Content uploaded by Dean L. Mamas
Author content
All content in this area was uploaded by Dean L. Mamas on Aug 29, 2022
Content may be subject to copyright.
Content uploaded by Dean L. Mamas
Author content
All content in this area was uploaded by Dean L. Mamas on Aug 29, 2022
Content may be subject to copyright.
Content uploaded by Dean L. Mamas
Author content
All content in this area was uploaded by Dean L. Mamas on Jun 06, 2020
Content may be subject to copyright.
An explanation for the cosmological redshift
Dean L. Mamasa兲
4415 Clwr. Hr. Dr. N., Largo, Florida 33770, USA
共Received 20 February 2009; accepted 27 March 2010; published online 29 April 2010兲
Abstract: A new theoretical model is presented which accounts for the cosmological redshift in a
static universe. In this model the photon is viewed as an electromagnetic wave whose electric field
component causes oscillations in deep space free electrons which then reradiate energy from the
photon, causing a redshift. The predicted redshift coincides with the data of the Hubble diagram.
The predicted redshift expression allows for the first time distance measurements to the furthest
observable objects, without having to rely on their apparent magnitudes which may be subject to
cosmic dust. This new theoretical model is not the same as, and is fundamentally different from,
Compton scattering, and therefore avoids any problems associated with Compton scattering such as
the blurring of images. © 2010 Physics Essays Publication.关DOI: 10.4006/1.3397803兴
Re
´sume
´:Un nouveau modèle théorique est présenté qui explique le décalage vers le rouge cos-
mologique dans un univers statique. Selon ce modèle le photon est visualisé comme une onde
électromagnétique, dont la composante électrique cause des oscillations dans les électrons libres
dans l’espace intergalactique qui ensuite diffusent l’énergie du photon, causant un décalage vers le
rouge. Le décalage vers le rouge prédit coïncide avec les données du diagramme de Hubble.
L’expression prédite du décalage vers le rouge permet pour la première fois la mesure des distances
aux objets les plus lointains observables, sans devoir tenir compte de leur magnitude apparente qui
peut être sujette à la poussière cosmique. Ce nouveau modèle théorique n’est pas le même, et il est
fondamentalement différent, de la diffusion Compton, et donc il évite tout problème associé à la
diffusion Compton tel que le brouillage des images.
Key words: Cosmology; Cosmological Redshift; Cosmological Models; Supernovae; Cosmic Dust.
I. INTRODUCTION
Compton scattering has long been rejected as an expla-
nation for the cosmological redshift because in this particle-
particle interaction, photons are scattered into various angles
at various frequencies, resulting in a blurring of images.1
Numerous other mechanisms have been attempted to explain
the cosmological redshift, such as an energy loss of the pho-
ton when traversing a radiation field,2an inelastic scattering
by gaseous atoms and molecules,3or a dispersive-extinction
effect by the space medium.4,5Previously unconsidered by
the principle of complementarity, a photon may also be
viewed as a wave, interacting with intergalactic free elec-
trons in a wave-particle fashion.
It is reasonable to assume that although very short wave-
length photons 共gamma rays兲can interact with electrons in a
particle-particle fashion 共Compton scattering兲, photons of
longer wavelengths than those of gamma rays could interact
with electrons in a wave-particle fashion, the electron react-
ing to the photon’s electric field. Being that a wavelength of
visible light is eight orders of magnitude larger than an elec-
tron, a visible wavelength photon should pass directly over
an electron with unchanging direction and with negligible
blurring of images. This would circumvent Zwicky’s above
mentioned historical objection to Compton scattering over
blurring of images and satisfy the consideration that photons
travel without appreciable transverse deflection.6Further-
more, any other objection to Compton scattering 共particle-
particle兲as an explanation for the cosmological redshift is
irrelevant to the thesis of this present article, which does not
propose a Compton scattering explanation but rather a fun-
damentally different redshift mechanism based on an instead
wave-particle interaction. The thesis of this present article is
a theoretical prediction of a new mechanism, a new fashion
in which a photon could interact with free electrons in deep
space. This new theoretical model is supported by the calcu-
lations provided below, the predicted cosmological redshift
coinciding with the data of the Hubble diagram.
A clear distinction is being drawn here between the case
of extremely high frequency 共gamma ray兲Compton scatter-
ing 共particle-particle兲interactions, and the different manner
in which photons of longer wavelengths than those of
gamma rays may interact with free electrons in an instead
wave-particle fashion. In the former case, the intensity 共pho-
ton flux兲of radiation is reduced as gamma ray photons are
simply scattered out of a beam of gamma radiation. In the
latter case, photons of longer wavelengths than those of
gamma rays are seen as passing directly over the free elec-
trons with therefore no change in a photon’s forward direc-
tion. Easily visualized as an example, a very long radio
wavelength photon which passes over a free electron will
certainly cause a radio frequency oscillation in the electron,
while the radio wavelength photon continues along in its
original straight path. In this long wavelength case, the in-
a兲deanmamas@yahoo.com
PHYSICS ESSAYS 23,2共2010兲
0836-1398/2010/23共2兲/326/4/$25.00 © 2010 Physics Essays Publication326
tensity 共photon flux兲of a beam of photons remains un-
changed. What is, however, expected is a minuscule reduc-
tion in each incident photon’s energy 共a redshift兲as the free
electrons are encountered, as will be demonstrated below by
calculation. This mode of interaction is expected to hold not
only for radio frequencies but over the entire frequency
range of observed spectral lines all the way into the x-ray
regime.
A further distinction is drawn here between these two
separate cases. In high frequency 共gamma ray兲Compton
scattering, photons can experience a change in their fre-
quency, but a strong unshifted component remains. In con-
trast, photons of longer wavelengths than those of gamma
rays as observed in the spectral lines from stars do not ex-
hibit both frequency shifted and unshifted light, rather these
photons are seen as all interacting with deep space free elec-
trons in a wave-particle fashion, where all photons are
equally redshifted by the law of large numbers, each photon
from a particular spectral line of a particular object encoun-
tering the same great number of free electrons in deep space.
As a note, in the situation of extremely dense radiation
fields such as where very powerful lasers are used in labora-
tory Thomson scattering measurements of plasma densities,
or in the extremely dense radiation fields in the interior of
stars, a new interpretation of the manner is suggested here in
which photons of longer wavelengths than those of gamma
rays are actually interacting with free electrons. In these
dense radiation fields, one has the impression that the pow-
erful laboratory laser beam’s photons can experience a
change in their direction and be subtracted from the beam, as
do gamma ray photons in Compton scattering. It is, however,
suggested here that in these very dense radiation fields, the
individual photons of longer wavelengths than those of
gamma rays are not actually deflected from their straight line
paths, rather the free electrons are so massively agitated by
radiation that a free electron reradiates photons at the same
frequency of the radiation field only after taking a tiny bit of
energy from each and every photon that passes directly over
the free electron. The incident laboratory laser beam would
then have no reduction in its photon flux but rather simply a
tiny reduction in the frequency of each incident photon. The
cosmological redshift might therefore be testable using labo-
ratory lasers, although conditions in dense radiation fields in
laboratory plasmas are radically different from those in deep
space.
II. ANALYSIS OF THE REDSHIFT MECHANISM
The following discussion analyzes by calculation the
共wave-particle兲fashion in which photons of longer wave-
lengths than those of gamma rays may interact with deep
space free electrons, resulting in the redshifted spectral lines
of astronomical objects.
A photon is an electromagnetic wave whose electric field
component should cause an oscillation in any free electron
over which passes the wave. The electron duly accelerated
must reradiate energy at the expense of the wave. A free
electron has been demonstrated by electromagnetic theory to
have an effective area for reradiating the energy of an inci-
dent electromagnetic wave, the Thomson scattering cross
section.7Applying Planck’s relation 共E=hf兲that the energy
of a quantum of electromagnetic energy be proportional to its
frequency, one expects then that the frequency of the photon
is lowered in proportion to this reduction in its energy, i.e., a
redshift. Much more massive are ions whose effect is ne-
glected.
From the point of view of electromagnetic wave theory,
as a photon passes over a single free electron the electron is
not displaced from its initial position but simply oscillates
about its fixed position with the electric field of the wave,
reradiating energy in a symmetric dipolar fashion, therefore
not causing the wave to alter its forward direction. Note that
in the calculation of the Thomson scattering cross section,
the electron is taken as fixed in that the random velocities of
free electrons are assumed small compared to the speed of
light of the incident photon. Also in the calculation of the
Thomson scattering cross section, the electron is taken as
reacting only to the photon’s electric field component, the
electron’s assumed subrelativistic velocity allowing one to
neglect the magnetic component of the Lorentz force. Any
effect of the electron’s dipole moment is also neglected.
If now a photon, viewed as in itself an incident electro-
magnetic wave, traverses the rarefied deep space of the cos-
mos for billions of years, the photon’s wavefront slowly and
eventually encounters vast numbers of free electrons one at a
time, resulting in a cumulative redshift which can be calcu-
lated. The following equation expresses a fractional decrease
共dI/I兲in a plane EM wave’s energy flux Ias the wave en-
counters an electron density n, where electrons have an ef-
fective cross-sectional area C, the well known standard value
for the Thomson scattering cross section of electrons. The
equation follows immediately from the definition of the Th-
omson scattering cross section, which is the effective area of
the free electron to reradiate energy from an incident electro-
magnetic wave 共the photon兲whose direction remains un-
changed.
dI/I=−Cndx.共1兲
We can now integrate this equation, the integral of the
right hand side being the total cross-sectional area of all the
electrons 共per m2of incident wave兲that the incident wave
would be intercepting over a distance x. Completing the in-
tegration of both sides of the equation and then solving for I
yield a standard exponential decay for I, the incident energy
flux, over a distance x, where the exponential decay constant
khas the value 共1/Cn兲.
I⬃exp共−x/k兲.共2兲
Assuming for illustrative purposes, an average electron
density of 100 e/m3in intergalactic space, the exponential
distance scale k共=1/Cn兲for the weakening 共redshifting兲
photon calculates to be 16⫻109light years. Dividing by the
speed of light gives an exponential redshifting time scale of
16⫻109years, which is approximately the hypothetical “age
of the universe” according to the Big Bang theory. This pro-
vides a simple alternative explanation for the extremely red-
Phys. Essays 23,2共2010兲327
shifted edge of the visible universe, due to wave-particle
scattering by free electrons, as opposed to the expansion hy-
pothesis of the Big Bang theory.
Regarding the above assumption of an estimated
100 free electrons/m3, note that any small uniform back-
ground of free electrons in deep space would have negligible
effect on the observed dynamics of astronomical systems.
Any higher or lower estimate for an average free electron
density in deep space would, respectively, decrease or in-
crease the above calculated redshifting distance scale. Esti-
mated values for Hubble’s constant have varied appreciably.
By choosing a higher or lower figure for the average free
electron density, one can precisely produce the same effect of
any estimated value for Hubble’s constant in that by either
redshifting mechanism the linear distance versus redshift
graphs for nearby measurable astronomical objects would
coincide.
III. AGREEMENT WITH THE HUBBLE DIAGRAM
The precise coinciding of redshift graphs is quickly seen
from the above exponential expression for the redshifting
photon, where the photon’s frequency fhas the following
dependence:
f⬃exp共−Cnx兲.共3兲
For nearby astronomical objects, the frequency is therefore
linear with distance.
f⬃共1−Cnx兲.共4兲
Calculating redshift we then arrive immediately at the fol-
lowing equation:
z= redshift = Cnx.共5兲
The Hubble expression for redshift is also linear with dis-
tance and precisely coincides with the above linear expres-
sion for redshift when simply equating the proportionality
constants.
Cn =H/共speed of light兲.共6兲
Taking one estimate of Hubble’s constant to be the in-
verse of 13.7⫻109years, the value of nis calculated to be
116 e/m3, the average free electron density that produces a
linear distance versus redshift behavior which precisely co-
incides with that from Hubble’s constant.
The above calculation demonstrates how just a small
amount of intergalactic free electrons can result in the cos-
mological redshift observed in the spectral lines of astro-
nomical objects.
Note that the emergent spectrum originates at the star’s
surface, and the cosmological redshift begins to increase
thereafter, as the photons pass over vast numbers of free
electrons in deep space after billions of years of travel.
Further regarding the above assumption of approxi-
mately 100 e/m3in deep space, the average electron density
in deep space has never been directly measured. The discov-
ery of voids and supervoids in deep space make even more
difficult the problem of directly measuring an effective aver-
age value for the density of electrons in deep space. The
arguments presented in this present article are based on the
implicit assumption that the electron density in deep space is
homogeneous in space and time. Models of the Big Bang
theory predict numbers for the mass density of the universe,
but if one rejects the Big Bang theory and proposes alterna-
tive theories, the Big Bang based predictions for mass den-
sity are meaningless. The above determination of an average
effective density of 116 e/m3is supported by the above cal-
culation which shows precise agreement with the current
value for Hubble’s constant.
As for laboratory confirmation of my above proposed
explanation for the cosmological redshift, to detect a redshift
in the laboratory would be difficult because electron densi-
ties normally attained in laboratory plasmas are far too low.
However, the effect does appear to exist over astronomical
distances where vast numbers of free electrons are available.
IV. CALCULATION OF THE DISTANCES TO THE
FURTHEST OBSERVABLE OBJECTS
One now returns to the above predicted redshifting fre-
quency dependence which was expressed by the following:
f⬃exp共−Cnx兲.共7兲
From this frequency dependence, the redshift of the weaken-
ing photon is then immediately calculated yielding the fol-
lowing general formula 共redshift=fractional change in fre-
quency兲which holds out to the furthest cosmological
distances.
z= redshift = exp共Cnx兲−1. 共8兲
This redshift formula is therefore independent of the ob-
served brightness of an astronomical object. It is also inde-
pendent of the photon’s frequency, thereby admitting the
same redshift measurement in any wavelength band of ob-
served spectral lines. Linear at nearby distances in precise
agreement with Hubble’s data, as shown above, we now find
that at great distances the redshift should increase exponen-
tially.
Solving this expression for redshift one finds the follow-
ing general equation for determining the distance xto cos-
mological objects based on their redshifts.
x=共1/Cn兲ln共redshift + 1兲.共9兲
At great distances, using the above calculated n
=116 free electrons/m3in deep space, one sees that for a
redshift of 1.72, the distance of an astronomical object re-
duces to the following:
x=1/Cn =共speed of light兲/H= 13.7 ⫻109light years.
共10兲
Type 1a supernovae with redshift of 1.72 should then be
at a distance of 13.7⫻109light years. Distant Type 1a su-
pernovae are observed to be much dimmer than their red-
shifts would normally indicate, leading one to believe them
to be further than 13.7⫻109light years. However, the cumu-
lative effect of cosmic dust at great distances is presumed to
be responsible for their dimness and for their divergence
from the linear Hubble relation at high redshifts.8,9Using
328 Phys. Essays 23,2共2010兲
distance modulus to calculate the distance of nearby astro-
nomical objects is reliable, but at great distances absorption
coefficients of cosmic dust make distance modulus measure-
ments uncertain. The above exponential expression for red-
shift allows distance calculations for the furthest observed
astronomical objects without needing any corrections for
cosmic dust. The arrival of a single photon from a particular
spectral line in principle allows the calculation of the dis-
tance to the furthest observable object. It matters not how
many photons arrive, the above redshift expressions being
independent of observed brightness. The above exponential
expression for redshift circumvents the problem of dust ex-
tinction when measuring the furthest cosmological distances.
Observations of time dilation in supernova light curves
are here regarded as inconclusive, such studies perhaps in-
volving systematic errors in their interpretation or treatment
of data, possibly in their sampling of intrinsically brighter
supernovae at high redshifts while ignoring these dimming
effects of cosmic dust. The surface brightness test is also
regarded here as inconclusive in view of these heretofore
neglected effects of cosmic dust at high redshifts.
V. FINAL COMMENTS
A new theoretical model has been presented here which
accounts for the cosmological redshift in a static universe.
This new theoretical redshift model is simpler than the hy-
pothesis of expanding space as derived from the gravitational
field equation. This new explanation for the cosmological
redshift also provides a solution to Olbers’ paradox, a photon
slowly redshifting to frequencies not capable of stimulating
the human eye.
This new non-Doppler explanation for the cosmological
redshift also permits for the first time distance measurements
to the furthest observable astronomical objects. Not only do
these newly allowed distance measurements circumvent the
problem of cosmic dust, they also are no longer subject to
the question of the Big Bang’s adjustable scale factors. With-
out the Big Bang theory comes a new postmodern cosmol-
ogy where the universe is seen as presumably infinite spa-
tially and temporally, which necessarily implies a new
dynamic equilibrium cosmology.
It is suggested here that research is directed into identi-
fying the processes which maintain this equilibrium, namely,
processes whereby entropy must be recycled and starlight
returns to matter, both these conditions possibly satisfied by
deep space pair production processes. The cosmic micro-
wave background should be reconsidered as due to the tem-
perature of space as first calculated in 1896 by Nobel Prize
winner Charles Édouard Guillaume.10 Without the Big Bang
theory, a symmetric universe with equal amounts of matter
and antimatter can now be considered, evidenced in the cos-
mic gamma ray background radiation. A picture then
emerges of matter-antimatter annihilation keeping an eternal
universe churning, all matter unable to coalesce to any par-
ticular point. This then immediately offers a new direction of
research into gamma ray bursts, quasars, blazars, and other
extremely energetic objects, possibly explainable by various
scenarios of matter-antimatter annihilation. This would avoid
having to use the unphysical mathematical singularities in-
herent in the gravitational field equation, on which have been
based models of astronomical black holes as well as the ini-
tial hypothetical Big Bang itself.
1F. Zwicky, Proc. Natl. Acad. Sci. U.S.A. 15, 773 共1929兲.
2E. Finlay-Freundlich, Proc. Phys. Soc., London, Sect. A 67,192共1954兲.
3P. Marmet, Phys. Essays 1,24共1988兲.
4L. J. Wang, Phys. Essays 18, 177 共2005兲.
5L. J. Wang, Phys. Essays 21, 233 共2008兲.
6E. Hubble and R. C. Tolman, Astrophys. J. 82, 302 共1935兲.
7J. J. Thomson, Conduction of Electricity Through Gases 共Cambridge Uni-
versity Press, Cambridge, London, 1906兲.
8R. P. Kirshner, Proc. Natl. Acad. Sci. U.S.A. 96, 4224 共1999兲.
9A. Aguirre, Astrophys. J. 525,583共1999兲.
10C.-E. Guillaume, La Nature 24,234共1896兲.
Phys. Essays 23,2共2010兲329
