LV.TTV,~V, AL NUOVO CIMENTO

VOL. 32, N. 12

21 Novembre 1981

Non-Doppler Red-shifts and Energy Decay of Elementary Particles. T. L. CHOW

Cali]ornia State College, Stanislaqzs . T~rloeb, Cal. 95380 (rieevuto 1'8 Settembre 1981)

The problem of the origin of the red-shifts of distant celestial objects has been with us for almost twenty years--since the large red-shifts in quasars were first discovered. Most astrophysicists tacitly assumed that the red-shifts were cosmological in origin (i.e., due to cosmological expansion). Alternative attempts were raised in several different contexts. The tired-light theory is perhaps the most commonly advocated non-Doppler alternative. It is based on the idea that the wave-length of the light from distant celestial objects such as galaxies or quasars is red-shifted because of changes in the photons which occur during the long journey before it reaches us. What is the plausible mechanism for producing changes in the photons? Much discussed mechanisms such as photon-photon interaction (1), photon-graviton interaction (2), or mechanism invoked photon rest mass (3) were shown to be not viable. I n this note we present a new attempt which is based on de Broglie's energy decay of elementary particles. According to de Broglie's causal and nonlinear interpretation of the wave mechanics known as the double-solution theory, the energy of every elementary particle undergoes spontaneously an exponential decay process (4). If this process is a fundamental feature and takes place for every elementary particle, then the energy of the light (i.e., frequencies of photons) decreases exponentially as it travels through space according to the following relation: (1)

v = v0 exp [-- p r ] ,

where v is the frequency of light at a distance r from a source which emits light at frequency ~0, P is an attenuation coefficient to be determined later. Corresponding to eq. (1), the law of the red-shift would be given by the relation

(2)

(1) (2) (s) (4)

Z : ~0__--~: exp [ / ~ r ] - 1 ,

~][. BORN: Proc. R. Soc. London Set. A, 67, 103 (1954:). J . F. WOODWARD a n d W . YOURGRAU: Nature (London), 241, 338 (1973). J . C. PECKER, A.. P. ROBERTS a n d J . P . VIGIER: -Nature (London), 237, 227 (1972). L. DE BROGLIE: Cab. Phys., 16, 425 (1962).

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T.L. c~ow

which is i n d e p e n d e n t of t h e initial f r e q u e n c y of light. T h i s f e a t u r e is also an essential c h a r a c t e r i s t i c of t h e D o p p l e r shift and was considered as an e v i d e n c e for t h e l e g i t i m a c y of i n t e r p r e t i n g t h e cosmological red-shifts as D o p p l e r effects. T h e v a l u e of t h e a t t e n u a t i o n coefficient can be e s t i m a t e d to be a b o u t 10 -~8 cm -1. As t h e o b s e r v e d ;red-shifts/ a p p a r e n t m a g n i t u d e r e l a t i o n is a linear one for Z < 0.2, we e x p a n d t h e e x p o n e n t i a l t e r m in eq. (2) to first order i n / ~ r : (3)

Z ~--/~r.

F r o m eq. (3) and H u b b l e ' s l a w Z = ( H / C ) r , w e o b t a i n H C T h e H u b b l c c o n s t a n t H lies b e t w e e n 50 to 100 k m s -I m p c -1. If we t a k e H---- 75 k m s -1 rope -1 = 2.43.10 -is s -1, t h e v a l u e of ~ is a b o u t 8.0.10 -29 c m - L T h e p r o p o s e d a l t e r n a t i v e e x p l a n a t i o n for t h e cosmic red-shifts is r o u g h l y consistent w i t h t h e o b s e r v a t i o n a l data. W e e m p l o y t h e c o m m o n m - z t e s t to d e m o n s t r a t e this. W e first o b t a i n a t h e o r e t i c a l m - z r e l a t i o n f r o m eq. (2) and t h e expression of t h e a p p a r e n t b o l o m e t r i c a l m a g n i t u d e (5)

(4)

mbo1 - Ambo I = 5 log (r) -~ ~ / - - 5 ,

w h e r e Ambol ---- 2.5 log (1 ~- z) is t h e correction t e r m to t h e b o l o m e t r i c m a g n i t u d e for t h e e n e r g y loss caused b y t h e r e d - s h i f t of t h e s p e c t r u m (6). Substituting eq. (2) into eq. (4), we o b t a i n

(5)

mbo I = 5 log (~/1"-+~ In (1 § z)) ~- 5 log (C/H) + M - - 5 .

I n general, calculations show t h a t r e l a t i o n (5) approaches v e r y closely t h e linear m-z relation. A t p r e s e n t d a t a are available up to red-shift as high as 0.5. F o r z---- 0.5, t h e difference b e t w e e n r e l a t i o n (5) and t h e linear m-z relation is about 0.01 magnit u d e w h i c h is a small difference. T h u s t h e p r o p o s e d e x p l a n a t i o n for t h e cosmic redshifts is n o t at v a r i a n c e w i t h p r e s e n t o b s e r v a t i o n a l data, and it is a v i a b l e explanation. A.. GERASIM: Cah. Phys., 19, 353 (1965). (*) E. HUBBLE: The Observational .Approach to Gosmology (Oxford, 1937). (6)

by Societ~ ItaUana di Fisica Propriet~ letteraria rfservata Direttore responsabfle: CARLO CASTAGNOLI

Stampato in Bologna dalla Tipografla Gompositori coi tipi della Tipografla Monograf Questo fascicolo ~ stato licenziato dai torchi il 17-XI-1931