Max Planck y El Nacimiento de La Teoria Cuantica.

FABIAN ANDRES HERNANDEZ CHARRIS SARENA BEATRIZ GONZALEZ MENDINUETA SANTIAGO FELIPE REALES GUERRA

PROYECTO INVESTIGA INVESTIG ATIVO FISICA III

MAX PLANCK Y EL NACIMIENTO DE LA TEORIA CUANTICA.

YALEIDYS YA LEIDYS PAOLA PAOLA HERNANDEZ H ERNANDEZ DIAZ

OBJETIVOS 



 

 

Encontrar a r!ac"#n $! %or&'! ('! Panc) o *'* !*t'$"o* ('!ron 'no $! o* !%"*o$"o* +,* "+%ortant!* !n a c"!nc"a !n *' -aa/o $! 'na %o*"0! -"%#t!*"* c',n1ca. R!a"ar ! !*t'$"o $! $"c-a* -"%#t!*"* a co+%ro0ac"#n %a*o a %a*o $! ca$a 'na $! !a*2 !* $!c"r c#+o %'$o '*ar a "n(or+ac"#n $! 3"!n2 Bot+an 4 Ma56! %ara $!*arroar *' !c'ac"#n 7na %ara c'!r%o* n!/ro*. D!*arroar -a0""$a$!* 4 conc'*"on!* ant! ! an1/'o %!n*a+"!nto $! a 8*"ca 4 !  act'a. D!$'c"r co+o Panc) %'$o to+ar 9!nta:a $! a* %ro%'!*ta* 8*"ca* o $!*arroo* %ant!a$o* ant!r"or!* a *' ;%oca2 %or !:!+%o ! t!or!+a $! K"rc--o<2 a $"*tr"0'c"#n $! 3"!n 4 a* !c'ac"on!* %ant!a$a* %or Ma56!. Po$!r !5%"car a $!r"9ac"#n (!no+!no#/"ca $! a !c'ac"#n $! Panc) %ara c'!r%o* n!/ro*. D!t!r+"nar a a%"cac"#n $! Panc) 4 a r!ac"#n $! Bot+ann !ntr! a !ntro%=a 4 a %ro0a0""$a$ $! a +!c,n"ca !*ta$=*1ca.

INTRODUCCION

La t!or=a c',n1ca nac"# co+o 'n "nt!nto $!*!*%!ra$o %or r!*o9!r ! %ro0!+a %ant!a$o %or a ra$"ac"#n $! c'!r%o n!/ro. In"c"a+!nt! %ro%'!*to %or G'*ta9 K"rc--o< !n >?@2 o* c"!n7co* $! 7na!* $! *"/o XIX o-n M"ton >?>J E Para=*o P!r$"$o a0or$aron !*t! %ro0!+a $!*$! a %!r*%!c19a $! a t!or=a !!ctro+a/n;1ca Ma56!J 4 $! a t!r+o$"n,+"ca Ca'*"'*K!9"nJ 4 -ac"a >? cr!4!ron t!n!r a r!*%'!*ta corr!cta. Soo $o* ao* $!*%';*2 -ac"a oct'0r! $! >2 a "n9!*1/ac"#n !5%!r"+!nta $!*%o+ar=a !*a !*%!rana. En oct'0r! $! >2 a "nt!ntar -aar 'na *a"$a a %ro0!+a2 Panc) %ro%'*o 'na (#r+'a $! "nt!r%oac"#n &'! concor$a0a con o* $ato* !5%!r"+!nta!*2 %!ro &'! *!/n ; car!c=a $! *!n1$o 8*"co. En $"c"!+0r! $! >2 !n *' "nt!nto $! ('n$a+!ntar a (#r+'a $! oct'0r!2 Panc) "ntro$':o 'n n'!9o !!+!nto !n ! an,"*"* $! %ro0!+a a a%"cac"#n $! %r"nc"%"o $! Bot+ann a a "nt!racc"#n !ntr! !n!r/=a 4 +at!r"a. Co+o r!*'ta$o $! !*ta "nc'r*"#n Panc) $!r"9# 'na (#r+'a !n a &'! a%ar!c=a 'na n'!9a con*tant! -J2 a c'a !5%r!*a0a ! car,ct!r $"*con1n'o $! !*a "nt!racc"#n. E *"/n"7ca$o 8*"co $! !*ta con*tant! &'!$a0a !n *'*%!n*o a no %o$!r *!r "ncor%ora$a a !ntra+a$o $! a 8*"ca c,*"ca2 %or o &'! a con*"$!r# ! r!*'ta$o $! 'n tr'co +at!+,1co. Ha*ta > Panc) +ant'9o 'na %o*"c"#n 0a*tant! -o*1 -ac"a a "$!a $! ac!%tar 'na $"*con1n'"$a$ r!a tanto !n a "nt!racc"#n ra$"ac"#n+at!r"a co+o !n a ra$"ac"#n !!ctro+a/n;1ca "0r!. E"n*t!"n ('! ! %r"+!ro !n to+ar !n *!r"o a* "+%"cac"on!* 8*"ca* $! tra0a:o $! Panc) 4 !n >@2 !n *' "nt!nto $! -aar n'!9o* ca+"no* %ara !/ar a a con*tant! -2 r!c-a# ! '*o &'! !*t! $"o !n $"c"!+0r! $! > a %r"nc"%"o $! Bot+ann. A %ar1r $! *'* !*t'$"o* ant!r"or!* a >@ *o0r! t!r+o$"n,+"ca !*ta$=*1ca !n !*%!c"a $! *' $!r"9ac"#n $! %r"nc"%"o $! Bot+ann2 a $!%!n$!nc"a r!*%!cto $! 9o'+!n $! a* can1$a$!* t!r+o$"n,+"ca* 4 a $!r"9ac"#n $! a (#r+'a $! a* 'ct'ac"on!* !n!r/;1ca*J2 a t!or=a c"n;1ca $! o* /a*!*2 a !4 $! 3"!n 4 $! a t!r+o$"n,+"ca2 E"n*t!"n ar1c'# 'n ar/'+!nto +!$"ant! ! c'a o/r# %ro%on!r ! car,ct!r cor%'*c'ar $! a ra$"ac"#n !!ctro+a/n;1ca "0r!. Para !*ta0!c!r a r'ta &'! con$'c! a a con7/'rac"#n $! %!r=o$o ('n$ac"ona $! a t!or=a c',n1ca 4 !*car!c!r o* *!n1$o* !n &'! Panc) 4 E"n*t!"n '1"aron ! %r"nc"%"o $! Bot+ann2 no* oc'%ar!+o* !n %r"+!r '/ar $! arc'o %'0"ca$o %or Panc) !n $"c"!+0r! $! > 4 %or 1+o $! arc'o $! E"n*t!"n $! :'n"o $! >@.

MARCO TEORICO

La $!%!n$!nc"a ('nc"ona $! a !ntro%=a !n a !n!r/=a2 4 !n a $"*tr"0'c"#n $! 3"!n %ara ! c'!r%o n!/ro Ma5 Panc) o0t'9o 'na (#r+'a %ara !*ta ra$"ac"#n +!$"ant! 'na r!ac"#n $! "nt!r%oac"#n &'! a:'*t# a* +!$"$a* !5%!r"+!nta!* $! a ra$"ac"#n t;r+"ca !n P-4*")a"*c- T!c-n"*-! R!"c-an*tat PTRJ !n B!r=n a 7na!* $! *"/o XIX. Sor%r!n$!nt!+!nt!2 *' car,ct!r %'ra+!nt! (!no+!no#/"co r!*'t# *!r no *#o 'na a%ro5"+ac"#n2 co+o *! -a0r=a !*%!ra$o2 *"no 'na !5acta r!ac"#n %ara o0t!n!r 'na "nt!r%r!tac"#n 8*"ca $! *' (#r+'a2 Panc) *! 9o9"# !ntonc!* a a $! Bot+ann >? *o0r! a "nt!r%r!tac"#n !*ta$=*1ca $! a !ntro%=a2 o &'! ! !9# a "ntro$'c"r ! conc!%to $! $"*cr!t!n!** $! a !n!r/=a !n a 8*"ca. Un n'!9o a*%!cto $! n'!*tra c'!nta &'! *! -a %!r$"$o !n o* !*t'$"o* -"*t#r"co* %r!9"o* $! $!*c'0r"+"!nto $! Panc) !* +o*trar &'! Panc) %o$r=a -a0!r !ncontra$o *' (#r+'a (!no+!no#/"ca $!r"9a$a %arc"a+!nt! !n ! tra0a:o $! Bot+ann !n t;r+"no* $! 'n %ar,+!tro2 %!ro a $!%!n$!nc"a $! !*t! %ar,+!tro *o0r! a t!+%!rat'ra no !*t, cont!n"$a !n !*t! t ra0a:o2 4 %r"+!ro ('! $!r"9a$o %or Panc).

Uno $! o* !%"*o$"o* +,* "nt!r!*ant!* $! a -"*tor"a $! a c"!nc"a ('! a "ntro$'cc"#n $! Ma5 Panc) $! a -"%#t!*"* c',n1ca2 a %r"nc"%"o* $! *"/o XX. E *'r/"+"!nto $! !*t! conc!%to r!9o'c"onar"o !n 8*"ca !* 'na -"*tor"a (a*c"nant! &'! *! -a $!*cr"to

ant!r"or+!nt!2 >> %!ro a*%!cto* "+%ortant!* $! !*t! $!*c'0r"+"!nto no *! !nc'!ntran /!n!ra+!nt! !n a $!*cr"%c"#n $! La* "$!a* $! Panc) !n o* "0ro* $! t!5to $! 8*"ca &'! +!c,n"ca. En %ar1c'ar2 a +a4or=a $! o* "0ro* $! t!5to $! 8*"ca no +!nc"onan c#+o ! conc!%to $! $"*cr!!nc"a !n a !n!r/=a2 ! r!9o'c"onar"o conc!%to "ntro$'c"$o %or Panc) %ara $!*cr"0"r !*%!ctro $! ra$"ac"#n $! c'!r%o n!/ro2 or"/"na$o !n a ? D! o* arc'o* 4 corr!*%on$!nc"a $! Panc) *o0r! *' t!or=a $! !*%!ctro $! a ra$"ac"#n $! c'!r%o n!/ro2 !*t, caro &'! to+# !*t! conc!%to $"r!cta+!nt! $! Bot+ann2 &'"!n !n *' %a%! *!+"na $! >? *o0r! +!c,n"ca !*ta$=*1ca $"*cr!1# !n!r/=a co+o 'n $"*%o*"19o %'ra+!nt! +at!+,1co %ara %o$!r contar a* %o*"0!* con7/'rac"on!* $! 'n /a* +o!c'ar !n !&'""0r"o t;r+"co2 %!ro !*ta "+%ortant! con!5"#n !ntr! a o0ra $! Panc) 4 Bot+ann no -a *"$o +!nc"ona$a "nc'*o !n o* "0ro* $! t!5to $! 8*"ca &'! -ac!n -"nca%"; !n 'na -"*tor"a %or !:!+%o2 !n a $!*cr"%c"#n $! $!*c'0r"+"!nto $! Panc) !n *' 0"o/ra8a $! E"n*t!"n2 A0ra-a+ Pa"* conc'4! &'!

"Su razonamiento [de Planck] estaba enojado, pero su la locura ene esa cualidad divina que sólo la las cifras más importantes de transición pueden aportar a la ciencia " E*t! co+!ntar"o no %ro%orc"ona +,* "'+"nac"#n *o0r! ! or"/!n $! a "$!a $! c'an17cac"#n !n 8*"ca &'! R"c-ar$ La *'c"nta $!carac"#n $! F!4n+an !n *'* conoc"$a* con(!r!nc"a* 8*"ca*2 &'!

"... jugando con [Planck] ncon!# un $%&'l d%(ac%#n ['aa $u )#&ula]. " La +a4or=a $! o* r!ato* $! $!*c'0r"+"!nto $! Panc) !n o* "0ro* $! t!5to $! 8*"ca *on -"*t#r"ca+!nt! "n!5acta*2 4 ! an,"*"* t!+%rano $! Mar1n K!"n $! a o0ra $! Panc) $!0""t# a/'no* +"to* cont!n"$o* !n !*to* "0ro*. Por !:!+%o2 'no $! o* +"to* +,* co+'n!* !* &'! Panc) !*ta0a r!*%on$"!n$o a %ro0!+a !n a t!or=a c,*"ca $! a ra$"ac"#n $! c'!r%o n!/ro conoc"$a co+o a cat,*tro(! 'tra9"o!taQ !*to oc'rr! c'an$o ! t!or!+a $! !&'"%ar1c"#n %ara 'n *"*t!+a !n !&'""0r"o t;r+"co *! a%"ca a a $"*tr"0'c"#n !*%!ctra $! Ra$"ac"#n t!r+a. P!ro !n !*! +o+!nto2 Panc) %ar!c! t!n!r $!*conoc"$o $! !*t! %ro0!+a2 &'! ('! no+0ra$o %or E-r!n(!*t 9ar"o* ao* $!*%';* $! $!*c'0r"+"!nto $! Panc). D! -!c-o2 ! a%"cac"#n $! t!or!+a $! !&'"%ar1c"#n a a ra$"ac"#n $! c'!r%o n!/ro ('! -!c-o %or Lor$ Ra4!"/- ca*" a +"*+o 1!+%o &'! Panc) o0t'9o *' (a+o*a (#r+'a %ara ! c'!r%o n!/ro !*%!ctro2 a'n&'! no -a4 n"n/'na !9"$!nc"a $! &'! Panc) !*t'9"!ra a tanto $! r!*'ta$o $! Ra4!"/-2 ! c'a !*t'9o $! ac'!r$o con n'!9o* !5%!r"+!nto* %ara ! !5tr!+o $! on/"t'$ $! on$a ar/a $! !*%!ctro o0*!r9a$o !n !*! 1!+%o.

K!"n conc'4# Pro0a0!+!nt! ('! a/o +'4 0'!no &'! Panc) ('!ra no "+"ta$o !n *' %!n*a+"!nto %or a a%r!ta$a t!a c,*"ca &'! Ra4!"/- -a0=a t!:"$o. 

En !*!nc"a2 ! !n(o&'! $! Panc) a a t!or=a $! a ra$"ac"#n $! c'!r%o n!/ro *! 0a*# !n o* *"/'"!nt!* %a*o*. A%ro9!c-an$o ! t!or!+a $! K"rc--o< $! &'! a $"*tr"0'c"#n $! c'!r%o n!/ro !* 'na ('nc"#n 'n"9!r*a "n$!%!n$"!nt! $! a nat'ra!a $! a ('!nt! $! ra$"ac"#n2 ! %r"+!r %a*o $! Panc) ('! o0t!n!r 'na r!ac"#n %ara a $"*tr"0'c"#n $! !n!r/=a $! !*ta ra$"ac"#n !n !&'""0r"o t;r+"co con 'n con:'nto $! o*c"a$or!* -!rt"ano* +"cro*c#%"co* con (r!c'!nc"a 9ar"a0!. M!$"ant! a a%"cac"#n $! a $"*tr"0'c"#n $! 3"!n &'! a:'*t# ! !5tr!+o $! ata (r!c'!nc"a $! !*ta ra$"ac"#n2 4 a* !c'ac"on!* $! Ma56! %ara ! ca+%o !!ctro+a/n;1co2 Panc) o0t'9o 'na !5%r!*"#n $! a !n!r/=a +!$"a $! ! *to* o*c"a$or!*.

METODO*O+IA. I. P*ANC,-S  SU DERIVACI/N 0ENOMENO*/+ICO DE SU 0/RMU*A DE CUERPO NE+RO Una $!*cr"%c"#n %!r*%"ca $! c#+o Panc) o0t'9o *' (a+o*a (#r+'a %ara ! !*%!ctro $! a ra$"ac"#n $! c'!r%o n!/ro *! %'!$! !ncontrar !n *' a'to0"o/ra8a c"!n7ca. E*t! r!ato ('! !*cr"to +'c-o* ao* $!*%';* $! a oc'rr!nc"a $! !*t! !9!nto2 4 %'!$! *'(r"r o* a%*o* -a0"t'a!* $! a +!+or"a 4 a a'*!nc"a $! $oc'+!nto* or"/"na!* 4 corr!*%on$!nc"a. Lo* %a%!!* 4 a corr!*%on$!nc"a $! Panc) ('!ron $!*tr'"$o* c'an$o B!r=n ('! 0o+0ar$!a$a !n a S!/'n$a G'!rra M'n$"a. S"n !+0ar/o2 %ar!c! *!r co-!r!nt! con a* %'0"cac"on!* or"/"na!* $! Panc). Por o tanto2 a&'= Panc) -a0ar, %or *= +"*+o2 +"!ntra* &'!2 %ara acarac"#n2 a/'no* $! o* $!ta!* +at!+,1co* *!r,n r!!na$o* +ant!n"!n$o *' notac"#n or"/"naJ !n 'na (or+a c!rcana a *'* arc'o* or"/"na!*. Panc) !*cr"0"# M"!ntra* &'! 'na /ran can1$a$ $! 8*"co* *o0r!*a"!nt!* tra0a:aron !n ! %ro0!+a $! a $"*tr"0'c"#n !*%!ctra2 tanto $!*$! ! %'nto $! 9"*ta !5%!r"+!nta co+o t!#r"co2 ca$a 'no $! !o* $"r"/"# *'* !*('!ro* n"ca+!nt! a +o*trar a $!%!n$!nc"a $! a "nt!n*"$a$ $! a ra$"ac"#n *o0r! a t!+%!rat'ra. Por otra %art!2 *o*%!c-a0a &'! a con!5"#n ('n$a+!nta ra$"ca !n a $!%!n$!nc"a $! a !ntro%=a con a !n!r/=a. Co+o a *"/n"7cac"#n $! a !ntro%=a no -a0=a !/a$o to$a9=a a *!r %!na+!nt! a%r!c"a$a2 na$"! +! %r!*t# at!nc"#n a +;to$o a$o%ta$o %or +=2 4 %'$! !a0orar +"* c,c'o* co+%!ta+!nt! a +" anto:o2 con a0*o'ta +"n'c"o*"$a$2 *"n t!+or a a "nt!r(!r!nc"a o a co+%!t!nc"a. P'!*to &'! %ara a "rr!9!r*"0""$a$ $! "nt!rca+0"o $! !n!r/=a !ntr! 'n o*c"a$or 4 a ra$"ac"#n &'! o ac19a2 ! *!/'n$o coc"!nt! $"(!r!nc"a $! *' !ntro%=a con r!*%!cto a *' !n!r/=a !* $! *"/n"7cac"#n caract!r=*1ca2 cac'; ! 9aor $! !*ta ('nc"#n *'%on"!n$o &'! a !4 $! 3"!n $! La D"*tr"0'c"#n E*%!ctra $! En!r/=a !* 9,"$a 'na !4 &'! !ntonc!* !*ta0a !n ! c!ntro $! "nt!r;* /!n!raQ O0t'9! ! nota0! r!*'ta$o $! &'! !n !*ta *'%o*"c"#n ! r!c=%roco $! !*! 9aor2 &'! a+ar; a&'= R2 !* %ro%orc"ona a a !n!r/=a. Por raon!* t!#r"ca*2 3"!n -a0=a %ro%'!*to &'! a $"*tr"0'c"#n $! !n!r/=a !*%!ctra %ara a ra$"ac"#n $! c'!r%o n!/ro con (r!c'!nc"a a a t!+%!rat'ra T t!n=a a (or+a $! !*caa

II. P*ANC,1 DICIEMBRE DE 2344 5UN SA*TO DESESPERADO6 E  $! oct'0r! $! >2 ! +"*+o $=a !n &'! H!"nr"c- R'0!n* >?@>J co+'n"c# a Panc) o* r!*'ta$o* !5%!r"+!nta!* &'! !*ta0!c=an a "ncorr!cc"#n $! a (#r+'a $! $"*tr"0'c"#n $! !n!r/=a ra$"ant! $! c'!r%o n!/ro &'! 3"-!+ 3"!n >?>?J -a0=a %ro%'!*to !n >?2 Panc) *! $!$"ca a 0'*car 'na *a"$a a %ro0!+a. E > $! oct'0r! $! > Panc) %r!*!nt# a o* +"!+0ro* $! a Aca$!+"a Pr'*"ana $! C"!nc"a* *' arc'o Ac!rca $! 'na +!:ora $! a !c'ac"#n $! 3"!n %ara ! !*%!ctro. En !*t! arc'o2 Panc) *'%'*o &'! a !ntro%=a SJ $! 'n r!*ona$or "n!a &'! "nt!ract'a0a con a ra$"ac"#n !ra 'na ('nc"#n $! *' !n!r/=a 9"0rac"ona UJ 4 !9a'# ! a'+!nto "n7n"t!*"+a $! !ntro%=a $! 'n *"*t!+a co+%'!*to %or n r!*ona$or!* "$;n1co* *"t'a$o* !n 'n ca+%o $! ra$"ac"#n !*tac"onar"o. Panc) no* $"c! &'! !n !*a 0*&'!$a $! at!rna19a* 7...8nal&n! 9

co&n:ado a con$!u% ;'$%on$ co&'l!a&n! a<%!a%a$ 'aa la n!o'=a la$ cual$> aun?u $on &@$ co&'l%cada$ ?u la ;'$%#n d %n> 'acn $a$)ac !oda(=a n una &ana ca$% co&'l!a !odo$ lo$ ?u%&%n!o$ d la !&od%n@&%ca  d la !o=a lc!o&agnca. Panc) *! *"n1# !*%!c"a+!nt! atra=$o %or a !5%r!*"#n

 a c'a !* a +,* *"+%! $! to$a* a* !5%r!*"on!* &'! con$'c!n a S co+o 'na ('nc"#n o/ar=t+"ca $! U a c'a !* *'/!r"$a %or con*"$!rac"on!* %ro0a0"=*1ca* 4 &'! %ara 9aor!* %!&'!o* $! U *! r!$'c! a a !5%r!*"#n $! 3"!n .... E -!c-o $! %ro%on!r 'na !5%r!*"#n %ara ! ca+0"o !n ! a'+!nto $! !ntro%=a 4 no 'na %ara a !ntro%=a *! $!0! a &'!2 %ara Panc)2 *oo ! a'+!nto $! !ntro%=a %o*!! *!n1$o 8*"co co+o +!$"$a $! a "rr!9!r*"0""$a$ $! 'n %roc!*oJ. Panc) '1"# !*ta !c'ac"#n %ara $!r"9ar 'na !5%r!*"#n %ara $S$U o0t!n"!$no

Co+0"nan$o a ant!r"or !5%r!*"#n con $S$U>T *! o01!n! %ara a !n!r/=a $! r!*ona$or !n !&'""0r"o con a ra$"ac"#n UJ

D! $on$!2 con otro* r!*'ta$o* o0t!n"$o* !n >?

E*ta (#r+'a2 $! ac'!r$o con Panc) ...conc'!r$a con o* $ato* o0*!r9ac"ona!* %'0"ca$o* -a*ta ! +o+!nto... %or o &'! +! %!r+"to a+ar *' at!nc"#n -ac"a !*ta n'!9a (#r+'a a c'a con*"$!ro *!r a +,* *"+%! %o*"0!2 a%art! $! a $! 3"!n2 $!*$! ! %'nto $! 9"*ta $! a t!or=a !!ctro+a/n;1ca $! a ra$"ac"#n

III. *A AP*ICACI/N DE P*ANC, DE *A RE*ACI/N DE BO*TFMANN ENTRE *A ENTROPGA  *A PROBABI*IDAD EN *A MECHNICA ESTADISTICA E*ta *!cc"#n r!9"*a a (a*! cr=1ca2 %ara !ncontrar ! *"/n"7ca$o 8*"ca$o $! *' (#r+'a %'ra+!nt! (!no+!no#/"ca %ara a ra$"ac"#n c'!r%o n!/ro $! a Ec'ac"#n

Panc) 9o9"# a %a%! *!+"na $! >? $! Bot+ann *o0r! o* ('n$a+!nto* $! a +!c,n"ca !*ta$=*1ca %ara a "'+"nac"#n. M,* tar$!2 co+o o $!*cr"0"# Panc) !n *' a'to0"o/ra8a2 P!ro "nc'*o *" a 9a"$! a0*o'ta 4 %r!c"*a $! a (#r+'a $! ra$"ac"#n *! $a %or *!nta$a2 *"!+%r! 4 c'an$o t!n=a *"+%!+!nt! ! %"! $! 'na !4 r!9!a$a %or a "nt'"c"#n a(ort'na$a2 no *! %o$r=a !*%!rar %ara %o*!!r +,* &'! 'n *"/n"7ca$o (or+a. Por !*ta ra#n2 ! +"*+o $=a !n &'! (or+'; !*ta !42 co+!nc; a $!$"car+! a a tar!a $! "n9!r1ra con 'n 9!r$a$!ro *"/n"7ca$o 8*"co. E*ta 0*&'!$a2 %or *'%'!*to2 +! !9# a !*t'$"ar a "nt!rr!ac"#n $! !ntro%=a 4 %ro0a0""$a$ !n otra* %aa0ra*2 %!r*!/'"r a =n!a $! %!n*a+"!nto "na'/'ra$a %or Bot+ann. En *' $"*c'r*o No0!2 Panc) a/r!/# a o0*!r9ac"#n D!*%';* $! 'na* *!+ana* $! a +,* ar$'a o0ra $! +" 9"$a2 a o*c'r"$a$ *! !9ant# 4 'na 9"*ta "n!*%!ra$a co+!n# a a%ar!c!r. Y con1n'# Co+o a !ntro%=a S !* 'na +a/n"t'$ a$"19a2 %!ro a %ro0a0""$a$ 3 !* +'1%"ca19a2 *"+%!+!nt! %o*t'; &'! 2 $on$! ) !* 'na con*tant! 'n"9!r*aQ ! "n9!*1/'; *" a (#r+'a %ara 32 &'! *! o01!n! c'an$o S *! *'*1t'4! %or *' 9aor corr!*%on$"!nt! a a !4 $! ra$"ac"#n ant!r"or %o$r=a "nt!r%r!tar*! co+o 'na +!$"$a $! %ro0a0""$a$. A "nt!/rar a !c'ac"#n S $!*a%ar!c! c'an$o U  2 Panc) o0t!n"$o

2 con a con$"c"#n =+"t! $! &'! a !ntro%=a

Don$! k ! #b !* a con*tant! $! Bot+ann. E*ta (or+a $! a $!%!n$!nc"a $! S !n $  4 v  *a1*(ac! a r!ac"#n $! !*caa $! 3"!n $! a r!ac"#n $#v

"n$"can$o &'! S $!%!n$! *#o

IV. RECONOCIMIENTOS DE P*ANC, EN 232 En %& &P%'(&(')* + P%&*(- + %& .%&(')* + /0%123&** *1. %& *1.0P4& 5  %& P.0/&/'%'+&+ * %& 3(6*'(& S1&+'S1'(&2 -!+o* -!c-o 'na r!con*tr'cc"#n %a'*"0! $! c#+o Panc) o0t'9o 'na $!r"9ac"#n -!r;1ca $! *' (#r+'a $! c'!r%o n!/ro 0a*a$a !n ! $!*arroo !*ta$=*1co $! Bot+ann !n >?. La "$!a $! "ntro$'c"r !!+!nto* $! !n!r/=a $"*cr!to* $! +a/n"t'$ *! or"/"n# con Bot+ann2 &'"!n o a%"c# co+o 'n $"*%o*"19o +at!+,1co %ara contar con7/'rac"on!* %ara 'n /a* $! +o;c'a*. Po*t!r"or+!nt!2 r!"ncor%or# ! c,*"co con1n'o $! !n!r/=a to+an$o ! =+"t! !. Panc) *!/'"$o E !n(o&'! $! Bot+ann +!$"ant! a a*"/nac"#n $! +1%o* $! !*to* !!+!nto* !n!r/;1co* $"*cr!to* a *'* o*c"a$or!* $! (r!c'!nc"a2 %!ro '!/o *! a%art# $! ; $! +an!ra ('n$a+!nta %or 7:ac"#n %ara t!n!r 'n 9aor con*tant!2 !-92 $on$! - !* 'n n'!9a con*tant! 'n"9!r*a2 !n '/ar $! $!:ar*! con9!r1r*! !n $!*a%ar!c!r %!&'!o co+o o !5"/=a a 8*"ca c,*"ca. Por &'! Panc) no to+# !*t! 1+o %a*o !  JW !* o09"o a *'%o*"c"#n $! 'n !!+!nto $! !n!r/=a $"*cr!ta $! +a/n"t'$ - ! $"o %r!c"*a+!nt! ! r!*'ta$o &'! 0'*ca0a %ara :'*17car *' car,ct!r (!no+!no#/"co (#r+'a $! c'!r%o n!/ro. P!ro co+o *!r=a !*%!ra$o2 ; no 4 no %o$r=a :'*17car ta $"*cr!%anc"a *o0r! 0a*!* a %r"or". Par!c! &'! !n ! corto 1!+%o ant!* $! &'! Panc) %r!*!ntara *' %on!nc"a a a Soc"!$a$2 ; no %o$r=a -a0!r *"$o con*c"!nt! $! a +,* a+%"a "+%"cac"on!* $! *' an*at *"n %r!c!$!nt!* %or&'! ; no o(r!c!r n"n/n co+!ntar"o &'! "n$"&'! &'! ; !*ta0a *a"!n$o $!*$! o* c,non!* $! a 8*"ca c,*"ca. Panc) *! 9o9"# -ac"a ! !n(o&'! $! Bot+ann 0a*tant! tar$! !n *' %ro/ra+a $! "n9!*1/ac"#n2 4 %or o tanto %ar!c! +'4 %ro0a0! &'! !n > to$a9=a no -'0"!ra $! o* $ato* +!c,n"co* !*ta$=*1co* $! Bot+ann. A !*t! r!*%!cto2 !* "nt!r!*ant! !5a+"nar a* c'!nta* $! *' $!*c'0r"+"!nto 'no* > ao* +,* tar$!. En r!*%'!*ta a 'na *o"c"t'$ $! 8*"co !*ta$o'n"$!n*! Ro0!rt 3""a+* 3oo$2 Panc) $!*cr"0"# a* con*"$!rac"on!* &'! o !9# a %ro%on!r a -"%#t!*"* $! o* c'anto* $! !n!r/=a !n 'na carta ! !*cr"0"# !  $! oct'0r! $! >>  @ Br!9!+!nt! r!*'+"$o2 o &'! -"c! *! %'!$! $!*cr"0"r co+o *"+%!+!nt! 'n acto $! $!*!*%!rac"#n. Por nat'ra!a *o4 %ac=7ca+!nt! "nc"na$o 4 r!c-aar to$o $'$o*o a9!nt'ra* P!ro %ara !ntonc!* 4a -a0=a !*ta$o 'c-an$o *"n ;5"to $'rant! *!"* ao* con ! %ro0!+a $! !&'""0r"o !ntr! ra$"ac"#n2 +at!r"a 4 ; *a0=a &'! ! %ro0!+a !ra ('n$a+!nta "+%ortanc"a %ara a 8*"caQ Ta+0";n *a0=a a (#r+'a &'! !5%r!*a a $"*tr"0'c"#n $! !n!r/=a !n a !*%!ctro. Por o tanto2 'na "nt!r%r!tac"#n t!#r"ca %ara *!r !ncontra$o a c'a&'"!r co*to2 no "+%orta c',n ato. Era caro &'! a 8*"ca c,*"ca no %o$r=a o(r!c!r 'na *o'c"#n a !*t! %ro0!+a 4 -a0r=a *"/n"7ca$o &'! to$a a !n!r/=a !9!nt'a+!nt! *! tran*(!r"r=a $! a +at!r"a !n ra$"ac"#n. Para !9"tar !*to2 'n *! r!&'"!r! 'na n'!9a con*tant! %ara a*!/'rar &'! a !n!r/=a no $!*"nt!/rar*! P!ro a n"ca +an!ra $! r!conoc!r c#+o !*to *! %'!$! -ac!r !* %ar1r $! 'n %'nto $!7n"$o $! 9"*ta. E*t! !n(o&'! +! ('! a0"!rto %or +ant!n"!n$o a* $o* !4!* $! a t!r+o$"n,+"ca. Lo* $o* !4!*2 +! %ar!c!2 $!0! *!r +ant!n"$o 0a:o c"rc'n*tanc"a*. Por o $!+,*2 !*ta0a $"*%'!*to a *acr"7car ca$a 'na $! +"* con9"cc"on!* ant!r"or!* *o0r! a* !4!*. Bot+ann -a0=a !5%"ca$o c#+o a t!r+o$"n,+"ca !&'""0r"o *! !*ta0!c! %or +!$"o $! !*ta$=*1ca* !&'""0r"o2 4 *" ta !n(o&'! *! a%"ca a ! !&'""0r"o !ntr! +at!r"a 4 ra$"ac"#n2 'no !nc'!ntra &'! a %;r$"$a con1n'a $! !n!r/=a !n ra$"ac"#n %'!$! *!r %r!9!n"$o *'%on"!n$o &'! a

!n!r/=a *! 9! o0"/a$o2 a %r"nc"%"o2 a %!r+an!c!r :'nto* !n &'anta E*to !ra %'ra+!nt! 'na *'%o*"c"#n (or+a 4 4o r!a+!nt! no ! $"o +'c-o %!n*a+"!nto2 !5c!%to &'! no "+%orta o &'! c'!*t!2 $!0o tra!r 'n %o*"19o r!*'ta$o.

BIB*IO+RA0IA. -%666.!-'.!'*c-!+"*tr4t-!or4+ar"o.%"r"*7!*7*"cac'an1ca.%$(  -%666.(%.'0a.ar!*nota*[$![c'r*o*nota*+!can"cac'an1caC'an1ca.%$(