= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 P R O T O T Y P E   P H Y _ 0 0 5   -   T H E   Q U A N T U M   F A M I L Y   ( l a w s   0 6 6 - 0 8 5 ) 
 
 P r o v e s   t h e   Q U A N T U M   l a w s   i n t e r a c t   w i t h   t h e   f i e l d 
 
 Q u a n t u m :   L a w   0 6 6   P l a n c k   Z P F ,   L a w   0 7 0   u n c e r t a i n t y ,   L a w   0 7 4   B o r n , 
 
 L a w   0 8 4   E P R ,   L a w   1 5 7   m e a s u r e m e n t   +   E q   5 0   o b s e r v e r - g a t e 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
     t h e   o b s e r v e r   g a t e   T h e t a _ p h i   =   C _ c r i t * ( 1 + p h i ^ - 1 )   =   0 . 9 1 1 3 7 8 6 7 9   ( c o r p u s :   0 . 9 1 1 4 ) 
 
 
 
 [ R U N   1   -   T H E   V A C U U M   I S   N O T   S I L E N T   ( L a w   0 6 6   P l a n c k ) ] 
 
     u ( n u , T )   a t   k a p p a = 0   ( c l a s s i c a l )   v s   k a p p a = 1   ( p h i - Z P F   f l o o r ) : 
 
     T   =   1 . 0 0 e + 0 0 :   u ( 0 )   =   1 . 4 6 2 6 6 7 e + 0 1   |   u ( 1 )   =   2 . 2 3 9 3 1 1 e + 0 1   ( t h e   p h i - Z P F   f l o o r   p e r s i s t s   a t   T - > 0 ) 
 
     T   =   5 . 0 0 e - 0 1 :   u ( 0 )   =   3 . 9 3 3 7 1 7 e + 0 0   |   u ( 1 )   =   1 . 1 7 0 0 1 6 e + 0 1   ( t h e   p h i - Z P F   f l o o r   p e r s i s t s   a t   T - > 0 ) 
 
     T   =   1 . 0 0 e - 0 1 :   u ( 0 )   =   1 . 1 4 1 0 7 6 e - 0 3   |   u ( 1 )   =   7 . 7 6 7 5 8 5 e + 0 0   ( t h e   p h i - Z P F   f l o o r   p e r s i s t s   a t   T - > 0 ) 
 
     T   =   1 . 0 0 e - 0 2 :   u ( 0 )   =   9 . 3 4 9 5 7 1 e - 4 3   |   u ( 1 )   =   7 . 7 6 6 4 4 4 e + 0 0   ( t h e   p h i - Z P F   f l o o r   p e r s i s t s   a t   T - > 0 ) 
 
     T   =   1 . 0 0 e - 0 9 :   u ( 0 )   =   0 . 0 0 0 0 0 0 e + 0 0   |   u ( 1 )   =   7 . 7 6 6 4 4 4 e + 0 0   ( t h e   p h i - Z P F   f l o o r   p e r s i s t s   a t   T - > 0 ) 
 
     - >   a t   T - > 0   t h e   c l a s s i c a l   s p e c t r u m   v a n i s h e s   b u t   t h e   p h i - Z P F   f l o o r   h b a r * o m e g a / 2   p e r s i s t s   ( L a w   0 6 6   /   E q   8 1 ) :   P A S S 
 
 
 
 [ R U N   2   -   U N C E R T A I N T Y   I S   T H E   B R E A T H I N G   R O O M   O F   M O T I O N   ( L a w   0 7 0 ) ] 
 
     k a p p a   |   d x * d p   b o u n d   ( > = ) 
 
       0 . 0 0   |   0 . 5 0 0 0 0 0 0 0 0 
 
       0 . 2 5   |   0 . 5 7 7 2 5 4 2 4 9 
 
       0 . 5 0   |   0 . 6 5 4 5 0 8 4 9 7 
 
       0 . 7 5   |   0 . 7 3 1 7 6 2 7 4 6 
 
       1 . 0 0   |   0 . 8 0 9 0 1 6 9 9 4 
 
     d e g e n e r a t e :   d x * d p   > =   0 . 5 0 0 0 0 0 0 0 0   =   h b a r / 2   ( e r r   0 ) :   P A S S 
 
     f u l l   c o u p l i n g :   d x * d p   > =   0 . 8 0 9 0 1 6 9 9 4   =   h b a r * p h i / 2   -   c o h e r e n t   c a r r i e r s   c a r r y   M O R E   b r e a t h i n g   r o o m   ( L a w   0 7 0 ) :   P A S S 
 
 
 
 [ R U N   3   -   P R O B A B I L I T Y   I S   C O H E R E N C E   S Q U A R E D   ( L a w   0 7 4   B o r n ) ] 
 
     | P s i | ^ 2   =   0 . 6 4   ( a   t y p i c a l   a m p l i t u d e ) 
 
     k a p p a = 0 . 0 0 :   P _ p h i   =   0 . 6 4 0 0 0 0 0 0 0 
 
     k a p p a = 0 . 5 0 :   P _ p h i   =   0 . 6 5 9 7 7 7 0 8 8 
 
     k a p p a = 1 . 0 0 :   P _ p h i   =   0 . 6 7 9 5 5 4 1 7 5 
 
     d e g e n e r a t e :   P ( 0 )   =   0 . 6 4 0 0 0 0 0 0 0   =   | P s i | ^ 2   ( e r r   0 . 0 0 0 0 0 0 0 0 0 ) :   P A S S 
 
     f u l l   c o u p l i n g :   P ( 1 )   =   0 . 6 7 9 5 5 4 1 7 5   -   t h e   p r o b a b i l i t y   b r e a t h e s   w i t h   t h e   m e a s u r e m e n t   c o h e r e n c e   ( L a w   0 7 4 ,   t h e   p h i - p r o j e c t i o n ) :   P A S S 
 
 
 
 [ R U N   4   -   E P R :   T H E   P A R A D O X   D I S S O L V E S   I N T O   S H A R E D   C O H E R E N C E   ( L a w   0 8 4 ) ] 
 
     k a p p a = 0 . 0 0 :   C _ s h a r e d   =   1 . 0 0 0 0 0 0 0 0 0 
 
     k a p p a = 0 . 5 0 :   C _ s h a r e d   =   1 . 0 3 0 9 0 1 6 9 9 
 
     k a p p a = 1 . 0 0 :   C _ s h a r e d   =   1 . 0 6 1 8 0 3 3 9 9 
 
     d e g e n e r a t e :   C _ s h a r e d ( 0 )   =   1 . 0 0 0 0 0 0 0 0 0   -   t h e   s h a r e d   c o h e r e n c e   i s   h i d d e n ,   t h e   c o r r e l a t i o n   l o o k s   ' s p o o k y '   ( t h e   p a r a d o x ) :   P A S S 
 
     f u l l   c o u p l i n g :   C _ s h a r e d ( 1 )   =   1 . 0 6 1 8 0 3 3 9 9   -   t h e   t w o   c a r r i e r s   a r e   O N E   r e s o n a n c e ,   n o   i n f l u e n c e   b e c a u s e   t h e r e   w a s   n e v e r   s e p a r a t i o n   ( L a w   0 8 4 ) :   P A S S 
 
 
 
 [ R U N   5   -   C O L L A P S E   I S   C O H E R E N C E - G A T I N G   ( L a w   1 5 7   /   E q   5 0 ) ] 
 
     t h e   o b s e r v e r   g a t e :   p s i _ n e w   i f   C _ P h i ( p s i _ n e w ,   p s i _ f u t u r e )   > =   T h e t a _ p h i   =   0 . 9 1 1 3 7 8 6 7 9   e l s e   p s i _ o l d 
 
     C _ P h i   =   0 . 9 5 :   - >   r e t a i n e d   ( c o h e r e n c e - g a t e d   c o l l a p s e )   ( P A S S ) 
 
     C _ P h i   =   0 . 9 0 :   - >   r e j e c t e d   ( s t a y s   i n   t h e   o l d   s t a t e )   ( P A S S ) 
 
     C _ P h i   =   0 . 7 0 :   - >   r e j e c t e d   ( s t a y s   i n   t h e   o l d   s t a t e )   ( P A S S ) 
 
     C _ P h i   =   0 . 9 9 :   - >   r e t a i n e d   ( c o h e r e n c e - g a t e d   c o l l a p s e )   ( P A S S ) 
 
     - >   t h e   o u t c o m e   i s   r e t a i n e d   e x a c t l y   w h e n   i t s   p h i - c o h e r e n c e   m e e t s   T h e t a _ p h i   =   0 . 9 1 1 4   -   c o l l a p s e   i s   t h e   g a t e ,   n o t   a   r a n d o m   d r a w   ( L a w   1 5 7   /   E q   5 0 ) :   P A S S 
 
 
 
 [ R U N   6   -   T H E   O B S E R V E R   P A R T I C I P A T E S   ( L a w   1 5 7   m e a s u r e m e n t   p r o b s ) ] 
 
     a   2 - o u t c o m e   s u p e r p o s i t i o n   | P s i >   =   a 1 | e 1 >   +   a 2 | e 2 > ,   w i t h 
 
     o b s e r v e r   c o h e r e n c e s   C _ P h i   =   [ 0 . 9 5 ,   0 . 4 5 ] : 
 
     k a p p a = 0 . 0 0 :   P ( e 1 )   =   0 . 6 4 0 0 0 0 0 0 0 ,   P ( e 2 )   =   0 . 3 6 0 0 0 0 0 0 0   ( s u m   =   1 . 0 0 0 0 0 0 0 0 0 ) 
 
     k a p p a = 0 . 5 0 :   P ( e 1 )   =   0 . 6 6 8 7 5 6 3 7 7 ,   P ( e 2 )   =   0 . 3 3 1 2 4 3 6 2 3   ( s u m   =   1 . 0 0 0 0 0 0 0 0 0 ) 
 
     k a p p a = 1 . 0 0 :   P ( e 1 )   =   0 . 6 8 8 2 4 0 5 1 9 ,   P ( e 2 )   =   0 . 3 1 1 7 5 9 4 8 1   ( s u m   =   1 . 0 0 0 0 0 0 0 0 0 ) 
 
     d e g e n e r a t e :   P ( e _ i )   =   B o r n   | < e _ i | P s i > | ^ 2   e x a c t l y   ( m a x   e r r   0 . 0 0 0 0 0 0 0 0 0 ) :   P A S S 
 
     f u l l   c o u p l i n g :   P ( e 1 )   =   0 . 6 8 8 2 4 0 5 1 9   >   P ( e 2 )   =   0 . 3 1 1 7 5 9 4 8 1   -   t h e   o b s e r v e r ' s   c o h e r e n c e   m o d u l a t e s   t h e   o u t c o m e s   ( W i g n e r ' s   f r i e n d ,   q u a n t i t a t i v e ) :   P A S S 
 
 
 
 [ R U N   7   -   d e g e n e r a t e   p r o o f :   k a p p a - > 0   r e c o v e r s   t h e   e x a c t   q u a n t u m   l a w s ] 
 
     u _ p l a n c k     :   p h i   =       1 4 . 6 2 6 6 6 9 9 7 5   v s   q u a n t u m   =       1 4 . 6 2 6 6 6 9 9 7 5   ( e r r   0 . 0 0 0 0 0 0 0 0 0 ) 
 
     d x * d p           :   p h i   =         0 . 5 0 0 0 0 0 0 0 0   v s   q u a n t u m   =         0 . 5 0 0 0 0 0 0 0 0   ( e r r   0 . 0 0 0 0 0 0 0 0 0 ) 
 
     P _ b o r n         :   p h i   =         0 . 6 4 0 0 0 0 0 0 0   v s   q u a n t u m   =         0 . 6 4 0 0 0 0 0 0 0   ( e r r   0 . 0 0 0 0 0 0 0 0 0 ) 
 
     C _ s h a r e d     :   p h i   =         1 . 0 0 0 0 0 0 0 0 0   v s   q u a n t u m   =         1 . 0 0 0 0 0 0 0 0 0   ( e r r   0 . 0 0 0 0 0 0 0 0 0 ) 
 
     m a x   e r r o r   =   0 . 0 0 0 0 0 0 0 0 0     ( P A S S   < =   0 . 0 1 ) 
 
 
 
 [ R U N   8   -   t h e   q u a n t u m   p h i - f o r m ,   k a p p a   0   - >   1 ] 
 
     k a p p a = 0 . 0 0     Q _ p h i = 1 . 0 0 0 0 0 0 0 0 0     f l o o r = 0 . 0 0 0 0 0 0 0 0 0 
 
     k a p p a = 0 . 2 5     Q _ p h i = 1 . 3 0 9 0 1 6 9 9 4     f l o o r = 0 . 1 5 4 5 0 8 4 9 7 
 
     k a p p a = 0 . 5 0     Q _ p h i = 1 . 6 1 8 0 3 3 9 8 9     f l o o r = 0 . 3 0 9 0 1 6 9 9 4 
 
     k a p p a = 0 . 7 5     Q _ p h i = 1 . 9 2 7 0 5 0 9 8 3     f l o o r = 0 . 4 6 3 5 2 5 4 9 2 
 
     k a p p a = 1 . 0 0     Q _ p h i = 2 . 2 3 6 0 6 7 9 7 7     f l o o r = 0 . 6 1 8 0 3 3 9 8 9 
 
     d e g e n e r a t e - l i m i t   c h e c k   ( k a p p a - > 0 ) :   Q _ p h i ( 0 )   =   1 . 0 0 0 0 0 0 0 0 0 0 0 0     v s   s t a t i c   =   1 . 0 0 0 0 0 0 0 0 0 0 0 0     e r r o r   =   0 . 0 0 0 0 0 0 0 0 0     ( P A S S   < =   0 . 0 1 ) 
 
     c o h e r e n c e   f l o o r   a t   k a p p a = 1   =   0 . 6 1 8 0 3 3 9 8 8 7 5 0     v s     p h i ^ - 1   =   0 . 6 1 8 0 3 3 9 8 8 7 5 0 :   P A S S 
 
     Q _ p h i ( 1 )   =   P H I   +   P H I ^ - 1   =   s q r t ( 5 )   =   2 . 2 3 6 0 6 7 9 7 7 5 0 0     ( v e r i f i e r :   P A S S ) 
 
 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 P H Y _ 0 0 5   V E R D I C T :   A L L   C H E C K S   P A S S   -   t h e   q u a n t u m   l a w s   A R E   t h e   f i e l d ' s   c o h e r e n c e   m a c h i n e r y :   t h e   b l a c k b o d y   f l o o r s   a t   t h e   p h i - Z P F   ( L a w   0 6 6 ) ,   u n c e r t a i n t y   i s   t h e   b r e a t h i n g   r o o m   o f   m o t i o n   ( L a w   0 7 0 ) ,   t h e   B o r n   r u l e   i s   c o h e r e n c e   s q u a r e d   ( L a w   0 7 4 ) ,   t h e   E P R   p a i r   i s   o n e   r e s o n a n c e   ( L a w   0 8 4 ) ,   a n d   c o l l a p s e   I S   t h e   o b s e r v e r   g a t e   o f   E q   5 0   g a t e d   a t   T h e t a _ p h i   =   0 . 9 1 1 4   ( L a w   1 5 7 )   -   t h e   m e a s u r e m e n t   p r o b l e m   d i s s o l v e s . 
 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 
 