Qu a n t u m W e i r d n e s s : Sc h r ö di n g er ’ s C a t , E P R , a n d Be l l ’ s T h e o r e m
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8 .2 2 5 / S T S .0 4 2 , P h y s ic s in t h e 2 0 t h C e n t u r y P r o f e s s o r D a v id K a is e r , 1 4 O c t o b e r 2 0 2 0
1. S u p e r p o si t i o n a n d Sc hröd i ng er ’ s C at
2. E P R a n d “ E l e m e n t s of R e al i t y ”
3. B e l l ’ s I n e q u a l i t y a n d En t a n g l e m e n t *
* S e e o p t i o n a l Le c t u r e N o t e s on B el l ’ s i neq u a l i t y
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In 1 9 2 6 , Er w i n S c h r ö d i n g e r dev el o p ed a n a p p r o a c h t o a f i r s t - pr i nc i pl e s qua n t um m e c h a n i c s , w h i c h a p p e a r e d ( a t f i r s t ) t o b e d i s t i n c t f r o m He i s e n b e r g ’ s ma t r i x me c h a n i c s . B u i l d i n g o n Lo u i s d e Br o g l i e ’ s su g g e st i o n a b o u t ma t t e r w a v e s , S c h r ö d i n g e r i n t r o d u c e d a wa v e e q u a t i o n fo r a n e w q u an t i t y , t h e
qua nt um w a v e f unc t i o n .
So l ut i o n s o b e y e d su p er p o si t i o n : i f 1 ( t , x ) an d 2 ( t , x ) we r e e a c h so l u t i o n s , t h e n so w a s 3 ( t , x ) = 1 ( t , x ) + 2 ( t , x ) . T h a t y i e l d s in t e r f e r e n c e .
in t e r f e r e n c e
In su m m e r 1 9 2 6 , Ma x Bo r n su g g e st e d t h a t ( t , x ) is a “ p r o b ab i l i t y am p l i t u d e . ” Pr o b a b i l i t y = | | 2 .
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Courtesy of Elsevier, Inc.,
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https://www.sciencedirect.com . Used with permission.
Su p er p o s i t i o n a n d Q u a n t u m St a t es
Br i t i s h p h y s i c i s t Pa u l D i r a c fu r t h e r fo r m al i z e d S c h r ö d i n g e r ’ s ap p r o ac h . I n ge n e r a l , a q u a n t u m s t a t e c o u l d b e r e p r e s e n t e d a s a ve c t o r in a n ( a b s t r a c t ) ve c t o r s p a c e . T h a t s t a t e ve c t o r c o u l d i t s e l f b e r e p r e s e n t e d a s a w e i g h t e d s u m
of “ e i g e ns t a t e s ” : s t a t e s w i t h a d e f i ni t e v a l u e f or a s pe c i f i c pr ope r t y :
(T h i s i s j u s t a m o r e f o r m a l o r a b s tr a c t w a y o f r e p r e s e n ti n g su p er p o si t i o n :
if e a c h o f t h e s t a t e s is a s o lu t io n , t h e n s o is t h e ir s u m . )
Ev en t h o u g h t h e i n d i v i d u a l ei g en s t a t es a r e in c o m p a t ib le w it h e a c h o t h e r , w e m a y c o n s t r u c t a v al i d q u an t u m s t at e v i a s u p e r p o s i t i o n .
T h e t w o s p i n s t at e s ar e o r th o g o n al ; t h e i r c o r r e s p o n di n g s t at e v e c t o r s h a v e v an i s h i n g o ve r lap :
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Su p er p o s i t i o n a n d Q u a n t u m St a t es
If w e pe r f or m a m e a su r e m e nt of spi n a l ong z fo r a p ar t i c l e p r e p ar e d in t h is s t a t e :
Ea c h t i m e t h e s p i n i s m ea s u r ed a l o n g z , w e a l w a y s f i n d a de f i n i te re s u l t : ei t h er s p i n u p o r s p i n do w n . W e n ev er f i n d a “ s m ea r ed o u t ” o r f u z z y r es u l t .
An d y e t , a c c o r d i n g t o Bo r n , Di r a c , Bo h r an d t h e ot he r s , q u a nt u m m e c ha ni c s c a n onl y be u s e d t o ca l cu l a t e pr o babi l i ti e s ; t h e e q u a t i o n s of f e r n o w a y t o kn ow in a d v a n c e wh e t h e r t h e p a r t i c l e w a s re a l l y sp i n u p o r sp i n d o w n , p r i o r t o t h e m e a su r e m e n t .
T h e t w o s p i n s t at e s ar e o r th o g o n al ; t h e i r c o r r e s p o n di n g s t at e v e c t o r s h a v e v an i s h i n g o ve r lap :
Su p er p o s i t i o n a n d Q u a n t u m St a t es
If w e pe r f or m a m e a su r e m e nt of spi n a l ong z fo r a p ar t i c l e p r e p ar e d in t h is s t a t e :
Bo h r w e n t f u r t h e r : w h a t if t h e p a r t ic le h a d n o d e fin it e v a lu e ( e . g ., o f
sp i n a l o n g z ) p r i o r to i ts m e as u r e m e n t? A s i f a p e r s o n h ad no
p a r t ic u la r w e ig h t un t i l s t e p p i n g o n a b a t h ro o m s c a l e .
y a de f i n i te re s u l t :
p n . W e n ev er f i n d a “ s m ea r ed o u t ” o r f u z z y r es u l t .
An d y e t , a c c o r d i n g t o Bo r n , Di r a c , Bo h r an d t h e ot he r s , q u a nt u m m e c ha ni c s c a n onl y be u s e d t o ca l cu l a t e pr o babi l i ti e s ; t h e e q u a t i o n s of f e r n o w a y t o kn ow in a d v a n c e wh e t h e r t h e p a r t i c l e w a s re a l l y sp i n u p o r sp i n d o w n , p r i o r t o t h e m e a su r e m e n t .
T h e t w o s p i n s t at e s ar e o r th o g o n al ; t h e i r c o r r e s p o n di n g s t at e v e c t o r s h a v e v an i s h i n g o ve r lap :
Sc h r ö di n g er ’ s C a t
Ei n s t e i n gr e w f r u s t r a t e d w i t h t h i s r e s t r i c t i o n t o o n l y c a l c u l a t i n g pr o babi l i ti e s . H e w r o t e to h i s g o o d f r i e n d Ma x B o r n in D e c e m b e r 1 9 2 6 :
“Q u a n tu m m e c h a n i c s i s c e r ta i n l y i m p o si n g . B u t a n i n n e r v o i c e te l l s m e i t i s n o t y e t th e r e a l th i n g . T h e th e o r y s a y s a l o t, b u t d o e s n o t r e a l l y b r i n g u s a n y c l o s e r to th e se c r e t o f t h e ‘ o l d o n e . ’ I, a t a n y r a t e , a m c o n v i n c e d t h a t He is n o t p la y in g a t d ic e . ”
Ei n s t ei n a n d S c h r ö d i n g er b eg a n d i s cu s s i n g t h es e p o i n t s t o g et h er a s w el l , o n ce Sc h r ö d i n g e r m o v e d t o B e r l i n i n 1 9 2 7 . ( H e s uc c e e d e d Ma x P l a n ck .) T h e y e n j o y e d Wi e n e r Wü r s t e l a b e n d e ev en i n g s t o g et h er ( V i en n es e s a u s a g e p a r t i es ) , a n d s a i l i n g o n t h e l a k e n ea r Ei n s t ei n ’ s s u m m er h o m e .
?
In one l e t t e r , E i nst e i n a sk e d S c hr öd i ng e r t o i m a g i ne t ha t a ba l l ha d be e n pl a c e d i n one of t w o i d e nt i c a l , c l os e d bo x e s .
Pr i o r t o o p e n i n g e i t h e r b o x , t h e p r o b a b i l i t y o f f i n d i n g t h e b a l l
in B o x 1 w a s 5 0 % . “ I s t h is a c o m p le t e d e s c r ip t io n ? NO : A co m p l et e s t a t em en t i s : t h e b a l l is (o r i s n o t) i n th e f i r s t b o x . ”
Sc h r ö di n g er ’ s C a t
Na z i b o o k - bu r ni ng r a l l y i n B e r l i n, s pr i ng 1 9 3 3
Image is in the public domain.
Bo t h E i n s t e i n a n d S c h r ö d i n g e r l e f t Ge r ma n y o n c e t h e Na z i s t o o k p o w e r i n 1 9 3 3 . Th e y c o n t i n u e d t h e i r d i s c u s s i o n s b y l e t t e r ; t h e i r ex a m p l es b eg a n t o r ef l ect t h e da r k er t i m es .
Ei n s t e i n to Sc hr ö d i n g e r , 8 A u g u s t 1 9 3 5 : I m a g i n e a c h a r g e o f gu n p o w d e r th a t w a s i n tr i n si c a l l y u n sta b l e , w i th 5 0 - 50 o d d s o f ex p l o di n g o v er t h e co u r s e o f o n e yea r . “ I n p r i n ci p l e t h i s ca n q u i t e ea s i l y b e r e p r es en t ed q u a n t u m - me c h a n i c a l l y ” :
“A f t e r t h e c o u r s e o f a y e a r t h i s i s n o l o n g e r t h e c a s e a t a l l . R a t h e r , t h e - fu n c t i o n t h e n des cr i b es a s o r t o f b l en d o f n o t - yet a n d o f a l r ea dy - ex p l o ded s ys t em s . [ . . . B u t ] i n r ea l i t y th e r e i s ju s t n o i n t e r m e d i a r y be t w e e n e x pl od e d a nd not - ex p l o ded. ”
Sc h r ö di n g er ’ s C a t
Sc hr ö d i n g e r re p l i e d t o Ei n s t e i n on 1 9 A u g u s t 1 9 3 5 , w i t h a t w i s t :
“C o n f i n e d i n a ste e l c h a m b e r i s a Ge i g e r c o u n t e r pr e pa r e d w i t h a t i ny am o u n t o f [ r ad i o ac t i v e ] u r an i u m , s o sm a l l t h a t i n t h e n e x t h o u r i t i s j u st a s pr oba bl e t o e x pe c t one a t om i c d e c a y a s none . A n am p l i f i e d r e l ay pr o v i d e s t ha t th e f i r s t a to m i c d e c a y s h a tte r s a s m a l l bo t t l e o f pr us s i c a c i d [c y a n i d e p o i s o n ]. Th i s a n d — cr u el l y — a c at i s al s o tr a p p e d i n th e s te e l c h a m b e r . ”
“A f t e r o n e h o u r , t h e l i v i n g a n d de a d c a t a r e s m e a r e d o ut i n e qua l me a s u r e . ”
© Dhatfield on Wikimedia Commons. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair- use/
Sc h r ö di n g er ’ s C a t
Sc hr ö d i n g e r re p l i e d t o Ei n s t e i n on 1 9 A u g u s t 1 9 3 5 , w i t h a t w i s t :
An i r o n y : B y e a r l y m i d - 1930s , S c h r ö d i n g e r h a d b e c o m e sk e p t i c a l of s om e of hi s o w n c ont r i bu t i ons t o q u a nt u m me c h a n i c s , a n d — al o n g w i t h E i n s t e i n — be c a m e a n ou t s pok e n c r i t i c . H e i n v e nt e d hi s c a t pa r a d o x a s a cr i t i q u e of th e c e n tr a l r o l e o f s u p e r p o s i ti o n a n d p r o b a b i l i ti e s i n qua n t um t h e o r y .
Ei n s t e i n ’ s re p l y ( 4 S e p t e m b e r 1 9 3 5 ) : “ Y o u r c a t s h o w s t h a t we a r e i n c o m p l e t e a g r e e m e n t . A - fu n c t i o n t h at c o n t ai n s th e l i v i n g a s w e l l a s th e d e a d c a t j u s t c a n n o t b e ta k e n a s a des cr i p t i o n o f t h e r ea l s t a t e o f a f f a i r s . ”
“C o n f i n e d i n a ste e l c h a m b e r i s a Ge i g e r c o u n t e r pr e pa r e d w i t h a t i ny am o u n t o f [ r ad i o ac t i v e ] u r an i u m , s o sm a l l t h a t i n t h e n e x t h o u r i t i s j u st a s pr oba bl e t o e x pe c t one a t om i c d e c a y a s none . A n am p l i f i e d r e l ay pr o v i d e s t ha t th e f i r s t a to m i c d e c a y s h a tte r s a s m a l l bo t t l e o f pr us s i c a c i d [c y a n i d e p o i s o n ]. Th i s a n d — cr u el l y — a c at i s al s o tr a p p e d i n th e s te e l c h a m b e r . ”
“A f t e r o n e h o u r , t h e l i v i n g a n d de a d c a t a r e s m e a r e d o ut i n e qua l me a s u r e . ”
Qu e s t i o n s ?
EP R a n d “ El e m e n t s o f R e a l i t y ”
Th a t s a m e y e a r ( 1 9 3 5 ) , Ei n s t e i n an d t w o y o u n g e r c o l l e ag u e s at t h e Inst i t u t e f or A d v a nc e d S t u d y i n P r i nc e t on ( Bo r i s P o d o l s k y an d Na t h a n Ro s e n ) pu bl i s he d a n e v e n m or e e l a bor a t e c r i t i q u e of q u a nt u m t he or y .
de t e c t o r 1 de t e c t o r 2
x p x
x p x
pa r t i cl e A
S
pa r t i cl e B
Th e q u a n t u m s t a t e d o e s n o t fa c t o r i z e : a c c o r d i n g t o q u a n t u m m e c h a n i c s , t h e r e i s n o w a y to d e s c r i b e th e b e h a v i o r o f p a r ti c l e A wi t h o u t r e f e r r i n g t o t h e b e h a v i o r o f p a r t i c l e B .
Ac c o r d i n g t o q u a n t u m m e c h a n i c s , p r i o r t o e i t h e r m e a s u r e m e n t t h e s y s t e m w o u l d be d e s c r i be d b y a su p er p o si t i o n of t w o d i f f e r e nt t w o - pa r t i c l e s t a t e s :
EP R a n d “ El e m e n t s o f R e a l i t y ”
Sup p o s e p h y s i c i s t 1 m e a s ur e s t h e po s i ti o n of pa r t i c l e A . T h e n , f r o m t h e co n s er v a t i o n o f m o m en t u m , s h e i m m edi a t el y k n o w s t h e po s i ti o n of pa r t i c l e
B . Or ph y s i c i s t 1 c ou l d c hoos e t o m e a s u r e t he mo me n t u m of pa r t i c l e A .
de t e c t o r 1 de t e c t o r 2
x p x
x p x
pa r t i cl e A
S
pa r t i cl e B
If she w a i t e d u nt i l t he l a st possi bl e m om e nt t o d e c i d e w hi c h m e a su r e m e nt t o pe r f or m , t he r e w ou l d not be e nou g h t i m e f or a s i g na l t o up d a t e pa r t i c l e B as t o w h at va l u e s i t s h o u l d h a ve f o r va r i o u s p r o p e r t i e s . S o p a r t i c l e B mu s t h a v e c a r r i e d i t s o w n se t o f d e f i n i t e p r o p e r t i e s on i t s ow n , p r i o r t o m e a s u r e m e n t .
Qu a n t u m me c h a n i c s d o e s n o t d e s c r i b e p a r t i c l e B ’s p r o p e r t i e s o n i t s o w n .
Th e r e f o r e quant um m e c h ani c s m us t be i nc o m pl e t e .
EP R a n d “ El e m e n t s o f R e a l i t y ”
Th e E P R c o n c l u s i o n r e l i e d u p o n tw o as s u m pti o n s :
de t e c t o r 2
de t e c t o r 1
x p x
x p x
pa r t i cl e A
S
pa r t i cl e B
Th i s i s a n a s s u m p t i o n t h a t q u a n t u m o b j e c t s p o s s e s s co m p l e t e s e t s o f pr o pe r ti e s o n th e i r o w n , p r i o r t o o u r e f f o r t s t o m e a s u r e t h e m .
“ Re a l i t y c r i t e r i o n ” (p . 7 7 7 ): “I f , w i th o u t i n a n y w a y d i stu r b i n g a sy ste m , w e c a n pr e d i c t w i t h c e r t a i nt y ( i . e . , w i t h pr oba bi l i t y e q u a l t o u ni t y ) t he v a l u e of a ph y s i c a l qua n t i t y , t h e n t h e r e e x i s t s a n e l e m e n t o f r e a l i t y c o r r e s p o n d i n g t o t h i s p h y s i c a l qua n t i t y . ”
“ Lo c a l i t y ” (p . 7 7 9 ): “S i n c e a t th e ti m e o f m e a su r e m e n t th e tw o sy ste m s [ p a r ti c l e s A an d B ] n o l o n g e r i n t e r a c t , n o r e a l c h a n g e c a n t a k e p l a c e i n t h e s e c o n d s y s t e m i n co n s eq u en ce o f a n yt h i n g t h a t m a y b e do n e t o t h e f i r s t s ys t em . ”
Th i s i s a n a s s u m p t i o n t h a t n o i n f l u e n c e c a n t r a v e l ar bi tr ar i l y q u i c k l y : lo c a l c a u s e s y ie ld lo c a l e f f e c t s .
EP R a n d “ El e m e n t s o f R e a l i t y ”
Th e E P R c o n c l u s i o n r e l i e d u p o n tw o as s u m pti o n s :
de t e c t o r 1
x
“ Re pr e d i
g sy ste m , w e c a n
w i t h pr oba bi l i t y e q u a l t o u ni t y ) t he v a l u e of a ph y s i c a l qua n t i t y , t h e n t h e r e e x i s t s a n e l e m e n t o f r e a l i t y c o r r e s p o n d i n g t o t h i s p h y s i c a l qua n t i t y . ”
Th i s i s a n a s s u m p t i o n t h a t q u a n t u m o b j e c t s p o s s e s s co m p l e t e s e t s o f pr o pe r ti e s o n th e i r o w n , p r i o r t o o u r e f f o r t s t o m e a s u r e t h e m .
E in s t e in to Ma x B o r n , 3 M a r c h 1 9 4 7 : “ I c a n n o t s e r io u s ly b e lie v e in
[qua n t um m e c h a n i c s ] b e c a us e t h e t h e o r y c a n n o t b e re c o n c i l e d w i t h
t h e id e a t h a t p h y s ic s s h o u ld r e p r e s e n t a r e a lit y in t im e a n d s p a c e , f r e e
.”
fro m
s p o o k y a c t io n s a t a d is t a n c e
“ Lo c a l i t y ” (p . 7 7 9 ): “S i n c e a t th e ti m e o f m e a su r e m e n t th e tw o sy ste m s [ p a r ti c l e s A an d B ] n o l o n g e r i n t e r a c t , n o r e a l c h a n g e c a n t a k e p l a c e i n t h e s e c o n d s y s t e m i n co n s eq u en ce o f a n yt h i n g t h a t m a y b e do n e t o t h e f i r s t s ys t em . ”
Th i s i s a n a s s u m p t i o n t h a t n o i n f l u e n c e c a n t r a v e l ar bi tr ar i l y q u i c k l y : lo c a l c a u s e s y ie ld lo c a l e f f e c t s .
Qu e s t i o n s ?
Be l l ’ s I n e q u a l i t y a n d En t a n g l e m e n t
“L o c al R e al i s m ”
In 1 9 6 4 , Ir i sh ph y si c i st Jo h n S . B e l l sc r u t i n i z e d t h e EP R p a p er , r et u r n i n g t o t h e t w o m a i n a s s u m p t i o n s t h a t th o s e a u th o r s h a d m a d e :
• E a c h pa r t i c l e ha s d e f i ni t e pr ope r t i e s , on i t s o w n, be f or e i t i s m e a s u r e d . ( Re a l i t y c r i t e r i o n )
• N o i nf l u e nc e c a n t r a v e l a c r oss spa c e a r bi t r a r i l y
A qui c k l y . ( Lo c a l i t y )
det ect o r s et t i n g s : a , b
me a s u r e me n t o u t c o me s : A , B
Be l l s u g g e s t e d : t h e s e a r e as s u m pti o n s , a n d we c a n t r y t o te s t th e m .
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Co r r e l a t i o n s a t a D i s t a n c e
Di c h o t o mi c o b s e r v a b l e s Co r r e l a t i o n f u n c t i o n s
B e ll: if
| S | ≤ 2.
S
th e n ( L ocal i t y : A does not depend on
b or B , and vi ce ver s a.)
QM p r e d i c t i o n :
S ma x = 2 √ 2
Be l l ’ s i n e q u a l i t y
Qu a n t u m me c h a n i c s p r e d i c t s t h a t q u a n t u m s y s t e ms c a n b e
mo r e s t r o n g l y c o r r e l a t e d th a n B e ll ’ s in e q u a lity w o u ld a llo w .
© source unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/ help/faq-fair-use/
Images © sources unknown. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/
Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
or
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
or
a
+1
- 1
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
- 1
+1
a
or
- 1
+1
a ’
or
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
- 1
+1
a
or
- 1
+1
a ’
or
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
- 1
+1
a
or
Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
- 1
+1
a ’
or
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
b
- 1
+1
a
or
Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
b ’
- 1
+1
a ’
or
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Al i c e
Ca m b r i d g e , M A
Bo b
Ca m b r i d g e , U K
“W h a t w o u l d y o u l i k e f o r d es s er t? ”
b
- 1
+1
a
or
Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
b ’
- 1
+1
a ’
or
Bo b c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
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Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Bo b c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Al i c e
Bo b
m b r i d g e , U K
b
a
Ca m b r i d g e ,
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Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Bo b c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Al i c e
Bo b
m b r i d g e , U K
b ’
a
b
a
Ca m b r i d g e ,
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Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Bo b c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Al i c e
Bo b
m b r i d g e , U K
b ’
a ’
b ’
a
b
a
Ca m b r i d g e ,
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Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Bo b c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
Al i c e
Bo b
m b r i d g e , U K
b ’
a ’
b ’
a
b
a
Ca m b r i d g e ,
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“Sp o o k y” co r r el at i o n s !
Al i c e Bo b
Ca m b r i d g e ,
m b r i d g e , U K
a
b
a
b ’
a ’
b ’
Bo b c h o o s e s th e fir s t o p tio n
ha l f t he t i B m e .
Al i c e c h o o s e s th e fir s t o p tio n ha l f t he t i m e .
?!
Co s m i c B e l l E x p e r i m e n t s
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Ro q u e d e l o s M u c h a c h o s O b s e r v a t o r y , L a P a l m a Phot o b y C a l v i n L e ung
Courtesy of Calvin Leung. Used with permission.
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Las er
No n l i n e a r cryst al
Bo b
Al i c e
ar X i v : 1 8 0 8 . 0 5 9 6 6
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2. 3 µ s
2. 2 µ s
Las er
No n l i n e a r cryst al
No t e n o u g h t i me f o r a s i n g l e lig h t b e a m to h a v e tr a v e le d fr o m o n e d e t e c t o r t o t h e o t h e r .
Bo b
Al i c e
3. 4 µ s
ar X i v : 1 8 0 8 . 0 5 9 6 6
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Ga l i l e o Na t i o n a l Wi l l i a m H e r s c h e l Te l e s c o p e Te l e s c o p e
Image is in the public domain.
© Nik Szymanek and Ian King. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq - fair-use/
ar X i v : 1 8 0 8 . 0 5 9 6 6
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WllT - Te eec‹›pe Bell test with entangled photons
TNC - Telescope
Color
RxB Tx- B Tx- A
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Th e m e a s u r e d c o r r e l a t i o n s ex c eed Be l l ’ s i n e q u a l i t y b y mo r e t h a n 9 s t a n d a r d d e v i a t i o n s , w i t h d e t e c t o r s e t t i n g s det er m i n ed b y ev en t s t h a t o ccu r r ed o n o p p o s i t e s i des of t he u ni v e r s e , 8 a nd 1 2 bi l l i on y e a r s a g o!
Th e w o r l d a p p e a r s t o b e j u s t a s “ sp o o k y ” a s q u a n tu m m e c h a n i c s des cr i b es !
Qu a n t u m W e i r d n e s s S u mma r y
2
Ev en t h o u g h t h e i n d i v i d u a l ei g en s t a t es a r e i n co m p a t i b l e w i t h ea c h
1 ot he r , w e m a y c ons t r u c t a v a l i d q u a nt u m s t a t e v i a su p er p o si t i o n :
1 2 3 4 5 6 7
- 1
- 2 co n s t r u ct i v e
2 in t e r f e r e n c e
1
-
-
4 5 6 7
de s tr u c ti v e in t e r f e r e n c e
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Ar e pr o babi l i ti e s ca l cu l a t ed fr o m su p er p o si t i o n s re a l l y e n o u g h to d e s c r i b e o u r w o r l d ?
Ca n w e m a k e s e n s e o f t h e be ha v i or of en t a n g l ed sy st e m s , w h i c h d o n o t o b e y “l o c a l r e a l i sm ”?
de t e c t o r 1 de t e c t o r 2
x p x
pa r t i cl e A
S
pa r t i cl e B
x p x
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STS.042J / 8.225J Einstein, Oppenheimer, Feynman: Physics in the 20th Century
Fall 202 0
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