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Foundations o f Physics, Vol. 13, N o. 12, 1983

P r o b l e m s o f S y n c h r o n iz a tio n

in Special Relat ivi ty:

A Reply to G. Caval ler i and G. Spinel l i

S t e fa n M a r i n o v 1

Received January 28, 1983

I defend the opinion that Cavalleri and Spinelli , who in the last years aban-

doned m an y of the relativity dogmas and embraced m any o f the absolute

conceptions, are still very fa r fr om an adequte understanding and interpretation

of physical reali ty .

I wa s o n e o f t h e r e f e r e e s o f C a v a l l e r i a n d Sp i n e l l i ' s p a p e r (1) i n t h e p r e s e n t

i s su e o f t h is j o u r n a l , a n d m y l e n g t h y a n d d e t a i le d c r i t ic i s m i s p u b l i s h e d i n

R e f . 2 , p . 2 2 8 . O f m y 1 7 c ri t ic a l r e m a r k s , C a v a l l e r i a n d S p i n e ll i ( C - S ) h a v e

t a k e n i n to a c c o u n t o n l y t w o , v i z . N o s . X I I I a n d X V I , a n d i n tr o d u c ed

r e l e v a n t c o r r e c t i o n s i n t h e i r p a p e r . T h e a u t h o r s h a v e n o t t a k e n i n t o a c c o u n t

t h e r e m a i n i n g 1 5 r e m a r k s , w h i c h r e m a i n v a l i d f o r t h e re v i s e d v e r s i o n o f t h e i r

p a p e r . H e r e I s h o u l d l i k e t o g i v e o n l y c e r t a i n g e n e r a l s t a t e m e n t s :

1. T H E M A R I N O V T R A N S F O R M A T I O N

A t t h e p r e s e n t t i m e t h e r e a r e t h r e e c o m p e t i t i v e s p a c e - t i m e t r a n s f o r -

m a t i o n s : t h o s e o f G a l i l e i, L o r e n t z , a n d M a r i n o v . W h i c h is t h e r i g h t o n e ?

B u t , f ir s t, c o n c e r n i n g t h e n a m e s o f t h e t r a n s f o r m a t i o n s : W a s t h e tr a n s -

f o r m a t i o n x ' = x - V t , t ' = t, i n v e n t e d b y G a l i l e i ? C e r t a i n l y n o t . G r e e k s ,

E g y p t i a n s , a n d C h i n e s e w o r k e d w i t h t h i s t r a n s f o r m a t i o n , a n d w h e n a

R e d s k i n i n a r e s e r v a t i o n s e e s h i s b o a t a t a d i s t a n c e x u p w a r d s i n a r i v e r , h e

1Labora tory for Fund amen ta l Ph ysica l Prob lems, So f ia , Bulgar ia . Pres ent address:Niedersch6cklstr. 62, A-8044 Graz, Austria.

1241

0015-9018/83/1200 1241503.00/0 © 1983 Plenum Publishing Corporation

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1242 Marinov

kno ws ve r y we l l t ha t a f t e r a t im e t the d i s t a n c e wi l l be x- Vt , i f V is the

v e l o c i ty o f w a t e r. T h e L o r e n t z t r a n s f o r m a t i o n w a s p r o p o s e d f i rs t b y V o ig t.

T h e M a r i n o v t r a n s f o r m a t i o n w a s p r o p o s e d f i r s t n o t b y T a n g h e r l i n i , a s C - S

a s s e rt , b u t b y I v es . I a m s u r e, h o w e v e r , t h a t t h e I v es t r a n s f o r m a t i o n w i llr e m a i n i n p h y s i c s u n d e r m y n a m e f o r t h e fo l l o w i n g r e a s o n s ( se e R e f s. 3 - 5 ) .

1. I ga ve fi r s t t he t r a n s f o r m a t io n f o r m u la s f o r the ve loc i t i e s , i nc lud ing

those f o r l i gh t .

2 . I g a v e fi r st t h e c o n n e c t i o n b e tw e e n t h e L o r e n t z v e l o c i t y t r a n s f o r -

m a t i o n a n d t h e M a r i n o v v e l o c i t y t r a n s fo r m a t i o n .

3 . I show e d f ir s t t ha t t he a bso lu te ve lo c i ty v a nd the r e l a t ive ve lo c i ty

v ' a r e p h y s i c a l l y a d e q u a t e q u a n t i t ie s , w h i l e t h e L o r e n t z r e l a t iv e v e l o c i t y v [

( a t e r m i n t r o d u c e d b y m e f o r t h e r e l a t iv e v e l o c i t y i n t h e L o r e n t z tr a n s f o r -m a t i o n ) i s n o t a n a c t u a l v e l o c i t y , b u t a m a t h e m a t i c a l r e s u l t f o l lo w i n g f r o m

t h e a r t i f i c i a l l y i n t r o d u c e d r e l a t i v e t i m e i n t h e L o r e n t z t r a n s f o r m a t i o n .

4 . I s h o w e d f ir s t t h a t t h e M a r i n o v t r a n s f o r m a t i o n s f o r m a g r o u p .

5 . I s h o w e d f ir s t t h a t a n y p a r t i c l e is a t ta c h e d t o a b s o l u t e s p a c e

t h r o u g h i ts p r o p e r m a s s a n d t h u s t h a t t h e l in k o f t h e M a r i n o v t r a n s f o r m a t i o n

t o a b s o l u t e s p a c e i s n o t o n l y k i n e m a t i c a l , b u t a l s o d y n a m i c a l .

6 . I m a d e f i rs t a s t r o n g d i f fe r e n c e b e t w e e n t h e n o t i o n s " L o r e n t z

i n v a r i a n c e " ( a v a i l a b l e t o a n o b s e r v e r a t r e s t i n a b s o l u t e s p a c e w h o d e s c r i b e st h e m o t i o n o f a p a r t i c l e m o v i n g f i r st w i th v e l o c i t y v w i t h r e s p e c t t o a b s o l u t e

s p a c e a n d t h e n w i t h a n o t h e r v e lo c i t y v ' ) a n d " M a r i n o v i n v a r i a n c e "

( a va i l a b le w he n th e r e is a pa r t i c l e m ov in g wi th a c e r t a in ve loc i ty v in

a b s o l u t e s p a c e a n d a n o b s e r v e r w h o f i r s t i s a t r e s t w i t h r e s p e c t t o a b s o l u t e

s p a c e a n d t h e n m o v e s w i t h a v e l o c i t y V ) . F o r C - S , a s f o r a n y c o n t e m p o r a r y

p h y s i c i s t , if t h e v e l o c i t y b e t w e e n a p a r t i c l e a n d a n o b s e r v e r c h a n g e s , i t is o f

n o i m p o r t a n c e w h e t h e r t h e p a r t i c l e o r t h e o b s e r v e r c h a n g e s i t s v e l o c i t y .

M e a nwhi le the se two c a se s a r e no t ide n t i c a l , be c a use , i n the f i r s t c a se , t he

p a r t i c l e c h a n g e s i ts v e l o c i t y w i th r e s p e c t t o d i s t a n t m a t t e r a n d t h u s i t s t i m ee n e r g y c h a n g e s t o o , w h i le i n t h e s e c o n d c a s e t h e t i m e e n e r g y o f t h e p a r t i c l e

r e m a i n s u n c h a n g e d . I t i s i m p o r t a n t t o n o t e t h a t t h e L o r e n t z i n v a r i a n c e

c o n c e r n s 4 - s c a l a r s , w h i l e t h e M a r i n o v i n v a r i a n c e c o n c e r n s 3 - s c a l a r s .

7 . I s h o w e d th a t " l e n g t h c o n t r a c t i o n " ( o r " d i l a t i o n " ) i n t h e L o r e n t z

a n d M a r i n o v t r a n s f o r m a t i o n s i s n o t a p h y s i c a l e f fe c t b u t a r e s u l t o f t h e

p e c u l i a r c h a r a c t e r o f li g h t v e lo c i t y . [ N . B . : T h e r e a s o n i n g s o f C - S o n

" n o n i n s t a n t a n e o u s L o r e n t z c o n t r a c t i o n , " o n " a c c e l e r a t i o n o f t h e a t o m s , " e tc .

a r e c o m i c a l : T o p r o d u c e a c c e l e ra t i o n o f a t o m s a n d d e f o r m a t i o n o f c r y s t al s

o n e m u s t i n v e s t energy. W h e r e d o e s t h is e n e r g y c o m e f r o m ? F o r E i n s te i n th ec o n t r a c t i o n s a r e s e e m i n g , b u t f o r a n a b s o l u t i s t ( s u c h a s C - S ) t h e y m u s t b e

r e a l , phys ic a l . ]

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Sy nch ronization in Spe cial R elativity 1243

8 . I show ed tha t t he pecu l i a r cha rac t e r o f l i gh t ve loc i ty cons i s t s in t he

f o l l o w i n g . A c c o r d i n g t o t h e N e w t o n ( G a l i l e i , R e d s k i n ) c o n c e p t i o n s , t h e

ve loc i ty o f l i gh t in a m oving f ram e m us t be c ' = (c 2 - V2 sin 2 0) 1/2 - V co s 0,

w he re c i s t he ve loc i ty o f l i gh t i n abso lu t e space , V i s t he ve loc i ty o f t hem o v i n g f r a m e , a n d 0 i s t h e a n g l e b e t w e e n e ' a n d V . M e a n w h i l e , t h e

p h y s i c a l l y a d e q u a t e f o r m u l a f o r t h e v e l o c i t y o f l i g h t i n a m o v i n g f r a m e i s

c ' = c 2 / ( c + V cos 0 ) , and w i th t h is fo r m ula one can exp la in a l l expe r imen t s

a v a i l a b l e . U n t i l n o w I c o u l d n o t f i n d a n e x p l a n a t i o n f o r t h i s s t r a n g e f a c t ;

a n d , a s I a l w a y s n o t e , t h e d e d u c t i o n w h i c h I g i v e o f t h e M a r i n o v t r a n s f o r -

m a t i o n d o e s n o t sa t i s fy me .

N o w l et u s r e tu r n t o t h e q u e s t io n , " W h i c h o f th e t h re e t r a n s f o r m a t i o n s

i s t he r i gh t one?" The G a l i l e i t r ans fo rma t ion i s no t t rue , a s i t i s a

" r e l a t i v i s t i c " t r a n s f o r m a t i o n ; i t i s n o t a t t a c h e d t o a b s o l u t e s p a c e a n d o fim por t ance i s on ly t he re l a t i ve ve loc i ty be tw een b o th f ram es . Then i t f a i ls to

g i v e r i g h t a n s w e r s f o r h ig h v e l o ci ti es . I s h o w e d t h a t t h e L o r e n t z a n d M a r i n o v

t r a n s f o r m a t i o n s c a n b e m a t h e m a t i c a l l y r e c o n c i l e d , s i n c e i n t h e L o r e n t z

t rans fo rma t ion t ime i s r e l a t i ve and the ve loc i ty o f l i gh t abso lu t e , w h i l e i n t he

M a r i n o v t r a n s f o r m a t i o n t i m e i s a b s o l u t e a n d v e l o c i t y o f l i g h t r e l a t i v e . I

show ed th a t i f one ca l cu l a t e s co r rec t ly ( i.e ., i f one d iv ide s t he space

d i f fe ren t ia l s by the d i f fe ren t i a ls o f ab so lu t e t ime , an d no t , a s E ins t e in d id , by

t h e d i f fe r e n ti a l o f r e l a ti v e t im e ) , t h e n t h e s p a c e -t im e L o r e n t z t r a n s f o r m a t i o n

l e a d s t o t h e c o r r e c t v e l o c i t y t r a n s f o r m a t i o n . I h a v e e x p e r i m e n t a l l y s h o w ntha t r e l a t i ve l i gh t ve loc i ty and abso lu t e t ime a re phys i ca l l y adequa te quan-

t i t i e s . T h u s I h a v e d e m o n s t r a t e d t h a t t h e M a r i n o v t r a n s f o r m a t i o n i s t h e

p h y s i c a l l y a d e q u a t e o n e .

2 . S L O W T R A N S P O R T O F C L O C K S

M a n y ( n a iv e ! ) a b s o lu t i s ts t h i n k t h a t b y a s l o w t ra n s p o r t o f c lo c k s o n e

c a n r e a l iz e a N e w t o n i a n ( a b s o lu t e ) t im e s y n c h r o n i z a t i o n b e tw e e n s p a t i a ll yremote c locks i n a f rame moving in abso lu t e space w i th ve loc i ty V . Such w as

a l so t h e v i e w p o i n t o f T o r r a n d K o t e n (6) w h o e v e n c a r r i e d o u t a n e x p e r i m e n t ,

h o p i n g t o b e a b l e to m e a s u r e t h e E a r t h ' s a b s o l u t e v e l o c it y b y s e n d i n g o n e -

w a y e l e c t r o m a g n e t i c s i g n a l s b e t w e e n a b s o l u t e l y s y n c h r o n i z e d c l o c k s a n d

regis te r ing the f i rs t -order ( in V / c ) e f fec t s . In h i s t a lk a t t he In t e rna t iona l

C o n f e r e n c e o n S p a c e - T i m e A b s o l u t e n e s s ( G e n o a , J u l y 1 9 8 2 ) P r o f e s s o r T o r r

s a i d h e h a d a r r i v e d a t t h e c o n c l u s i o n t h a t d u r i n g t h e t r a n s p o r t t h e c l o c k

suf fe r s a t ime d i l a t i on such tha t t he expec t ed f i r s t -o rde r e f fec t i n t he

a n i s o t ro p i c l i g h t v e l o c it y w i ll b e c o m p e n s a t e d . H o w e v e r , T o r r w a s o f th eo p i n i o n t h a t a t h i r d - o r d e r e f f e ct m a y b e o b s e r v ed . A s h i s e x p e r i m e n t h a d

g iven a da i ly s inu so ida t e f fec t (ove r a d i s t ance o f 500 m ) co r re l a t ed t o

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1244 Marinov

sideral t i m e , h e a c c e p t e d i t a s a t h i r d - o r d e r e f f e c t a n d c a l c u l a t e d a n a b s o l u t e

E a r t h v e l o c i t y o f t h e o r d e r o f t e n s o f t h o u s a n d s o f k m / s e c . I s h o w e d (v) t h a t ,

w h e n w o r k i n g w i t h t h e M a r i n o v t r a n s f o r m a t i o n , t h e c o m p e n s a t i o n c o n t i n u e s

t o t h e t h i r d o r d e r i n V/c.C - S h a v e a l s o u n d e r s t o o d t h a t t h e r e is a c o m p e n s a t i o n o f t h e f i rs t - o r d e r

e f f e c t . B u t w h e n t h e y w r i t e , " T h e s e s i m p l e c o n s i d e r a t i o n s s e e m n o t y e t t o

h a v e b e e n u n d e r s t o o d b y M a r i n o v , " I c a n o n l y e x p r e s s m y r e g r e t t h a t t h e y

d i d n o t a t t en d t h e I C S T A c o n f e r e n c e i n G e n o a a n d t a k e p a r t in th e

d i s c u s s i o n o f t h e e n g i n e e r i n g a s p e c t o f th e p r o b l e m a n d i n t h e d i s c u s s io n n o

l o n g e r o f t h e f i r s t- o r d e r e f f e c t (t h e r e a l m o s t a ll g o o d s p a c e - t i m e s p e c i a li s ts

a r r i v e d a t t h e c o m p e n s a t i o n c o n c l u s i o n ) , b u t o f t h e t h i r d - o r d e r e ff e ct .

3 . E X P E R I M E N T A L M E A S U R E M E N T O F T H E E A R T H ' S A B S O L U T E

V E L O C I T Y

C - S r e p l a c e d t h e n a i v e e t h e r o f t h e 1 9 t h c e n t u r y b y a n e w e t h e r w h i c h i s

n o t n a i v e . V e r y g o o d . H o w e v e r , i n a n y e t h e r ( n a i v e o r n o n - n a i v e ) t h e

v e l o c i t y o f l i g h t i n a m o v i n g f r a m e m u s t b e d i r e c t i o n - d e p e n d e n t . T h u s , w i t h

t h e h e l p o f a r o t a t i n g s h a f t a n d t w o o p p o s i t e l y d i r e c t e d l i g h t b e a m s , o n e i s

a b l e t o m e a s u r e t h e E a r t h ' s a b s o l u t e v e l o c i t y . I m e a s u r e d t h i s v e l o c i t y

t w i c e ( 8'9 ) a n d c o n s t r u c t e d a t h i r d v e r y s i m p l e a p p a r a t u s f o r i ts

m e a s u r e m e n t . ~ t° ) C - S a s s e r t t h a t i f m y e x p e r i m e n t s g a v e p o s i t i v e r e s u lt s , I

s h o u l d a b a n d o n t h e " M a r i n o v t r a n s f o r m a t i o n " ( w h i c h p r e d ic t s t h o s e r es u lt s) .

S t r a n g e l o g i c ! B u t C - S a s s e r t t h a t m y e x p e r i m e n t s e e m s n o t t o b e r e l i a b l e ,

w i t h o u t s t a t i n g w h a t i s t h e p r e d i c t i o n o f their t he o r y . I t i s i n t e r e s t ing ,

h o w e v e r , t o n o t e t h a t w h e n I i n v i t e d P r o f e s s o r C a v a l l e r i t o s e e m y

e xp e r im e n t a n d to c h e c k i t s re l i a b i l i t y , he de c l ine d ( se e R e f . 2 , p . 236) .

R E F E R E N C E S

1. G . Cava lleri and G . Spinelli,Found. Phys. 13, 122 1 (1983).2. S. Marinov, The Thorny Way of Truth (East-West, Graz, 1982).3. S. Marinov, Found. Phys. 9, 445 (1979).4. S. Marinov, Eppur si Muove (Ce ntre Beige de Docu mentation Scientifique, Bruxelles,

1977, 2nd edn ., East-W est, G raz , 1981).5. S. Marinov, Classical Physics (East--West, Graz , 1981 .6. P. Ko len and D. G. To rr, Found. Phys. 12, 401 (i982).7. S. M arinov and J. P. Wesley,Proceedings of the International Conference on Space-Time

Absoluteness, Genoa, 8- 11 Ju ly, 1982 (East-West, Graz, 1982).8. S. Marinov, Czech. J. Phys. B 24, 965 (1974).

9. S. Marinov, Gen. Relativ. Gravit. 12, 57 (1980).10. S. Marinov, Spec. Sci. TechnoL 3, 57 (1980).