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