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
Abstract 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. Introduction 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
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 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 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 Examining Space-Time Expansion 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 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 The Quantized Redshift 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 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 The Stability Of A Static Universe 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 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: http://www.orionfdn.org. 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 Zero-Point Energy And Atomic
Stability 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 ZPE And Lightspeed 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" The Testimony Of The Bible 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:
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:
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: Isaiah 40:22. Translated in a
past time context by the LXX. In Hebrew it reads: 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: Isaiah 45:12. Translated in a
past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB. In
Hebrew it reads: Isaiah 48:13. Translated in a
past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB. Isaiah 51:13. Translated in a
past time context by the LXX, KJV, NAS, NIV, NKJ, RSV, TLB. 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: 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:
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. Arp, H. 1987. Quasars, Redshifts
and Controversies. Interstellar Media, Berkeley, * * * * * 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."
* * * * * 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. REFERENCE: Cooperstock, F. I., Faraoni, V.,
Vollick, D. N. 1998, Astrophys. J. 503:61 NOTE: an interesting part of the Discussion page on stellar brightness, which is often used as an indication of an expanding universe is here.
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