The Cosmological Constant and the Redshift of Quasars

( Last checked 2016/02/21 - The estate of Paul Marmet )

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Paul Marmet

This work was supported by the 
National Science and Engineering Research Council and 
The Herzberg Institute of Astrophysics of 
the National Research Council of Canada

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Abstract
          We discuss how the cosmological constant that is used in Einstein's model has an equivalent in the Big Bang model.  That model requires a critical density of matter that leads to the problem of dark matter.  We show that data on new cosmological structure and on a non-Doppler redshift mechanism lead to an unlimited and ageless universe.  We also explain why quasars appear to be unusual objects and have a large redshift while being physically much closer to us than usually claimed.  One can see that their luminosity is about the same as standard galaxies and not as millions of galaxies as believed previously.  One can also explain why the luminosity distance relationship observed in galaxies is not observed in quasars.

I. Introduction
          There is a serious controversy about the Big Bang model because it shows an increasing number of deficiencies.  This is illustrated by Flam, who states [1] "As doubts built about the once-favored model explaining how structures are formed in the Universe, new theories are jockeying in a cosmological free-for-all". 
          Let us compare some models.  The steady-state model uses "the perfect cosmological principle," in which the universe presents the same large-scale view to all fundamental observers at all times.  We will also consider Einstein's model, which adds a cosmological constant L to balance the attraction of matter.  An important point, common to those models, is of course the universal law of gravitation.  All matter is attracted with a force proportional to the Cavendish constant GC, and inversely proportional to the square of the distance.  It did not seem possible in the past to observe gravitational forces at very large cosmological distances.  Therefore, gravitational forces were not tested at cosmological distances.  Recent observations of gravitational interaction at cosmological distances now suggest a solution based on these new observations. 
          The use of the universal law of gravitation in the Big Bang model leads to a prediction of the critical density r, of the universe that differs from observations by about two orders of magnitude.  This difference is interpreted to be caused by some "missing mass". 
          We will see that the problem of critical density of matter in the universe (and missing mass) is related to a common problem for which all popular models (the Big Bang, Einstein's and steady state model) require an equivalent correction (the cosmological constant L) related to a common phenomenon: The range of gravitational forces.

II. Reason that Led to the Big Bang Model.
          An important reason that led astrophysicists to prefer the Big Bang model (of Friedmann cosmology of a close universe) is because the first Einstein model (the geometrodynamical model) is clearly unstable without the cosmological constant.  This instability is a consequence of the use of the standard universal law of gravitation.  Two suggestions have been given in order to try to solve this problem.  Einstein suggested adding a cosmological constant L to his field equations.  That constant adds a repulsive force at large distances [2].  This second Einstein model with 0 has another problem of stability.  It is stable only for a critical value of LC.  For any increase in size, the universe expands forever.  For any decrease, it will recontract forever.  This Einstein universe has therefore another kind of instability.
          An equivalent of Einstein's cosmological constant has been presented in various forms by different authors, but most cosmologists have rejected it.  George Gamow and many astronomers refer to the cosmological term as the biggest blunder of Einstein's life.  Even very recently, Hawking states [3] that the addition of a cosmological constant L is: ". . . the biggest mistake of his (Einstein's) life." In 1917, de Sitter suggested [4] another model that includes a cosmological repulsion term of the Einstein type to balance the attraction of gravity at large distances. Another hypothesis considers that L=0.  This is the Big Bang model, a model that is unstable in time, since it starts with a Big Bang and ends with the Big Crunch. 
          Following those considerations, many astrophysicists have preferred the Big Bang model because it was hoped that this alternative would lead to predictions compatible with the universal law of gravitation without being obliged to add any gravitational repulsive constant as was suggested by Einstein.
          After more than 60 years of development of this theory and decades of observation, it is calculated that an equivalent of the cosmological constant is still necessary.  There is no way to avoid it. 

III. A Force Equivalent to the Cosmological Constant
          We have seen that an arbitrary constant L is required in Einstein's static universe.  However, it is not always realized that an equivalent cosmological constant is now necessary in the Big Bang model.
          Hawking recently stated [3]: "In order to find a model of the universe in which many different initial configurations could have evolved to something like the present universe, a scientist at the Massachusetts Institute of Technology, Alan Guth, suggested that the early universe might have gone through a period of vey rapid expansion. This expansion is said to be inflationary."
          Hawking goes on writing [3] that the inflationary model requires special extra energy and writes:
"This special extra energy can be shown to have an antigravitational effect: it would have acted just like the cosmological constant that Einstein introduced into general gravity when he was trying to construct a static model of the universe"
          Hawking then discusses that force, and writes: ". . . the repulsion of (matter due to) the effective cosmological constant".  This clearly shows that a repulsive force, acting just like the cosmological constant L, is absolutely necessary in the Big Bang model.
          The Big Bang model also leads to a critical density of matter r, in the universe.  Since that density is not observed, one has assumed that there is some unobserved dark matter.  Some dark matter may also be necessary to explain the recently discovered huge structure called "The Great Attractor".  Lindley [5] concludes: ". . . that the Cold Dark Matter can be saved at least in modified form, if a non-zero cosmological constant is resurrected." 
          How can so many astrophysics reject Einstein's model so easily because of the cosmological constant, and then later use an equivalent constant of repulsion "just like the Einstein's cosmological constant" [3] to try to save the Big Bang model?  How can cosmologists repeat that a cosmological constant was "the biggest mistake of his (Einstein's) life" [3] when the equivalent of such a constant is now copied by the new cosmologists?

IV.  Main Unsolvable Difficulties of the Big Bang Model.
          Apart from the fact that the Big Bang model does not solve the problem of the cosmological constant, many more proofs exist showing that the Big Bang model in unacceptable.  Only a few examples are recalled here.
A. Time Zero.
          When the universe was at time t=0, the density of the universe was infinite.  This is a singularity.  It is argued [6] that space-time itself did not exist for times less than zero.  How could the universe be created from nothing [6] (no space, no time)?  The universe cannot be the result of a quantum fluctuation [6] that appeared before the existence of space and time 
B. Critical Value of G.
          From the Big Bang model, the first natural length of the universe is the Planck length.  Then the typical radius of the universe was about 10-33 cm.  However, we observe today that the universe has a radius of 1028 cm.  This is a decrease of 1061 times in curvature.  It corresponds to an extreme flatness of Euclidean geometry [6].
          The fundamental mechanism of the Big Bang is that it started by a fast expansion that was slowed down by the forces of gravity.  Cosmologists find interesting the question whether the forces of gravity are weak enough so that the universe will end in a dispersion of matter into an infinite space or if the forces of gravity are strong enough so that the universe will collapse rapidly into a Crunch.
          Consequently, in the Big Bang model, it is assumed that two completely independent mechanisms balance forces of expansion and retention of matter acting in opposite directions. From the Big Bang hypothesis [6], one must conclude that the universal gravitation constant G, is such that it happens (by chance) that all 61 digits of the parameter used to calculate the gravity necessary to stop the expansion of the universe is exactly the same as the first 61 digits of the parameter required in the calculation of the energy of expansion that appeared at the instant of the Big Bang.  The probability of having two, so nearly identical physical constants in nature, resulting from two completely unrelated hypotheses is extremely suspicious.  This difficulty is mentioned by Linde [6].  The problem of the critical value of G does not exist in the model presented here.
          In fact, this highly critical constant cannot exist with an accuracy of 61 digits because the Cavendish constant GC, is not considered to be a constant and varies by many more orders of magnitude, as will be seen in subsection V-A.
C. Age and Isotope Problems.
          There are hundred of papers and books with examples showing that the Big Bang model is not compatible with observations.  Recent data show striking incompatibility.  For example, certain galaxies appearing completely mature were observed by Simon Lilly [7] in 1988 at the enormous redshift of 3.395.  This puts these galaxies so far back in time that the Big Bang scheme does not allow sufficient time for their formation.  The report [8] mentions: ''the appearance of a mature galaxy so soon after the Big Bang poses a serious threat."
          The discovery in 1989 of the Great Wall, 700 million light years across, is also incompatible with the Big Bang model.  Margaret Geller of the Harvard-Smithsonian Center for Astrophysics comments [9] on her discovery: "No known force could produce a structure this big since the universe was formed."  Very recently, Paul Steinhardt [10] states the equivalent: "There wasn't enough time in the history of the universe for gravity to pull together these structures." There is a general consensus on this point. 
          Finally, the distribution of isotopes in the universe, claimed to be a consequence of the Big Bang, also does not agree with many observations.  The most recent disagreement is the case of the Sun, where a reliable measurement can be made.  Only 1% of the predicted amount of lithium is observed in the Sun [11]. Discussions related to the above problems have been published [12], [13].

V. Variation of Gravitational Constant
          Considering that the gravitational constant is so critical (up to the 61st digit), one cannot conceive that it is (relativity) greatly varying as a function of time or space.  This variation leads to new difficulties.

A. Non-Constancy of the Cavendish Constant 
          It is claimed that just at the moment of the Big Bang, all forces (weak, strong, electromagnetic, and gravity) were unified.  This is the basic argument to establish the Grand Unified Theory (GUT).  All the individual fundamental forces of nature appeared later.  Therefore, at the time of the Big Bang, gravity did not exist as it does now.
          Some time after the Big Bang, gravitational forces developed.  Therefore G is not constant.  Many articles have been written about the non-constancy of the Cavendish constant GC [4]. Dirac [2] was among the first to formulate a change of gravitational constant.  As early as 1937, Dirac, using numerology, suggested that the gravitational Cavendish constant GC was varying in time.  Dirac pointed out that the ratio between the age of the universe and the atomic unit of time (e2/mc3) is the same as the ration between the electrical force between the proton and the electron and the gravitational force between these particles.  Since the first ratio is a function of the age of the universe, GC is continuously changing.  Dirac chose the equation:

(1)
          Where Ho is the Hubble parameter and GC the Cavendish gravitational constant [2].
          Many other models with changing G have been suggested.  For example, the Dicke-Brans-Jordan theory [4] assumes that the gravitational constant depends on where and when the experiment is performed (as well as on mass and the radius of the gravitational source). Other models (of a change of the Cavendish constant) were studied [14]. Ni's theory of gravity [15] and other two-tensor or vector-tensor theories [16] have preferred a "universal rest frame" and give a velocity dependence on the gravitational constant.
          Even very recently [17], the variation of G has been used in cosmology and particle physics to relate constants with space-time of ten dimensions.  Wang [17] uses the equation (dG/G)@-10-11 per year.  The reader should realize how big this variation of 10-11 per year is in comparison with the required criticality of 10-61 seen in subsection IV-B.

B. Energy Conservation
          It might not be possible to follow the logic that inspired Dirac about the near mathematical coincidence related to the variation of G, but this hypothesis, used for five decades, illustrates another serious difficulty.  When G is changing, the energy of the system is changing. Consequently, the change of the Cavendish constant G contradicts the most fundamental law of physics: "The Principle of Mass-Energy Conservation". Hawking states: [3]  "The total energy of the universe is zero." It cannot stay zero if G is changing with time.
          The change of the Cavendish constant G (assumed here) has nothing to do with the change of gravitational force when radiation is generated (and a corresponding amount of mass disappears).  Of course, radiation pressure prevents the collapse of parts of the universe and contributes to the decrease of the gravitational pull. 
          Let us recall that the transformation of mass into radiation does not change the total energy of the system when everything is taken into account, and when one considers that there is energy conservation in any close system.

C. A Second Big Bang?
          Following the problems raised by the Big Bang hypothesis, Hawking uses the equivalent of a second Big Bang in an attempt to explain the inflationary universe.  He explains [3] that the total mass-energy of the universe in the first Big Bang is zero.   Then he writes: "Twice zero is also zero." Then he states [3] "Thus the universe can double the amount of positive matter energy and also the negative gravitational energy . . .". This is equivalent of a second Big Bang.  It is this way that the inflationary expansion of the universe is explained [3]
          What is the probability of a second Big Bang at the same place over such a short time interval (a small fraction of a second)? How many Big Bangs should we expect?

VI. Characteristics of a Gravitational Field
A. Finite Range of Gravitational Forces
          We have seen in section IV that the equivalent of a cosmological constant is just as necessary in the case of the Big Bang model as in the case of Einstein's static universe. This means that all models require, at large distances, that the strength of the gravitational field go down more rapidly than the 1/r2 function predicted by Newton's law.  In other words, a gravitational field with an infinite with an infinite range is not acceptable?
          In principle, it is not necessary to use a cosmological constant that neutralizes the gravitational forces at large distances.  One shows that strong and weak nuclear forces have a finite range.  We do not say that there is another force at large distance that neutralizes nuclear forces.  We might use the same terminology but, of course, an appropriate description must be given to the field. 
          The importance of a finite range of gravitational interaction is that it does not lead to an infinite potential in an infinite universe. Before describing a test to determine the range of interaction of gravitational forces, we need to explain the exact meaning of the phenomenon we are looking for. 

B. Definition of a Finite Range
          When we say that a gravitational field has a finite range, we mean that this gravitational field at cosmological distances decreases more rapidly that the 1/r2 function and produces no observable effect beyond this range.  We do not specify here whether the rapid decrease of the gravitational field at large distances is due to: 
a) The property of the gravitational field itself (for example curvature); 
b) The property of space that supports the gravitational field; 
c) matter that might damp the gravitational field in space; 
d) the disappearance in time (annihilation) of some matter that produced the gravitational field (for example due to the transformation of matter into radiation that has escaped the original location); 
e) the possibility that the graviton has a non-zero mass; or 
f) any other cause.

VII. Evaluation of the "Range of Gravitational Forces"
          Since we mentioned that the gravitational force has an effective limited range of interaction, let us evaluate that range.  It is generally agreed that this range is enormously longer that the finite range of weak and strong nuclear forces.  Since all planets in the solar system follow (almost perfectly) the inverse quadratic law of gravitation, the 1/r2 law is substantiated in the solar system.
          The next range to consider is that of galaxies.  At distances up to about 50 000 light years, galactic rotation appears around a center.  It is well known that galactic rotation does not follow Kepler laws. Hypotheses have been presented to explain the motion of stars around the nucleus of galaxies. For example, some suggest the dark matter hypothesis while others use a change in the gravitational force (Milgrom [18]-[20]).
          One can conclude that for a range of the order of the radius of galaxies (about 50 000 light-years) at least some gravitational interaction certainly exist but some might argue that gravity may not behave strictly as Newton's law.
          The largest observed structures in the universe, showing central gravitational interaction, are clusters of galaxies. One can estimate that the approximate practical maximum range of gravitational interaction is about 10 to 20 million light years [21]. This range seems large, but it is about (1/1000) of the size of the universe (as calculated assuming the Big Bang model).
Beyond this limit is the Great Wall, discovered by M. J. Geller and J. P. Huchra [13] in 1988. Its name suggests that it may not have a spherical geometry; its pattern stretches over 700 million light years.  It does not appear to be associated with a central gravitational force.
          On an even larger scale, P. J. E. Pebbles plotted the locations of nearly one million galaxies.  The plot shows lines or threads of clusters of galaxies forming superclusters.  Charles Bennett [22] produced a similar plot of a million galaxies "Splashed across a section of the cosmos." Those threads of galaxies are interwoven in a complicated way to form a pattern that astrophysicists have dubbed the cosmic tapestry. It is clear that this tapestry does not reveal the existence of a central gravitational attraction.  The distribution of galaxies looks in fact, like what one expects for the distribution of atoms that form complex molecules.  The lines of galaxies are similar to chains of atoms in certain molecules. In these plots, one can almost see rings (of superclusters) as in molecule benzene.
          One must conclude that astrophysical data cease to show the effect of gravitational attraction for distances larger than about 10 or 20 million light-years.
          It can also be seen that the universe is much older that predicted by the Big Bang theory.  Here are a few examples.  In the case of certain superclusters, Tully and Fisher state [13]. "They were just too big to have formed in the twenty billion years since the Big Bang". Paul Steinhardt, [1] a cosmologist at the university of Pennsylvania explains: "There wasn't enough time in the history of the universe for gravity to pull together these structures".  In the case of the Great Wall, it is estimated to have taken about 150 billion years to form [13]. These observations support the notion that the universe is much older than 15 billion years.  Powell [24] concludes recently: "Globular clusters such as M13 appear to be older than the latest estimate of the age of the universe".  John Gribbin [25], studying the spectrum of quasars entitled his paper: "Astronomers Double the Age of the Universe".

VIII. Controversies on Infinities.
          Forces with a limited range of interaction are not new in physics.  It is a useless argument to insist that a force has an infinite range, if that force exists until only 16 billion years (according to the Big Bang).  Astrophysicists have difficulties accepting that the universe is "infinite" in size, while, at the same time, they readily accept that the range of interaction of gravitational forces in infinite.  Even if cosmologists believe that the range of gravitational forces in infinite, this hypothesis is applied in a finite universe when the Big Bang model is used.

 IX. Proposed Model
           The Big Bang theory uses certain observations to justify its existence.  However, an unlimited and ageless universe better explains astrophysical observations.  Here the word ageless is as defined in Webster's dictionary [26]: "Valid or existing unaltered at all times". The universe described by W. D. MacMillan [27] is more compatible with current observations than the Big Bang model. According to MacMillan, it is not necessary that "the universe as a whole has ever been or ever will be essentially different from what it is today"[28].  MacMillan believed that radiation emitted by stars could be reconverted into matter.  This excellent model also satisfies the "Perfect Cosmological Principle". This description was written well before Dirac's first statement of the theory of pair production.  MacMillan's theory was rejected because of the lack of evidence then, that gamma rays could be converted into matter.  However, two decades later, Bondi, Gold and Hoyle developed an almost similar model, "The Steady-State Theory" [29], in which matter in the universe is not formed from gamma rays, but is formed from "nothing" (of course, certainly, without physical evidence).  Finally, our choice of an unlimited space is not foreign to the philosophical difficulty of conceiving an end to space.  Another argument is given in subsection X, below.

X. Deficiencies of the Big Bang Model
          Scientifically, it can be shown that the best proofs claimed to support the Big Bang model are unjustified.  These proofs can easily be interpreted in favor of another model.  Let us discuss the following arguments: a) The cosmological Red Shift and the Doppler effect: b) The 3K background radiation; c) The critical density of the universe; and d) The Olbers paradox. Other arguments have been discussed above in subsection IV-c
          a) The cosmological redshift can be logically explained by a mechanism other than the Doppler effect.  There is another natural mechanism that can produce a non-Doppler Red Shift [30].  It is based on the non-elastic collision of photons on atoms or molecules in space.  This non-Doppler Redshift has been successful in explaining a Redshift on the Sun [31], [32] and in many other observations [33]-[36]. A similar effect is expected everywhere else in the universe.
          b) The origin of the 3 K radiation is more logically explained [34]-[36] by the Planck radiation emitted by cold matter in an unlimited universe.  Since the universe (and the plasma it contains) is at 3K, therefore blackbody radiation is emitted by that matter.  The problem of a lack of thickness of plasma does not exist since the universe is unlimited.  This interpretation is compatible with the high homogeneity of the 3K radiation observed, with an inhomogeneity smaller than 1/25000 [22].
          c) The problem of the critical density r, of matter in the universe has been mentioned above in discussing dark matter.  Our unlimited ageless universe does not require such a critical value.
          d) Olbers paradox can be explained without the Big Bang. In fact, Olbers paradox does not exist [36] since the sky is uniformly bright when one looks at the correct wavelength (»1mm) generated by its temperature of 3K.  The full amplitude of the Planck blackbody spectrum received from space is caused by the emission of radiation of the universe at 3K and proves that the universe has a depth of at least several trillion light-years.

XI. Transparent Matter in the Universe.
          With the choice of the unlimited ageless universe, one has to explain the observed red shift by a mechanism other than a Doppler shift.  One has seen that from the inelastic transmission of photons in space [30], [35], a red shift similar to a Doppler effect is always produced.
          There have been many discussions about non-detectable gases (or dark matter) in the universe. Cold atomic hydrogen is easy to observe in the universe, because it has a transition in the radio range due to the coupling between the spin of the electron and the spin of the proton (forming atomic hydrogen). A transition between those configurations produces radiation at 21 cm, and is easily detected in the radio range.  There are however, serious indirect observations (in galaxies or with the Great Attractor) that show that there is still a much larger amount of matter in the universe.  That undetected matter is called Dark Matter.  David Lindley [5] defines Dark Matter in the following way; "Dark Matter is the invisible stuff that dynamical studies of galaxies and clusters of galaxies indicate must be there, but which can't be seen".
          With regard to H2 and its extreme transparency, it is known that the most abundant atom in the universe is hydrogen.  Atomic hydrogen is chemically active, much more than molecular hydrogen.  For example, two colliding atomic hydrogen atoms (H) can combine to from molecular hydrogen (H+H®H2+hn). This mechanism of formation of H2 is highly probable during three-body collisions.   However, because of the strong binding energy of the atoms in H2 and due to the low temperature of the interstellar gas (»3K), two colliding H2 particles at 3 K do not have enough energy and will not dissociate back into atomic hydrogen atoms.  This illustrates how molecular hydrogen H2 is much more stable than H.  Of course, when these particles (H and H2) are bombarded with photons, they might react to produce ionization, excitation and induced dissociation.  Other mechanisms are also possible, especially the Compton effect as mentioned by Kierein [37].
          Consequently, since the universe has an average temperature of 3K, for the reason given above and during the unlimited age of the universe, one expects that, at equilibrium, much hydrogen must have passed from the atomic form, into the form of molecular hydrogen H2.
          Spectroscopy shows that molecular hydrogen is one of the most transparent gases in the universe.  It has no dipole transition in the radio range, in the infrared, in the visible, and even in the UV, up to the far UV at 110.8 nm [2].  Even rotation and vibration states of the ground state cannot be observed because they are all forbidden dipole transitions.  The second and third UV lines of H2 are located at 109.2 and 107.7 nm.  These three lines correspond to transitions B1Su-X1Su in states (0,0), (1,0) and (2,0).  Thanks to the transparence of H2 one is able to view the universe at very large distances.  However, H2 cannot be detected by spectroscopic means.  The only observable radiation from H2 at 3K is the wide Planck spectrum at its own temperature (already observed but erroneously interpreted as a background cosmic radiation).
          There are many misleading statements about the detection of hydrogen in the universe.  Without making the distinction between the atoms and the molecules, it is stated [38] that: "masses of hydrogen are easily detectible out to considerable distances in the universe". This is awful error, since the molecular form of hydrogen (H2) is possibly the most transparent gas in the universe.
          Furthermore one cannot argue that H2 does not exist in space because it would be dissociated by UV radiation.  If there were actually a large intensity of far-UV radiation in the universe, neutral atomic hydrogen would ionize.  This is not the case, since the 21 cm radiation is well observed and therefore proves that H is not generally ionized.  Consequently, in those circumstances, we expect that the far-UV radiation in space, which does not have enough intensity to ionize most of the atomic hydrogen, will also not have enough intensity to react and dissociate most of H2.  It is well known that it takes more energy to ionize molecular hydrogen than atomic hydrogen.
          We have seen that molecular hydrogen in space is responsible for another interaction: Collisions of photons on hydrogen are always slightly inelastic [30], [35] in transmission and lead to a non-Doppler red shift.  It has been measured that more than one atom/cm3 of atomic hydrogen has been measured between stars inside our galaxy.  Due to the transparency of H2, there might be, on the average, the equivalent of 0.01 mol/cm3 of the much more abundent H2 in the universe, which would account for the observed cosmological red shift in the universe [30].

XII. Distance of Quasars
A. Dependence of Red Shift on Source Temperature
          It has been calculated [30], [35] that photons have a very slightly inelastic interaction when transmitted through the gases of space, which gives them a redshift compatible with the observed redshift in the cosmos.  This is done using electromagnetic theory and quantum mechanics without the need of any new "ad hoc" physical hypotheses.  This red shift generally appears indistinguishable from the Doppler shift. The energy lost is transformed into very low frequency radio waves.  It has been seen that this mechanism [30], [35] leads to red shifts which explain the red shift on the Solar limb [31], the apparent velocity of recession of some early type stars (K-Term) [33]-[35], the different average shift of binary stars, and others red shifts [33]-[35] of astrophysical interest.  This mechanism uses the well known Larmor equation:

(2)
to calculate the energy loss W, during the interaction of light with particles like hydrogen.  In this equation, a=Dv/Dt is the acceleration, e is the electron charge, Dv is the change of velocity due to momentum transfer, Dt is the time during which the electron is interacting (the coherence time of the interacting light), eo is the permittivity of vacuum, and c is the velocity of light in vacuum.
          It is clear that this mechanism depends on the coherence time of the emitted radiation.   It is also known that the length of coherence of radiation in the case of blackbody radiation is a function of temperature T of the emitter.  The relative energy loss R per interaction is:
(3)
          One calculates [30], [35], that
(4)
          where M=e2h/(3peoc5me2C4), h is the Planck constant. Thus, M=2.73´10-21 K-2
          From this mechanism, it has been calculated that an average density of 0.01 atom/cm3 is sufficient to produce a red shift equal to the Hubble parameter.  In other words, it is no longer necessary to assume an expansion of the universe, because there is enough gas in the universe to produce the same red shift.  The calculations have been made using a typical effective temperature T of 50 000 K, compatible with the temperature of very bright stars in galaxies [30], [32].

B. Redshift of Quasars
          The case of a light source having a much higher equivalent temperature as in quasars has not been previously considered.  It is observed that quasars emit a spectrum with an extraordinary wide spectral band.  The continuum of radiation extends up to the far UV and even into the soft X-ray range.  It is reported [39]¸ that there is: "a blue bump peaks somewhere in the extreme ultra violet and probably into the soft X-ray around 40 Angstrom".
          Synchrotron radiation is believed to be the source of such a spectrum.   The length of coherence of the radiation is much smaller that the length of coherence of the Planck spectrum of an ordinary hot star (since the bandwidth is larger).  This is easily understood considering the physical meaning of the Fourier transform.  One finds that the equivalent temperature of the quasar is then a few million degrees.  Let us consider an efficient temperature of about 2 million degrees for a typical quasar.
          Theory [30], [32] shows that due to the short length of coherence, quasars must naturally show a much larger redshift than other stars located at the same distance (i.e. light going through an equal thickness of gas).  Equation (4) shows that the red shift produced by hydrogen is proportional to the square of the temperature.  From (4), the relative red shift (per interaction) of the two objects is:

(5)
          Where R is the relative energy loss of photons and the subscripts Q and S refer to a quasar and a star respectively.
One finds that the relative red shift (with respect to the star temperature of 50 000K) is equal to:
(6)

C. Comparison with Observations
          Quasars have then, a redshift about 1600 times larger than a typical star whose light intersects the same column density of gas.  That quasar would then be 1600 times closer than expected from their red shift (when one has used the Doppler instead of the Hubble interpretation).  This result is of interest because the standard model shows several difficulties related to quasars:
a) The unacceptable red shift-distance relationship,
b) their unphysical brightness, and
c) the abnormal red shift of quasars that are physically associated with closer galaxies as reported by Arp [12].
          A) Narlikar shows that when the red shift of galaxies is plotted against their faintness, a straight line is obtained [40].  However, the corresponding plot for quasars plotted against their faintness produces a random scatter of points [40].  It is surprising that quasars located at larger distances do not appear less bright, unless the redshift of quasars is not due to their great distance.  The model calculated here shows that the red shifts of quasars do not primarily depend on the distance, but depend on their equivalent temperature.  This explains why the red shift-distance relationship is seriously defective in quasars.
          B) The belief that gamma-ray quasars can be as bright as 100 trillion suns [41] is more than astonishing.  In July 1991, the discovery in Virgo of a Quasar (3C279) emitting 10 million times more energy than the entire Milky Way was announced [42].  More recently, HS1946+7658 in Drago was reported to emit "more energy that 1.5 quadrillion suns" [43].  However, from the above calculations, the same quasar can be at least about 1000 times closer. Therefore its absolute brightness should be at least one million times less.  This solves the problem of the unacceptable brightness of quasars and brings their absolute brightness to about the same magnitude as normal galaxies.
          C) The large red shifts of quasars, interpreted as a Doppler phenomenon, are called into question when they are found to be associated with galaxies.  Many years ago, Burbidge [44] suggested non-cosmological redshifts of quasars.  Many of those associations have been reported by Arp [12], [37], suggesting that quasars are much closer.  One prominent example is the case of Stephan's quintet. This close association of galaxies shows that NGC 7331 and other high red shifted members are linked [12] to the low red shifted NGC 7320.  Also, in the chain of galaxies VV172, one of them has an excess redshift of 21 000 km/s. Numerous other examples have been observed [12].
          A systematic study should be done.  If the distance of quasars is corrected due to their high effective temperature, one should be able to verify that the red shift-distance relationship of quasars fits the expected linear function (as in the case of galaxies) as expected by Narlikar [40].

XIII. Conclusion
          New observations are compatible with the unlimited-ageless universe model.  It is unnecessary and unrealistic to invent a new principle after each new discovery.  For example, in defending the Big Bang cosmology, Davis states: "In some of the newer (Big Bang) theories, we are inventing a new physical principle for every new observational fact" [1].
          We do not agree, as stated [3], that: "a scientific theory is just a mathematical model we make to describe our observations: is exist only in our minds".

Acknowledgment
          The author wished to thank Dr. Y. Varshni and Dr. L. Marmet for reading and commenting on this manuscript.

References
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This is an updated version of:
IEEE Transactions on Plasma Science,
Vol. 20. No: 6, pp. 958-964, 1992

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