Preprint (05.10.2002)
Date: Sat, 05 Oct 2002 16:22:18 GMT
From: redshift0@narod.ru (Alex Chepick)
Organization:
Newsgroups: sci.physics, sci.astro
Subject: Doppler Effect Against
Scale-Factor
Key words: Doppler effect scale-factor expanding universe Hubble constant
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The formula of Doppler effect does not fit for definition of a Hubble
constant
Alex M.
Chepick, Nizhni Novgorod
05.10.2002
Abstract
The impossibility of usage of the Doppler effect's relativistic formula for definition of a Hubble constant in the expanding Universe is demonstrated most shortly and simply.
1. Introduction
When
Hubble inferred his famous law v=HD, he with clean conscience has used
the relativistic formula of Doppler effect for definition of a radial velocity v of object:
(z+1)2= (z +v)/(cv) (1)
where z is redshift, c - speed of
light.
2. Role of the formula of Doppler in definition of the Hubble constant
Many
methods of definition of the Hubble constant have appeared since then, but for
the Static Universe the definition of a radial velocity of objects and distance
up to it lies in the basis of the most of it. The methods of definition of
distance D can be miscellaneous. But the radial velocity v is
determining only under the relativistic formula of Doppler effect (1) or by its
approaching for low speeds: v = cz.
For
models of the expanding Universe the methods of definition of Hubble parameter are
based in the majority on the formula H(t)=a'(t)/a(t), where a(t) is
time-depending scale factor.
And
as the formula of Doppler is deduced for static Universe and is tested only in
it, then it is impossible to apply this formula in expanding Universe.
Really,
let for some source of light we have measured redshift z. Guessing
applicability of the formula (1) we determine speed v of moving of this object in our
system of reference: v=(2z+z2)/(2+2z+z2). Then under relativity theory the
pace of time in a system of reference of the source grater in (1(v/c)2)-1/2 of times than pace of time in our system of
reference. But under the theory of expanding Universe the pace of time in a
system of reference of this source grater in (z+1) times concerning pace of time in
our system of reference. [1]
Compare
two expressions for pace of time:
(1(v/c)2)-1/2 = (z+1) (2)
We
obtain with the help of the formula (1), the equality (2) is executed only at z=0, v=0.
3. Conclusions
1. The
formula of Doppler effect deduced for the static Universe, it is defaulted in
the expanding Universe.
2. The
formula of Doppler effect in the expanding Universe should in addition depend
on time of radiation, reception time and scale factor.
Reference:
1.
Postnov K.A. Lectures on Astrophysics for
Students of MSU
[http://info.phys.msu.su/AstroPhysic/Lecture5/html/lecture5.html]
2.
Sten
Odenwald and Rick Fienberg Galaxy
Redshifts Reconsidered
[http://www2.ari.net/home/odenwald/anthol/expan.html]
( I can E-mail You this article. Reference was taken at address: [http://ursa.irk.ru/cosmo/part2dl.html])
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Last correction 22.11.2002 22:18