Research Article Does the Hubble Constant Really Represent Recession Velocity? A New Interpretation of the Cosmic Redshift

Abstract

The tired-light redshift (RS) theory in a static or slowly expanding universe is re-examined in connection with novel theories of the physical properties of the quantum vacuum by assuming thermalization of starlight into a homogeneous black-body energy distribution. A new redshift /photon travel time (RS/t) relation is deduced and predictions of the theory are compared with those of the lambda-cold dark matter (ΛCDM) model and with supernovae RS data.

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Mai 30. 2012
Research Article
Does the Hubble Constant Really Represent Recession Velocity?
A New Interpretation of the Cosmic Redshift.
Laszlo A. Marosi
67061 Ludwigshafen, Germany
E-Mail: LaszloMarosi@aol.com
Copyright © 2012 Laszlo A. Marosi
Abstract
The tired-light redshift (RS) theory in a static or slowly expanding universe is re-
examined in connection with novel theories of the physical properties of the
quantum vacuum by assuming thermalization of starlight into a homogeneous
black-body energy distribution. A new redshift /photon travel time (RS/t)
relation is deduced and predictions of the theory are compared with those of the
lambda-cold dark matter (ΛCDM) model and with supernovae RS data.
Key words: Tired-light theory, redshift, Hubble constant, energy equilibration,
quantum vacuum, cosmic microwave background, diffuse background radiation,
energy conservation.
1 Introduction
The interpretation of the RS of atomic spectral lines emitted by distant galaxies as
recession velocity was probably the most important contribution leading to the
conception of the big-bang theory; a highly successful theory for explaining the origin
and expansion of the universe, the abundance of light elements, and the existence of the
2.7K cosmic microwave background (CMB), demonstrating that its basic assumption,
i.e. the expansion of the universe, is a legitimate global concept.
At the same time, however, we have to bear in mind that, as the counterpart to its great
success, this interpretation was the most compelling evidence for introducing the
elusive dark components dark matter (DM) and dark energy (DE) into cosmology.
Nearly all the major problems of modern cosmology have their origin in this hypothesis.
To mention only a few:
Firstly: Accurate observations of the CMB anisotropy show, that the universe is flat [1].
Following the paradigm of the big-bang theory, kinetic energy = ½ gravitational
energy, the critical mass for a flat universe G
H
cr
π
ρ
8
32
= (H0=72.6 km s-1 Mpc-1)
corresponds to a mass density of ≈ 10-29 g cm-3. In contrast, the density of matter which
has been observed so far amounts only to a few percent of the critical value.

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For comparison: Inferring the Hubble constant from the observable mass density of
some 10-31g cm-3 (instead of ~ 10-29g cm-3 as calculated on the basis of the still
controversial interpretation of RS as recession velocity) leads to 3
8
0
G
obs
H
π
ρ
×
= ~
7-15 km s1 Mpc-1 and the missing mass problem on the cosmic scale does not arise.
Secondly: A further problem is related to the age of the universe which nearly
corresponds to the age of its oldest stars. The problem is that galaxy formation in a
purely baryonic universe does not work. It is impossible for baryonic matter to form
galaxies and large scale structure in a time as short as 10 - 20 billion years. Estimates
show that the time necessary for the formation of galaxy clusters amounts to roughly
200 billion years [2].
For comparison: Inferring the age of the universe from 1/H0 with H0 ~ 7 km s-1 Mpc-1
yields ~ 170 billion years, and with this, galaxies may have been evolved over time in
some regular way without the need for DM or DE.
Finally: Another problem with the cosmological expansion relates to the loss of energy
associated with the RS. Contemporary big-bang cosmology ignores this problem and
often, this still unexplainable loss of energy is explained by some physically
questionable arguments like the universe is an open system to which, on the cosmic
scale, energy conservation does not apply, or simply using the fuzzy statement that the
redshifted energy disappears in the quantum vacuum.
An alternate answer to the problems described above might be found in the hypothesis,
that RS of spectral lines is composed of a velocity and a superimposed RS component
[3, 4] of as yet unknown origin and the rate of expansion is much lower, say, the
universe expands according to the Friedmann equation with ρM, obs ≈ 10-31g cm-3, Λ = 0,
k = 0.
Contemporary big-bang cosmology adheres to the purely velocity interpretation and
surmises DM and DE for explaining the missing mass and age problems. Many
cosmologists consider the postulate of DM and DE as the main finding of present
astrophysics. Speculations about the physical nature of these unknown particles and
energy are numerous but not successful as yet. If search for DM and DE turns out
unsuccessful, the whole construction will break down and we shall unavoidable face the
question what is the real mechanism that produces the observed values of the RS.
2 Tired – Light Redshift Theories
The tired-light scenario assumes that the photon loses energy due to some unknown
process when travels through space. The idea was first suggested by Zwicky [5] to
explain the Hubble relation. The major problem with this theory is the identification of a
convincing physical process responsible for the observed loss of energy.
Since that time several theories appeared in scientific literature, by which photons in
transit might lose energy. To mention only a few: Photon-photon scattering [6 – 9],
absorption of starlight by luminiferous ether [10, 11], interaction of photons with
vacuum particles [12], with intergalactic matter [13], dispersive extinction [14], photon
decay in curved space-time [15] have been proposed but for lack of supporting physical
and astronomical evidence not accepted by mainstream cosmology.
In this paper I will describe a new tired light mechanism that explains the observed
RS/d (distance) relation in a static or slowly expanding universe by assuming
thermalization of starlight into a homogeneous black-body energy distribution.
This idea is not really new. Its conceptual origin can be traced back to early ideas of
Eddington, Regener, Nernst, and Finlay-Freundlich [16, 17] predicting a temperature of

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the interstellar space of ~ 3 K for a static universe in thermal equilibrium. The proposed
mechanism, explicitly the loss of energy of starlight by photon-photon scattering was
widely criticized [18] and because no convincing mechanism could be identified at that
time the tired light model for explaining intergalactic RS was discarded.
During the last few decades, however, new theories of the physical nature and structure
of the quantum vacuum have become available, so a reconsideration of the tired model
in light of these theories appears warranted.
3 New Interpretation of the Cosmic Redshift
3 1 Main Hypothesis
We assume thermalization of the energy of atomic spectral photons into the equilibrium
blackbody energy distribution. In extension of previous ideas mentioned above we
further assume that energy equilibration is a natural quantum mechanical process,
inherent in the energetically excited quantum vacuum itself and thus, equilibration does
not require any material mediator for transfer of energy from the starlight into the CMB.
Supporting physical theories in favor of the proposed energy equilibration without
material mediator are discussed in Section 5.
To illustrate the concept let us assume that an emitted photon having energy hν travels
through the CMB radiation field. According to the proposed energy equilibration there
is a transfer of energy from the travelling photon into the CMB radiation field.
The rate of energy transfer is given by
dνt/dt = H0νt (1)
where νt is the frequency of the photon at time t (sec.) after emission, H0 is the Hubble
constant, and hν = ν; h = 1).
According to this schema the energy of an emitted photon after a second flight time is νe
– νeH0 = νe(1-H0), after two seconds νe(1-H0) - νe(1-H0)H0 = νe(1-H0)2 and after t
seconds the observed frequency νobs is
νobs = νem(1-H0)t (2)
and with (2) the RS
1
1
)()(
)(
00
0
1
1
1−=
−
=
−
−
−
HH
Htt
t
e
ee
z
ν
νν
(3)
Eq.(3) leads to an exponential increase of RS with increasing flight-time t. This is
essentially the tired light model. For short distances, z << 1, eq. (3) can be approximated
by the linear relation z ≈ H0t.
With this interpretation, of course, H0 does not represent the velocity of expansion, km
s-1 Mpc-1, but the rate of energy transfer from starlight into CMB and has the dimension
Hz s-1 Hz-1 according to the presented energy equilibration theory.
3 2 The Exponential RS/t Relation
The ΛCDM model with H0 = 72 km s-1 Mpc-1, ΩM = 0.266, ΩΛ = 0.732 and k = 0 leads
to a mathematically correct solution for the evolution of an expanding universe; the
universe has expanded from its beginning to the present time to an extent of about DC =
46 billion ly, where DC is the co-moving proper distance.

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However, the ΛCDM model, though cosmologically important, has by itself no physical
basis and requires a choice of free parameters (DM and DE) in order to fit the
underlying expansion theory to the observed RS/d data.
An alternative procedure is to choose a static (or slowly expanding) space and analyze
cosmological observations exclusively on the basis of observable quantities, i. e.: ρM,
obs., the experimentally measured RS – distance relation, and the experimentally
confirmed Euclidean geometry of the universe, instead of introducing unknown
particles and energy.
Imagine now that, although the result obtained on the basis of the ΛCDM model is a
mathematically correct description of the present radius and distances in an expanding
universe, nevertheless, the expanding space interpretation is physically fictitious and the
universe is static, or slowly expanding, and infinite, or very large, in extent. In this case,
the ΛCDM-model represents only a mathematical fit to the observed RS data, but in
reality, the calculated distances represent non-expanding distances between observer
and the emitting objects in a static universe. With this assumption the flight-time of
photons between emission and reception is t = DC/c.
The resulting RS/t relation, derived from the distances DC, as obtained from the ΛCDM-
model with H0 = 68 km s-1 Mpc-1 and k = 0 is represented by the solid line in Figure 1
[19].
Figure 1: Redshift of type Ia supernovae as function of t =DC/c. Plane line: ΛCDM-
model with H0 = 68 km s-1 Mpc-1. Diamonds: RS/t relation inferred from eq. (3) with H0
= 1.95×10-18 Hz s-1 Hz-1. Triangles: representative ‘gold set’ data [20]; luminosity
distances were converted into DC by DC = DL/(1 + z).
One can see from Fig. 1 that the two approaches, the ΛCDM-model, supposing
expansion, and the static universe model, supposing energy equilibration, although
fundamentally different, lead to similar results and show a fairly good fit to the
observed redshifts.
An advantage of the equilibration model compared with ΛCDM is that the equilibration
model does not require unknown constituents and that there is no real loss of energy
associated with this process: The energy of the redshifted photons is merely converted
into CMB energy and the total energy (Eλ + ECMB) has not changed.

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4 The Missing Diffuse Background Radiation
Beside the CMB the universe also contains a considerable amount of radiation not
belonging to the blackbody spectrum, called diffuse background radiation (DBR). DBR
is expected to arise from cumulative emissions of pregalactic, protogalactic, and
evolved galactic systems over the history of the universe, assuming that star formation
is the major source of the observed background [21].
It is to be expected that similar to CMB, also DBR would establish a certain radiation
temperature of the interstellar space. There are numerous estimates to determine this
temperature. A compilation of these results is shown in Table 1.
Guillaume 5-6
Eddington 3.18
Regener 2.8
Herzberg 2.3
Nernst 2.8
Finlay-Freundlich 1.9-6
Table 1: Estimates of the temperature of the interstellar space (K).
Data are taken from [16, 17]
It is a surprising fact that all these unanimous estimates deviate considerably from
experimental data: Sky brightness measurements by COBE, DIRBE, and FIRAS have
permitted the first quantitative results of the diffuse cosmic background (DBR) at all
wavelengths showing that infrared radiation in the range from 0.3 to - 200 μm is the
major contribution to the total DBR energy. It amounts to only 10 % of the expected
value [22 – 24].
Thus, it is legitimate to ask, if all these careful estimates carried out by notable
physicists are really so much in error, or as a more likely explanation, the lack of DBR
energy is to be seen as an indication in favor of the presented theory, namely as a
steadily flow of energy from the starlight into the CMB by the proposed energy
equilibration process.
5 Thermalization of Starlight into Black - Body Radiation
The interpretation of RS of atomic spectral lines suffers from the fact that none of the
proposed mechanisms, including the expanding space paradigm, can be verified
experimentally. Thus, the confidence in each theory must be measured by its success in
explaining the observational phenomena. In Section 3.2 we have shown that observed
RS date agree well with data inferred from eq. (3).
In order to give a supporting physical basis for the proposed energy equilibration it is
necessary to answer the following question:
Is the transfer of energy from starlight into CMB without any material mediator a
physically acceptable concept?
To answer this question we can present the following reasons:
(1) Theories that support energy equilibration of starlight into CMB without material
mediator are described by Opher and Pelinson [25] and Lima and M. Trodden [26].
They describe the possible decay of vacuum energy into CMB photons. The process
corresponds to a continuous flow of energy from the vacuum to the created CMB
radiation field. It leads to a Planckian type form of the spectrum, which is preserved in

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the course of evolution. Further literature supporting the theory of energy equilibration
can be found in [27 – 33].
In generalization of these theories we claim, that similar to the decay of vacuum energy
into black body radiation, also the energy of the excited vacuum state has the tendency
to equilibrate into the Planckian black body distribution.
(2) Energy equilibration also follows from the principle of maximum entropy, which
states that the probability distribution has the the largest entropy and herewith the
thermodynamically favored distribution of energy. For photons (the excited quantum
vacuum), the equilibrium state is the well known Planckian black-body energy
distribution [34].
(3) In quantum field theory the vacuum state is defined as the ground state of interacting
quantum fields that can exist in various excited states. The vacuum is described as a
quantized, fine grained, evolving, dynamical medium; waves propagating in this
medium can be described as excitation of specific quantum states. Photons, for example,
are interpreted as elementary excitations in a fine grained space whose ground state is
the vacuum [35]. Because all constituents of the excited vacuum, photons, virtual
particles, and possible also space and time are quantum mechanical, it is consequent to
assume that between these constituents energy exchange will occur and, further, that the
equilibrium state of these energetically intimately interacting fields is the probability
energy distribution, i.e. the black-body energy distribution.
We assume that Planck’s formula continues to be valid in every quantum system, in
atomic, solid state systems and even also in the excited quantum vacuum itself and thus,
energy equilibration is rather an inevitable physical process than a theoretically
unfounded physical assumption.
Admittedly, the presented theory remains incomplete to an extent as it does not include
explicit physical micromechanism according to portions of energy of the photon can be
transferred into the CMB black body energy distribution. However, this lack of
knowledge is inherent in the expanding space paradigm, too. Classical physics tells us
that the energy of a photon depends on its wavelength by E = hc/λ. It is assumed that the
expanding space stretches the photon’s wavelength and consequently, its energy
decreases. However, the explanation given above simply describes what will happen to
the energy when the wavelengths of photons increase under certain conditions, but
similar to the proposed energy equilibration the expanding space hypothesis can neither
provide an explicit micromechanism for the energy transfer, nor can it tell us where the
redshifted energy has gone.
In the presented theory, at least, there is no real loss of energy, the energy of the
redshifted photons is merely converted into CMB energy and the total energy (Eλ +
ECMB) has not changed.
6 Conclusions
In this paper we reconsider and extend the tired light theory for the explanation of the
cosmic RS by utilizing the principle of energy equilibration between starlight and CMB.
We present a new RS/t relation and novel scientific theories supporting our assumption,
which shows that the proposed equilibration process might take place without any
material mediator. The equilibration follows from the interaction between quantum
states of the excited space-time entity and therefore, energy equilibration has to be
looked at as a natural quantum physical process rather than being physically unlikely.
We further show that (i) redshifts calculated with equation (3) are in agreement with the
observed supernovae RS data, (ii) the model avoids the missing mass problem on the
cosmic scale and (iii) the age problem of galaxy formation by assuming a static or

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slowly expanding universe and (iv) explains the RS in accordance with the law of
energy conservation.
We do not expect that all the results presented in this paper will turn out to be correct in
every detail on closer examination. The theory, however, makes provable predictions:
The energy equilibration theory predicts RS of spectral lines even inside of non-
expanding galactic systems. Moreover, if the correct form of eq. (1) should turn out to
be νt = H0(νt – νCMB) a possible blueshift of radio signals as suspected by Anderson et al.
[36]. Thus, in experiments similar to the Pioneer mission the validity of our theory
could be proved experimentally.
Acknowledgment
I am grateful to Professor Rainer Mattes from the Westfälische Wilhelms-Universität,
Münster, Germany, for proofreading and for his continuous interest in this work.
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