|
By Barry Setterfield
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. At the end of the page is an email address
where comments regarding this article, the CRSQ letter, and the
Setterfield response are welcomed. Many of these responses will
be posted here along with Setterfield's responses to them.
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
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 [Couderc, 1960 p.10, 91; Audouze
& Israel, 1985 p.382, 356]
z = Dl/l
(1)
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 [Audouze & Israel, p.382]
r = cz/H = v/H
(4)
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 z by lightspeed c. 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 modelling.
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 travelled 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: 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
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. 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 also holds good. 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 c
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.
References.
Arp, H. 1987. Quasars, Redshifts
and Controversies. Interstellar Media, Berkeley,
California
___. 1998. Seeing Red: Redshifts, Cosmology and Academic Science.
Apeiron,
Montreal, Canada.
Arp & Sulentic, 1985. Astrophysical Journal 291:88
Audouze & Israel, 1985. Cambridge Atlas of Astronomy.
Cambridge University Press.
Barnett, S. 1990. Nature, 344:289.
Boyer, T. H. 1985. Scientific American,
pp.70-78, August.
Corliss, W. R. 1996. Science Frontiers, No. 105: May-June.
Couderc, 1960. The Wider Universe. Translated by Martin
Davidson. Hutchinson &
Co. Ltd., London.
Davies, P. C. W. 2001. New Scientist, pp.30-34, 3 November.
De la Pena, L. 1983 in Stochastic Processes Applied to Physics
and other Related
Fields, p.428, B. Gomez et al. eds., World Scientific
Publishing Co. Pty. Ltd.,
Singapore.
Fisher, J. R. & Tully, R. B. 1981. Astrophysical Journal
Supplement 47:139.
Friedmann, A. 1922. Zeitschrift fur Physik 10:377; For
English translation see
reference below under Lang and Gingerich, pp. 838-843.
Gentry, R. V. 2001a. arXiv:physics/0102092 28 Feb. Part 1.
___. 2001b. arXiv:physics/0102094 28 Feb. Part 3.
___. 2001c. arXiv:physics/0102096 28 Feb. Part 5.
Harrison, E. R. 1981. Cosmology, The Science of the Universe.
Cambridge University
Press.
Hoyle, F. 1956. Frontiers of Astronomy. William Heinemann
Ltd., London.
Hubble, E. P. 1929. Proceedings of the National Academy of
Sciences 15:168.
___. 1936. The Realm of the Nebulae. Yale University Press.
Landsberg, P. T. & Evans, D. A. 1979, Mathematical Cosmology,
Clarendon Press, Oxford.
Lang, K. R. & Gingerich, O. (editors) 1979. A Sourcebook
in Astronomy and
Astrophysics. Harvard University Press.
Latorre, J. I., Pascual, P. and Tarrach, R. 1995. Nuclear
Physics B 437:60.
Lemaitre, G. 1927. Annales Societe Scientifique Bruxelles A47:49.
For English
translation see reference above under Lang and Gingerich, pp.844-848.
Lewis, B. M. 1987. Observatory, 107:201.
Longair, M. S. 1995. The Physics of Background Radiation.
In Binggeli, B. and
Buser, R. (editors) The Deep Universe. Springer, Berlin.
Matthews, R. 1995. New Scientist, p.30, 25th February.
Matthews, R. 1996. Science, 271:759.
Milonni, P. W., Cook, R. J., and Goggin, M. E., 1988. Phys
Rev A 38:1621.
Misner, C. W., Thorne, K. S. & Wheeler, J. A. 1997. Gravitation.
W. H. Freeman &
Company, USA.
Narliker, J. and Arp, H. 1993. Astrophysical Journal, 405:51.
Noerdlinger, P. D. and Petrosian, V. 1971, Astrophysical Journal,
168:1.
Norman, T. and Setterfield, B. 1987. The Atomic Constants, Light
and Time,
Research Report for SRI International & Flinders University,
pp.1-88.
Northrup, B. E. 2001. e-mail, 8 Sept. 12:20 pm.
Novikov, I. D. 1983. Evolution of the Universe. Cambridge
University Press.
Parker, B. 1993. The Vindication of the Big Bang. Plenum
Press.
Peacock, J. A. 1999. Cosmological Physics. Cambridge University
Press.
Puthoff, H. E. 1987. Physical Review D, 35:3266.
Schewe, P. F. & Stein, B. 1992a. American Institute of Physics,
Physics News
Update, No.61, January 3.
___. 1992b. American Institute of Physics, Physics News Update,
No. 104, Nov. 25.
Schmidt, M. 1972. Astrophysical Journal 176:273-287
Sumner, W. Q. 1994. Astrophysical Journal, 429:491.
Tifft, W. G. 1977. Astrophysical Journal, 211:31.
___. 1979. Astrophysical Journal, 233:799.
___. 1991. Astrophysical Journal, 382:396.
Tifft, W. G. & Cocke, W. J. 1984. Astrophysical Journal,
287:492.
Troitskii, V. S., 1987. Astrophysics and Space Science,
139:389.
Van Flandern, T. C., 1984, in Precision Measurements and Fundamental
Constants II, National Bureau of Standards Special Publication
617, B. N. Taylor & W. D. Phillips eds.
Weinberg, S. 1972. Gravitation and Cosmology. John Wiley
& Sons.
___. 1983. The First Three Minutes. Flamingo edition,
Fontana Paperbacks, London.
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 myself 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."
The full response to Chaffin's objections using this article follows.
RESPONSE TO DR. CHAFFIN'S
CRITICISM
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.
REFERENCE:
Cooperstock, F. I., Faraoni, V.,
Vollick, D. N. 1998, Astrophys. J. 503:61
Available on the web at:
http://arxiv.org/PS_cache/astro-ph/pdf/9803/9803097.pdf
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.
|