REDSHIFT IN A STABLE UNIVERSE
From: Marcel Luttgens (mluttgens_at_wanadoo.fr)
Date: 10/27/04
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Date: Wed, 27 Oct 2004 15:55:34 +0000 (UTC)
REDSHIFT IN A STABLE UNIVERSE
_____________________________
INTRODUCTION
____________
Old massives galaxies, giant strings of galaxies, or iron-rich quasars
can be observed at enormous distances.
Those findings contradict the big bang theory, according to which
the universe should appear very young at such distances.
Here are a few pertinent references:
- Is the Universe older than expected? (1)
10 July 2002
"An analysis of 13.5 thousand million-year-old X-rays (from
quasar APM 8279+5255) , captured by ESA's XMM-Newton satellite,
has shown that either the Universe may be older than astronomers
had thought or that mysterious, undiscovered "iron factories"
litter the early Universe."
And also,
A Universe Older Than Itself?, by Tom Van Flandern (2)
"The large iron content of the quasar is therefore a major puzzle.
Only two explanations appear possible, and either one is going to
upset some theorists:
(1) the Big Bang redshift-distance-age relationship is wrong; or
(2) the early universe contained "iron factories" producing
extra iron by an unknown physical means."
Notice that a third explanation is plausible:
The universe is stable, and the Big Bang never happenend.
- Very Large Telescope unravels new population of very old
massive galaxies (3)
"Those galaxies must have formed when the Universe was only about
2,000 million years old, that is some 12,000 million years ago."
"... these galaxies have structures and shapes more or less identical
to those of the present-day massive elliptical galaxies"
"Says Andrea Cimatti (INAF, Firenze, Italy), leader of the team:
"Our new study now raises fundamental questions about our understanding
and knowledge of the processes that regulated the genesis and
the evolutionary history of the Universe and its structures."
- GIANT GALAXY STRING DEFIES MODELS OF HOW UNIVERSE EVOLVED (4)
"Wide-field telescope observations of the remote and therefore
early Universe, looking back to a time when it was a fifth of
its present age (redshift = 2.38), have revealed an enormous
string of galaxies about 300 million light-years long. This new
structure defies current models of how the Universe evolved,
which can't explain how a string this big could have formed so early."
"The team compared their observations to supercomputer simulations
of the early Universe, which could not reproduce strings this large.
"The simulations tell us that you cannot take the matter in the early
Universe and line it up in strings this large," said Francis.
"There simply hasn't been enough time since the Big Bang for it
to form structures this colossal".
POSTULATES:
__________
1) The universe is infinite, Euclidean, stable (non-expanding),
homogeneous and isotropic.
2) The range of the gravitational force is finite.
3) The Cosmological Principle, according to which the universe,
when viewed on sufficiently large distance scales, has no preferred
directions or preferred places, applies.
CONSEQUENCES OF THE POSTULATES:
______________________________
At each point of their trajectory, light and material objects are
subject to a negative acceleration cK.
Indeed, each point of the trajectory can be considered as the center
of a sphere of radius R and mean density rho, which corresponds to
the mean density of the universe itself. This is valid according to
the second and third postulates.
At the surface of the sphere, the acceleration of gravity is given
by the formula a = GM/R^2, where G is the gravitational constant.
As rho = M/V and V = (4/3)*pi*R^3, M/R^3 = (4/3)*pi*rho, hence
a = (4/3)*G*pi*rho * R
As the dimension of a is L/T^2, the dimension of (4/3)*G*pi*rho
is 1/T^2, and the square root of this expression corresponds to
the inverse of a time.
The formula a = (4/3)*G*pi*rho * R can thus be written
a = K^2 * d, where K = sqrt((4/3)*G*pi*rho).
To the maximum possible value of R corresponds
a = c^2/R = K^2 * R, hence R(max) = c/K.
Replacing R by c/K in the formula a = K^2 * R, one gets
a = cK, which is the acceleration of gravity at the surface
of a sphere of radius c/K.
As, according to the above postulates, the trajectory of a photon
corresponds to an infinity of such centers, the moving photon will
be subject to a constant negative acceleration cK during its whole
trip, which will lead to its reddening.
THE REDSHIFT IN A STABLE UNIVERSE
_________________________________
A light ray of wavelength lambda is sent from a point P.
At a distance d from P, the energy loss of a photon of
frequency Nu is
(hNu/c^2) * cK * d = hNu * (K/c) * d,
where h is the Plank constant.
The residual energy hNu(o) of the photon at the distance d is
hNu(o) = hNu - hNu * (K/c) * d = hNu (1 - K*d/c), hence
Nu(o) = Nu (1 - (K*d/c), and
lambda(o) = (1 - (K*d/c) / lambda
Thus, in a stable homogeneous universe,
z = (lambda(o) - lambda) / lambda
= (K/c)d * (1+z), and
d = (c/K) * z/(1+z)
z = d / ((c/K)-d),
where d is the distance between the observer and
the emitter at the instant when the light was emitted.
Interestingly enough, the formula d = (c/K) * z/(1+z), which gives
the light travel time, leads, assuming c/K = 15 Gly, to results which
are very close to those obtained by Ned Wright's calculator when
hypothetizing a flat universe, c/H0 = 13.7 Gly and Omega M = 0.27
z d Calculator (5,6)
0.1 1.36 1.29
0.5 5.00 5.02
1.0 7.50 7.73
3.0 11.25 11.48
6.0 12.86 12.72
The correlation coefficient between those two series of results
is 0.999.
CONCLUSION
__________
Recent cosmological observations are so much at variance with the
predictions of the big bang theory, that an alternative should be
considered. The most obvious one is a stable, non-expanding universe.
The existence of a cosmological negative acceleration explains
the reddening of light relatively to the distance of its source,
according to the relation d = (c/K) * z/(1+z).
Such relation leads to distances which are very close to those
calculated with the help of general relativity.
On the other hand, a negative acceleration cK would explain the Pioneer
anomaly (7,8), that the ESA intends "to put to the test". (9)
Marcel Luttgens
Oct. 9, 2004
REFERENCES:
__________
(1) http://www.esa.int/esaSC/Pr_5_2002_s_en.html
(2) Apeiron, Vol. 9, No. 3, July 2002
(3) http://www.rednova.com/news/stories/1/2004/07/07/story003.html
(4) http://www.gsfc.nasa.gov/topstory/2004/0107filament.html
(5) http://www.astro.ucla.edu/~wright/CosmoCalc.html
(6) Formula used in the calculator: see
http://www.astro.ucla.edu/~wright/Distances_details.gif
(7) Study of the anomalous acceleration of Pioneer 10 and 11, by
John D. Anderson et al., gr- qc/ 0104064 19 Apr 2001
(8) http://perso.wanadoo.fr/mluttgens/pioneer1.htm
(9) http://physicsweb.org/articles/world/17/9/3
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