Paul Marmet, Herzberg Institute of Astrophysics

National Research Council, Ottawa, Ontario, Canada, K1A 0R6

( Last
checked 2012/07/02 - The estate of Paul Marmet
)

Updated from: Physics Essays, Vol. 1,
No: 1, p. 24-32, 1988
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A new mechanism must be looked for, in order to explain those inconsistent redshifts and many other observations related to the “redshift controversy”.

It is possible to calculate a very slight inelastic scattering phenomenon compatible with observed redshifts using electromagnetic theory and quantum mechanics, without the need to introduce

A careful study of the mechanism for the scattering of electromagnetic radiation by gaseous atoms and molecules shows that an electron is always momentarily accelerated as a consequence of the momentum transfer imparted by a photon. Such an acceleration of an electric charge produces bremsstrahlung.

It is shown in the present work that this phenomenon has a very large cross section in the forward direction and that the energy lost by bremsstrahlung causes a slight redshift. It is also demonstrated that the relative energy loss of the electromagnetic wave for blackbody radiation, such as for many celestial objects, follows the same “Dn/n = constant” law as if it were a Doppler law.

This redshift appears indistinguishable from the Doppler shift except when resonant states are present in the scattering gas. It is also shown that the lost energy should be detectable mostly as low frequency radio waves. The proposed mechanism leads to results consistent with many redshifts reported in astrophysical data.

** 1. Introduction**

Astrophysical observations show that the
electromagnetic radiation originating from cosmological objects
is often redshifted. Except for some hypothesis such as
assuming that it is a gravitational redshift, this has always
been interpreted as a Doppler shift. To date, the
interaction of light with interstellar gas has not been
seriously considered as a possible mechanism responsible for the
observed redshift because no known forward scattering process
could be demonstrated to lead to an effect compatible with
common astronomical observations. The redshift observed in
astronomy that agrees with a shift of Doppler origin, follows
the relationship:

(1) |

Thomson scattering however does not lead to Eq. (1). In this case, electrons accelerated by the transverse electric field of the incident electromagnetic radiation emit radiation due to their transversal acceleration. For example, the polarized blue radiation scattered by the daytime sky results from the transverse acceleration of bound electrons by visible light. It is well known that the cross section leading to such scattering increases very rapidly as a function of frequency n and therefore cannot lead to a red shift following Eq. (1).

Let us now consider the photon momentum in the direction of the propagation of the wave. It is this momentum which produces the Compton effect. In this case, the momentum transfer from the photon to the electron is taken into account. However, no one has ever fully taken into account the bremsstrahlung resulting from the momentum transferred to an electric charge, when the energy of the electromagnetic radiation is imparted to electrons or atoms. Although Boekelheide

Maxwell’s equations predict that radiation is emitted as a consequence of the change of velocity (acceleration) of the electron impinged on, due to momentum transfer. That point has been taken into account in quantum electrodynamics as explained by Jauch and Rohrlich

(2) |

From Eq. (2), we must notice that at any angle of scattering, bremsstrahlung is completely neglected. However, the electron is accelerated during the scattering. In order to illustrate the basic principle leading to an energy loss due to bremsstrahlung, let us examine the case of 90

According to electromagnetic theory, any accelerated charge must emit bremsstrahlung. Since the Compton electron has been accelerated, it must emit bremsstrahlung. Although the energy emitted due to such acceleration is extremely small, it is not zero and should not be neglected as done at low energy. It will be seen that this energy loss adds a slight correction to Eq. (2). The case of interaction at q = 0 requires special considerations. It can be considered either as an extreme case of Compton scattering (q = 0) or better as the simple transmission of radiation through the particles of a gas. In the latter case, the scattering angle is essentially zero degrees, but the physical reality of interaction with atoms is evident because the observed average speed of light is reduced in gases.

This reduced speed of light in gases is frequently calculated with the help of the index of refraction. In this paper, that parameter will be calculated as the group velocity and will be considered in more detail below. The interaction during transmission (or the scattering angle q = 0) is the only one that will be treated in this paper, since it leads to measurable predictions of light traveling through space.

In order to be able to evaluate the energy loss due to such a phenomenon, one needs to calculate different parameters such as the time of coherence of the electromagnetic radiation, the index of refraction of gases, and several other quantities. These parameters will be calculated in Appendices A and B.

** 2. Bremsstrahlung Due to Axial Momentum Transfer.**

** 2.1
Basic Mechanism**

In the corpuscular description of light, it
is considered that a particle, called a photon, is emitted from
an excited state after its average lifetime Dt.
This corresponds in electromagnetic theory to an oscillating
dipole continuously emitting coherent electromagnetic radiation
whose amplitude is uniformly damped to a fraction 1/*e *of
its initial value during the lifetime of the excited
state. This lifetime is equivalent to the time of
coherence of the radiation. During absorption, the
phenomenon is reversed and the time of coherence Dt becomes the time of interaction of the
wave with the atom.

This time of interaction Dt characterizes the wave as its time of
coherence. In the case of the emitter, this characteristic
can be considered as the average time taken by the emitter to
emit a photon. When using a wave description, it is
physically possible to deduce the time of coherence which is the
pulse duration of the wave packet. Therefore Dt appears to belong not only to the
emitter but also to the wave.

One must recognize another property of the
waves: Electromagnetic waves not only have energy but also
momentum. If one considers that the electromagnetic wave
imparts its energy during an effective pulse duration Dt, one must remember that it also
imparts its momentum during that time.

When an atom absorbs a wave train (photon),
the total momentum is conserved and therefore must appear within
the atom. The electron is therefore accelerated due to the
momentum transfer from the photon to the mobile electron.
The much smaller fraction of momentum imparted to the nucleus is
much smaller and can be neglected here. The electron is
then accelerated during a length of time equal to the time of
coherence of the absorbed radiation. After absorption, the
energy stays in the atom for a short interval of time which
explains the apparent reduced speed of light in gases.
Finally, the mechanism is reversed and the energy absorbed of
the wave is re-emitted. This short time interval accounts
for the index of refraction of gases as explained in Appendix
B. This selective forward reemission is obviously
necessary to explain the transparency of gases and the
straight-line propagation of light through them.

** 2.2 Transmission with Bremsstrahlung.**

It is known that, according to
electrodynamics, any accelerated electron must emit
radiation. Let us recall that we consider here an electron
that is accelerated due to the axial momentum transfer of
electromagnetic radiation. Classical electromagnetic
theory used here to treat the acceleration of an electron should
lead to an excellent approximation. This is because the
same classical energy leads to an equally excellent answer when
we calculate, at a similar energy, the electron inside an atom
related to the Thompson scattering or Compton effect.

We must realize that classical
considerations are valid here because of the "Correspondence
Principle" ^{(4)}. The
Correspondence Principle can be applied here because one deals
with very low energy electromagnetic radiation polarizing a
continuum of atomic hydrogen. A better proof of validity
of these semi classical considerations will be given in Appendix
B using an experimental value with the value deduced from this
theory (at similar energies).

Let us calculate the energy radiated due to
the photon momentum transfer given to the electron. The
total power radiated by an accelerated charge e is:

(3) |

The time of coherence Dt is calculated in Appendix A. The power radiated is:

(4) |

(5) |

The momentum P of the wave train is:

(6) |

where n is the frequency of the incoming radiation. Since this phenomenon is transferred to the electron, the change in velocity (Dv=P/m) gives:

(7) |

(8) |

(9) |

Combining Eqs. (8) and (9) gives:

(10) |

(11) |

(12) |

Numerically, we calculate that M=2.73 ´ 10

This energy loss can be applied to either bound or free electrons, but the cross sections differ greatly between these two cases, as shown in Appendix B.

** 2.3 Characteristics of the Energy Loss Equation.**

It is
interesting to note that in Equation (12), the relative energy
loss is independent of the frequency n
of the incoming radiation in the case stated (blackbody
radiation). Therefore, the whole spectrum will undergo a
constant relative displacement in energy toward lower
frequencies. This displacement of the spectrum is exactly
similar to the redshift produced when a source of radiation
recedes from the observer (Doppler effect). For example, the fractional redshift ^{(5)} for astronomical objects can be described by the fractional redshift constant:

(13) |

Since the relative energy loss is independent of n in both cases, the new redshift described by Eq. (12) is undistinguishable from the Doppler redshift described by Eq. (13) in the energy range studied. As a consequence, all absorption lines of a blackbody spectrum will be redshifted with the same dependence as Z as long as they are away from resonant frequencies.

On the other hand if narrow emission lines, which have a much longer time of coherence (see Appendix A), are superimposed on the spectrum, their redshift is smaller than that given by Equation (12). However, if the emitted light appears at the same frequency as the resonant absorption line of the interacting gas, the cross section becomes very much larger. This problem related to emission lines (instead of absorption lines) is much more complicated, requires a different treatment and is outside the scope of this paper.

It may at least be realized that the redshift is emission should be, in general, different from that in absorption and also influenced by the energy of the quantum states that characterize the absorption medium.

One must then conclude that a redshift is produced due to hydrogen in space according to Eq. (12). This redshift appears undistinguishable from Doppler redshift for radiation with a short coherence time. The energy loss of the initial radiation appears separately as very low frequency radio waves.

** 3. Application to Astrophysical Data.**

** 3.1
Interstellar and Intergalactic gases**.

Let us
apply this energy loss R to astrophysical data. First, we
calculate the average density D (atom/m^{3}) of gas in space required to produce a redshift
coherent with the Hubble constant Ho. The average number of
collisions N produced on a path one parsec long is:

(14) |

Since the energy loss per collision is very small compared with unity, let us consider the so-called thin-target condition. From Eq. (12):

(15) |

(16) |

Since Eqs. (15) and (16) give the relative energy loss per parsec, they lead to:

(17) |

(18) |

19 |

This value includes the contribution of the very large gaseous nebulae or galaxies located in the line of sight or concentrated around the light source itself. Consequently, depending on the temperature of the source and the nature of the intergalactic gas, an average density of the order of 0.01 atom per cubic centimeter is sufficient to produce, on the Planck spectrum, an effect equivalent to that of a Doppler shift in agreement with the Hubble constant.

** 3.2 Angular Spread**

We know
experimentally, that light travels in straight line in a medium
as in water or air. Even after traveling one meter in air, we
can calculate that photons have interacted with numerous
molecules since they are delayed, as given by the index of
refraction. However, after millions of collisions in air, most
of the photons still maintain a parallel direction of
propagation. It is easy to evaluate the angular deviation of the
incident radiation due to the axial acceleration of the
electron. It is known that bremsstrahlung radiation is emitted
in the direction perpendicular to the acceleration of the
electron. Since we are dealing with the problem of the momentum
transfer of a wave train to an electron accelerated in the same
direction as the incident wave, the total transverse momentum
component given to the electron is zero (Newton's law). Then the
sum of the transverse momentum component of the two
electromagnetic wave trains re-emitted must be zero. The initial
photon cannot get a large deviation when it is interacting with
the hydrogen because the secondary photon generated during the
interaction has too small energy and momentum to provide a
sufficient recoil to the initial photon. Since the very soft
bremsstrahlung emitted at 90^{o}
has momentum, the initial transmitted wave receives an extremely
slight recoil in order to satisfy the law of conservation of
transverse momentum components. Consequently, the transmitted
radiation will be very slightly deviated from the incident
direction. From geometrical considerations and equation 12, one
can see that:

20 |

21 |

22 |

23 |

** 3.3 Line Broadening**

Let us
also briefly discuss how multiple transmission interactions can
make absorption lines wider and fuzzier. It is known that the
redshift is proportional to the number of collisions *n*,
but not all photons have undergone statistically the same number
of collisions. Thus, the statistical spread in the number of
collisions widens the absorption lines of very redshifted
objects emitting blackbody radiation. Such observations are
reported by Hewitt and Burbridge ^{(6)} who reports quasi-stellar objects being discovered
with very broad absorption structures.

** 3.4 Redshift on the Sun**

Let us
consider the surface of our Sun. When observing its photosphere
at the center of the disk, light reaching us on Earth crosses a
much smaller amount of gas above the Sun’s surface than when
light is coming from the limb and travels tangentially above the
surface. Therefore, according to the theory described above, a
larger redshift should appear near the limb.

Such a
redshift near the limb has been known for about 80 years ^{(7-12)
}and has been confirmed by at least 50
independent papers. It has never received a clear explanation.
We have calculated that this redshift agrees quantitatively with
the theoretical predictions explained above, taking into account
the Sun’s temperature and the amount of gas above its surface.
More details will be published on that work elsewhere.

** 3.5 Binary Stars**

Since
it is difficult to distinguish a Doppler redshift from the new
redshift described above, one must look for special
circumstances where the Doppler component of the phenomenon can
be clearly identified. An ideal case is seen in binary stars.
Celestial mechanics shows that spectral lines from components of
binary stars must oscillate around the central position since
the average radial velocity of the stars must be the same.
Observations ^{(9),(13)} show
that it is not so. Hot stars (O-stars) show a larger redshift
than the cooler (A and B) stars ^{(9),(13)}. When one applies the theory stated above, one sees
that the extra redshift observed in the high-temperature star
agrees exactly with the value deduced from such a star, taking
into account the temperature and the amount of gas on its
surface. This is another confirmation of the above theory.

** 3.6 K-Term**

It is
known that hot stars in the Sun’s neighborhood are moving away
from us in all directions, while cooler stars do not. This
phenomenon has been called K-effect. ^{(9),(14)}. The apparent velocity of recession is larger for
hotter stars ^{(14)}. We have
calculated that this effect agrees with the new redshift theory
described above, knowing the amount of gas on the surface of the
star and the measured temperatures of their surfaces.

** 3.7 Direct Detection of Bremsstrahlung Radiation**

When
visible light travels through gases, the mechanism described
above leads to an energy loss that appears as bremsstrahlung
with wavelengths several hundred meters or even kilometers long.
Grote Reber, ^{(15)} with his
hectometer telescope, has observed radiation from the sky in
that wavelength range. He has been able to measure the map of
southern sky ^{(15)} at 144
meters wavelength and is now getting data for a map of the
northern sky. This radiation is compatible with the one expected
from the mechanism described above.

** 3.8 Different Redshift in Absorption and in Emission**

It has
been seen [equation 12] that radiation emitted according to
Planck’s law is redshifted when it is transmitted in the forward
direction through an interacting gas. Emission lines, which
necessarily have a much longer time of coherence than that of
blackbody radiation, are also observed in the spectra of some
galaxies or quasars. Their time of coherence Dt is generally much longer than that of
blackbody radiation. Consequently, the emission lines due to the
phenomenon described above will show a different redshift that
that of the blackbody radiation.

This
agrees very well with the fact that the observed absorption
redshift are different from those observed in emission for all
109 quasi-stellar objects for which absorption and emission
lines (of the same object) have been measured ^{(6)}. It is observed that the redshift in absorption is
always larger than the one in emission.

** 3.9
Pairs of Quasars and Multiple Absorption Redshift**

Walsh,
Carswell, and Weymann ^{(16)}
have recently reported the discovery of a close pair of quasars
having the same absorption redshift. They argue that this is
extremely improbable. However, according to the present model, a
double source located inside of behind the same very thick and
dense nebula must show a similar redshift.

Oke ^{(17)} has reported
recently that "surprisingly" the number of quasars increases as
the redshift increases. Assuming the redshift mechanism
described above, it is clear that an object surrounded by an
extremely large amount of gas will display an important redshift
and will automatically be interpreted as being at a large
distance. This might explain the apparent lack of quasars at
short distances.

It is
also stated by Oke ^{(17)} that
in some cases, different redshifted absorption lines are
observed superimposed on the spectrum of one and the same star.
Quasi-stellar object 0424-131 shows ^{(6)} as many as 18 different redshifts in the same
spectra. We cannot ignore that 18 stars at different
temperatures and surrounded by the same amount of gas would
produce such a similar effect. The same phenomenon can also
explain the well-observed forest of spectral Ha lines.

**
3.10 Implications on the Big Bang Model**

In
section 3.1, it is seen that an average concentration of about
10^{-2 }particle cm^{-3} of gas is enough to produce a redshift that would be
indistinguishable from the effect resulting from the Doppler
shift attributed to the expansion of the universe. Such an
average concentration of intergalactic gas is larger than
usually accepted, although an almost similar concentration (10^{3} cm^{-3}) of gas has
recently been reported ^{(18)}
in some intergalactic clouds. However, the density accepted
comes out of the hypothesis of a Doppler interpretation using
Einstein's relativity. Such a calculation of the density of
matter is space is irrelevant here, since it is based on the
Doppler interpretation of the redshift, while the results
obtained here are based on the energy lost due to interstellar
gases which is a Non-Doppler interpretation. Therefore, the
density calculated is erroneous if the universe is not
expanding, as it seems to be.

The
actual density of gases observed lead to higher densities that
predicted. Mean concentrations of the order of one particle per
cm-3 have been
measured in galaxies. Consequently, radiation having a path
across the diameter of a galaxy and traveling through such a
large density of gas would undergo a measurable spectral
redshift. Furthermore, Scoville and Sanders ^{(19)} have measured huge molecular clouds with masses up to
10^{6} solar masses and diameters
up to 80 parsecs, giving a density of 200 hydrogen molecules cm-3. The amount of gas
discovered inside and outside galaxies is becoming increasingly
important. Should we expect new discoveries? Is this related to
the missing mass that would stabilize galaxies? From the
increasing rate of discoveries of gas in space, it does not
appear improbable that a particular light path will have its
light interacting a sufficiently large number of times in the
forward direction to produce an important atomic or molecular
redshift.

However, when the redshift obtained from the measurement of
absorption lines is different from the one deduced from emission
lines, as appears to be the results reported by Hewitt and
Burbidge ^{(6)} and Arp and
Sulentic ^{(20)}, it must be
concluded that this is another agreement with this paper. Many
other interesting observations ^{(21)} should be considered in order to find new proofs of
the new model that lead to a new interpretation of the redshift.
This is consistent with the observation that large-scale
structures of the universe get larger ^{(22)} so that "** … theorists know of no way such a
monster could have condensed in the time available since the
Big Bang …** "

** 4.
Laboratory Verification of Such a Redshift.**

Some
laboratory experiments could be considered in order to prove
actual redshifts in gases. Could the necessary conditions to
generate redshifts be produced in a lab in order to demonstrate
this phenomenon? Could this phenomenon be measured when
radiation passes through air at atmospheric pressure? It is well
known that laser light can be tested very efficiently through
great distances in air in order to detect micro-redshifts. We
have seen that a more important redshift is produced when the
length of coherence is short. Therefore, the long time of
coherence, which is a fundamental characteristic of lasers, is
specially inappropriate for the measurement of redshifts in
gases. Therefore, such a test is useless, because the time of
coherence of laser radiation is much too long.

Although narrow absorption lines are more difficult to measure
accurately, they might help to solve this problem. However,
further considerations show that they do not seem to offer much
hope of yielding a positive measurement when transmitted through
long distances in air. Since the average distance between
molecules at atmospheric pressure is much smaller than that of
the length of coherence of the radiation used, the
electromagnetic field is applied in phase on many molecules.
Therefore, the photon momentum is distributed simultaneously on
the total mass of the molecules. A similar phenomenon is
explained by Feynmann, Leighton, and Sands, ^{(23)} for Thompson scattering of light in air. This
phenomenon also corresponds to a description of the
Mössbauer effect at low temperature, where the atoms recoil
in phase. Consequently, the bremsstrahlung produced in a gas at
high pressure is extremely small, because the radiation is
simultaneously accelerating many electrons in phase within the
length of coherence of the radiation. Therefore, the combined
mass of all the electrons emits much less bremsstrahlung
radiation. Such an experiment would have to be done at pressures
lower than atmospheric, but the path length would have to be
correspondingly long in order to produce a detectable signal.

<><><><><><><><><><><><>

**Appendix A:**

**Time of Coherence or Pulse Duration of
Blackbody Radiation.**

A1 |

A pulse having Planck’s spectrum F(n )=d A(n ) will have an amplitude

A2 |

A3 |

It can be shown that the integral of A3 is approximately equal to:

A4 |

P=[8p

The limit

A5 |

A6 |

In order to determine the properties of this function, let us use the variables :

and | A7 |

A8 |

A9 |

The most probable frequency n

A10 |

The time Dt described in A9 is characteristic of the duration of the wave packet emitted by the blackbody at a given temperature T and therefore, it is mainly influenced mainly by the most probable frequency component n

We also wish to show that, within a spectrum at a given temperature, Planck’s quantum postulate leads to different values of pulse duration depending on the wavelength considered. According to Planck, the blackbody spectrum is composed of a finite number of frequencies

A11 |

As a consequence of the finite number of frequencies, Planck’s spectrum must be represented as a sum of discrete frequencies. All these frequency components must be coherent, and the signal must be non-interrupted during the full interval of time of emission, since it is necessary to reproduce exactly the Planck’s spectrum.

Let us consider two independent emitters of electromagnetic radiation at different frequencies n

A12 |

From the law of energy conservation:

A13 |

A14 |

Equation A14 shows that within a given spectrum of blackbody radiation, the effective wave duration Dt is proportional to its frequency n .

There remains to combine A9 and A14. Let us examine A14. For n =n

A15 |

A16 |

A17 |

A18 |

One must finally recall that these conclusions depend directly on the fact that the spectrum is made of discrete values following Planck’s quantum postulate described in A11. Consequently, A18 gives the relation between the time of coherence Dt at any frequency n in the case of blackbody radiation.

Figure 1

<><><><><><><><><><><><>

**Appendix B:**

** Relevant Cross Section of Hydrogen.**

Let us consider hydrogen at an extremely low pressure, a condition prevailing in outer space. If the radiation undergoes only one collision per week, it is then completely inappropriate to consider that the velocity of propagation is simply slightly smaller than c. In that case, it is evident that the index of refraction is exactly one during six of the seven days and also 23 of the 24 hours of the exceptional day, and so on during the last minute, second, and its fraction, until one has to arrive at a non zero interval of time of interaction between the absorption of radiation and its reemission.

Between absorption and reemission, the atoms must then momentarily retain the absorbed energy and momentum. This mechanism leads to identical times of propagation whether one considers a change of index of refraction or individual collisions with delayed energy reemission. Therefore, there is certainly a delay during the interaction of the photon with the particle. The latter model, however, is closer to the atomic nature of matter.

It is known that the index of refraction

B1 |

It is also known that the velocity of propagation of energy corresponds to the group velocity

It is well known

B2 |

Since we know that the energy is transmitted with a velocity equal to the group velocity

B3 |

B4 |

Equation B4 has been derived here in order to point out that the quantity 9pr

Therefore equation B4 shows that the time taken for the electromagnetic radiation to cross a given distance inside a volume containing N atoms per cubic meter is equal to the time the light would take in a vacuum to cross the same volume, to which one must add a virtual volume V

B5 |

B6 |

B7 |

B8 |

It is known that the virtual volume is a function of the polarizability of the atom. One must not be surprised that the cross section s found here remains finite and s¹0 when n®0. This cross section is of course completely different from the scattering cross section used in Thomson scattering. It is related to the index of refraction for which light propagates in straight line.

Finally, for the case of a single free electron, the Thomson scattering cross section may be considered. It is s =6.65 x 10

** New Verification and Supporting Evidence.**

Several
new papers with experimental proofs supporting the energy loss
of photons due to the traces of hydrogen in space have been
published more recently. For example, a paper entitled: *The
Cosmological Constant and the Red Shift of Quasars* ^{(27)}, explains the consequences of a redshift due the
traces of hydrogen in outer space. Furthermore, another paper
entitled: *Non-Doppler Redshift of Some Galactic Object"*^{(28)} shows that
the difference of redshift between the components of binary
stars systems can only be explained by the difference of
temperature responsible for the change of coherence of blackbody
radiation as explained above. Furthermore, that same paper shows
that the K effect and other astronomical observations require
that photons are redshifted when moving through traces of
hydrogen gas. Also, the solar atmosphere shows a redshift which
varies as a function of the radial distance as seen from he
Earth. That is explained in the paper^{(29)}: "*Redshift of Spectral Lines in the Sun's
Chromosphere*". That redshift remained unexplainable until
it was realized that the hydrogen in the solar atmosphere has
exactly the correct concentration to explain its redshift (as
explained above). Finally, various other descriptions of that
phenomena have been presented ^{(30)}.

<><><><><><><><><><><><>

==================== =====================

Back cover of the Book (Printed in June 1981)

**A New Non-Doppler Redshift.**

This is clearly contrary to the Doppler hypothesis.

Many more observations lead to results, which are incompatible with the interpretation that redshifts are due to relative velocity.

This book shows that taking into account the change in momentum of the electrons of gas molecules scattering light in space leads to bremsstrahlung and a slightly inelastic forward scattering.

This is the first Non-Doppler redshift theory, which when combined with the usual Doppler phenomenon, would explain consistently all spectral shifts observed in astronomy.

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27 P. Marmet, *The Cosmological Constant and
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28 P. Marmet, *Non-Doppler Redshift of Some
Galactic Objects.* IEEE Transactions on Plasma
Science,Vol. 18, No. 1, p. 56-60, 1990.

29 P. Marmet, *Redshift of Spectral
Lines in the Sun's Chromosphere*, IEEE Transactions
on Plasma Science, Vol. 17. No. 2, p. 238-244, 1989.

30 P. Marmet, *Big Bang Cosmology Meets an
Astronomical Death. *21^{st} Century,
Science and Technology, Vol 3, No: 2, 1990.

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