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