Physics | Mechanics, Quantum mechanics » Benedict Mihály - Kvantummechanika

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" / 7 ( * & * C ( ( # / + ! " # " # $% & Fotonok polarizációja A+ Az A berendezés sajátirányai Kalcit A- A B+ Más sajátirányok tartoznak B-hez Kalcit B- B & / % % 27 & * 1 7 # ! % # ( !( & !# 7 *2 & * # R ( & * ( ( / B +C ' " S # & & $ # ) / * & " / & '# & & ( ' ( / $ 5 " ' & 2 ( ( ' / ! # @ "! / )# / B ;C ! 2 ( #2 ' @ ( / ! " # " # / ( " # 2/ ; $% & * !# (& & # / " ! / @ & ( !! * # ! #2 / ( & " ' ( & " ' ( 0 ( % ! # # " / % # & " ' ( / *2 * ' % #2 ! ! * " ) 27 & 7 % - & " ' ( ! !# " & " ' ( ! !# * ( / & " ' ( / 2 @ # / 7 & ! "& " ' ( ! & " ' ( # < ) "- = 7 ! )

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' )# # # % 7 ! ( C ! - # # " & # #2 ( % ' / ) @ B $ # # % " # ' #2 / ! ) "# B C ' ( ) $ % & *+ , -( ' 5 $ ( ) * & ( . 2 !& ( ' 9 $ * * & ' & ' #"& ( # T ! * ( # / ! & ( % # 2 * / # * ! / & " ' ( ' &( ! ) " / - ! # ( !! ( ! ) " ' " % " * % $ " % ! & ' ' " ' " & ! ) " ! ) "# / ! ) " # ' ' " ' % " " ( / % ' B$ C " " " / ' " " ' " " ! " 7& " " ! 0 " & / " ' # & / / ' ' " & 7 # # ( / / ! / / * ! 7 !" ! &' ! * ! ( / & " ( 0 2 7 ( *2 ( 2 & ! ' ( D 7 ( ( ( 2 ! & ( "/ ( 7 * * & / ! $ % & % * / . / ! & *

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

& 2 @ ! ) "# " # / ( " # !! / / & ! ! & " '" & /' # # ! " C () ( ( & " ' ( ' ! ( - * * % B$ ;C ) " 7 , % / " % )- $ /& ! / % / ! / #2 / ( " ! * !# & " 7& / / @ # ! ! . - $ / & & ! / & #2 8 " - # " ! 0 "& (& / & " % & # 7 / # / 6 " ' * # & & ( ' ' % ( * ! / ( # * " / & 7 7 / "/ ." & 7 7 @ " 7 = '& 7 '& / !! ! 0 ! 0 / ' - . =& & ' . / " " . " & " (6 '&/ " / " . " # / '&/ JJ . " ' " " "/ " ) * 0" @ & * % ( * # ( ! *+ / ! J " $ ! 7& L 7 2 " ' , & # . ' # " & " " / " /. / " 7 7 ./ "

& 27 , *2 ' % ' ' ) * # & 2 /% ' ' ' ' ' ' # 2 & !! "/ 7 @ ( & " ' "# & 2 ' *2 *2 7 *2 ( *2 ) % & & *2 ' % & 6 ! - " / / ' # ' ) & & ! 0 & "' & 2 " 7 7 ( ( ' # - && " ' 7 & ) 7& / " ' * # B+ C "' # . - $ % # ' 7& 6 V & & " ." ' . "' B+ +C E ! " & @ ' & ! % & 7 ( *2 & % * & / / B ' & / *7 ( *2 ' 2 E ' ( ( 2 & # ' / / E /@ M *7 " / ' ( 2 # " % / / & " # % *7 / ' P / # & & / & & M & ' ( ' " " & @ & 2 ! " & & / / / # & & ( " / " ! 0 & & & ' %

"" B+ ;C " " C/ ' / / & ( # ( & # B+ $C # ' B+ C . "' '" & ( " .' "' "" & "- ! 0 "" / & /& ' $ % *7 "" & "/ ( & % "' ( % & " # ( +$ ( *+ - ( " $ & 2 %& @ / < & " 8 # 7 & / # / " /8 * 2 ( "# * *7 & / # 7 '& ( ' # 7 # & / & / + . - & & $ % "' ! 0 # ! *2 & / ( * 8 & " & # 7& & # 7 & # ( H * /' # 7 # . " V& E 1 & # ' ( ' % ' / # / * - " ' B+ 5C # B 7& / " / 2 1 1 *7 / & & ! " % *2 ! B !# / *2 # *2 / ( / & " B+ 9C ' % / * !! & " /! ( C & & / 6 ! / / # ( / 6 '# @ " ( & &

! * ( & " ' ' ' ' ' # ) / 0 & 2 , # / ' ' # 27 & C & B+ C / ' A "' % ' % ( ) # ( * & # 7 " & ( ( % - ( *7 / 8 = % % 7 & G ) *+ ) /* & ." =' * # $ ( & & & "'" ' &' * # " ! / . - $ ! & 2 # / " 7& 4 - 7& ( 7 &- & ' ! " &' & # 2 +37 / ' &' & ) & ' P " & &' && # ( " < ! 3' # '& / & ! " ' ' * " ! ! / / &' & 2 / ( ' ! *2 / % & ! ( B& ! # ( & ! " # & B+ 3C &' 2 & " - / ( "/ *2 ! ' - = ; & C / % &' / ' & 2 *+ # 2 &' % $ &' / ( ! / * / ' # ( %

& ! " 7& ) 6 ' # W! ' % & & C & & 7 & 3 '& % & # 7 *7 " ' # " " & 7& 3 ' & ' & ' & ' 7& 7 ( '&- & 3 * / & 2 *7 ' ( / ( " & " ! & * ( " / & 3 ! B % 7 & " 6 & & ' " @ (* ( (* - 3 ' " 3 !! & & & * # " B+ C B+ C '& & & ' - & " &" " ! ! " < ! '& U . - $ 6 # & 3 6 ' "& - % # 7 ! # / " > & & ; , # / &3 / B+ & ( "/ 2 '& " * # " % # * # " 2 ( " * # / " # # ' " B+ $C # " " & & ! "' , " # # ' "' * " % & ! " / % ( # " & " # " / %8 &

& < " % 3 & !# J / & ! / ' & " & # # ! & / " 2 C / & &3 " ( & 3& 3& & / 1 3 ( *7 , & & 3 & ' / & ! & & && & & ! @ / % & # & & " &3 *+ ! ! 3 &3 $ &3' & 3' % 7 &3' 3&' 27 7 ( & *7 & ( 1 & ! J & & & / # '& ' / # # 7& " # & " & 7& - / # ( !! "# # B+ +C ' ! & ' / (- # < " # # % . - $ * # / 2 # " 5 % "/ ( *2 / '& ( 2 # / !# ( " # & 7 # & / = # 2 # " 7 # *2 ) " ) ! B+ ;C # & '! ) ' ! " ! ( # / # & , " & # / & ( & / & & # # *+ *2 / *7 7 $ ( D * # ( B+ C & # & , ! 0 . / ' " & # . ( #

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

,$ # !# 3 & 0 ' ) - & BE @ & # # & # &3 3 % 4 4 B+ 5C , =& 44 4 , - / $ / ,, : + ( $ # % & ! / & , " & & & & " & 2 & " " & / & *7 =X / 7& " " 8 ' ) * '& / / & #7&( & / # " " " = " " " & " / ' B+ 3C " " 7 *2 " / * & / & '( ! # ! ! ( " ! ! R ' ' % ! # !# & 2 ( ! @ / ' & "/ " ' ' # ! ! / / " & ! # " " B+ 9C ( # ' " / ! " 7 ' #2 "& # ' " ' " ' & " !! " " " ( % *7 " & 2 " 7 @ 7 " " ! ' ! ( @ " " & / / 7 ' / *7 ! '# & "# & = ' " *2 " ' / / 7 ) $

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

) ( ) $ ( & ) ) ( P ' & / / ' / # 7& & ( (! & & ! " " ! % 7 & 2 / $ 2 # ! $ / 4 ! % # # & ! " 7 $ & / & " & & ( " , 7 )& ' ! / / & (/ / & & ' 7 * / ! 0 % & & / & ' 2 ' & & ' ! 0 2 & ! ' # & % B ' # & / - P / C& & ! ' & / # " " '/ I & ! & & ' & 2 & # & 1 ' - P 2 *7 ' & 2 / ' ( * # / *7 " % # & * # % & ' 2 & ' ( *7 / - ' ' 7 % / % *2 & % & % . % % B; +C ' B; ;C 0 *7 & B ! C / + ( $ # $ # / $ ( #7 * ! 0 = - S / & = 7 # & 7 7/ # # & ' !# "# % *7 2 ' ) ! & % # & 7 B; C 7 * ( & - 0 % 7 $$ ) $ 0 . 1 $ ;; J / & # &

! ! # & " - & ' ' ' ' ' &' &' ' ' ' - S # ! B; 5C ' ' B; 9C ' ' 27 7 ( # " ' & " # & - & ' ' & ' ' &' ' ' &' ' B; 3C ' ' B; ' ' ' ' C 2 # " & % ! ' # & 1 ' & # "# # ( - % ( ( 5 # % # = # / / &" # & / # & & ! # / & "& / 7 # & & & & ! & # & & ( & " &# & . "# & & , &" ( # " " ( #2 / $+ / + ( $ # # J & & # &7 % # & 7 / & # ! 0 . *2 !! # *7 # ! (* 5 # / 7 @ 6 7 / ! & & # & 27 & *2 C / !# & ! & 7 7( 5 # P / B; 5 " & '( ! # # 7 2 !! & " # C * & ! &7 " # & " 27 7 ( # 6

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! ! ) " @ & " = ! ) " 8:; < * )Q ! 1 ( 6 ( /1 4 (/ 6 % # & " ' ( ( 2 " ( & " > . # / 6 ' 3$; # & & " ' ( 6 & " *7 6 * / # & Q / / / * 2 @ 0 Q 6 ' " / & " = & " # 2 # ! G * & * # , & & " ' ( & ! ) " ! ) " # @ / ) ) # * ! ( - $ < B 3 +;C # *2 & & ( / #2 ! "/ ! & " # 2 *2 & ( / 7& " ( ) ! 7& B C & ( . ' / / ! ! / 0 . 2 (7 ' B . ( " / C 9 !4 # # + 5 * # ( *2 $% & * 2 !' 2 / ! % / ! / / . ( 7 7 ! 1 * & ! ! - - ! ! < !2 ( " ' " & B C / 5 8 B $C 8 5 B +C 8 8 '& " 5 8 D * 5 5 5 8 %! ( *2 2 / ( # 4. D & ] ( * # B & L 1 !2 ( < 2/ # # ! # / / M & ! # ( 27 7 ! # 4. ! C # # &

/ 2 ( / & H/ 7 ! # 2 " ) / 3 + # & * 6 ' / #2 B! (/ ( ! & 2 *7 ( / " *2 2 C & # 3 & / ! !4 # # + 5 * # 9 $% & * A.Einstein, B Podolsky, N Rosen (EPR) 1935, bizonyítják(?), hogy a kvantummechanika nem teljes D. Bohm 1957 AKalcit Fotonpár forrás A B+ Kalcit A+ Kalcit A Fotonpár forrás B B- Kalcit B Szigorú korreláció van a két oldal eredményei között, ha ugyanolyan berendezés van mindkét oldalon. Különbözo berendezések a két oldalon Aforrás A- B- B+ forrás A+ A+ forrás B- forrás B+ 9 !4 ) & # # + 5 * # $% & * ! # & / # " ! % ! !2 ( ! # '! # '! ! 9/ # 7 #2 ! & # & & 3 3 ! ! ! ! ! ! ! ! 2 ! *7 3 / ! & & 3 & /# # # " ! & ! ! ! & 2 ! ! < !# / ! & ! & 3 & / ' & & " ' ( *7 , & ! / / B ! 3 ! ' *7 / = ( / *7 ;C 7 & /*

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

Bell: N(A+,C+) < N(B+,C+) + N(A+,B+) P(A+,C+) < P(B+,C+) + P(A+,B+) ( sin2 600 = sin2 300 + sin2 300 0,75 = 2· 0,25 =0,5 ?? A+ C- #( A kvantummechanika sérti a Bell egyenlotlenséget! N(A+,C+) = N(össz) P(A+,C+)/18 (kapcsolat a valószínuséggel) Bell : #$ B+ ÖSZZEVETÉS A KVANTUMMECHANIKÁVAL C+ P(A+,C+) = sin2 (A+,C+) A- P(B+,C+ ) = sin2 (B+,C+) P(A+, B+) = sin2 (A+,B+) B- ; <' ' 1 A kvantummechanika sérti a Bell egyenlotlenséget! * / & & ( & ( : % ! ! " # " * ' . ! # & & ! 9 = B & ! # ' !# ' ! ! ! 2 ! ! ! " ! # % * * "# & / * & " 7 ( 7 / / ! 7 ! = & 2 C # = ! & / ! / ! & 2 / 7 2 B * < * 7 * # " / & # * ( " 6 ' "# B C 7& #2 ( " I# ! #$ *7 #( ! 9; ( & 7 7 ( = % * 2 B * ( 7 " = & ' ) & '# / # J 7 & / !

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

& , ( # - % 0( ;+ % *2 & & ( & " , & ! 7 *2 & (# 2 % ; , *2 & & ; % 7 / *2 & & B # ! 0( 7 "! 7& ) @ 6 *2 I & & " / (B , ' , ! 7 & ; 7 $ C ' , ! I *2 & 7& & " # 6 $ C + *2 & " 7 7 7 * + ; ; ! + % H $ C 7 H ;+ & & 7 ( *2 & / " *2 ( , + B , + * *2 ;+ + + B ( ! * $$C !! # 5 93 $ . 5 %! D ' " & ! ! ! & ! # & / " ! 8 6 # B $ $ ! & $ " $ 2 7 " = % C * )= " = )= " = ( B C B $C = * & ( B +C B ;C )= *2 & 1 "/ # *2 & $ ! $ = $7 ! # " ! *2 & $ / & ( $" # 7& =$ $ = / $ 2$ 2 $ $2 $ $ % # ) ! ! & ! ! # & ! / & ! / ! ! / ( *2 ! ! # & 2 O / & 2 *7 ( ! ( $& ! # @ & $ 7 7 & ! # & ! / 7 7 3 !! 9

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

"/ ! ! & 39 !0 ! % & & " ' ( / # - & # % "" # & ( & / " ! & * % ( ( & "# # & # *2 & *2 ( * 77 / / ) : J= )! * % 7 H ' & & / % & ! " / H * H * % % H * ( *2 ( ( ( = & # + J= = + = *2 & 6 & & / # + J= ;+ = *2 ( " H & & - 6 : * # *2 & ' = .* * % & H ' H *2 & # * " + 7 & # *2 & # + J= = *2 & * )! / * .* *2 & + = % " % ! 0 ! .* J= H / # ! ' # *2 & / ) / 7 ( 27 B H C + % *( & P "# * / # ! * ( * # & "# *7 " / # * # # & ! # / & & % ;9 # *2 & 6 & *7 / '& / < J 2 K % ! !(K & 1 ( I = . J=!& " ! J 2 B $C !0 - # * # !# 33 ( / . ) * # & "#) & 1 % / & *7 ' +C B ;C B C B 5C # . " B " #

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

#7&( 5 '# @ & 6 ' "# ! 27 7 & # ( 7( ! & #2 . ' S W! / & @ " & " & / # / 2 & ( 7 ! " % ' - ' ' $ " ' ) @ ! ! / ! ! " $ B 5 C !1 % ( ' ' < 27 & # 7 $ " ' 7 ( ) 27 (/ " ( & % & 4 27 7 ! ' 7 (* & & 7 , " " ! & ( 7 7 ' " ( 7 7 B 5 C ' " 6 & 27 7 4 2 / ) ! / < ( " 2 / 7 27 2 / " @ ' 7 2 " 27 ! 2 *7 " % 27 7 & ' 2 ' ! " ! "" ! , " / % / ' ! 4 " / ( & ' 1 ! / & " ' / " > / #2 2 / % B 5 $C % & % & ! ! 27 7 27 7 / ( @ B 5 +C % Y Y ( / / / / !# / & ! @ & ( 7 2 ( "# % 3 =& 6 B & / " & "# B 5 ;C % ( * # C 27 " 7 (& ( !1 & 2 (

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

$# + 2 B 7& * P & ! # & 3 6 * / # & 3 & , ! / " & / @ & / '4 ! ! & " # / ( 7 # ! - " " *7 & ( ! ! # ! + " = & $" $ $ ! I & $7 # "$ 7& / ! ! & " 0 / P "# ( 7 2 ( & " ! * " C # C 0 ' & ! ! ! " " / "& ! ! ! # " # " 7& / / B$ ;C " # " ( ( H# ! ) 7 H B & "& & ) / " + 6 ' "# " & " " / ( !" # & & # & / $" ( 7 7 ! ! ' "# % !" & "" *7 " 27 - 7 ( 7& / "/ / 0 & / *7 # ! " / H !" 2 & 7* 7* & & ! ! ' "/ ( *2 ( " 1 & & ( ! ! " # ( / ) & # / !" & !# B$ " " " " " " ' & " " ! # 7 & " ! & & , ( ! 2

* ( <5 & B$ 5C " " * # / C " *7 '4 "" / ( 5 ( ! 0 ( 2 " " " " 2 % 1 C C !( ! % *7 7 2 < =& ' < ( 2 / & ! 2 7 < " / / & 2 *7 " + ) ! <" 7 7 # & " " 0 / ( & < B$ 3C <" + + ) 2 !" # % / / B$ C B$ C ! ; '# C < ! " + & & ! # ; ) ( ' < / ) # C 7 ! / / ( ! ; ! B$ 9C B 2 ! !# B ( ( ( ' # & ( " !! * 0 0 < 1 # # < + # /' / ; < ; < ! ! " - " & ! ( 7 & ' ( " # + " + " + B$ C B$ " + $C 7 7 " + ) " + 9 '4 7& ( " # ( / " + + / " / <" " 0 C 2 " " " 0 " " " " 0 < " " B$ ;C )=) ), B$ C ; ) ), " " ! " = +C &

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