TEMAS 43 Fronteras de La Fisica



   

                                       

                                                

   

   5    0    0    2    o    r    e    r    b    e    F    /    o    r    e    n    E

                                                                                                       

 

                                    

                

          

      

   

             

           

       

                

         

          

                      

        

 

                                          



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

 

                                       

   



      

                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                                                                                                      







                             



                      



                              

                                                                     

                                                                                                                                                                                                                                                                                                  

                                                                                                                                                                                                                                                                                                                                                                                                                             

    



                                                                                                 

                                                              







                                                                          

                                                                               



 





                                       

                                                                                          

                                                                                                                                              

     

     

                                       

                                                                                                                                               

                                                                                                                                                   

                                                                                                                                                     

                                                                                                                                



   

 



 

 

                                                                                                        



 

   



                                                                                                            

 

   

                                       



                                                                                                                                            

                                                                                                                                                                                                                                                                           

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               

                           







                                        

                                                                                                                              

                                                             

                              

 

                                                                       

                                       

   



                                                                                                                                                                              Λ                                 Λ                                                                                                                                                                                                            

                                                      Λ              Λ                                                                               Λ                                            Λ         × Λ                                                Λ                                                                                                                      Λ                                                                                                                                                                                                                                                                                                                                                                           Λ           Λ                                                        

                                                                                                                                                                                                                                                                                                    

                                          

                                                                                                                                                               

                                   

                                                                                     

                                                           

                              

 

    

       





 

                                                         

                        

  

                                    

                                                                                                                                      

  

       

                                        

   



                   



                                                                                                                                                                                                                                                                                                                    ×                                                                                                                    



 

                                                                            

   



                                                                                                                         

                                                                                                                                                  

                                                                                                                                                                                                                                                                                                        

         





                                                                                          



                                                               

                                                                                                                                                                                                                                                                                                                                                                                                                      

                                                                            

                                      ×                       

                                                 

  

 ×  

        

 

                                                            

   

   

 

  

                             

                        

         

                                                               ×  

  



   ×  

  

   



                                                                                                                                                                                

                                                                                                                                                            

                                  

    



 

   

  











  

                                                                      

                                                                                                                                                                                                                                         

                                                                                                                                                     

 

                                                                                               

                                                                  

                                                                                   









     

                                                                  

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                                                                                                                                                                                                                                        

                                               

                                         

   

 

    

    

                                               

                                                                                 

   

                                                                                         





                                                                                                                                                 

                             

 

     



                                                                                                                                                       

  

       

    

  

    

 

   

    

         



                                                                                                                                                                                                                                                                                                                                                                                                   

                                                                                                                                                                                                                                                                                                                                                                             ×          ×                                                           ×                                                                                                                                                                                                                                                                                                                                                                        

                                                                        

                                                 

                                        

                                                                                           



   

                                                                                       

                                                                                       

   



                                                                                                                                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                                                                                                                                                                                                                         

                                                                                                                                                                                                                                                                                                                                                                                                

                                                                                                                                                                                                                                                          

                                                                                                                                                                                                                                             

                                                                      ×                                                                                                                                                                         

                           

                                                                                                                                                                        

                                       

                                                                                                                                                                                                         

                                                                              

   

                                                                                                                                                                                                                                                                       





                                                                                                          

                                                                                     





                                                                                                       



 

                                                                                                                

                                                                                                                                                                                                             π                                                                                                                                                                                   

                                                               

                                                                                                                                                                                                                                                                                                                            

                                                                                                                                                                                                                                                                                                                                                                                                            

                                                                                                                                                                                                                                                                                                                                                                                                



 

                            



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     



                                                      

   

                                              

                         

                                  

                                        

                                                                                                                                                                                                                                                                                                                                                                                                               

                                                                                                                                                                                 

                                                                                         

                                                                                                                                                                                                                                                                                              

        

                                

 

                                           



                                                      



                                                                          

                                

                                                                   

                                                                                                                                                                                 



                                  





   

              

  

                                                                                          

                                                                                                                                                                                   



  



                                                                                         



                                                                                                           

                                                                                                                                                                                                                                      

                                                                                                             

                             

  

  

                                                                                              

  

                                  

   

                                                                                                                                                                       

                                                                                                                                                                       

                                                                                                       

                                                       

                                                                          







                                                                                              

                                                                                                                                                                                                              

                                                                                                                                                                                                       

                                                                                                           

                                                                                          

                                                                                                                               

                                                                                                                                 

                                                                                                                        

                                                                                                

                  

                                   





                                                                                              

   

                                        



                                                                                       



         







                                                                                                        

                                       

                                

                                                                                                        

                                                                                                                                   

                                                                                                                                                                                                                                                                                                                                                                                                           

 

   

                                           



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     

 

                                                                                                                                                                                                                                         

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           

                                                                

   



   

     

    

                                                                

                                                                                                                                                                                                                                                                                                                        

                                                                                                            

                                                                                                                                                                                                                                                                                                                                                                     

                                                                

                                                                                                            

  

                                                                                                                                                                                                                                                                                                           

                                                                                                                                                                                                                                                                                             

                                                                                                                                                                                                                                                                                                             

                                                     

                                   

                                       

                        

      

                                                                                                            ×                                                                                                                                                                                                                      

                                                                                                                                                    

                                                                                                                                                               

                                                            

                                                                                                                                                                                                                                                                                                                                                                       

                                                    







                                                                

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    



                                     



                                                                                                                                                                                                                                                                                                                                                                                                                            



 

                                                                            

   



  

                                                                                                                                                                                                                                                                                                

                                                                                                                                                                                                                                                                                                  

                       

                                                       

 

                                                             





                    

                                                                                                                                                                                                                                                                                                                      

                                                                 

                                                                                                                                                                                                                                                                                                                                                                                                                                        

     

    

   

                                                                                                                               

                                                                                                                                                                      

                                                                            

                                                                                                                                                                          

                                                                                                                                              

            

                                                                                                                 

                                                                                                                                                                             

          



 

   

      

 

 

                                                                                                                                    

                                              

   



 

                       

 

 







 



                                                                                                                                                                                                                                                                                                



  

                             



 

                                                                                 

                                                                            

                                                                                                                                                                                                   

                                                                                                                                                                                                                                                                                                                                                                                                  

                                                                                                                                                                                                                              

                                                                                                                                                                                                               

     

     

  

 

                                                                                                                                                                                                               

 

                                                                                                                                                       

                                        

                                                                                                                                                                                                                                                                                                                                                                                                                                 

               

                                                                            

                                                                 

                                                                                                                                              

                                                                                                                                                                                          



                                      



                                                                                                                                                                                                                                                                                        

                                                                                                                                                                    

                                                                                                                    

                                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                                                                                                                

                                                                

                                                               

                                                                                                                                                                                                                                                                                 

                                         

                                                                                                                                                                                                              

                

                                                        





                                                  



                                                       

   

                                                                                                                                                                                                                                                                                                                                                                                                                

                                                                                                                                                                                                                      

                                                                                                                                                                   

                                                                                                                                                                                                                                                                                                                                                                                                                                                 

                                                                                         

                                                                            



                                                                                                                                                  

                                                                                                                                                                                                                                                                                                             

                         





    

                             

                                                                                                                                                                           

                                                                                                                                                                      

                                                                                                                                                                     

                                                                                                                                                                                                                                                                                                                                                                                                          

                                                                                           

                                                                                  

                                                     

     

                                                  

                                                        

    

              

    

                                                                                  



                                                                          

 

                                               

  

                             

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

                                                                                                                                                                                                                                                                                                                                                                      

 

         

                                                 



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

 

                                                                                                                                             ×                                                                                                                                                                                                                                                                        



     

  

   

                                                                                                                    

h

   

    

                 h                                h                                      

                                                                                                                                                                                 

                   

          h                                                                                            h          h →     h                                            h                                                    



                                                                           



                                                                                                                                                        →    →                               Δ      Δ                                                                                                                                   ≈ h                  

                                                                                                     

                                                                                  Δ      Δ               Δ  Δ ≥ h                      ×                                    Δ  →          Δ → ∞                                  

        Δ          h  Δ                                                                                                                ×        ×            h                 h                                              

 

                                          γ                                                                                                                                              

                                                                                                                                                                       →                                                          h                                         





 



 

 



  













 





                                                                                                                                    

                                                     h                                         

                                                                                                     

                                                                                                                                                                                                                                              √h      

                                                                                                                 h                                              h                                                        h                                                          h                                                                                                                     h                                                                                   

                                                                                                     

                                                                                                                                                                         



                                                                                                                                                                                                                                                                                                                                                        

                 

 

                                                                                                                                                                                   √h                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

                                                                                                     

   



                                                                                                                                                                                                                                                                                                                                                                                       

                            α  β        α  β           α  β                       β  α   β  α                                                                                                                     

  

  

  

      













                                                                                                          









            

                                                                                                                                                                                                                                                                                                                                    Δ  Δ ≥                                                 

                                                                      h                                                     h            Δ     Δ  h           Δ  Δ ≥ h       Δ  Δ ≥ θ                                           

                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                            

 



                                                                                                       



                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                   

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

                                                                                                                                                                                                                                                                                                

                                                                     

 

                                    



                                                                                                                                               

                                                                                                            

                       

                                                                                                                                                                        

 

                                                                                                                                                                          

                                                                                                                                             

                                                                                                                                                   

                                                                                                                                                                           

                                                                                                        

                                                                                                                                                                                                                                                                        

       





                                              



                                                               



                                                              

                                       

                        

         

                                                                                                                                                                                                                                       

        

 

  



                                                                                                                                                     

                                                                                                                            

                                                                                                                                                                                 

                                                                                                                                                

                                       

                             

                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                            



                                     

                                                                                                                                                                                            

                                                                                 

                                                                                     

                                                                                                                                                                                                                                         







 





 



 

 

     



                                                                





   

                                                                                                                                                                        

 

                                                                                                                                                                                                                                                                                                                                                                                                    

 

                                                                                                                                                                                                                                                                                                                                                                                                                     

                                                                

           

                            

                                                                                                                                                                                                                                             

                                                                                                                                                                                                                                                                

                                                                

           

                                                                                                                                                      

                                                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                                                                                             



                                                                                                                                                                                                                                                                                                                                                                                                                        

                                                                                                 



              

                                                       

                

                                                                                       

                                                                                                           

                                                                                          

 

 

                                                                  

       

                                                                                                                                                                                                                                       

                                                                                                                                                                                                                                                   

                                                                                                                                                                                                                                                       

                                                                

            

                                                                                                                                                                                                                                                                                   ×             

                                                                        

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

  

                                                           

 

                                     

   



                                                                                                                                                                                                                                                                                   

                                            

                     

                    

                   

           

          

                  

        

        

         

                 

   

                                                                                                                                                     

                                                                                                                                                                                                                                                                                                                         

                                                                                                                                                                                                                                                                    

                                            

                       

                                    





                                                  



                                         

                                                                                                                                                                                                                                                                                                                                                                                                                                               

           

              

             

           

  

  

                                                                                                          

                                               





    

   

    

                                                                                                                                                                                                                                                                                                                                                                                                                                    

  

                                                                                                                                                                                                                 





     





 



                                                                                                                                                                                                                              

     

   





 











  



  









  

 











 

 

 

   









 

 

                                                                                              

  

  



      

                                                   

                                                                                                                                                                                                                                                                                                                                                                                                                             





                                                                                                                                                                                                                                                                            

    

                                                                                                                                                                                                                                                                                                                                                                                   

                                                                                                                                                                                                                                                                              

                                                                                                           

  

  

                                                  

   

    

                                                                                              

                                     

                                                                                                                                 



                                                                                                         

                                                                                                                                                                                     

                                                                                                                                                                                                           

                                                                                                                                          

                                    

                                                                                                                                                                                                                                                                                                   

                                                                                                                                                                                                                                                                                                                                                                                                                             

                                                                                                                                                                                                                                                                      

                                                                                                                                           

                                                                                                                                                                                                                                                       

                                                                   





                                                                                                                                                                   

                                                                                                                                                                                                                 

 

                                                    

                                            

   



 

                                                                                                                                                                                                                                                                                                               

                                                                                                                                                                                                                                                                                                                  

            

                                  

 

                                                     

 

                                                             



                                                                                                                                                                                                                                                                                                                                                                                              

              

                                                                                                                                                                                                                                                                                                                                                                                                                                         

                                                                                                                                                                                                                      

                                                                                     

                                                                                                   

                                                                                                              

                                                                                   

  

   

  

   

 

   

   

   

   

 

 

   

                                                                                   

            

                                            



                                                                                                                                                                                                                                   

 

  

    

  

 



 

 

  

 

 

     

    

   



                                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                                          

                                                                                                                                                                                                                                                                                                                             

                                                           





                     



                        

                         

                    

 

                                                                                                                                                                                                                                                                                                                 



                                                                                                                                                                                                                                                                       

                                    

                                                                                                                                                                                                                                                                                                                                  



              

                         

   

                    

                     



             

                     

           



                                                                                                                                                                                          

                                                                                                                                                                                                                                                    

                                                                                                                                                                                               

                                                                                                                                                                                                                                  

                                                                                                                                                                                                                     

 

           



                                                                                                                                                                                                                                                                                                                                                                                                                   Λ                                                  Λ                                                                                   



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

                                                                              η                                             ν                                             η               η          ν                     ν             ν                       ν                                                                             ν                      ν                                                         ν                                                                         ν                    

























                                                 







                   

                                                                                                                                     















 