In June of 2002 an article was submitted to CRSQ regarding evidence that the universe may not be expanding. On 16 July a response with the peer review suggestions was received. The article, as is common, was then partially re-written and amended to comply with the peer review suggestions and resubmitted. It was refused on some very curious grounds. What follows here is the article itself, an explanation of the letter of refusal, and Barry Setterfield's response to the points brought up in that refusal. Questions are welcomed.  The question and answer section is linked at the bottom of the page.

Is The Universe Static Or Expanding?

Barry Setterfield, 4th August 2002

Historical Background
Noting Some Problems
The Second Interpretation
The Ambiguity
Examining Space-Time Expansion
Problems With Space-Time Expansion
Summarising The Interpretations
The Quantized Redshift
Attempting To Settle The Issue
Galaxy Motion Smears Out The Quantization
The Stability Of A Static Universe
The Redshift And Energy Conservation
Properties Of The Vacuum
Zero-Point Energy And Atomic Stability
ZPE And The Redshift
ZPE And Lightspeed
Quantised Redshift "Shells"
The Testimony Of The Bible
An explanation of CRSQ's letter of refusal
Setterfield's Response
Questions and Answers


Both the Big Bang and the Biblical presentation of creation indicate the universe expanded.  The current mainstream thinking in science is that it is still expanding.  This is based primarily on the way that redshift data is currently interpreted.  Was Hubble correct in multiplying the redshift, z, by the speed of light, c thereby implying that the redshift was a Doppler recession effect?  He may not have been.  The alternative explanation of the redshift as being due to an assumed expansion of the entire fabric of space may also be seriously questioned as a result of the ongoing work of Tifft and others working with the redshift measurements.  Instead of indicating universal expansion, the quantised redshift may have a cause that is inherent to the atomic emitters of light within the galaxies themselves.  The Bible seems to indicate that expansion of the universe was completed in the distant past.  There is a growing body of data being collected which apparently indicates the same thing.

   In today's scientific climate, it almost seems an impertinence to even pose this question, impinging as it does upon one of the bases of modern cosmology.  Nevertheless, in the history of astronomy since 1929, there has consistently been a minority of astronomers who have questioned the prevailing paradigm of universal expansion.  Furthermore, there are certain pertinent facts which, when examined, lead to the conclusion that it might be wise to reconsider the evidence upon which the whole idea of an expanding cosmos is based.

   One of the key pieces of evidence that cosmologists use to indicate universal expansion is the redshift of light from distant galaxies. The redshift is an astronomical term that describes the shifting of the spectral lines of atoms towards the red end of the spectrum when compared with a laboratory standard here on earth. Consequently, the redshift, z, is defined as the measured change in wavelength, when compared with the standard, divided by that laboratory standard wavelength. If the change in wavelength is given by Dl and the laboratory standard wavelength is represented by l, then the redshift is defined as

                            z = Dl/l                                                             (1)

   [Couderc, 1960 p.10, 91; Audouze & Israel, 1985 p.382, 356]

It is important to remember in all that follows throughout this paper that this is the quantity that astronomers actually measure.  Notice that z is a dimensionless number as the units of wavelength cancel out. One might reasonably ask how this dimensionless number came to represent the expansion of the universe. Two ideas were running concurrent with each other on this matter, namely a Doppler shift interpretation and the expansion of space-time. However, instead of running these two interpretations side by side, they are individually followed through here to their main conclusions.

Historical Background
   The historical development of the Doppler shift idea, which is also the more common of the two explanations, began with the work of Vesto Slipher and Francis Pease between 1912 and 1922 at the Lowell Observatory in Flagstaff, Arizona.  They measured the redshift of forty-two galaxies [Couderc, 1960, p.92]. In 1919, Harlow Shapley noted that the vast majority of those redshifts were positive, with the only exceptions being those in our own galactic neighbourhood [Audouze & Israel, 1985, p.382].  Then during the period 1923-24, Edwin Hubble discovered Cepheid variables in neighbouring galaxies [Couderc, 1960, p.93].  These stars vary in light output in such a way that their intrinsic luminosity and the period of variability are linked.  Measuring the period of variability can thereby in principle establish their intrinsic luminosity.  Comparing the observed luminosity with the intrinsic luminosity should allow their distance to be found.  Hubble then used these stars to measure the distances to all forty-two galaxies that Slipher and Pease had examined.  In so doing, he discovered that the observed redshifts were proportional to distance.  In 1929 he published the law of spectral displacements, which is now called Hubble's Law [Hubble, 1929, p.168].  If astronomical distance is r and redshift is z, then in mathematical terms Hubble's Law can be written  as

r=z/h                                                                         (2)

where h is a constant of proportionality.

   Essentially Hubble's Law is a redshift/distance relationship, and as such simply notes that the redshift of galaxies is proportional to their distance.  That is the hard core of data that astronomers and cosmologists have to deal with.  However, once they go beyond these data and begin the "interpretation" of the data, the problems seem to begin.  Although cautious about the procedure until more data came in, Hubble suggested that z could be multiplied by the speed of light, c, thereby transforming the dimensionless number into a velocity.  Hubble pointed out that this procedure allowed the redshift to be interpreted as a Doppler effect of galactic recessional velocities, v [Hubble, 1936, p.121]. This was done by analogy with the effect heard when a police car passes you with its siren going. As it pulls away from you, the pitch of the siren drops. In a similar way, Hubble suggested that the redshift, which lengthened the wavelengths of light from distant galaxies, might indicate they are moving away from us also. This is one possible interpretation of the redshift data. As such the basic equation in (1) was interpreted to became

                        zc = v    or re-arranging   z = v/c    which suggested    v/c = Dl/l                   (3)

This then allowed equation (2) to be re-written as

                        r = cz/H = v/H                                                                          (4)

   [Audouze & Israel, p.382]

where H is the new constant of proportionality called the Hubble constant. This was the situation up until the early 1960's. By 1960, the highest value of z obtained was around 0.4. From the interpretation of equation (3) this meant these galaxies were receding at two-fifths of the velocity of light, and an essentially linear relationship was being maintained on the Hubble graph of redshift/distance from (2) or (4) [Couderc, 1960, p.103; Hoyle, 1956, pp.311-312].

However, soon after 1960, redshifts greater than about 0.4 were observed and a departure from linearity began to be noted as galaxy 'velocities' became more relativistic. Consequently, by the mid-1960's, the relativistic Doppler formula was applied and it was later found to be a reasonably accurate description of even the most distant known objects.  Thus equation (3) came to be re-written as [Audouze & Israel, 1985, p.356]

                     z = {[1+(v/c)] / [1 - (v2/c2)]-1/2} -1                                                                  (5)

Noting Some Problems
   Equation (5) is the end result of a process that Hubble started when he multiplied the redshift by lightspeed.  This procedure forced a Doppler shift interpretation on the data.  Furthermore, because this explanation had originated with Hubble himself, an important element of authority had been given to it.  Hubble's procedure effectively led to the interpretation that galaxies are racing away from each other at speeds which increase with distance.  Indeed, near the frontiers of the cosmos, those speeds are thought to be close to the current speed of light.  This is claimed to support current Big Bang modeling.  But was Hubble justified in multiplying z by c in the first place?  Some professional comment seems desirable.  In 1995, Malcolm Longair wrote: "Thus, redshift does not really have anything to do with velocities at all in cosmology.  The redshift is a...dimensionless number which...tells us the relative distance between galaxies when the light was emitted compared with that distance now.  It is a great pity that Hubble multiplied z by c. I hope we will eventually get rid of the c." [Longair, 1995, p.369].

   Using quasars of high redshifts with z greater than 1 as examples, Misner, Thorne and Wheeler use an argument similar to Schmidt [1972, p.273-287] to reject Doppler shifts on different grounds. They state: "Nor are the quasar redshifts likely to be Doppler; how could so massive an object be accelerated to v ~ 1 [the speed of light] without complete disruption?"  In thus rejecting the redshifts as Doppler effects, they also point out the problem that exists with another possible explanation that has been proposed to account for the data, namely gravitational redshifts.  They state: "Observed quasar redshifts of z ~ 1 to 3 cannot be gravitational in origin; objects with gravitational redshifts larger than z ~ 0.5 are unstable against collapse."  So in knocking out Doppler shifts and gravitation as the origin of the observed redshifts they come to what they see as the only other solution, namely a "cosmological redshift" [Misner, Thorne & Wheeler, 1997, p.767].

The Second Interpretation
   This cosmological redshift introduces the second interpretation commonly used to explain the observed lengthening of wavelengths.  About the time that the initial redshift and distance measurements were being made in the mid 1920's, the mathematician Alexander Friedmann was examining Einstein's field equations describing a static universe.  Friedmann found that these equations describing the behaviour of the cosmos were capable of an infinite number of solutions if Einstein's model of a static universe was abandoned [Friedmann, 1922, p.377].  Then in 1927, the Abbe Georges Lemaitre produced equations describing a universe which exploded out of an infinitely dense state and continued to expand ever since [Lemaitre, 1927, p.49].  In Einstein's case, the equations required the very 'fabric' of space-time to be static.  By contrast, Friedmann and Lemaitre's universe had this 'fabric' of space-time expanding.  In scientific terminology it is said that the universe's spatial co-ordinates are time dependent.  Importantly, Lemaitre pointed out that if the fabric of space was itself expanding, then photons of light in transit should have their wavelengths stretched in a manner proportional to the expansion.  These hypothesized space-time expansion redshifts can then be described mathematically as

                    z = (R2/R1) ­ 1                                                                   (6)

where R1 and R2 are the values of the space-time expansion factor at emission and reception respectively [Lang & Gingerich, 1979, pp.844 ff.].  This equation plays a crucial role in big-bang cosmology.  Consequently, it might be expected that the expression R2/R1 in this equation has been proven to be a valid representation of a physical reality.  But, as Robert Gentry points out, the problem is that no one has ever found a way to measure R.  Even more worrying is the fact that its actual existence has never been specifically verified.  It might simply be a mathematical construct [Gentry, 2001a, p.5; 2001c, p.2].

   As a possible explanation for redshifts, (6) should be compared with (5).  It is on this basis that the balloon analogy is often used to describe the redshift.  As it is being inflated, the fabric of the balloon expands in the same way that the fabric of space-time is proposed to be expanding.  Wavelengths of light in transit through space are meant to be stretched proportionally resulting in the redshift when that light is compared with the laboratory standard.  This is obviously a very different explanation for the redshift of light waves from distant galaxies when compared with Doppler shifts, just as (6) is conceptually different from (5).  Both result in a stretching of light waves, but for entirely different reasons.

   While it is true that this second interpretation has always been accepted, the Doppler shift interpretation has often been the one that was publicly espoused, at least until recently.  As difficulties with the Doppler shift model, such as those noted by Misner, Thorne and Wheeler, became more widely known, alternative statements appeared.  For instance, in 1993, Barry Parker stated: "We shouldn't think of galaxies as moving through space as they expand away from each other.  In reality, it's the space between them that is expanding. ...Because recessional velocity is not a true velocity, in the usual sense of the word, it is incorrect to think of the redshift of galaxies as due to the Doppler effect.  The Doppler effect applies only to objects that actually move through space.  The redshift of galaxies exists because their light waves are stretched as space is stretched, and therefore their wavelength is increased" [Parker, 1993, pp.76,77].  This emphasis is reinforced in a 1999 comment by John Peacock who considers that "Photon wavelengths therefore stretch with the universe, as is intuitively reasonable...This is the only correct interpretation of the redshift at large distances; it is common but misleading to convert a large redshift to a recession velocity using the special-relativistic [Doppler] formula..." [Peacock, 1999, pp.71-72].

The Ambiguity
   However, not every professional in this area agrees.  The Cambridge Atlas of Astronomy, whose topics were written by experts in the field, ignores the expansion of space-time and its photon stretching procedure in its discussion of redshifts and maintains the Doppler shift position [Audouze & Israel, 1985, p. 356, 382].  This might be considered a concession that allows ease of explanation, except for one thing. In the definition section of the Atlas under the heading "redshift", a choice of explanation is given to account for the phenomenon.  Amazingly, photon stretching is not one of them.  Rather, the third possibility, namely a gravitational redshift, is substituted, despite the fact that it was shown to be flawed by Misner, Thorne and Wheeler as noted above.  The Atlas states the redshift is "The shift of spectral lines towards longer wavelengths either because of a Doppler effect...or because of the Einstein effect (gravitational redshift)"  [Audouze & Israel, 1985, p.426].  These are not isolated instances.  Novikov was convinced that the origin of cosmological redshifts was to be found in the Doppler effect [Novikov, 1983, pp.48-49], and so was Weinberg [1972, p.417].  Interestingly, by 1983 Weinberg adopted both the stretching explanation as well as the Doppler shift definition [1983, pp.28, 30, 35, 172 cf 37-40].  In this he reflects the general ambiguity on the issue. This suggests that a closer examination of this matter is needed.

Examining Space-Time Expansion
   In the first place, if the expansion of space-time does cause light waves in transit to be lengthened, it might be fully expected that atoms, intimately involved with this very fabric of space, would likewise undergo such expansion.  If it is accepted that this is occurring, the customary explanation states that the expansion would not then be observable since everything would be expanding, including our measuring sticks, telescopes, and the observers themselves.  In order to save the existing paradigm, it is then concluded that the expansion does not occur within the galaxies themselves, but rather is external to them.  However, legitimate doubts can be raised whether the expansion of space-time would really be as unobservable as this customary explanation suggests.  In 1994, Sumner undertook a thorough examination of the physics and maths involved if space-time expansion were truly universal.  He established that, due to the effects of cosmological expansion on the atom, the results would indeed be observable and would lead to a blue-shift of light received from such atoms [Sumner 1994, p.491].  If the Friedmann equations are logically followed through, as Sumner did, the observed redshift implies that the very fabric of space must therefore be contracting and not expanding at all.

   These results from Sumner's analysis re-emphasise the fact that if cosmological expansion is really occurring a redshift can only be obtained if galaxies, stars, atoms and matter do not expand also.  This proviso therefore becomes a vital necessity to maintain the existing paradigm whichever approach is taken to the expanding space-time scenario.  The customary explanation suggests that there is no observable result unless matter does not expand, while the strict mathematical analysis of the situation results in a blue-shift, unless again matter does not expand.  In both cases, therefore, unacceptable results are obtained if matter partakes of the cosmological expansion.  Without this crucial proviso the whole idea of space-time expansion flies in the face of the observational evidence.

   For this reason, Sumner was accused of a conceptual error because he failed to follow the accepted position that not everything expands.  In a segment whose side-bar reads "What expands in the universe and what does not," Misner, Thorne and Wheeler refer to this conceptual problem that many a student has on the topic and then comment: "Only later does he realize that the atom does not expand, the meter stick does not expand, the distance between the sun and earth does not expand.  Only distances between clusters of galaxies and greater distances are subject to the expansion.  No model more quickly illustrates the actual situation than a rubber balloon with pennies affixed to it, each by a drop of glue.  As the balloon is inflated the pennies increase their separation one from another but not a single one of them expands!" [MTW, 1997, p.719].

Problems With Space-Time Expansion
   Well, that is the analogy, but there are no maths or physics presented to justify that idea.  Misner, Thorne and Wheeler were in an ideal position to present the evidence for space-time expansion if that evidence were available.  But nothing is there.  Instead, it seems that Sumner was basically correct in applying the effects of expansion to the atom, because if space-time is really expanding, then nothing should be exempt from the process.  This is often countered by the argument that gravity overcomes the expansion locally, thereby allowing solar systems, galaxies, and clusters of galaxies to remain unaffected by the expansion process.  The Misner, Thorne and Wheeler tome on gravity was an excellent place to outline the details of any such argument, but again nothing is presented.  Their key and only defence for this position is to give a reference to a paper by Noerdlinger and Petrosian [1971, p.1].  One would have thought that this paper would give the definitive proof required.  However, when this paper is examined in detail, it is seen to be ambiguous in addressing the matter of the expansion of galaxies.

   It is at this point that Robert Gentry makes a significant contribution to the discussion.  He calculates the gravitational force, Fc, between two clusters of 500 Milky Way sized galaxies, where each galaxy has a mass of about 2 x 1011 times the mass of the Sun.  From Newtonian mechanics Fc = -GMc2/rc2, where the centre to centre distance between clusters rc is of the order of 108 light years and the mass of each cluster is given by Mc = 1014 times Ms, the mass of the Sun, and where Ms = 2 x 1033 grams.  Then, using the spherical mass approximation for the Galaxy, the gravitational force Fs exerted on the Sun by our Galaxy's mass interior to the Sun's position is given by the standard Newtonian formula Fs = -4pGMsrrs/3, where the Sun's position from the centre of the Galaxy rs is roughly 3 x 104 light-years, and the average matter density r is 10-24 grams per cubic centimetre.  The result is that the gravitational force on the clusters Fc turns out to be close to 2 x 1010 times greater than the gravitational force, Fs, exerted on the Sun by the mass of our Galaxy interior to the Sun's position [Gentry, 2001b, p.6].  We can therefore write Fc/Fs = 2 x 1010.  However, it is also important to find out the relative sizes of the cosmological expansion factor R with which to compare this figure.  Since Gentry's distance between clusters rc is of the order of 108 light-years, while he gives the distance of the Sun from our galactic centre rs as about 3 x 104 light-years, the ratio of rc/rs = 3.3 x 103.  Since at any given time R is essentially linear in distance over the scales being considered here [Landsberg and Evans, 1979, p.33], then it follows that the cosmological expansion factor is only about 3.3 x 103 greater between clusters of galaxies than compared with the Sun.  However, the G force acting on the clusters is 1010 times greater than the G force on the Sun.

   The conclusion is, therefore, that if the expansion factor is sufficient to act over inter-cluster distances with the gravitational forces involved, it should also act within our Galaxy where the gravitational forces are relatively weaker.  Alternatively, if the gravitational forces acting on the Sun in our Galaxy are too strong for the cosmological expansion factor to affect it, then, by the same token, the even stronger gravitational forces acting between clusters will also prevent the expansion factor from operating there.  It is therefore incorrect to state that gravitational forces prevent galaxies and smaller scale objects from partaking in cosmological expansion.  While it might also be true that the effect could be masked by local processes, that is substantially different to saying it does not occur locally at all.  Over time, the effect would build up and become observable.  In other words, if space-time were expanding as the Friedmann-Lemaitre equations suggest, atoms and galaxies would expand too, and as Sumner [op. cit.] has pointed out, this would lead to a blueshifting rather than a redshifting of light from distant objects.

Summarising The Interpretations
   In summary, it might be stated that there are three main interpretations of the redshift data.  The first is the Doppler shift argument whereby the galaxies themselves are moving through static space-time.  Misner, Thorne and Wheeler point out that this concept has the problem of how galaxies could be accelerated to near the speed of light without disruption.  Another, albeit minority, interpretation is that the Einstein effect gives redshifts that result from gravitational forces.  Misner, Thorne and Wheeler also dismiss this possibility since objects with gravitational redshifts greater than z = 0.5 are unstable against collapse.  Finally, there is the expansion of space-time under the Friedmann equations, which fail to give results in accord with observation unless an important proviso is imposed.  However, that proviso, based on the assumption that gravitational forces prevent cosmological expansion occurring from the scale of galaxies downward, does not seem to stand up to simple analysis using Newtonian mechanics.  In addition, the cosmological expansion factor R in the Friedmann equations has never had its existence verified, and it has never actually been measured.  It may simply be a mathematical abstraction.  Despite these results, it would appear to be important to have some observational evidence from an entirely independent line of enquiry that might settle the issue once and for all.  It is at this point that the work of William Tifft at Steward Observatory in Tucson, Arizona comes into focus.

The Quantized Redshift
   From 1975 onward, after a long, careful series of measurements on binary galaxies and galaxies in the Coma cluster, Tifft published several papers indicating that redshift differences between galaxies were not smooth but went in jumps, or were quantised [Tifft, 1977, p.31].  The Coma cluster exhibited this effect in such a way that bands of redshift ran through the whole cluster.  Some little time later, Tifft was on sabbatical leave in Italy and lectured on the puzzling quantization effects he had been observing.  At one of these lectures he was presented with a list of accurate redshifts using radio measurements of hydrogen with the comment "I am sure you will not find periodicity in here."  (In this case, the word "periodicity" is referring to the quantisation effect.)  Astronomer Halton Arp reports on the outcome of Tifft's analysis of this data set by stating: "Not only did the quantization appear in this independent set of very accurate double galaxy measurements, but it was the most clear cut, obviously significant demonstration of the effect yet seen. ...The results were later reconfirmed by optical measures in the Southern Hemisphere..." [Arp, 1987, p. 112].

   These results have important consequences.  If the redshift was indeed due to galaxies racing away from each other as the Doppler shift interpretation requires, or due to the expansion of space-time, then these speeds of recession should be systematically increasing with distance like cars accelerating smoothly up to a maximum speed on a highway.  Furthermore, the overall redshift function should be a smooth curve. The results that Tifft had obtained indicated that the redshift went in jumps from one plateau to another like a set of steps and stairs.  It was as if every car on the highway traveled only at speeds that were multiples of, say, 5 miles per hour, no matter what pressure was placed on the accelerator.  Even more puzzling was the fact that some jumps actually occurred within galaxies.  On either the Friedmann-Lemaitre or the Doppler model, it was difficult to see how any cosmological expansion or recession could go in jumps.  In fact these results did not fit either concept at all.  As a result, astronomers were incredulous and very dismissive.  The editor of the Astrophysical Journal, which published Tifft's initial papers, apologetically added a footnote to many of Tifft's title pages.  They mostly read after this style: "After an extensive independent statistical analysis, the referee could not demonstrate that the bands discussed in this and previous papers do not exist, but he was also not convinced by the author's analyses that the bands and cross-bands do exist.  In this stalemate on a question of possible considerable importance, we will permit the author to present his evidence in hopes that an open forum will encourage research and a resolution of this disagreement." [Tifft, 1979, p.799].

   In 1981, the results of an extensive redshift survey by astronomers Fisher and Tully were published [Fisher & Tully, 1981, p.139].  The redshifts did not appear to be clumped in the way that Tifft had claimed, so astronomers dismissed Tifft's quantizations as merely due to a small data set.  The idea was that if the data set was enlarged, the effect would go away, as seemed to have happened with the large Fisher-Tully catalogue.  However, Tifft and Cocke conducted an analysis of the catalogue, and in 1984 they published their findings.  They noted that the motion of the Solar System through space imparted a genuine Doppler shift of its own to all measurements of redshift.  When this Solar System Doppler component was subtracted from the survey results, redshift quantization appeared globally across the whole sky [Tifft & Cocke, 1984, p.492].  Despite the size of the data set that the Fisher-Tully catalogue provided, the 'noisy data' argument continued as the official reason for rejection of the results.  However, in 1985, there was an unexpected and independent confirmation of the quantization effects.  Sulentic and Arp used radio-telescopes to accurately measure the redshifts of over 260 galaxies from more than 80 different groups for an entirely different purpose.  As they did their analysis, the same quantizations that Tifft and Cocke had discovered surprisingly appeared in their data, and the measurement error was only 1/9th of the size of the quantization [Arp & Sulentic, 1985, p. 88; also Arp, 1987, pp.108, 110, 112-113, 119].

Attempting To Settle The Issue
   These developments were disturbing to astronomers and cosmologists alike.  In the early 1990's two astronomers in Scotland decided to prove Tifft wrong once and for all.  Bruce Guthrie and William Napier from the Royal Observatory in Edinburgh used the most accurate hydrogen line redshift data.  By the end of 1991 they had studied 106 spiral galaxies and detected a quantization of about 37.5 km/s, very close to Tifft's quantum multiple of 36.2 km/s [Schewe & Stein, 1992a, No.61].  By November 1992, a further 89 spiral galaxies had been examined in which a quantization of 37.2 km/s emerged [Schewe & Stein, 1992b, No. 104].  In 1995 they submitted a paper to Astronomy and Astrophysics with the results from a further 97 spiral galaxies showing a 37.5 km/s quantization.  Because the prevailing wisdom said the quantization only appeared because of small number statistics, the referees asked them to repeat their analysis with another set of galaxies.  This Guthrie and Napier did with an additional set of 117 other galaxies.  The same 37.5 km/s quantization was plainly in evidence in this 1996 data set, and the referees accepted the paper [Matthews, 1996, p.759; Corliss, 1996, No. 105, Arp, 1998, p.199-200].  A Fourier analysis of all 399 data points showed a huge spike at 37.5 km/s with a significance of one in a million.  The measurement error was about 1/10th the size of the quantization.  One comment on the redshift quantization plot stated: "One can see at a glance how accurately the troughs and peaks of redshift march metronomically outward from 0 to over 2000 km/s." [Arp, 1998, p.199].  Despite this observational evidence, cosmologists like James Peebles of Princeton are reluctant to accept it.  He stated: "I'm not being dogmatic and saying it cannot happen, but if it does, it's a real shocker." [Corliss, op. cit; Arp, 1998, p.200].

   The outcome of the most accurate studies by Tifft indicates a possible basic redshift quantization of about 8/3 km/s [Tifft, 1991, p.396] with a claim by Brian Murray Lewis that the redshift measurements used had an accuracy of 0.1 km/s at a very high signal to noise ratio [Lewis, 1987, p.201].  Tifft demonstrated that higher redshift quantum values were simply multiples of this basic figure.  As Peebles noted, these results are a "real shocker" no matter which model is used.  If changes in the Friedmann radius really are occurring and are the prime cause of the redshift, then the quantised redshift shows it must be changing in jumps.  This is virtually impossible.  At the same time, the quantised redshift also precludes changes in the Friedmann radius from occurring concurrently with any other proposed quantisation process.  This conclusion follows since the stretching or contracting of light photons in transit as the Friedmann radius changes would immediately obliterate or 'smear out' any sign of a precise redshift (or blue shift) quantization.  In other words, the very fact that this z quantization exists at all necessarily implies that the Friedmann radius is fixed.

   On the Doppler model, the galaxies are themselves moving away through static space-time, but the quantised redshift requires this to be in such a way that their velocities are in fixed units.  This is unlikely.  However, when it is considered that the quantum jumps in redshift values have been observed to even go through individual galaxies [Tifft, 1977, p.31], it becomes apparent that the redshift can have little to do with either space-time expansion or galactic velocities through space, nor can it have anything to do with galaxy size or distribution.

Galaxy Motion Smears Out The Quantization
   One final piece of observational evidence is pertinent to this matter.  Tifft and others have pointed out that, as far as clusters of galaxies are concerned, the quantised redshift means that the actual velocities of galaxies must be minimal except in the very centre of the clusters [Tifft, 1977, p. 31; Arp, 1987, p.119].  Observational evidence that this is indeed the case was mentioned at the Tucson conference on quantization in April 1996.  Observations of the Virgo cluster and other clusters have shown that in the innermost parts of the clusters "deeper in the potential well, [galaxies] were moving fast enough to wash out the periodicity" [Arp, 1998, p.199].  (Again the word 'periodicity' is being used as an alternative to 'quantization'.)  In other words, if galaxies really had a significant velocity, it would actually smear out the quantization.  As a consequence, these observations reveal that redshifts are not basically due to galaxy motion at all, but must have some other primary cause, with any Doppler effects from motion being secondary.  This conclusion also resolves one matter that has puzzled astronomers for years.  Use of the redshift to determine galaxy motion in clusters has given a false impression of the actual velocities of galaxies involved.  If the redshift is interpreted as a velocity, the outer galaxies in clusters are moving too fast to be held by the gravitational field of the cluster.  As a result, astronomers have looked for the 'missing mass' which should hold such clusters together.  The quantisation of the redshift reveals that actual galaxy motions are so low that there is no mass 'missing' at all.  A thorny problem is thereby resolved by these observations.

The Stability Of A Static Universe
   Since the observed quantized redshifts rule out Doppler shifts from galactic velocities or from cosmological expansion of space-time, then the evidence indicates that the cosmos has probably remained static after an initial period of expansion, and that the minor motions of galaxies are merely a secondary addition to the redshift.  This raises two issues. The first matter is the stability of a static universe, while the second issue is the origin of the quantised redshift itself.  On the first count, Narliker and Arp [1993, p.51] demonstrated that a static, matter-filled universe was stable against gravitational collapse without the action of a cosmological constant, provided that mass increases with time.  They point out that "stability is guaranteed by the mass-dependent terms...Small perturbations of the flat Minkowski spacetime would lead to small oscillations about the line element rather than to a collapse."

   This is not the only possible model.  In 1987, V. S. Troitskii from the Radiophysical Research Institute in Gorky, presented a different concept for stability in a universe in which the radius of curvature of space also remained constant.  Stability in this static cosmos was maintained in a manner expressed in the Abstract thus: "The agreement with the fundamental physics laws is achieved by introducing the evolution of a number of other fundamental constants synchronously with the variation of the speed of light" [Troitskii, 1987, p.389].  Some three years earlier, T. C. Van Flandern from the US Naval Observatory in Washington, made a similar observation.  He said "For example, if the universe had constant linear dimensions in both dynamical and atomic units, the increase in redshift with distance (or equivalently, with lookback time) would imply an increase in c at past epochs, or that c was decreasing as time moves forward" [Van Flandern, 1984, p.625].  In this scenario, stability was maintained by variation in some atomic quantities.  In other words, these three examples reveal that a static cosmos can be stable against collapse even without the action of Einstein's cosmological constant.

The Redshift And Energy Conservation
   Second, the question of the origin of the quantised redshift must be addressed.  With galactic motion and space expansion ruled out, and a static cosmos indicated instead, the options must be reconsidered.  The Einstein gravitational redshift is one possibility, but, as Misner, Thorne and Wheeler point out, gravitational redshifts greater than about z = 0.5 indicate an instability that would seem to preclude this option.  With all three likely external causes for the redshift thereby removed from contention, it would seem that the prime option left is to seek a cause that is inherent to the atomic emitters of light within the galaxies themselves.  This would at least account for Tifft's observation that quantum changes in redshift occur within galaxies.  If this were the case, there would be no need to change the wavelength of the light in transit as the wavelength would be fixed at the moment of emission.  This overcomes a difficulty faced by all processes that give redshifts to photons in transit.  This difficulty was noted by Hubble in 1936.  He stated: "redshifts, by increasing wavelengths, must reduce the energy in the quanta. Any plausible interpretation of redshifts must account for the loss of energy" [Hubble, 1936, p.121].  The conservation of energy of light photons (quanta) in transit has been a problem for cosmologists ever since.  In fact some are openly willing to claim that this is one case where energy is not conserved [Harrison, 1981, p.275-276].  By contrast, any model that implicates the atomic emitters themselves changes the problem around and energy conservation in transit is no longer an issue.

   At this stage, I am aware of only a few cosmological models that are in line with the observational features mentioned in this article.  Among the most recent is the New Redshift Interpretation (NRI) by Robert Gentry, who uses a combination of gravitational and Doppler effects.  His proposals may be viewed at the following URL:  Another is the variable lightspeed (Vc) or c decay (cDK) model in which both atomic emitters and light are jointly affected by the changing properties of the vacuum.  A brief exploration of this possibility now follows.

Properties Of The Vacuum
   One of the key properties of the vacuum is the Zero-Point Energy (ZPE), so-called because this electromagnetic energy is present even at zero degrees Kelvin [Boyer, 1985, p.70].  The amount of this energy that permeates every cubic centimetre of the universe is absolutely enormous.  Recently, Professor Paul Davies estimated the energy density of the ZPE as around 10110 Joules per cubic centimetre, a fairly typical figure [Davies, 2001, p.30].  We are unaware of the presence of the Zero-Point Energy for the same reason that we are unaware of the 15 pounds per square inch of atmospheric pressure on our bodies at sea level ­ its presence is balanced both inside and outside our bodies, and it permeates our instruments as well.  Nevertheless experimental evidence confirms the presence of the ZPE in a number of ways including the Casimir effect [Boyer, 1985, p.70].  When two metal plates are brought very close together in a vacuum, there is a measurable force, the Casimir force, pushing the plates together.  Since these plates exclude all wavelengths of the electromagnetic ZPE other than those which fit between the plates, all those excluded longer waves exert a radiation pressure on the plates forcing them together [Milonni, Cook & Goggin, 1988, p.1621].  The same effect occurs at the atomic and molecular level and is the origin of the feebly attractive Van der Waals forces.  The Zero-Point Energy is also the cause of random "noise" in electronic circuits that puts a limit on the levels to which signals can be amplified [Matthews, 1995, p.30].  The same vacuum energy also explains why cooling alone will never freeze liquid helium.  Unless pressure is applied, the vacuum energy fluctuations prevent the atoms from getting close enough to trigger solidification [Ibid].

Zero-Point Energy And Atomic Stability
   The all-pervasive ZPE 'sea' also turns out to be a physical necessity to maintain atomic structures throughout the cosmos.  In 1987 an interesting paper was written on this matter by Hal Puthoff.  According to classical physics, an electron in orbit around a proton should be radiating energy and so spiral into the nucleus and the whole structure disappear in a flash of light.  Obviously this does not happen.  But when you ask why it does not happen it is usual to invoke quantum laws and explain that on quantum concepts electrons do not radiate energy when in a stable orbit.  Quantum laws are one thing, but an actual physical explanation is still desirable.  It was at this point that the 1987 paper appeared.  The author assumed that classical physics was correct and he calculated the energy that electrons radiated as they orbited around their protons.  He then calculated the energy that such an electron received from the all-pervasive ZPE sea in which it was immersed. It turns out that the two were identical.  The Abstract summarizes the results as follows: "the ground state of the hydrogen atom can be precisely defined as resulting from a dynamic equilibrium between radiation emitted due to acceleration of the electron in its ground state orbit and radiation absorbed from the zero-point fluctuations of the background vacuum electromagnetic field" [Puthoff, 1987, p.3266].  In the same way that a child on a swing receives resonantly times pushes from an adult to keep the swing going, so also the electron received resonantly timed pushes from the ZPE.

   It has also been explained another way.  If an electron is orbiting too far out from the nucleus, it radiates more energy than it receives from the ZPE and spirals inwards to the position of stability.  However, if the electron is orbiting too far in, it receives more energy from the ZPE than it is radiating, and so moves outwards to its stable position [de la Pena, 1982, p.428].  The concluding comment in the 1987 paper carries unusual significance.  It reads: "Finally, it is seen that a well-defined, precise quantitative argument can be made that the ground state of the hydrogen atom is defined by a dynamic equilibrium in which the collapse of the state is prevented by the presence of the zero-point fluctuations of the electromagnetic field.  This carries with it the attendant implication that the stability of matter itself is largely mediated by ZPF phenomena in the manner described here, a concept that transcends the usual interpretation of the role and significance of zero-point fluctuations of the vacuum electromagnetic field" [Puthoff, 1987, p.3266].  In a word, it appears that the very existence of atoms and atomic structures depends on this underlying sea of the electromagnetic ZPE.  Without the ZPE all matter in the universe would undergo instantaneous collapse.

ZPE And The Redshift
   On this basis, then, it seems that atomic orbit energies are sustained by the ZPE.  It is therefore possible that, if the energy density of the ZPE were to vary significantly, then all atomic structures throughout the cosmos might be expected to adjust their orbit energies to be in accord with the sustaining power available from the vacuum.  In view of the fact that orbit energies go in quantum jumps, it might also be anticipated that any such change in the energy density of the ZPE might have to cross a quantum threshold before the atoms actually took up their new energy state.  For example, if the ZPE was systematically lower the further back in time we went, then, as a series of quantum thresholds was reached, atomic orbit energies might also be expected to become lower in a set of jumps.  The light emitted by atomic processes would therefore be redder in a series of steps and stairs as we look back in time, since the red end of the spectrum is the low energy end.  The quantised redshift of light from distant galaxies may in fact be evidence for this very phenomenon.

ZPE And Lightspeed
   At the same time, a lower energy density for the ZPE would also mean a higher value for the speed of light.  This conclusion results from an analysis done in 1995 on the speed of light in 'modified vacua' including the Casimir vacuum in which the energy density of the ZPE is lowered between the plates.  The Abstract of the analysis reads in part: "Whether photons move faster or slower than c depends only on the lower or higher energy density of the modified vacuum respectively."  The analysis concluded that for all vacua "It follows automatically that if the vacuum has a lower energy density than the standard vacuum, [lightspeed] v >1, and vice versa", where v = 1 is the current speed of light [Latorre, Pascual and Tarrach, 1995, p60].  This follows since lower vacuum energy densities effectively mean lower values for the electric permittivity and magnetic permeability of the vacuum, and lightspeed is inversely dependent upon these quantities.

   The reason why the permittivity and permeability of the vacuum, and hence lightspeed, is dependent upon the strength of the ZPE requires an addition piece of information.  Because of Einstein's equation linking matter and energy, the very presence of the ZPE allows virtual particle-antiparticle pairs (such as electron-positron pairs) to flip in and out of existence on a timescale determined by Planck's quantum constant h.  As a photon of light travels through the vacuum, it becomes absorbed by such virtual particles and then re-emitted as the particle pairs annihilate.  The process, while fast, does take a finite time.  The progress of the photon is therefore like that of a runner on a track with hurdles; the more hurdles in a given distance, the longer the runner takes to complete the course.  In practice, a lower energy density for the ZPE also means fewer virtual particles per unit distance in the path of a photon.  Consequently, fewer absorptions and re-emissions of the photon would occur over that distance, so light would reach its destination more quickly.  The converse is also true.  Stephen Barnett picks up on this point and explains further: "The role of virtual particles in determining the permittivity [and permeability] of the vacuum is analogous to that of atoms or molecules in determining the relative permittivity of a dielectric material.  The light propagating in the material can be absorbed...[but] the atoms remain in their excited states for only a very short time before re-emitting the light.  This absorption and re-emission is responsible for the refractive index of the material and results in the well-known reduction of the speed of light...A [similar] modification of the vacuum can produce a change in its permittivity [and permeability] with a resulting change in the speed of light." [Barnett, 1990, p.289].

   As a result of these considerations, it becomes apparent that atomic behaviour, the redshift and lightspeed should be linked via the ZPE.  Since Planck's constant h can be considered a measure of the strength of the ZPE with c inversely related to it, this scenario suggesting that the ZPE has increased with time finds some support from the measured values of c and h as in the Report by Norman and Setterfield [1987].  The observational evidence presented there indicated that h was measured as increasing during the 20th century with c decreasing in such a way that hc was invariant.  This suggests that the ZPE is increasing with time, for reasons that are related to the stretching out of the cosmos at Creation, and that the quantised redshift results along with a drop in lightspeed over the lifetime of the universe.  Furthermore, since looking out into astronomical distance is equivalent to looking back in time, and since redshift and lightspeed can be shown to be directly related via the ZPE, the graph of redshift against distance should be the same as the graph of lightspeed against time.  All that is required to change from one to the other is to re-scale the axes. These important matters are currently undergoing further investigation.

Quantised Redshift "Shells"
   If these results are followed through, the appearance of quantised redshift "shells" centred on our Galaxy or Solar System is the perfectly natural result.  It stems from the fact that light photons travelling from equal distances to the earth will carry the same information about the physical conditions at the time of emission.  As the ZPE steadily increased isotropically with time, and atoms emitted bluer light, objects equidistant from any given point in the cosmos will have emitted light with the same redshift information.  Thus, the appearance of redshift "shells" centred on the observer is a universal phenomenon on this model, and not an indication of a preferred position for the Solar System.  Note that this argument does not apply to models where the quantised redshift is due to gravitational phenomena such as those that Robert Gentry or Russ Humphreys propose.

The Testimony Of The Bible
   The key issue for the Christian, in the long run however, is whether or not the Bible has anything to say on any particular issue.  This issue of an expanding or static cosmos is no different.  It may seem strange to think the Bible might have a word on whether the universe is static or continues to expand, but it is always necessary to check.

   In this case, there does appear to be some evidence supporting a universe that was expanded out to its current size quickly at the time of creation and was then held at that size so that it is now static. Look at the following quotes:

This is what God the Lord says ­
He who created the heavens and stretched them out,
Who spread out the earth and all that comes out of it,
Who gives breath to its people
And life to those who walk on it.

Isaiah 42:5 NIV

I am the Lord who has made all things,
Who alone stretched out the heavens,
Who spread out the earth by myself
Isaiah 44:24 NIV

It is I who made the earth and created mankind upon it.
My own hands stretched out the heavens;
I marshaled their starry hosts.

Isaiah 45:12 NIV

   The Big Bang and the Bible agree on one thing: the universe expanded.  The Big Bang postulates an internal energy giving rise to this expansion.  The Bible says God did it.  The Big Bang says it continues, but the Bible seems to say it was in the past.  If the context is examined in these passages as well as others which talk about the stretching of the heavens, it can be seen that the action is being paired with other actions which are in the past and long since completed: the earth has been spread out, the stars have been formed, mankind has been created, and so forth.  The indication is that all these things were fully completed long ago.

   Let us examine this issue in a little more detail.  There are 12 instances in the Old Testament where it talks about the heavens being "stretched out."  A consistent picture emerges from this collection.  In every case except one in Job, which is fuzzy, a Hebrew construction is used which indicates a past time context for this process; the stretching out does not appear to continue after the acts of Creation.  In this matter I acknowledge the valuable contribution of the Hebrew scholar, Dr. Bernard Northrup as he has provided the literal Hebrew translations given below. He notes:

"Where the shewa (a "u" sound like that in "cup") occurs, I have transliterated with a 'u' to avoid other uses of the "u." I have used the single quotation mark ['] for both the Aleph and the Ayin in Hebrew.  In Hebrew, in spite of the shambles found in our English translations, it is always the context of a verb or participle that determines the time setting in which it must be translated.  I have noted the participles and identified the perfect tense verbs used in these sentences that speak of God's having stretched out the heavens in the past."

Let us examine these Scriptural statements in turn with the help of Dr. Northrup [2001].

Psalm 104:2. This has been translated in a past time context by the RSV and TLB. In Hebrew it reads:
noteh[qal. participle] shamayim kayuriy'ah,
"[The One] having stretched out heavens like a curtain"

Isaiah 40:22. Translated in a past time context by the LXX. In Hebrew it reads:
hannoteh[qal. participle & article] haddoq shamayim,
"The One Who has stretched out the heavens like a curtain" ("and Who has spread them out like a tent for dwelling")

Isaiah 42:5. Translated in a past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB. This is a united testimony from all the main translations. The verse is quoted in the comments at the beginning of this section.

Isaiah 44:24. Translated in a past time context by the LXX, NIV, RSV. In Hebrew it reads:
'anoki [pronoun in emphatic position] YHWH 'oseh [participle] kol,
("I Myself am the Eternal Lord, the One having made everything")
noteh[participle] shamayim Lubadiy,
"having stretched out the heavens by Myself,"

Isaiah 45:12. Translated in a past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB. In Hebrew it reads:
'ani yaday natu shamayim,
"I, by My hands, stretched out heavens"

Isaiah 48:13. Translated in a past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB.
In Hebrew it reads:
("Surely My hand laid the foundation of the earth.)
wiymiyniy tephchah [perfect tense] shamayim
"And My right hand spread out heavens. (In My calling upon them, they stood up together.)"

Isaiah 51:13. Translated in a past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB.
In Hebrew it reads:
("And you have forgotten the Eternal Lord, your Maker),
noteh[participle] shamayim wuyosed [participle] 'aretz,
"the One having stretched out heavens and having laid the foundation of the earth."

Jeremiah 10:12. Translated in a past time context by LXX, KJV, NAS, NIV, NKJ, RSV, TLB.  This is a united testimony from all major translations indicating that the Hebrew represents a completed action.  In the NKJ it reads: "He has made the earth by His power, He has established the world by His wisdom, and has stretched out the heavens at His discretion."

Jeremiah 51:15. Translated in a past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB.  Again all major translations have a united testimony.  Note: this verse appears in the LXX as Jer. 28:15).  In the NKJ it reads: "He has made the earth by His power; He has established the world by His wisdom, and stretched out the heavens by His understanding."

Zechariah 12:1. Translated in a past time context by the RSV and TLB. In Hebrew it reads:
n'oom YHWH, noteh [participle] shamayim wuyosed [participle] 'aretz,
"[This is] The declaration of the Eternal Lord, the One having stretched out heavens and having laid the foundations of earth."

Job 9:8. Translated in a past time context by the LXX, RSV, TLB. The LXX translation reads: "He alone has stretched out the heavens and walks on the sea as on firm ground."

Job 37:18. Translated in the past context by KJV, NKJ, RSV.  Most modern translations use "sky" and read like the NKJ: "With Him, have you spread out the skies, strong as a cast metal mirror?"  However, the LXX reads: "Will you establish with Him the ancient heavens, strong as a molten mirror?"

Bernard Northrup concludes:

"I do not find any excuse whatsoever in the context of any of the uses of the participle phrase noteh shamayim, "stretching out the heavens", or any of the perfect verbs [finished, single action] for translating them without acknowledging their past time context.  Again I say that I see no justification for attempting to support the concept of the continuing spreading out of the heavenly bodies today.  I would only see references to the great creative acts that were concluded and completed in the past."

   To conclude, one smaller matter needs to be mentioned.  In most examples used above it should be noted that the heavens are 'stretched out' while the earth is 'spread out'.  The word translated 'spread out' for the earth is raqa' which has a basic meaning "to pound out".  This is in contrast to the word translated 'stretch out' for the heavens, which is natah whose basic meaning is "to stretch or extend".  This implies a different action by the Lord in stretching out the fabric of space, compared with 'pounding' the earth into shape.  The only time that raqa' is used to describe the process for the heavens is in the Job 37 passage.  Interestingly, the Greek LXX has come down to us differently; the word used there is stereoo meaning to "establish or confirm" the ancient heavens.  Also of note is that most modern translations use "sky" in this passage rather than "heavens", and the raqia is applied to mean "sky" instead of "heavens" exclusively in Genesis 1 by the NIV, TLB and the New English Translation.  A consistent picture thereby seems to emerge on this matter.

   On the basis of this examination of Scripture, it therefore appears that, from the use of the past time context, God stretched out the heavens at the time of Creation, and that the action was completed then and is not continuing.  This implies that the universe is not currently expanding, but is static, in line with the scientific evidence presented above.  If this is indeed the case, we need to conform our cosmological modeling to these precepts.


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An explanation of CRSQ's letter of refusal, dated 15 August, 2002:

   In his letter of rejection, Dr. Eugene Chaffin (who requested the text of the letter be removed from the net), stated that despite the revisions to the manuscript, he had two problems with it which would prevent him from allowing publication.

   The first problem he stated was that there was, to use his words, "significant new material [that] has appeared at the end of the paper, which had not been in the version that the reviewers saw."  That new material was in response to requests made by the reviewers and by Chaffin himself in the original letter when the reviewers' reports were returned to me.  The material involved a requested further explanation of Gentry's material as I referenced it.  It also involved a requested explanation of why there is no blue shift if the universe is not expanding, as that reviewer felt that then there must be gravitational collapse instead.  That reviewer also requested an explanation for the cause of the redshift if it did not have a Doppler or cosmological cause.  This is exactly what I responded to in the new version.

   Chaffin's second reason for rejecting the paper was because he thought that maybe he had found a "mistake in logic" in the paper and was therefore obliged, as he put it, to reject it in order to save both myself and CRSQ "embarrassment."

   He then stated that "I would think the author would wish to withdraw the paper but in any case, the editor would be obliged to reject the manuscript."

   After his official signature on the letterhead page, he added another page of argument refuting, as he had referred to it, the "erroneous material" which triggered his rejection despite my having answered all requests made by both him and the reviewers in the original communication.

   The second page opens with his admission that I was correct with the calculation that I had done showing that the force between galactic clusters may be 1010 times bigger than the force exerted on the sun by our galaxy.  But he then claimed that comparing these two things was an "apples and oranges" situation.  To support his claim he referred to an article by Cooperstock, Varaoni, and Vollick which is part of my response below.  However he had only sent me the first three pages and it was not until I downloaded the entire referenced article by Cooperstock et al off the net that I was able to see the full extent of what they were saying.  This was not made evident by the excerpt sent to me by Chaffin in his letter of rejection.  His conclusion regarding my calculations in the paper was, "In my opinion, this comparison, when done correctly, will not be fruitful."  This comment, as well as his statements on the front page of the communication, seemed to further close the door on all possibility of him passing the manuscript for publication.

   However, I had thought that was what publication was for -- to allow this kind of thing on the table for open discussion.

   As a result, all that was left was to open this to the public and add my response to his objections using the Cooperstock article.  In Chaffin's response to me, which he does not want in full on the web, he used an equation given in the Cooperstock article and, using that equation, showed that the cosmological expansion correction was greater than the gravitational one between clusters of galaxies.  But the equation Chaffin used is the exact one which Cooperstock et al pointed out later in the paper was not valid over large distances.  Cooperstock et al pointed out "In this case, the approximation used in this paper becomes invalid [over large distances.]"  They finalise by saying, "The magnitude of the effect [of the expansion] is essentially negligible for local systems, even at the scale of galactic clusters."


*     *     *     *     *

Setterfield's Response

   In his rejection of this paper, Dr. Chaffin states, "I believe I have discovered a mistake in the logic concerning the comparison of the cosmological expansion to the gravitational binding effects.  Once one realizes that this mistake is there, then I would think the author would wish to withdraw the paper, but in any case the editor would [be] obliged to reject the manuscript."  This "mistake in logic" concerns the effects of cosmological expansion.  In this current paper, it was pointed out that one of the explanations for the redshift was that, according to the Friedmann equations, the wavelengths of light were being stretched in transit as the fabric of space expanded.  The logic is that if such things as small as the wavelengths of light are being stretched as the fabric of space expands, so also must things like atoms, our measuring devices, star systems, and galaxies.  However, there are a number of problems that this introduces as discussed in the body of the paper.  The usual way to overcome these problems and save the existing paradigm is to claim that expansion only occurs between clusters of galaxies.  The explanation is that expansion does not occur on smaller scales due solely to the effect of gravity.  This is the position taken by a number of theorists.

   However, the problem is not nearly as settled as many believe. Cooperstock, Faraoni and Vollick acknowledged in 1998 "The recurrent attention paid to this issue indicates that to this point a definitive answer is still lacking."  They point out that it was first raised by McVittie in 1933, by Jarnefelt in 1940 and 1942, then Pachner in 1963, Dicke and Peebles in 1964, plus both Callan et al. and Irvine in 1965 with Noerdlinger and Petrosian in 1971 and so on until the discussion conducted in 1995 by Anderson.  In order to assist a decision on this matter, an equivalent system was then studied in 1996 by Bonnor who examined the distribution of pressureless charged dust in equilibrium between electrical repulsion and gravitational attraction.  He concluded that the lesser systems participated in universal expansion despite gravitational acceleration.  This led on to an admission by Cooperstock, Faraoni and Vollick in 1998 that the Friedmann equations do not dictate a scale for expansion, "and in principle, it could be present at the smallest practical scale as a real...expansion and observable in principle. ...Thus in this debate we are in agreement...that it is most reasonable to assume that the expansion does indeed proceed at all scales." However, if cosmologists accept these conclusions that atoms, stars and galaxies partake of universal expansion, Sumner's unacceptable result of a blue-shift of light from these atoms necessarily follows as explained in this current paper.

   It is against this background that the alleged "mistake in logic" comes in.  This current paper notes that the gravitational force between the clusters is 1010 times greater than the force exerted on the Sun by the Milky Way.  Dr. Chaffin concedes this is correct.  Consequently, one would expect that if the cosmological expansion force is not strong enough to overcome the gravitational force on the Sun by the Milky Way system, it will have even less effect on clusters of galaxies, even when the distance factor over which it operates is taken into account.  In other words, the space between the clusters of galaxies should not expand either.  But Dr. Chaffin (in a separate note he included in his letter of rejection) states that this "is like comparing apples and oranges since the mass of a galactic cluster is not the same as the mass of either the Sun or of a galaxy.  A more relevant quantity is the magnitude of the accelerations caused by the gravitational binding compared to that caused by cosmic expansion."  It is here that Dr. Chaffin calls attention to the paper by Cooperstock, Faraoni and Vollick, for which he is thanked.  This calculates both the gravitational acceleration of the Sun by our Galaxy, and the acceleration between clusters of galaxies and compares them with the acceleration of the cosmological expansion.  In this case, the cosmological acceleration is largest for the clusters of galaxies.  The conclusion drawn from this by Dr. Chaffin was that only the space between clusters of galaxies would expand under these conditions in contradiction to the calculation performed in the current paper, therefore there exists a "mistake in logic."

   But this is probably the wrong conclusion for Dr. Chaffin to draw for two reasons.  First, in their 'Discussion and Conclusions' section, Cooperstock, Faraoni and Vollick examine the numerical results obtained for the magnitude of the correction to the acceleration of objects subject to external forces.  They specifically conclude: "The numerical estimates obtained in Sec. 3 suggest that the correction is extremely small and unobservable for galaxy clusters, galaxies and the solar system, and negligible for smaller systems such as stars and even more so for molecules and atoms."  The actual figures tell the story.  For the best case, that is with galaxy clusters, the gravitational acceleration is about 8 x 10-11 metres per second per second, while the acceleration due to cosmological expansion is merely 5.6 x 10-18 metres per second per second.  Thus, as Cooperstock, Faraoni and Vollick state, the correction is extremely small and unobservable.  These figures indicate that the gravitational acceleration for galaxy clusters is 7 orders of magnitude greater than that of the cosmological acceleration, a point that Cooperstock, Faraoni and Vollick actually make.  Despite the fact that it is the best result obtainable, they also state "it is still nevertheless essentially ignorable."  In other words this calculation suggests that even when comparing the gravitational and cosmological accelerations, not only do the stars and galaxies not expand, it seems that even the space between clusters does not expand either.  This does not contradict the conclusion reached in the current paper using the forces argument that if the atoms, stars, and galaxies do not expand, neither does the space between the clusters.  So Dr. Chaffin appears to have come to the wrong conclusion.

   There is a second reason why this may be the wrong conclusion for Dr. Chaffin to draw.  Cooperstock, Faraoni and Vollick try to overcome their problem with the magnitude of the expansion effect by doing a different calculation using the local equations of motion applied to two bodies under Newtonian conditions.  Here, the cumulative effect of cosmological expansion on the Sun-Earth system is essentially negligible.  However, it becomes increasingly significant for larger systems over the lifetime of the cosmos.  But there is then a problem, because Cooperstock, Faraoni and Vollick admit: "In this case, the approximation used in this paper becomes invalid."  They finalise by saying: "As a conclusion, it is reasonable to assume that the expansion of the universe affects all scales, but the magnitude of the effect is essentially negligible for local systems, even at the scale of galactic clusters."  In other words, if the gravitational binding argument is accepted at all, it leads to the conclusion that the expansion effect "is essentially negligible" even between clusters of galaxies, so there will never be any observational proof for cosmological expansion.  In other words, it becomes an unfalsifiable theory.  In this case, the weight of observational evidence presented in this current paper assumes a greater priority, and it all points in one specific direction.  Under these circumstances, Dr Chaffin's rejection of this current paper on the basis of a "mistake in logic" seems unduly harsh.

   Dr. Chaffin also asked in his additionally enclosed note "Would [cosmic expansion] become predominate at larger scales? I think the answer is yes. To say otherwise is to say that Friedmann and Lemaitre did their calculations wrong, and that many others who repeated these calculations, such as Landau & Lifshitz, 'Classical Theory of Fields', got the arithmetic wrong."  Dr. Chaffin was kind enough to supply some relevant pages there.  However, his comments seem undiscerning.  Far from showing that cosmic expansion became predominate at large scales, Cooperstock, Faraoni and Vollick show that even at the scale of clusters of galaxies it is still "essentially negligible."  Dr. Chaffin then makes the accusation that "To say otherwise is to say that Friedmann and Lemaitre did their calculations wrong,"  This is incorrect.  Cooperstock, Faraoni and Vollick show that the cosmic expansion does not predominate in the way Dr. Chaffin expected, but their calculations are not therefore wrong.  They merely show that the effect that Friedmann and Lemaitre theoretically envisioned was not behaving in the way they assumed.

   However, there exists one final problem.  Dr. Chaffin sent me the first three pages of the Cooperstock, Faraoni and Vollick article, upon which he based his rejection.  I initially accepted this gratuity as an act of kindness, and was grateful.  However, when the full article was obtained from the web, it became apparent that the other pages in the article largely counteract Dr. Chaffin's reasons for rejection as outlined above.  Consequently, I am left to wonder at the rationale behind both his rejection of this current paper, and his forwarding of only three pages.

Barry Setterfield ­ 23rd August 2002. Changes August 25, 2002.


Cooperstock, F. I., Faraoni, V., Vollick, D. N. 1998, Astrophys. J. 503:61

References supplied by Cooperstock, Faraoni, and Vollick:
Anderson, J. L. 1995, Phys Rev. Lett. 75, 3602.
Bonnor, W. B. 1996, Mon. Not. Roy. Ast. Soc 282, 1467.
Callan, C. et al. 1965, Am. J. Phys. 33, 105.
Dicke, R. H. and Peebles, P. J. E. 1964, Phys. Rev. Lett. 12, 435.
Irvine, W. M. 1965, Ann. Phys. (NY) 32, 322.
Jarnefelt, G. 1940, Ann. Acad. Sci. Fenn. Series A, 55, Paper 3.
Jarnefelt, G. 1942. Ann. Acad. Sci. Fenn. Series A, 1, Paper 12.
McVittie, G. C. 1933, Mon. Not. Roy. Ast. Soc. 93, 325.
Noerdlinger, P. D. and Petrosian, V. 1971, Astrophys. J. 168, 1.
Pachner, J. 1963, Phys. Rev. 132, 1837.

NOTE: an interesting part of the Discussion page on stellar brightness, which is often used as an indication of an expanding universe is here.