#
Is there any evidence for a change in *c*?

## Implications for creationist cosmology

Recent astronomical observations of spectral lines in starlight from distant quasars
suggest that the fine structure constant was lower in the past. Astrophysicists
have claimed that this means the speed of light (*c*) may have been higher
in the early universe. Observations by Webb may be interpreted in this way back
to redshift *z* = 3.5, assuming the usual long-age evolutionary cosmology.
Creationist cosmologists, however, place a different interpretation on the timescales
relating to these reported redshift values. As a result, a model is explored where
c was enormously greater at Creation. From the moment of Creation on, *c *
very rapidly decreased. By redshift *z* = 1 it had reached its current value
except for very small residual changes. The model however doesn’t provide
an explanation to the starlight-travel-time issue in creationist cosmology. Nor
does it provide a mechanism to explain rapid stellar aging in the early universe,
which could account for the deficit of old dwarf stars in nearby galaxies in Humphreys’
model. More significantly, the model clearly shows that no variable-speed-of-light
model consistent with current observations on the fine structure constant can explain
a young universe.

Creationists have been concerned about the issue of the time of flight of light
across the vast distances of the visible universe in the 6,000 years since the Creation.^{1,2}
Specifically the Humphreys’ model^{1} attempts to answer this problem.
It seems that one difficulty facing that model is the observation of apparently
old stellar objects such as white dwarf stars in the halos of galaxies near our
own. In Humphreys’ model nearby stars would have aged very little compared
to stars on the edge of the universe. Therefore we shouldn’t see any ‘old’
stars nearby. This objection may be answered by rejecting models of stellar evolution
that are all based on million-year time scales. But is there an alternative explanation?

In this paper I present the hypothesis that if the speed of light (*c*) was
shown to decrease over cosmological time, then it is also possible that the speed
of light was enormously greater at Creation. The decrease in the value of c may
have resulted from changes in values of some parameters or ‘constants’
related to the fabric of space itself. In this model, the process causing the decrease
ceased long ago but the effects may still be observed in astronomical data at cosmological
distances. The process described here may have gone hand-in-hand with a very rapid
expansion of space, something like the ‘inflation’ period invoked by
the big-bang cosmologists. Note that these very same evolutionary cosmologists are
abandoning inflation for a superluminal or variable-speed-of-light model with c
as much as a billion times its current value. The question can then be asked: Does
such a model explain the light travel time problem or explain the abundance of ‘old’
dwarf stars in galaxies that are in our local galactic neighbourhood? I will attempt
to answer these questions.

## The speed of light c, the limiting constant of the universe

The two-way speed of light, usually specified by the letter *c*, is the quantity
measured in all tests of Relativity and is the quantity under consideration in this
paper. It has been described as the limiting constant for all causally related events
in the universe and is related to two important parameters by

where ε_{0} and µ_{0} are the permittivity and permeability
of free space, respectively. The permittivity and permeability of free space really
describe properties of the fabric of space that permit wave propagation, something
analogous to the stiffness of a medium to sound propagation. Therefore, the constant
c has been called Einstein’s constant as it imposes a limit on all forms of
energy propagation in the universe.

## Drift in dimensionless constants

Since Dirac conjectured about the ratio of certain constants varying on the timescale
of the age of the universe, the search has been on to measure variation in the three
main contenders. They are the electron to proton mass ratio (*m*_{e}
*/m*_{p} ), the fine structure constant (*α)*, and the
quantity *α*^{2} *γ*_{p} (*m*_{e}
*/m*_{p} ), where *γ*_{p} is the proton gyromagnetic
ratio. Generally the search has been for temporal variation in these constants^{3–6} and can be divided into cosmological
observations and modern atomic clock measurements. Variation of these non-gravitational
constants is forbidden in General Relativity and other metric theories of gravitation.
In those theories gravitation is described as a result of the geometry of space-time.
String theories, however, suppose that, as the universe expanded over time, compact
(extra) dimensions have unraveled a little, causing ‘constants’ as seen
in our 3-dimensional space to vary.^{7}

Cosmological observations have set upper bounds on these ratios generally back to
about a redshift, *z* = 3. Spectroscopic observations of molecular hydrogen
in quasar absorption-line systems has set a limit on *m*_{e} */m*_{p}
= *y* of *δy/y* ≤ 8 × 10^{–5} at the 95% confidence limit, back to *z*
= 2.811.^{8} The ratio of the
frequencies of the hyperfine 21 cm absorption transition of neutral hydrogen and
an optical resonance transition is the dimensionless constant *α*^{2}
*γ*_{p} (*m*_{e} */m*_{p} ) =
*x*. Lennox
used absorption-line data from a system involving a quasar at a redshift *z*
= 1.77644 to set an upper limit of *δx/x* ≤ 7 × 10^{–6}
at the 95% confidence limit.^{4}

## Fine structure constant

There is experimental evidence^{6} suggesting that the fine structure ‘constant’
(*α*) has increased over the lifetime of the observed universe by about
1 part in 100,000. It is related by

where e is the charge on the electron and (pronounced ‘h-bar’) is Planck’s
constant divided by 2π. The current value of the fine structure ‘constant’
*α*_{0} = 1/137.0359895. This dimensionless ‘constant’
specifies the extent of the splitting of some spectral lines resulting from the
fine structure of energy levels in atoms caused by spin-orbit coupling. The starlight
from distant quasars intersects line-of-sight absorption systems and the spectral
lines of certain elements are compared to laboratory spectra of specific ions. *New
Scientist* recently reported Webb’s work stating in regard to this
discovery ‘The ground is shifting under our feet. Fundamental properties of
the universe are changing, and physicists can’t explain how or why. Now researchers
say an as yet undiscovered fifth force could be behind these mysterious changes’.^{9} So it could be interpreted
in two ways: either the universe has extra dimensions suggested by Kaluza-Klein
and Superstring theories or ‘if the universe is four dimensional then a fifth
force is the only thing capable of triggering these changes’.^{9}
This new force would be repelling and about 100,000 fainter than gravity, it is
claimed. They report that ‘light may be slowing down’. In another article
entitled ‘Light may have slowed down’, the on-line Newscientist.com
quotes John Webb as saying ‘If it holds up, it surely has to be one of the
more important discoveries in fundamental physics’.^{10}

Electronic transitions between excitation states in alkaline ions are the usual
choice to measure the fine structure constant in cosmological sources. Ionized atoms
of elements like Ni, Cr, Zn, Al, Si, Mg, Fe etc. are observed and identified in
gas/dust clouds in the interstellar medium by their spectral characteristic lines.
The separation between the wavelength *λ*_{1} of the ^{2}S_{1/2} *→* ^{2}P_{3/2} transition and the
wavelength *λ*_{2} of the ^{2}S_{1/2} *→*
^{2}P_{1/2} transition is proportional to *α*^{2}
to lowest order in *α*. Therefore after defining the mean wavelength
we can write

Any change in *α* will result in a change in the mean separation of
the doublets (pairs of spectral lines) in high-*z* quasar absorption systems.
From Si IV doublets, observed with the Keck HIRES spectrograph, Lennox^{4}
(in 1995) was able to set a limit *δα*/*α* <
± 3.5 × 10^{–4} at *z* = 2.78. The main uncertainty
in the measurement comes from the uncertainty in the laboratory determination of
the doublet separation. Webb (in 1999) was able to achieve greatly improved sensitivities
by applying a multiplet^{11}
technique to the relativistic fine-structure splitting of certain doublets. He made
further gain by comparing the wavelengths of different species. Still the limiting
accuracy was due to an uncertainty in the laboratory reference. For example, the
limit *δα*/*α* ~ 10^{–5} results from uncertainty
in the laboratory frequency of ~ 0.03 cm^{–1} (unit: 1 cm^{–1} =
30 GHz), which is typical for accurately known lines.^{5} In Webb’s
2001 paper, he combined three large data sets and two 21 cm and mm absorption systems,
resulting in four independent samples producing 72 individual estimates of *δα/α*.
Each sample showed *α* smaller in the past and the optical sample shows
a 4*σ* deviation. Rigorous statistical analyses were applied to the
data sets, resulting in *δα/α* = −0.72 ± 0.18
× 10^{–5} over the redshift range 0.5 < *z* < 3.5. The
most recent analysis of the cosmic microwave background (CMB)^{12} taken from BOOMERANG and MAXIMA data also suggest
*α* may have been smaller in the past. However I would not apply too
much weight to the interpretation placed on that data as it is much more open to
alternative interpretation than the fine structure constant data described here.^{13}

It is believed it may be possible to measure the current ‘drift’ in
*α* with carefully constructed modern laboratory experiments. Prestage^{3}
describes a test by comparisons of the rates of atomic clocks based on the hyperfine
transitions in alkali atoms with different atomic number Z. Hydrogen-maser^{14} , cesium and Hg^{+}
ion clocks have different dependence on *α* via relativistic contributions
of order (Z*α*)^{2} . Prestage set a limit on the fractional
temporal change^{15} in *α
*of *α/α* ≤ 3.7 × 10^{–14} /yr using
a comparison of H-maser and a Hg^{+} ion clock. Further tests are planned
using the world’s best cesium and rubidium atomic fountain clocks^{16} and another using monolithic crystal resonators.^{17}

## Effect on the speed of light

From (1) and (2) it follows that

The term on the right of (4) is called the impedance of free space and currently
evaluates to approximately 377 ohms. It is something like a resistance to electromagnetic
wave propagation. If the data for an increase of *α* over cosmological
time proves to be true, it could imply that this parameter too has increased. The
data from Webb^{6} have been plotted in Figure 1. From (4) it can be seen
that for an increase in *α*, the impedance of free space would decrease
provided the electron charge and Planck’s constant remained constant. By making
assumptions of cosmological parameters and choosing a value for the Hubble constant
*H*_{0} = 68 km s^{–1} Mpc^{–1} , Webb claims
that *α* has changed by 1 part in 10^{5} over the past 12 billion
years. However, the same data indicate the ‘drift’ now has become very
small in our galactic neighborhood at least. From atomic clock experiments the local
drift in *α* it is expected to be less than 1 part in 10^{16}
per day. This is at the very limit of current experimental precision.

I explore in this paper a creationist model where the increase in the fine structure
constant is related to a relaxation mechanism of the expansion of space. Hence the
expected functional form for the fractional change in *α* is exponential
and may be expressed

where *z* is the redshift due to the expansion of space. This was fit to
Webb’s data and is shown in Figure 1, where *α* = 3.895 ±
0.917 × 10^{–6} was evaluated from the fit. This is a reasonable expectation
for this model. The fit is consistent with an annual change less than 10^{–14}
at the present epoch
(*z* ≤ 10^{–10} ) and is good back to when the universe was
a quarter its current size. As space expanded, *α*(*z*) increased
from a zero value (at large *z*) to its current value *α*_{0}
(at *z* = 0). A reduced spacing between spectral lines would be observed
with increasing *z*. From (4), it follows that an increase in *α*
as *z* decreases would also result in an increase in the impedance of free
space and a decrease in c. Therefore these parameters respond also to the relaxation
process, which could be described by String theorists as an unravelling of extra
spatial dimensions.

Assuming the change in *α* is totally due to a change in *c*,
then from (2) and (5) we can write

where *c*_{0} is the current value of the speed of light at
*z* = 0. The form of the dependence on *z* is plotted in Figure 2.
Note the asymptote at approximately *z* = 2 ×10^{5}. Due to
the uncertainties arising from the small domain of the data this exercise is only
meant to give us a functional form of this dependence.

The expansion redshift is the redshift that according to General Relativity results from the stretching of space itself and is usually defined by

where *R*_{0} is the scale factor of the universe now, and *R
*at some time in the past. According to the Friedmann-Lemaître solution
of Einstein’s field equations, the expansion redshift only depends on the
scale factor of the universe at the time the light was emitted and the time it was
received. The fabric of space itself stretches between emission and reception. This
is what is usually referred to as Hubble flow. The expansion redshift doesn’t
depend on the rate of this expansion. Other types of redshift are Doppler shift,
due to the absolute motion of the source itself with respect to space, and gravitational
redshift, which results from the pull of the gravitational field on a photon at
the moment of emission from the surface of a star. The latter two forms of redshift
are not involved in these data, assuming careful measurements were made to separate
out any such effects. Therefore the farther we look back in space the greater *z*
and the further into the past. For example, if we look at light coming from a source,
emitted at the time when the universe was half its current size, 1 + *z*
= 2, or *z* = 1. Because the speed of light is finite, the redshifts we observe
on Earth have time delays built in. Therefore, *z* more correctly describes
some convolution of distance with time.

The location of the source in space is determined by the expansion redshift (*z*)
measured by a comparison of the absolute shift of a group of spectral lines as compared
to a laboratory reference. The separation between or the splitting of certain spectral
lines as compared to the laboratory reference determines the value of *α*
at that value of *z*. Then using (2) the value for c locally at redshift
*z* is determined. Now at any time in the past, or at a specific value of
*z* the fractional scale factor is 1/(1+*z*). In other words, the
greater the value of *z*, the smaller the size of the universe. This means
the distance between two points was smaller in the past. In young universe creationist
cosmology, it is assumed the larger *z* is, the closer the epoch is to Creation
week and the beginning of time. For example in the Humphreys’ model, the universe
started as a ball of the size of about a light-year in radius. Now if the universe
is 10^{10} light-years in radius, the origin was at about *z* = 10^{10}.

In understanding this data it is best to divorce the redshift values from any universal
time scale. The Hubble parameter (*H*_{0} ), the space curvature
parameter (*k* =–1,0 or +1) and the universal deceleration parameter
(*q*_{0} ) predetermine the distance scale of the universe. These
parameters, however, are not well known and even less is known about their dependence
on *z*. The type of cosmological model assumed in turn determines the timescale
based on constant c, or in other words, how R evolves with time. The chosen model
includes the form of the space-time metric and values for the cosmological constant
(*Λ*), the amount of dark matter or dark energy (*Ω*_{Λ}
) and the baryonic mass (*Ω*_{M} ), which can only be assumed
(see Hartnett^{13} ).

For small *z*, the Hubble relation is usually written for a flat space (*k*
= 0) cosmology

where *v* is the light source recession velocity and r the radial distance
to the source. This is the relation Edwin Hubble originally fitted to his data.
The value of *H*_{0} is the asymptotic value of the normalised rate
of change of the expansion of the universe, or at any value of *z*. For all
cosmologies, *H*(*z*) approaches *H*_{0} for *z≤*
0.2 (see Hoyle *et al*^{18}
). The Hubble relation (8) has been extremely well established by observational
evidence out to *z* = 0.2. It follows from (8) that we would measure a recession
velocity (v) for a galaxy at *z* = 1 equal to the speed of light. Therefore
any creationist model must account for (8) valid to *z* = 0.2 at least. Creationist
models need to solve the issue of the correct time calibration with *z*,
which obviously cannot be the billion year scale that evolutionist determine from
(8), because from a simple reading of Genesis the beginning was about 6 thousand
years ago as measured by Earth clocks. The only creationist model, to my knowledge,
which has attempted to do this, is Humphreys’ model.

In order to evaluate if (6) could explain the light-travel-time problem in a recent-Creation
cosmology, it is important to calculate the time for a photon to travel across the
universe as measured by Earth clocks. Assuming the Hubble relation to be a correct
conversion for distance, it follows from (8) and constant c that the time of flight
of a photon emitted with redshift *z*, is

for small *z*. For all *z*, the general form of this equation must
be used. For simplicity, and for a comparison with evolutionary cosmology, I have
chosen the Hubble distance relation in a flat universe,

which approximates to (8) for small *z*. Now, after dividing *r* by
*c*(*z*) from (6) and integrating out to redshift *z*, the
look-back time to *z* is

The result of (11) has been expressed as a percentage of the look-back time with
constant c (see Figure 3). *It is obvious that this doesn’t explain the light
travel time problem*.^{19}
Though the increase in *c* is very great near *z* = 10^{5}
it does not reduce the transit times of light across the universe to six thousand
years. In fact, any creationist cosmology based on a higher value of the two-way
speed of light cannot, except by fantasizing about incredibly higher values of c
in the very recent past. Such ideas are not based on observational evidence.

From (2) and Webb’s data, it is possible to envisage an early universe where
the speed of light decreased enormously to its present value. I suggest that the
data present *the possibility*, that early in the Creation week, enormous
changes occurred that are now only seen as a very small residual ‘drift’
in dimensionless constants. I am not suggesting any connection to the work of Setterfield
and Norman (*c*-decay). The astronomical measurements of the fine structure
constant show that any significant changes to the value of *c* occurred in
the very early universe and if any ‘drift’ remains today it is extremely
small, well below the resolution of all early measurements of the speed of light.
Only in the last few years have atomic clocks achieved the precision and accuracy
to make such measurements.

The ‘light-year’ in this paper is a fixed length based on approximately
3 × 10^{8} meter/second × 365.25 days × 24 hours ×
60 minutes × 60 seconds, where meters and seconds are defined in the Earth
frame of reference. In fact, on 20 October 1983, the General Conference (CGPM),
as recommended by the International Committee on Weights and Measures (CIPM), formally
redefined the meter so as to make the speed of light an exact unmeasurable quantity,
determined by convention. The value of c therefore has been defined to be 2.99792458
×10^{8} ms^{–1} . As a result, now it all depends on the ‘second’.
The second in turn is determined from a certain frequency of light from a specific
transition in an excited cesium atom. This brings it back to the fine structure
constant and the energy of hyperfine transitions.

## A more rapid star formation rate?

The product *ε*_{0} *µ*_{0}
more correctly relates matter and energy in Einstein’s famous equation

If we suppose total energy (*E*) is conserved, then the total energy of all
matter is described by (12). As a consequence of (12), the mass of any body of matter
would rapidly increase with decreasing *c*. This meant a rapid ‘switching
on’ of stars as they gained mass and as the accompanying nuclear ‘fires’
started from increasing gravitational compression. By the time *c *slowed
to the current value the mass of the stars would be approximately as we currently
observe. Because luminosity and hence age is directly related to the mass of a star,
*the model does not provide a rapid aging mechanism for stars in any region of the
universe and as a result does not provide an answer for the abundance of white dwarfs
stars nearby in a Humphreys’ type cosmology. *

## The light-travel-time problem explained?

Recent astronomical evidence suggests that the speed of light *c* may have
changed over cosmological time. Though variation in the value of *c *would
violate General and Special Relativity, modern experimental evidence as yet cannot
decisively exclude the possibility. A ‘drift’ may be observed in some
dimensionless ‘constants’ of physics that contain *c*, because
*c* itself, as a result of the way it was conveniently defined in 1983, is
truly a constant. I have proposed a model with *c* enormously greater in
the past, particularly during Creation week, yet consistent with recent observational
data. Such a model, however, cannot provide an explanation for the light-travel-time
problem in creationist cosmology. In fact, a significant point is made that no variable-speed-of-light
model consistent with current observations can explain a young universe.

### References

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and variation of the fine structure constant,
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evolution of dimensionless physical constants over cosmological time,
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and Barrow, J.D., Search for time variation of the fine structure constant,
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- A multiplet technique compares a number of doublet lines in an atomic species. The technique significantly reduces systematic errors. Return to text.
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*a*in the cosmic microwave background,*Phys. Rev.D***62**(123508), 2000. Return to text. - Hartnett, J.G., Recent cosmic
microwave background data supports creationist cosmologies,
*Journal of Creation***15**(1):8–12, 2001. Return to text. - A maser is a microwave frequency laser. MASER means microwave amplification by stimulated emission of radiation. A hydrogen maser is built around a resonant cavity filled with hydrogen gas. When stimulated at about 1.4 GHz maser activity is observed. Once atoms enter the resonant cavity, they find other atoms radiating and they fall in step with each other. They ‘start to talk to each other’ and echo what they hear. This produces a highly coherent oscillation. Because the frequency of this oscillation is determined by the atomic transition (the 21 cm line) it is called an atomic clock. Return to text.
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*Rubidium and cesium in one*fountain: A new tool for the search of the time variation of the fine structure constant, in*2001 IEEE International Frequency Control Symposium*, Seattle, pp. 22–24, 2001. Return to text. - Braxmaier, C., Pradl, O., Muller, H., Peters, A. and Mlynek,
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*a*and me/mpusing monolithic resonators,*Phys. Rev. D***64**:042001, 2001. Return to text. - Hoyle, F., Burbidge, G. and Narlikar, J. V.,
*A different approach to*cosmology:*From a static universe through the big bang towards reality*Cambridge University Press, Cambridge, UK, 2000. Return to text. - If the fractional change of 1/
*e*_{0}in (4) was not small in comparison to the change in the impedance of free space then an additional exponent may be added to (6). That is if*e*_{0}/*e*_{0}(*z*) ~ ebz, then the value of c was even greater in the past. For comparison, if b = 10, the value of c would be 20,000 times greater at*z*= 1and the look back time reduced to 15%. Still this is a billion years and does not solve the problem. Return to text.