1979.11.20 - stefan marinov - the quasi-doppler experiment according to absolute space-time theory

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Foundations o f Physic s, Vol. 11, Nos . 1/2, t981

The Quasi-Doppler Experiment According to Absolute

Space-Time Theory

S t e f a n M a r i n o v ~

Received November 20, 1979

W e find the relation between the frequen cies received by two observers pla ced

at a git'en par allel with 180 ° difference in longitude when they observe a dista nt

light (radio) source. This relation depends o n the absolute velo city o f the

Earth ; however, because o f the occurrence o f aberration, the effect cannot be

registered in pra ctice.

Poinca r6 ~5) poin ted out that the h is tor ic Brad ley ex per iment , wi th w hose

help the ab er ra t io n of l ight was d iscovered, can be used for the es tabl ishment

o f the Ear th ' s abso lu te ve loc i ty , i f t he ae ther mod e l o f ligh t p ropag a t ion

is the t rue one. We call such a modif icat ion o f the B radley exper im ent the

quasi -Bradley exper iment , and we show ~4) that , acco rding to our absolute

space- t ime theory , the quasi -Bradley exper iment must g ive a posi t ive resul t .

The Brad ley exper imen t cons i st s o f a change o f the d i r ec t ion under

which a d is tant l ight source (a s tar ) i s seen when the observer changes h is

veloci ty . However , when the observer changes h is veloci ty the received

frequ enc y a lso changes. This represents the wel l -known Do pple r ef fect. In

the p resen t paper we cons ider the p rob lem of whe ther the observa t ion o f the

Doppler shi f t s in the f requencies of d is tant s tars dur ing the d iurnal ro ta t ion

of the E ar th can g ive in fo rma t ion abou t the Ear th ' s abso lu te ve loc i ty .

We cal l the a b e r r a ti o n in f r e q u e n c y ( in contrast to the a b e r r a t i o n i n

d i rec t i on d i scovered by Brad ley) the change in the f r equen cy o f ligh t coming

fro m a d is tant l ight source when the observ er changes h is veloci ty . I f we cal l

1 Laboratory for Fundamental Physical Problems, Sofia, Bulgaria.

115

0015-9018/8110200-0115503.00]0© 1981 PlenumPubllshh'tgCorporation

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116 M ar i n ov

th e Dopp le r e x pe r ime n t 2 t h e d e t e rmi n a t i o n o f l i gh t v e l o c i t y wh e n o b s e rv i n g

t h e a b e r r a t i o n i n f r e q u e n c y , t h e n t h e D o p p l e r e x p e r i m e n t p e r f o r m e d w i t h th e

a i m o f meas u r i n g t h e E a r t h ' s ab s o l u t e v e l o c i t y wi ll b e ca l led t h e quasi-

Doppler exper iment .

T h e t r e a t m e n t o f t h e q u a s i - D o p p l e r e x p e r i m e n t in t h e f r a m e w o r k o f o u r

ab s o l u t e s p ace - t i me t h eo ry i s v e ry s i mp l e . L e t u s h av e (F i g . l ) a d i s t an t

l i g h t s o u rce ( a s t a r ) S an d t wo o b s e rv e r s 0 2 , 0 2 wh o ro t a t e wi t h r e l a t i v e

ve loc i t i es v~ , v , .2 (U~'1 = /31"2 = / ) 0 a b o u t s o m e c e n t e r C w h i c h m o v e s w i t h

an ab s o l u t e v e l o c i t y v. T h e ab s o l u t e v e l oc i ti e s o f O 1 an d 0 2 , wh i ch li e o n

t h e s am e l in e wi t h t h e cen t e r o f r o t a t i o n , a r e

Vl 2 = 1)2 -7- I)r2 ~ 2vvr c o s %

/)2 2 = /)2 _~ Vr 2 __ 2VUr COS C/9

(1)

whe re q0 i s the ang le be twee n the ve loc i ty v an d the ve loc i ty o f the f i r s t

o b s e r v e r v ~ . D e n o t e b y ~ t h e a ng l e b e t w e e n t h e s o u r c e - o b s e r v e r l in e a n d t h e

v e l o c i ty v a t t h e m o m en t o f r ecep ti o n . Ob v i o u s l y S is a co n s t an t an g l e, wh i l e

q0 chan ges by 27r dur ing the pe r io d o f ro ta t ion o f O2 an d 02 • Al l ang les a re

t ak en p o s i t i v e c l o ck wi s e an d n eg a t i v e co u n t e r c l o ck wi s e .

Ac co r d i n g t o o u r ab s o l u t e s p ace - t i me t h eo ry c3~ i f l i gh t w i t h f r eq u e n cy v

i s emi t t ed b y a s o u rce mo v i n g a t v e l o c i t y v , t h e f r eq u en cy r ece i v ed b y an

o b s e rv e r mo v i n g a t v e l o c i t y v0 will be

1 - - (Vo/C) co sO o ( 1 - - v2/e 2 )~/~

v o = v 1 + ( v / c ) c o s O ' - 1 - - v 0 U / c 2- (2 )

wh e re 00 is t h e an g l e b e t w een t h e l in e co n n e c t i n g t h e em i s s io n p o s i t i o n o f

t h e s o u rce w i t h t h e r ecep t i o n p o s i t i o n o f t h e o b s e rv e r an d t h e v e l o c i t y o f t h eo b s e rv e r a t t h e r ecep t i o n mo men t , wh i l e 0 ' i s t h e an g l e b e t ween t h e l i n e co n -

n ec t i n g t h e r ecep t i o n p o s i t i o n o f t h e o b s e rv e r wi t h t h e emi s s i o n p o s i t i o n o f

t h e s o u rce an d t h e v e l o c i t y o f t h e s o u rce a t t h e emi s s io n mo me n t .

W r i t i n g i n fo rmu l a (2 ) f i r s t v0 = v s , v 0 = v l , 00 = 02 , an d then

2 The Do pple r experiment was been pe rform ed seven years ago by Hoff. (1) Let us note

that if Bradley had had a prism with resolution better than Av/v = 10 4, he co uld have

discovered the yearly aberration in frequency, which is Av/v = 2v/c = 2 × 10 4, where

v = 30 km/sec is the velocity of the Ea rth a ro und the Sun. The Dopp ler experiment ismuch easier than the Bradley experiment because only two photographs of the spectrum

of light coming from a certain star are to be taken with a time difference of six months.

Of course, Bradley did not have a camera, and even if a suitable prism had been at his

disposal, he would have been unable to measure the shift in the frequencies.

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The Quasi-Doppler Experiment According to Absolute Spa ce-T ime Theory 117

o,

vr2

Fig. 1.

8

The quasi-Doppler experiment.

Vo = v2, Vo = v2, 0o = 02 (see Fig. 1), an d div idin g th e fo rm ul as ob tain ed ,

we ge t

v l _ 1 - - ( v l / c ) co s 01 { 1 -- v 2 2 / c 2 ~ 1 / 2(3)

7 1 - -

(v/c)co s 0~ ~ 1 --

v12/c~!

Thu s the r e l a t ion be tween the f r equency / ;1 r ece ived by the f ir st obse rve r

and the f r equency vz r ece ived by the second obse rv e r does no t de pend on the

ve loc i ty o f t he source .

8as / , I / i /a -8

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118 Marinov

F r o m t h e f i g u r e w e h a v e

vl cos 01 = v cos 3 + vr cos(3 + 9)

v2 co s 02 = v co s 3 - - v~ co s(3 + 9)(4)

Subs t i tu t ing (1) and (4) in to (3 ), we f ind wi th in an a ccu rac y o f seco nd

o rd e r i n 1/ c

- - 2 vv~ [ c o s - - c o s S c o s ( S q - c p ) ]l __ 1 - - 2 V ~ c o s ( ~ + q o ) + ~P2 C

v~ cos~(~ + ~o) (5)- 2 ~ -

This f ina l express ion i s conven ien t fo r d i scuss ion . Le t us measure u l and

v 2 receiv ed f ro m a giv en l ight ( rad io) sour ce f or w hic h 3 + c? = zr/2 . I f

(3 = 0, we will hav e v1 = v2 fo r q0 = ~/2 ; h ow ev er , if ~ = zr/2, we will hav e

vl = v~(1 q- 2vvr/e 2) fo r q~ = 0 . Th i s resu l t l eads to th e c onc lus io n tha t we

can meas u re t h e E a r t h ' s ab s o l u t e v e l o c i t y i n t h e fo l l o wi n g ma n n e r : L e t u s

have two rece ivers p laced a t a para l l e l wi th 180 ° d i f fe rence in long i tude . Le t

u s o b s e rv e a r ad i o s o u rce wh en i t " c ro s s e s " t h e l in e O1 0 2 an d l e t t h e f r eq u en -

c i e s r ece i v ed b e s en t t o s o me mi d d l e p o i n t an d t h e re co mp ared . Imag i n e fo r

s i mp l i c i t y t h a t t h i s mi d d l e p o i n t i s a t t h e p o l e an d t h a t t h e E a r t h r ep re s en t s

a f l a t d i s k . As we s h o wed i n Re f . 3 wh en co n s i d e r i n g t h e s o -ca l l ed " ro t o r -

ro t o r " ex p e r i men t , i f l i gh t is s en t f ro m t h e r i m o f a ro t a t i n g d i s k t o it s c en t e r,

t h en t h e ch an g e i n t h e f r eq u en cy d ep en d s o n l y o n t h e ro t a t i o n a l v e l o c i t y , n o t

o n t h e v e l o c i t y o f t h e d i s k a s a wh o l e . Hen ce v l an d v2 wh e n r ece iv ed a t t h e

p o l e wi ll su f fe r eq u a l ch an g es , d u e t o t h e d a i l y ro t a t i o n o f th e E a r t h . I f n o w

w e c o m p a r e v1 an d vz fo r an y r ad i o s o u rce wh i ch "c ro s s e s " t h e li n e O1 0 2 ,

then fo r ~ - - 0 the f requencie s v l and v2 wi ll be equa l p re c i se ly a t the m ome n~

wh en the rad io source i s on the l ine O109 , i . e. , fo r ~ + ~ = z r/2; how ever ,

fo r ~ = ~r /2 the f requ encies v l and v2 wi l l be equa l w hen [ see (5) and t ake

into ac co un t tha t fo r the case con side red cos(S + ~p) ,-~ 0]

cos( 3 + 9) ----v/c (6 )

Ta kin g v = 300 km/se c, (~) we ob tain

c o s ( ~ + 9 ) = s i n ~ c ~ = 10 -a = 3 ' , 4 (7)

wh ere ~ is t h e an g l e b e t ween t h e li n e O2 0 1 an d t h e s o u rc e -o b s e rv e r l in e.

Su ch a n an g l e i s l a rg e en o u g h t o b e r e l iab l y r eg i st e r ed . Ho w ev e r , t h e an g l e

is exact ly eq u a l t o t h e ab e r r a t i o n an g l e d u e t o t h e mo t i o n o f t h e E a r t h w i t h

ve loc i ty v. Th i s s igni fi es tha t wh en the l ine O 201 make s an ang le c~ wi th the

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The Quasi-Doppler Experiment According to Absolute Space-Time Theory 1 1 9

source -obse rve r l i ne , t he source w i l t b e s e e n a l o n g t h e d i re c t i o n O ~ O 2 . T h u s ,

b e c a u s e o f t h e o c c u r r e n c e o f t h e a b e r r a t i o n , t h e q u a s i - D o p p l e r e x p e r i m e n t

leads in prac t ice to a nul l resul t .

The p ro b le m so lved in th i s pap e r was cons ide r ed by R ob e r t so n , ~6~ wh o

used the ap pa ra tus o f spec ia l r e la t iv i ty , o r ra the r , t he t ech n ique o f the

L o r e n t z t r a n s f o r m a t i o n s . R o b e r t s o n c a m e t o t h e c o n c lu s i o n t h a t t h e r e l at i o n

be tween v~ and v2 depend s on ly o n the v e loc i ty o f 02 in the ine r t i a l f r am e

where O 1 i s a t r e st , o r on the v e loc i ty o f O~ in the ine r t ia l f r am e where 02

is at rest , i .e . , only on the r e l a t i v e v e l o c it y o f b o t h o b s e r v e rs : h o w e v e r ( w e

shou ld l i ke to em phas ize th i s) , re l a t ive w i th r e spec t to abso lu te space bu t no t

to the Ea r th , s ince w i th r e spec t t o the l a t t e r t he r e l a tive ve loc i ty o f bo th

observers i s equal to zero. In the case considered this re la t ive ve loc i ty i s

e q u a l t o 2 v r . W e s h o w w i t h o u r f o r m u l a ( 5) t h a t t h e c o n c lu s i o n o f R o b e r t s o n

is n o t t r ue . The r e l a t ion v l / v 2 depend s a l so on the abs o lu te ve loc i ty v ; howev e r ,

the occur r ence o f the abe r r a t ion in d i rec t ion does no t pe rm i t t h i s depe nden ce

to be e x p e r i m e n t a l l y revea led.

N ow we sha ll show tha t , for v = 0 , ou r for m ul a (5) [ see a lso (3) ] whic h

reduces to

_ _ l d 2

v~ ...... 1 - - 2 v~ cos(S ÷ ~ ) ÷ 2 -~ -c o s 2 (S + ~)P 2 C

= 1 - ( v # e ) c o s ( ~ 4- ~) (8)

1 4 - ( v r / c ) c o s ( 3 4 - q ~ )

i s i den t ica l w i th bo th fo rm u las o b ta ined by R obe r t son , (6)

, , 1 - - ( V / c ) c o s c?~' , , 1 - - ( V / c ) c o s qo1'v~ - - v~ (1 - - V '~/e~) 1/2 ' u2 = vl (1 - - V 2/cZ ) ~/~ (9 )

wh ere V = 2v, . i s the re la t ive ve loc i ty of 01 w i th res pec t to 02 (an d vice

versa) , q~l' i s the angle be twee n th e ve loc i ty o f O1 an d the d i rec t ion in which

the sou rce is seen i f m ea sured in a f r am e in which 02 i s a t r es t , and % ' i s t he

ang le be tween the ve loc i ty o f 02 and the d i r ec t ion in which the source is seen

i f me asu red in a f ram e in which O1 is a t res t . O ur angle 3 + q~ i s be tw een

the sou rce -o bse rve r l i ne an d the v e loc i ty v~.l • Thu s th i s i s the ang le b e tween

the ve loc i ty o f O~ and the o p p o s i t e di r ec t ion in which the source i s seen i f

m easured in a f r am e in which the Ea r th were a t r e s t , i . e . , i n abso lu te space .

I t is o b v i o u s t h a t, b e c a u s e o f t h e a b e r r a t i o n i n d i r ec t io n d u e t o t h e m o t i o n

o f O 1 a n d O 2 , w e h a v e

q ) l' - - ~ - - [ 3 + cp 4 - ( v ~ / c ) s i n ( 3 + q v ) ]

cp2' = 3 4 - ~ -- (v , . /c) sin( 3 + qv)(10)

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120 Marinov

Pu t t i n g (1 0 ) i n t o (9 ) an d t ak i n g i n t o acco u n t t h a t t h e ab e r r a t i o n an g l e

(v,/c) s in(S -k ~o) i s a smal l qua nt i ty , we ob tai n (8).

R E F E R E N C E S

1. D. Hoff, Sky and Telescope43, 9 (1972).

2. S. Marinov, in Abstracts of the 8th International Conference on General Relativity andGravitation, Canada, 1977, p. 244.

3. S. Marinov, Found. Phys. 8, 637 (1978).

4. S. Marinov , The quasi-R6mer and quasi-Bradley experiments accord ing to absolute

space-time theory, to appear.

5. H. Poincard, Bulletin des Sciences Mathematiques 28, 32 (1904).6. D. S, Robertson. Nature 257, 467 (1975).