The Decaying Speed of Light

Summary

• In 1987 Trevor Norman and Barry Setterfield tabulated 163 measurements of the speed of light made between 1675 and 1983 and argued that they show a real decline.  If the speed of light was once enormously higher, light from a galaxy a billion light years away could reach Earth in days.  For a few years this was the most popular young-earth answer to the distant-starlight problem, and its appeal was that it solved the problem with a physical mechanism instead of a miracle.

• The argument was destroyed a few months later by a creationist using Setterfield's own numbers.  Gerald Aardsma was head of the Astro/Geophysics Department at the Institute for Creation Research graduate school.  Norman and Setterfield had fitted a straight line through all 163 points giving every point the same weight, even though the quoted uncertainties "range from ± 20,000 km/s to ± 0.0003 km/s."  Weighting properly, Aardsma got a decay of 0.0000140 ± 0.0000596 km/s per year — zero, within the error.

• Most of the apparent trend came from a single seventeenth-century point, and the report handled that point inconsistently.  Norman and Setterfield's Table 1 lists Rømer's 1675 value as 307,600 km/s — a modern correction of his raw observation — and Cassini's 1693 value as 352,000 km/s, which their own footnote calls "Uncorrected observations by Cassini."  Cassini's raw number is 17.4 % above the modern speed of light.  Rømer's raw number is 24.4 % below it.  Correcting one and not the other manufactured the slope.

• Three more creationists reached the same verdict in the same year, in the same journal.  The Creation Research Society Quarterly ran a two-part "Minisymposium on the Speed of Light" in June and September 1988.  D. Russell Humphreys, a physicist at Sandia National Laboratories who wanted the result to be true, wrote that the book "is misleading" and set four minimum standards for the analysis, none of which it met.  Roy Holt showed that the model's own scaling laws imply a twelve-hour day in AD 1000.  Robert Brown recomputed every significance claim in the report and rejected each one.

• In 1992 a creationist physicist showed that the report's biggest number was not real.  Setterfield's 1675 Rømer value was a 2.6 %-high figure obtained by private letter from Bernard Goldstein.  Eugene Chaffin redid the seventeenth-century orbital mechanics from published eclipse timings, using his own 1988–1991 observations of Io as a control, and found "the 2.6% was not real, and that any real effect that might be present must be smaller than about 1%, at most."

• Even a real trend in the numbers would not have meant what the argument needed it to mean.  The speed of light is a dimensional constant:  its numerical value depends on which units are chosen for length and time.  "c was different" is therefore not, by itself, a claim about the world.  Michael Duff:  the time variation of dimensional constants "has no operational meaning."  Dirac said the same thing decades earlier.  The physically meaningful question is whether a dimensionless number has changed.

• The relevant dimensionless number is the fine-structure constant, and whether it has varied is a live and legitimate research question.  John Webb's group has reported small variations from quasar absorption spectra since 1999, including a claimed 4.1σ dipole across the sky.  Other groups, other instruments, and a systematic-error study by one of Webb's own collaborators have failed to confirm it.  The best single-absorber measurement to date is Δα/α = −1.42 ± 0.55 ± 0.65 parts per million, and the best combined limit is −0.5 ± 0.5 ± 0.4 ppm.

• The scale is the point.  Every claimed or excluded variation in the fine-structure constant is at the level of parts per million.  A speed of light large enough to cross the observable universe in a few days is a change of ten or more orders of magnitude.  Nothing in the varying-constants literature is remotely that size, in either direction.

• The proposal also required rewriting most of physics, and Setterfield said so.  His report has atomic rest masses varying as 1/c², Planck's constant as 1/c, and radioactive decay rates as c.  He then argued that all of these changes cancel exactly, so that "the atom sees no change in c!"  A model tuned so that nothing observable changes has bought its safety at the price of its content.

• There is a direct empirical check and it fails for c decay.  In 2012 the INTEGRAL satellite detected the two hard X-ray escape lines of titanium-44 in the remnant of SN 1987A at 67.9 and 78.4 keV — the laboratory energies, from 168,000 light years away.

• Setterfield's own answer to that objection concedes it.  Writing in 2015, he explains that in his model hc is constant and e²/ε₀ is constant, so "Alpha will never register any change, no matter how the speed of light or the other three quantities vary."  On supernova 1987A he adds that "the slowing of light exactly counteracts the faster decay rate," and that "it is therefore impossible to deal with the speed of light issue in this fashion."  A model built so that no dimensionless quantity ever changes is, in Jean-Philippe Uzan's words, "just a redefinition of units."

• The measurement the model rested on has been superseded by one thousands of times tighter.  Setterfield's third line of evidence was Thomas Van Flandern's 1981 claim that atomic and gravitational clocks were drifting apart, Ġ/G = (−6.4 ± 2.2) × 10⁻¹¹ per year.  Van Flandern named the result that would disprove it.  Fifty years of lunar laser ranging now give Ġ/G = (−5.0 ± 9.6) × 10⁻¹⁵ per year — consistent with zero.

• The verdict was reached by creationists, in creationist journals, and creationists should stop making the argument.  Andrew Repp's 2022 survey in the Creation Research Society Quarterly records that "a general consensus has emerged … that the purported evidence for such decay is artifactual in nature."  Creation Ministries International lists "The speed of light has decreased over time (c decay)" among arguments that are "doubtful, hence inadvisable to use."

• This article's verdict:  refuted, and ill-posed besides.  The historical data do not support it, the claim as usually stated is not a claim about physics, and the dimensionless version of the claim is constrained to parts per million where ten orders of magnitude were needed.  The distant-starlight problem is not solved this way.  See Young-Universe Cosmologies for the seven other answers and how each of them fares.

The proposal, at its strongest

The distant-starlight problem is simple to state.  The Andromeda galaxy is about 2.5 million light years away.  Light travels one light year per year.  If the universe is about 6,000 years old, that light should not have arrived.  It has.

Barry Setterfield's answer was that the premise is wrong.  Light does not travel one light year per year and never has.  It travels one light year per year now.  It used to travel much faster, and it has been slowing down ever since — slowly enough that the change is hard to see, fast enough that a galaxy two and a half million light years away was visible on the evening of Day Four.

That is a physical answer, not a miracle and not a redefinition.  It is testable in principle, because people have been measuring the speed of light for three and a half centuries and writing the numbers down.  This is what made it attractive.  Every other young-earth answer to distant starlight either invokes a miracle, rearranges spacetime, or changes the meaning of the word "now."  This one made a prediction about a table of numbers that already existed.

The 1987 report

The case was set out in a technical report by Trevor Norman of the School of Mathematical Sciences at Flinders University of South Australia and Barry Setterfield, dated August 1987 and titled The Atomic Constants, Light, and Time.¹  It was an invited research report prepared for Lambert T. Dolphin, then a senior research physicist at SRI International, and it runs to about 40,000 words with nineteen data tables and 360 references.

Its central empirical claim is one sentence:

"A systematic, non-linear decay trend is revealed by 163 measurements of c in dynamical time by 16 methods over 300 years."¹

The report says its evidence stands on three legs, at three different scales:

"These variations have thus been recorded at three different levels of measurement:  the microscopic world of the atom, the intermediate level of the c measurements, and finally on an astronomical scale."¹

The three are:  475 measurements of eleven other atomic quantities, said to drift in the way a changing c would require;  the 163 direct measurements of c itself;  and Thomas Van Flandern's 1984 comparison of lunar and planetary orbital periods against atomic clocks, which Setterfield read as showing that atomic clocks are running slow relative to gravitational ones.¹

The historical observation the argument was built on

The report's most persuasive material is not its own statistics.  It is the fact — and it is a fact — that physicists in the first half of the twentieth century noticed their own measurements drifting downward and said so in print.

Norman and Setterfield quote Maurice E. J. Gheury de Bray, writing in Nature in 1931:

"If the velocity of light is constant, how is it that, INVARIABLY, new determinations give values which are lower than the last one obtained, …There are twenty-two coincidences in favor of a decrease of the velocity of light, while there is not a single one against it."¹

And N. E. Dorsey, whose 1944 review of the field was written specifically to argue against a real change:

"As is well known to those acquainted with the several determinations of the velocity of light, the definitive values successively reported…have, in general, decreased monotonously from Cornu's 300.4 megameters per second in 1874 to Anderson's 299.776 in 1940."¹

One thing has to be said about de Bray, though, and the report does not say it.  His argument had already been run, answered and closed, fifty years before Setterfield revived it.  De Bray pressed the case in Nature through a string of letters from 1927 to 1934 — and by 1934 he had shifted from a decay to an oscillation.  Other physicists replied at the time that the discrepancies were systematic and instrumental, and better instruments settled it.  Jim Lippard's summary names the replies:  Vrkljan and Wilson in 1931, Kennedy in 1932, Birge in 1934, Kitchener in 1939, followed by Bergstrand, Essen and Houston at mid-century converging on a constant value.²  Norman and Setterfield cite both de Bray and Birge's 1934 Nature reply in their own reference list.¹

That is the strongest thing in the report, and it should not be waved away.  Careful people looking at the same numbers in the 1930s and 1940s found the downward drift striking enough to write about.  De Bray thought it was real.  Dorsey thought it was not, and set out to show that the older experiments had underestimated their own errors.  Dorsey was right, but he had to do a hundred pages of work to show it.

The numbers the report reported

On the full data set, Norman and Setterfield stated their result plainly:

"When all 163 values involving 16 different methods are used, the linear fit to the data gives a decay of 38 Km/s per year."¹

They also ran the analysis on a hand-picked subset:

"The data mean is 753 Km/s above c now and the hypothesis that c has been constant at today's value over the last 300 years can be rejected with a confidence interval of 97.2%."¹

and on a "refined" list of the fifty-seven values they judged most reliable:

"The 57 best possible data points that were left still show a decay in c with time.  The drop is something like 1500 kilometers per second over a period of 300 years."¹

That last figure is the one to hold onto.  Fifteen hundred kilometres per second over three hundred years is five kilometres per second per year — a drop of one part in two hundred over the whole span.  It is nowhere near enough to get light from Andromeda to Earth in a week.  The enormous speeds the model needs come from extrapolating a fitted curve backwards, far outside the range of any measurement.  The report offers two curves, an exponentially damped sinusoid and a polynomial:

"This is born out by the c observations which follow the equation c = [a + e^-19."[dt)]^-19."[ere one solution gives k = -0.0048, a = 9.029 x 10^-19."[ 4.59 x 10^-19."[ -2.60 x 10^-19."[s the year.  However, most properties of this complex expression are closely reproduced by a much simpler polynomial c = a + bt^-19."[8, where a = 299792, b = 0.01866 and d = 3.8 x 10^-19."[norman-1987:curve]

A degree-eight polynomial fitted over three centuries and then run back six thousand years is not evidence about six thousand years ago.  It is arithmetic about the shape of the fitting function.  The report is aware that it needs an independent anchor at the far end, and supplies one:

"The only difference he noted was that the microwave differed from the x-ray by a wavelength factor of ten million.  This being the case, we get a value for c virtually at the time of the Big Bang of about 10 million times c now."¹

The reasoning is that the cosmic microwave background and the cosmic X-ray background differ in wavelength by a factor of ten million, that both are the same starlight seen at different epochs, and that the ratio therefore measures how much faster light once travelled.  This is not an argument that survives contact with the two backgrounds' actual spectra, which have different shapes and different sources, and in the CMB's case a blackbody form measured to extraordinary precision by the COBE satellite's FIRAS instrument.  But it is the report's own stated basis for the initial value of c, and it deserves to be quoted rather than paraphrased, because the number is otherwise unexplained.

The refutation, and it came from inside

On 1 May 1988, nine months after the report appeared, the Institute for Creation Research published a two-page article by Gerald A. Aardsma, then head of the Astro/Geophysics Department at the ICR Graduate School.³  It is titled "Has the Speed of Light Decayed?" and its answer is no.

Aardsma had no interest in defending an old universe.  He closes by saying that the creation of the stars "was a supernatural event which God accomplished by the power of His spoken Word in six solar days about 10,000 years ago."³  His objection is purely technical, and it is decisive.

Why weighting a fit is not optional

Norman and Setterfield's headline number came from an unweighted least-squares fit:  a straight line drawn through all 163 points with every point counting the same.  Aardsma's objection:

"For a data set consisting of measurements having error bars of varying lengths, it is not appropriate to give every data point equal weight as Norman and Setterfield have done.  It is standard practice to weight the data points in inverse proportion to the size of their error bars. … This is especially important for the current data set, since the reported error bars range from ± 20,000 km/s to ± 0.0003 km/s."³

Here is what that means, in a case with no physics in it.

Suppose two people measure a friend's height.  One uses a tape measure and reports 180.2 ± 0.1 cm.  The other squints at him from across a car park and reports 165 ± 20 cm.  Averaging the two numbers gives 172.6 cm — a height that neither measurement supports and that the tape measure rules out by more than a hundred standard deviations.  The plain average is wrong because it pretends the two measurements are equally informative.

The standard fix is to weight each measurement by 1/σ², the inverse square of its stated uncertainty.  The tape measure gets weight 1/0.1² = 100.  The squint gets 1/20² = 0.0025.  The tape measure counts 40,000 times as much, and the weighted average is 180.20 cm — the tape measure's answer, essentially untouched.  That is the correct answer, and the squint contributes almost nothing to it, which is exactly right, because it knows almost nothing.

Now apply the same arithmetic to Setterfield's table.  The best measurement in it is quoted to ± 0.0003 km/s.  The worst is quoted to ± 20,000 km/s.  The ratio of their weights is:

(20,000 / 0.0003)² = 4.4 × 10¹⁵

Four thousand million million to one.  In the unweighted fit, they count the same.

Aardsma redid the fit properly:

"When I analyzed the entire data set of 163 points using the standard, weighted, linear least squares method, the decay of c was determined to be:  decay of c = 0.0000140 ± 0.0000596 km/s/year.  This result says pretty plainly that there is no discernible decay trend in the data set presented by Norman and Setterfield."³

Read the result carefully.  The central value is 0.0000140 km/s per year.  The uncertainty on it is 0.0000596 — more than four times the central value.  A result smaller than its own error bar is a null result.  The measured decay rate is consistent with exactly zero, and it is also 2.7 million times smaller than the 38 km/s per year the report claimed.

One point did most of the work

Aardsma's second finding was that the unweighted fit was not merely undisciplined;  it was being driven by a single seventeenth-century number that Norman and Setterfield had handled inconsistently.

Both Rømer's 1675 determination and Cassini's 1693 one work the same way.  Jupiter's moon Io is eclipsed on a schedule.  The eclipses fall behind as Earth moves away from Jupiter and catch up as Earth approaches, and the size of that swing is the time light takes to cross the radius of Earth's orbit.  Divide the orbit radius by that time and you have the speed of light.

Rømer put the delay at 11 minutes.  Cassini put it at 7 minutes 5 seconds.  The modern value is 8 minutes 19 seconds.  Rømer was too slow;  Cassini was too fast;  Edmond Halley said so in 1694, and Norman and Setterfield quote him saying it:

"Observations by Cassini (1693 and 1736) gave the orbit radius delay as 7 minutes 5 seconds.  Roemer in 1675 gave it as 11 minutes from selected observations.  Halley in 1694 noted that Roemer's 1675 figure for the time delay was too large while Cassini's was too small."¹

What the report then did with those two numbers is visible in its own Table 1:

Table 1 of The Atomic Constants, Light, and Time, reproduced as printed, with the percentage deviations added.¹  The report's own footnote to the Rømer row reads "Provisional correction only (see text)";  its footnote to the Cassini row reads "Uncorrected observations by Cassini."¹

The Rømer entry is not Rømer's number.  It is Bernard Goldstein's 1975 reworking of Rømer's raw observations, which found a light travel time 2.6 % lower than the modern value and produced 307,600 ± 5,400 km/s.¹  The Cassini entry is Cassini's raw number, corrected by nobody.

That asymmetry is the whole trend.  Aardsma:

"Norman and Setterfield have chosen to use a reworked or 'corrected' value for Roemer's c determination (this is the earliest measurement shown on the graph), and an uncorrected value for Cassini's. … It is also unfortunate, since this single, anomalous point is responsible for most of the apparent 38 km/s/year decay which they report.  Furthermore, Roemer's uncorrected c determination would graph below the line at -24%, more than offsetting the uncorrected Cassini value."³

Aardsma's -24% is easy to check, and it is exactly right.  Take the orbit radius the report itself uses, 1.4959787 × 10⁸ km, and Rømer's raw 11-minute delay:

1.4959787 × 10⁸ km / 660 s = 226,663 km/s
(226,663 − 299,792) / 299,792 = −24.4 %

Do the same for Cassini's 425.0 seconds and you get 351,995 km/s, which is +17.4 % — the report's 352,000, to the last digit it prints.  So the two seventeenth-century observations, treated the same way, sit on opposite sides of the modern value and roughly cancel.  Treated differently — one corrected, one not — they produce a decline.

The same effect, demonstrated on the report's own smallest table

Table 1 above is small enough to check by hand, and it settles the question of how much leverage one point has.

Fitting a straight line to the six entries from 1738 onward gives a slope of −25.93 km/s per year with a correlation coefficient of −0.982, and those six values average 1,701 km/s above the modern speed of light.  Norman and Setterfield print exactly these numbers:  "the data mean is 1701 Km/s above c now," and "a least squares linear fit to the data gives a decay of 25.9 Km/s per year, with r = - 0.982."¹  The arithmetic reproduces, so the transcribed table is the real one and the report's own procedure can be replicated.

Now put the two seventeenth-century points back in and refit all eight:

Adding one uncorrected 1693 estimate nearly quintuples the apparent decay rate and cuts the correlation almost in half.⁴  That is what a high-leverage outlier does to an unweighted straight-line fit, and it is a scale model of what Aardsma says happened to the 163-point fit.

There is a sharper way to put it.  Norman and Setterfield knew the two earliest Rømer-method points were unreliable.  They said so:  "In view of initial uncertainties, only the Glasenapp and Harvard values are included in the final analysis of Table 11."¹  Six of the eight values in Table 1, including Cassini's, were excluded from their own refined data set.  But the 163-point fit that produced the headline 38 km/s per year included them all.

A last arithmetic check makes the inconsistency visible without any statistics at all.  A decay of 38 km/s per year, sustained across the 308 years the table spans, is a total change of about 11,700 km/s.  The report's own refined analysis says the total change over 300 years was "something like 1500 kilometers per second."  The two figures differ by a factor of eight.  They are computed from overlapping data by the same authors in the same document.

The obvious objection, and Aardsma's answer to it

There is a fair question to ask about a weighted fit, and it is the first thing a sceptic should ask.  A weighted least-squares fit needs an uncertainty for every point.  Many of the early measurements were reported without one.  Assign them generous error bars and they drop out of the fit — which is most of how the trend disappears.  How did Aardsma choose?

The two-page Impact article does not say.  It notes only that "the range of uncertainty was not reported for many of the earliest measurements, so some of the data points are plotted without error bars."³  A longer paper published the same month in the Creation Research Society Quarterly answers the question in full.⁵

Twenty-eight of the 163 points had no error estimate.⁵  For those, Aardsma took a group of three to eight neighbouring measurements made by the same experimental method within a twenty-year window and used their scatter as the error bar.  That is an objective rule, applied without reference to the answer, and he argues that its precision barely matters:

"The absolute lengths of the error bars do not need to be known very accurately.  Even if the estimates of the standard deviation are off from the true error bar length by a factor of two or three, the resultant weighted fit will be a vastly superior representation of the true nature of the data than was the unweighted fit which treated all data points equally, even though they differed in precision by orders of magnitude."⁵

He is right, and the reason is the ratio computed above.  When the weights span fifteen orders of magnitude, being wrong by a factor of three changes nothing.

Applying the same idea to Cassini's 1693 point gives the number that settles the matter.  Rømer and Cassini used the same method eighteen years apart and disagreed by 166 seconds on the light travel time.  Treat that as the method's scatter and Cassini's speed of light carries an error bar of ± 138,000 km/s — about ± 39 %.⁵  A measurement with a 39 % error bar has essentially no vote in a weighted fit.  In the unweighted fit it had the loudest voice in the room, because it sat furthest from everything else.

Aardsma then quantified the leverage directly, in a footnote:

"Had they removed this single data point and analyzed the remaining 162 data points in the same way, they would have found an apparent c decay rate of only 11 ± 6 km/s/year.  This result would have suggested that support for the hypothesis from the historical data is marginal, at best."⁵

One point out of 163 carries the result from 38 ± 8 down to 11 ± 6 — from a near-five-sigma result to a sub-two-sigma one — before any weighting is applied at all.  Weight the points properly and even the hint is gone.

He also anticipated the other obvious objection:  that the post-1972 laser measurements are so precise they swamp everything else and force a flat line by construction.  So he threw them out and refit:

"I have analyzed the data set exclusive of these suspect data points, since they could possibly obscure an earlier decay trend in the c data by their constancy and very high precision.  Using the same weighted linear least squares technique, the result is:  decay of c = 0.0101 ± 0.0068 km/s/year.  Thus, there is still no discernible, statistically significant decay trend."⁵

0.0101 ± 0.0068 is a one-and-a-half-sigma result.  It is not a detection, and it is 3,700 times smaller than the claimed 38 km/s per year.

The coincidence Aardsma noticed

One more argument from the same paper, because it is the kind of test a hypothesis should be made to pass and this one fails it:

"According to Norman and Setterfield's theory, the rate of decay of c was greater than 1 km/s/year for the entire span of time from creation until about 1920 A.D.  Experimental precision has been such that a decay rate of 1 km/s/year would have been easily and unquestionably verified from about 1950 A.D. onward.  It seems a remarkable coincidence that direct experimental corroboration of the theory, open for thousands of years as a theoretical possibility, should have eluded us by just 30 years."⁵

The decay is always large enough to matter and always just too small to catch.  It was thousands of kilometres per second per year during creation week, tens of kilometres per second per year through the era of crude measurement, and indistinguishable from zero in the era of precise measurement.  A curve shaped exactly so as to be undetectable whenever anyone can check it is not a strong hypothesis, whatever the fitting does.

The June 1988 minisymposium: four creationists, one verdict

The Impact article was the popular version.  The serious one ran in the Creation Research Society Quarterly, which devoted a two-part Minisymposium on the Speed of Light to the report across its June and September 1988 issues.⁶  Four papers, four authors, one conclusion.

None of these authors was an opponent of a young earth.  All four were publishing in the flagship journal of the Creation Research Society.  This matters for how the episode should be read, and it is the reason this article exists.

Humphreys: a physicist who wanted it to be true

D. Russell Humphreys was a physicist at Sandia National Laboratories and would later publish his own young-earth cosmology.  He had been corresponding with Setterfield since 1985 and had reviewed early drafts of the manuscript.  He wanted the result.  His abstract:

"Because its historical research and statistical analyses have no depth, this book (Norman and Setterfield, 1987) fails to prove that the speed of light has decreased over the past three centuries.  Its theoretical interpretations are flawed, and in some parts do not make sense."⁷⁷

He set out four minimum standards any such analysis has to meet:

"In my opinion, the minimum acceptable analysis must do the following:  (1) Use the correct Roemer point, (2) Correct or exclude the Cassini point, (3) Give each point a weight proportional to its estimated accuracy and (4) Treat all the data from the different experimental methods together with as many points as possible.  Norman and Setterfield have not done these things in their published work.  When the minimum standards are applied, it appears that no statistically significant decay in the speed of light can be found."⁷

Standards (1) and (2) are the Rømer/Cassini asymmetry.  Standard (3) is the weighting.  Standard (4) is a separate objection worth spelling out:  the report analyses each measurement method in its own small group, looking for a downward trend within each, and Humphreys thinks that is where the systematic error hides.

"The authors' practice of separating data into various groups seems to have made their analysis susceptible to distortion from systematic errors.  One likely candidate for such error is the psychological bias each experimenter has when selecting data, as Dorsey pointed out.  Such a bias would explain both the seeming downward trend within each group and the steady flattening out of the data curve as experimental accuracy improves.  Norman and Setterfield offered no alternative explanation for the flattening trend, as far as I can tell."⁷

That is the strongest single argument in the whole exchange, and it is worth dwelling on.  A real decay in the speed of light should produce a trend that is there whatever the measuring technique and however accurate it is.  Experimenter bias produces something different:  a downward drift inside each technique as it matures, and a flattening as precision improves and there is no longer any room to be pulled toward a wrong prior answer.  What the data show is the second pattern.  Setterfield never offered an alternative explanation of the flattening, and Faulkner's "trending" argument thirty-three years later is the same observation again.

Humphreys also caught a presentational problem that matters to anyone weighing the report by its heft:  its 377 references are "very redundant, with many entries repeated three or more times," which "tend to give the reader a mistaken impression that nearly 400 books and articles back up the monograph, instead of much fewer."⁷

And his verdict, which is the most quotable thing any creationist has written about this argument:

"The problem with this book is that it is misleading.  If one reads it naively, assuming that the authors are presenting their case fairly and objectively, one gets the impression that the speed of light has decayed.  However, if one examines it critically, carefully checking out the assumptions and calculations, one arrives at the opposite conclusion. …  Also the reader should know that I actually favor the possibility that c has decayed sometime in the past, so that if anything I should welcome the book.  But the underlying facts just do not support the hypothesis.  The speed of light may well have decreased either during Creation week, after the Fall, or during the Flood.  But after critically examining this book, I can find no statistically significant evidence that c has decayed during the last three centuries."⁷

Brown: the significance claims, checked one at a time

Robert H. Brown recomputed the report's individual statistical claims and found that they did not survive.  Take the one Norman and Setterfield lead with, that constancy from 1879.5 to 1926.5 can be rejected at 98.2 % confidence.  Brown works it out:  those six determinations have a mean of 299,845.5 km/s and a standard error of 41.5 km/s, so the 5 % points sit 83.5 units either side of the mean.  The 1926.5 value is 47.5 units below the mean — 57 % of the way there.  The modern value is 53.0 units below — 63 % of the way there.  Neither is anywhere near significant.  His question:

"It is true that these six measurements declined monotonously during the time interval over which they were made, but the maximum difference is only 112 and the observers claimed standard errors ranging from ± 15 to ± 90 km/s for their reported means.  How can one claim 98.2% confidence that this set of data represents measurement of a steadily decreasing quantity, rather than the influence of subjective factors and normal error of measurement on the determination of a constant quantity?"⁸⁸

Brown also disposes of de Bray's "invariably lower" claim — the single most rhetorically effective line in the report — by counting entries in the report's own table:

"On p. 9 a statement made in 1931 is quoted which affirms that new values for the speed of light are 'invariably . . . lower than the last one obtained.'  In the selected listing on p. 26, 21 examples out of 56 succeeding measurements are greater than the preceding, five of which were made prior to 1931."⁸

Twenty-one increases out of fifty-six, in Setterfield's own hand-picked list.  De Bray in 1931 said there was "not a single one against it."  There were at least five before he wrote.

Brown's conclusion, on the whole data set:

"These observations provide strong evidence that within the precision and accuracy of measurements made up to the middle of this century the speed of light has been essentially constant."⁸

Holt: pulsars, and a point about testability

Roy Holt took a different route entirely.  Pulsars are neutron stars that emit radio pulses with extraordinary regularity;  the millisecond pulsar PSR 1937+21 is among the most stable natural clocks known.  Their pulses have been travelling for tens of thousands of years on any reckoning, so their arrival times constrain how much the speed of light can have changed over that span.

"If one assumes the first law does not hold, pulsar timing measurements indicate the speed of light has been a constant to 10⁻¹⁰ since the time light left the pulsars (the pulsars appear to be 30,000 light years and farther away).  If one assumes the first law holds, 1,000 years ago a day would only be 12 dynamic hours and there would be 730.5 days in a dynamic year—an historical absurdity.  In addition the Norman-Setterfield model gives pulsar values that are six to 15 orders of magnitude different from what is observed."⁹⁹

The dilemma is real, and it comes straight out of Setterfield's own scheme.  If the rotation rate of a spinning body scales as 1/c, as the model needs it to for the pulsar timings to come out right, then the Earth's rotation scaled that way too — and a thousand years ago the day was twelve hours long and the year had 730 days.  No historical record says any such thing.  Escape that by letting rotational kinetic energy vary instead, and the first law of thermodynamics goes.

Holt's closing paragraph reaches, from pulsar data in 1988, the same place Duff reached from dimensional analysis in 2002:

"One could imagine everything changing with the speed of light in such a way that it would not be detectable, but there would be no way to prove this type of a decay.  Such a model would only be speculation.  If something cannot be detected and measured, it is not subject to the scientific method."⁹

1992: the anchor point itself was not real

Every argument above concerns how the 163 numbers were fitted.  In 1992 Eugene F. Chaffin, a creationist physicist then at Bluefield College and later the head of the RATE project's variable-decay work, went after the biggest number itself.¹⁰

Recall the Rømer entry in Table 1:  307,600 ± 5,400 km/s, 2.6 % above the modern value, the earliest and highest-leverage point in the whole set.  It is not a seventeenth-century number.  It comes from a modern reanalysis of Rømer's raw eclipse timings, and Chaffin tracked down where it came from:

"Norman and Setterfield (1987) attributed a value of 3.076 x 10⁸ m/sec to Roemer's 1675 data point.  This value is 2.6% higher than today's value, and is a result of a private communication with Goldstein.  Only Goldstein et al. (1973) dealt with the possible variation of the speed of light, not the 1975 paper which was concerned with possible variation of Io's period.  Since the 1975 paper included some improvements over the 1973 paper, it was necessary to communicate privately with Goldstein to obtain the 2.6%."¹⁰

So the anchor was an unpublished figure obtained by letter.  Chaffin redid the calculation from scratch:  he took Jean Lieske's published seventeenth-century eclipse timings, rebuilt the orbital model including the perturbation of Io's longitude by Europa, and — this is the good part — used his own observations of Io from 1988 to 1991 as a control, so the method's systematic error could be measured rather than guessed.

Chaffin's Table II.¹⁰  Read the bottom row first.  Chaffin observed Io himself, with a six-inch Newtonian reflector and WWV time signals, in a decade when the speed of light was known to nine decimal places — and the method returned a value 0.297 % low.  That is the method's own noise floor.  The two seventeenth-century values sit within it, on the same side.  The 1878–1880 Harvard value is 0.77 % high, which Chaffin also rejects as unreal, because Michelson measured 299,910 ± 50 km/s in 1878 by a better technique.¹⁰

His verdict:

"It is apparent that the results do not speak in favor of any variation of the speed of light over the last 300 years. …  The results presented here show that the 2.6% was not real, and that any real effect that might be present must be smaller than about 1%, at most."¹⁰

And the figure caption states it in the plainest possible way:

"Since all of the error bars overlap the horizontal line, the results are consistent with a constant value for the speed of light over the last 300 years, and any systematic errors must be small."¹⁰

Two things about this paper deserve notice.

The first is that Chaffin was correcting himself.  He had published a more favourable analysis of Rømer's method at the Second International Conference on Creationism in 1990, and he says so:  "This is a change from what Chaffin (1990b) said, but the improvements in the computer analysis forced a fresh analysis."¹⁰

The second is that when his iterative procedure was allowed to solve for c and the orbital parameters together, it drifted to values implying the speed of light was smaller in the 1670s, not larger.  He does not use this as an argument.  He says plainly that "Table III does not seem to represent any real effect."¹⁰  That is the correct call, and reporting it is a good sign about the paper:  a result pointing the opposite way from the author's sympathies, published rather than buried, and then honestly discounted.

Chaffin is also, elsewhere, the strongest creationist voice for the possibility of varying constants — see the section on the Oklo reactor below, where he argues that the published limits are weaker than they look.  He is not a hostile witness.  He killed the anchor point anyway.

Faulkner's version: trending, and the asymmetry test

Danny Faulkner is an astronomer who writes for Answers in Genesis and has published in the Answers Research Journal on every young-earth approach to distant starlight.  In 2021 he wrote a survey of every young-earth answer to the light travel time problem, and his treatment of c decay reaches Aardsma's conclusion by a different route.¹¹

His first point is the same one about error bars, put without the statistics:

"This trend shows up only if one treats all measurements of the speed of light as having equal errors of measurement, but this is not the case.  The earliest measurements of the speed of light were subject to the greatest amount of error."¹¹

His second is about the people doing the measuring:

"When making measurements, people do not operate in a vacuum.  Rather, they generally are aware of the work that preceded them and hence 'know' what the right answer is.  If researchers' measurements are at variance with previous results, there is a tendency to interpret new measurements in the direction of the 'known' value.  Some people call this trending."¹¹

He then illustrates it with an anecdote about his own undergraduate physics labs, where a lab partner looked up the established values in advance and insisted on repeating any measurement that missed them.¹¹  This is not a hostile characterisation of experimenters.  It is a well-documented feature of the history of measured constants, and the speed of light is one of the standard examples.  It is also, incidentally, what Dorsey concluded in 1944 after reworking the original experiments' error budgets.

His third point is the one to draw with a ruler:

"Aware of trending, I have drawn a red horizontal line that fits all the data well.  A horizontal line means that the speed of light has not changed."¹¹

A fit is only evidence against a hypothesis if the hypothesis it is being compared against fails.  "No change at all" passes through the error bars of every point in Setterfield's table.  A decaying curve also passes through them.  When two models both fit, the data have not chosen between them, and the one that adds a mechanism is the one that has to earn its keep.

And then Faulkner makes a point that is worth more than all the statistics, because it is a check on his own side's motives:

"If an increasing speed of light were indicated by historical data, we wouldn't be having this discussion because it would exacerbate the light travel time problem, not possibly solve it."¹¹

That is the test.  Suppose the seventeenth-century measurements had come out low rather than high — Rømer's uncorrected number, in fact, comes out 24 % low.  Nobody would have proposed that the speed of light was rising, because a rising c makes the starlight problem worse.  The historical scatter was read as a trend because a trend in one particular direction was useful.  A creationist astronomer said that in print, about creationists, and it is the single most credible sentence in the whole literature on this argument.

The deeper problem: "the speed of light changed" is not yet a claim about the world

Everything above concerns whether the historical numbers show a trend.  They do not.  But there is a prior difficulty, and it is the more important one, because it applies even to a version of the argument with perfect data.

The speed of light is a dimensional constant.  Its numerical value depends on the units chosen for length and time.  In metres per second it is 299,792,458.  In miles per second it is 186,282.  In furlongs per fortnight it is about 1.8 × 10¹².  None of those numbers is more correct than the others, and none of them is a fact about light.  They are facts about metres, miles and furlongs.

This is not a debating trick, and it matters more than it looks.  Since 1983 the metre has been defined as the distance light travels in 1/299,792,458 of a second.¹²  The speed of light in metres per second is therefore fixed by definition and cannot be measured.  Anyone who reports having measured it since 1983 has measured a length.  Norman and Setterfield note the 1983 redefinition themselves.¹

So what would "the speed of light was higher" even mean?  Higher compared to what ruler and what clock?

Duff's answer

The clearest statement of the problem is a 2002 paper by Michael Duff, then at the University of Michigan and later at Imperial College London.  His abstract:

"The possible time variation of dimensionless fundamental constants of nature, such as the fine-structure constant α, is a legitimate subject of physical enquiry.  By contrast, the time variation of dimensional constants, such as ℏ, c, G, e, k…, which are merely human constructs whose number and values differ from one choice of units to the next, has no operational meaning."¹³

An appendix reproduces a lecture by Paul Dirac making the same point decades earlier:

"Talking about whether a thing is constant or not does not have any absolute meaning unless that quantity is dimensionless."¹³

Duff also supplies the thought experiment that makes it concrete for a reader who does not want the algebra.  Imagine you want to catch light slowing down.  You build a ruler and a clock and you keep measuring:

"First take a ruler with notches one Planck length apart and a clock with ticks one Planck time apart.  Next measure the speed of light in vacuum by counting how many notches light travels in between ticks.  You will find the answer c = 1.  You may repeat the experiment till the cows come home and you will always find c = 1!  Repeat the experiment using Stoney length and Stoney time, and again you will find c = 1.  But if the notches on your ruler are one Schrodinger length apart and the ticks on your clock one Schrodinger time apart, you will find c = 1/α and c will now have the same time dependence as 1/α.  Once again we see that the time dependence of c is entirely unit-dependent."¹³

Read that once more slowly.  In one system of units the answer is a constant, forever.  In another it drifts, and it drifts exactly like 1/α.  Same universe, same light, same experiment.  The difference is the ruler.  Duff's conclusion is that when you think you are measuring a dimensional quantity, "you are really measuring dimensionless ones."¹³

He puts the moral less gently a page later, answering the objection that this is a quibble about semantics:

"The failure to tell the difference between changing units and changing physics is more than just semantics.  It brings to mind the old lady who, when asked by the TV interviewer whether she believed in global warming, responded:  'If you ask me, it's all this changing from Fahrenheit to Centigrade that's causing it'."¹³

The people who build varying-c theories agree

It would be fair to suspect that this is one physicist's idiosyncratic position, adopted to shut down an inconvenient idea.  It is not.  The physicists who actually publish varying-speed-of-light cosmologies say the same thing about their own work, and Duff quotes them saying it.

Andreas Albrecht and João Magueijo, whose 1999 paper is the founding document of modern varying-speed-of-light cosmology:

"Our conclusion that physical experiments are only sensitive to dimensionless combinations of dimensional constants is hardly a new one.  This idea has been often stressed by Dicke…and we believe this is not controversial."¹³

And Magueijo with John Barrow and Håvard Sandvik:

"Undoubtedly…one has to make an operationally 'meaningless' choice of which dimensional constant is to become a dynamical variable."¹³

Duff's verdict on those papers is worth repeating because it is not dismissive:  "I might criticize these papers for being confusing, but not wrong."¹³  A varying-c theory can be a perfectly good physical theory.  What makes it good is not the letter c.  It is the dimensionless numbers the theory predicts will change, and the units in which it is written are a labelling convention on top of that.

Magueijo has pushed back on Duff in print, arguing that the constancy of c was established by experiment rather than adopted as a definition.  Duff's reply is narrow and hard to argue with:  he never claimed logical necessity, only that whether a dimensional number varies "is a matter [of] human convention…In neither case is it something to be determined by experiment."¹³  This corner of physics is not settled in the sense that everyone likes the phrasing.  It is settled in the sense that both sides agree the observable content lives in the dimensionless numbers.

What this does to Setterfield's argument, and what survives it

The naive form of c decay — "light used to go faster, full stop" — is not a physical hypothesis at all.  It is a statement about units, and the units are ours.

Setterfield's actual proposal is more sophisticated than that, and it should be given credit for it.  He did not claim c alone changed.  His report has Planck's constant varying as 1/c, electron rest mass as 1/c², radioactive decay constants as c, and several other quantities moving in step, all constrained by energy conservation.¹  That is a specific scheme, not a bare assertion, and a specific scheme can be tested.

But he then draws the conclusion himself, and it is fatal:

"Summarizing the above approach, we may say that the atom sees no change in c!  Atomic time is based on the time an electron takes to travel its orbit once. …  For the atom, light has always traveled the same distance in one of its seconds, its light emitting frequency has always been constant, Planck's constant never varies and radioactive decay rates remain unchanged."¹

And, in the same document:

"Dimensionless constants and those with mutually canceling time dependent terms remain invariant if conservation laws are to be upheld."¹

Those two sentences concede the whole of Duff's point in advance.  If every dimensionless number is invariant, then by construction no experiment done inside the physics can detect the change.  There is exactly one measurable quantity left over — the ratio between the rate of an atomic clock and the rate of a gravitational one.  That ratio is dimensionless, and it is the entire empirical content of the proposal.

Setterfield knew that too, which is why the report leans on Van Flandern's 1984 comparison of lunar and planetary orbital periods against caesium clocks:

"The number of atomic seconds in a dynamical interval is becoming fewer.  Presumably, if the result has any generality to it, this means that atomic phenomena are slowing down with respect to dynamical phenomena … (though) we cannot tell from the existing data whether the changes are occurring on the atomic or dynamical level."¹

Note Van Flandern's own hedge, quoted in the report and worth keeping:  he could not tell which clock was drifting.  That is the dimensional ambiguity again, in the one place where the theory has something real to say.  What has happened to that measurement since 1984 is taken up below.

So has the fine-structure constant varied?

Everything so far has been negative.  This section is not, because the question Duff says is legitimate — has a dimensionless constant changed? — is being actively worked on, with big telescopes, and the answer is not yet fully settled.  A reader who is told that c decay is dead deserves to know exactly what the live version of the question looks like, and how far it is from what Setterfield needed.

The quantity to watch is the fine-structure constant:

α = e² / (4πε₀ℏc) ≈ 1 / 137.036

It is built out of the electron charge, the electric constant, Planck's constant and the speed of light — and all the units cancel.  It is a pure number.  It is 1/137.036 in SI units, in CGS units, in Planck units, and in any other units anyone cares to invent.  Nothing you can do to your rulers or clocks will change it.  That is exactly why it is the right thing to measure:  if α is the same now as it was ten billion years ago, then no reshuffling of c, ℏ and e among themselves is doing anything observable to atoms.

How you measure a constant ten billion light years away

α sets the fine-structure splitting of atomic energy levels — the small separations between spectral lines that give the constant its name.  Different transitions in different ions respond to a change in α by different amounts and in different directions.  That is the whole trick.

Light from a distant quasar passes through gas clouds on its way here.  Each cloud stamps absorption lines onto the spectrum.  If α inside that cloud differed from α in the laboratory, the lines shift relative to each other in a specific, predictable pattern.  Because the pattern is a relative one, an overall shift from the cloud's redshift or its motion cancels out.  This is the "many-multiplet" method, and it can reach parts-per-million sensitivity.¹⁴

The claim

John Webb's group at the University of New South Wales has been reporting small variations since 1999.  By 2004 the Keck sample had grown to 143 absorption systems, and the weighted mean was Δα/α = (−0.57 ± 0.11) × 10⁻⁵ — a smaller α in the distant past, at five standard deviations.¹⁴

Then it got strange.  When the same group turned the Very Large Telescope in Chile on the southern sky, α came out larger at high redshift, not smaller.  Their 2011 interpretation was that α varies across the sky rather than only with time:

"We previously reported Keck telescope observations suggesting a smaller value of the fine structure constant, α, at high redshift.  New Very Large Telescope (VLT) data, probing a different direction in the universe, shows an inverse evolution;  α increases at high redshift.  Although the pattern could be due to as yet undetected systematic effects, with the systematics as presently understood the combined dataset fits a spatial dipole, significant at the 4.2σ level, in the direction right ascension 17.5 ± 0.9 hours, declination −58 ± 9 degrees."¹⁵

The full analysis followed in 2012:  154 VLT absorbers plus 141 Keck absorbers, a dipole of amplitude 0.97 × 10⁻⁵ pointing at RA 17.3 ± 1.0 h, dec. −61 ± 10°, preferred over a uniform-α model at 4.1σ.¹⁴  The paper's own summary of its standing was confident:  "To the best of our knowledge, this result is not in conflict with any other observational or experimental result."¹⁴

Note the caveat Webb's team put in their own abstract:  "the pattern could be due to as yet undetected systematic effects."  They were right to.

The trouble

Three things have happened since.

Another group got a null result, and the two sides disagree about why.  Hum Chand and colleagues analysed 23 absorption systems with the VLT in 2004 and reported a statistical error on Δα/α of just 0.06 × 10⁻⁵ — consistent with no variation, and tighter than anything Webb had.  Murphy's group responded that "the errors were under-estimated by a factor of 6 and that the optimisation algorithm was demonstrably unreliable, failing to reach a solution in most of the absorbers."¹⁴  That dispute has never been fully resolved to everyone's satisfaction, and it is a fair summary of the field's condition:  two teams, two answers, and an argument about error bars.  This should sound familiar.

A systematic error big enough to fake the result was found — by one of Webb's own co-authors.  Jonathan Whitmore and Michael Murphy — Murphy is a co-author on both the 2011 dipole paper and the 2012 analysis — built a "supercalibration" technique that checks a spectrograph's wavelength scale against sunlight reflected off asteroids and solar-twin stars.  What they found:

"We find that systematic errors in their wavelength scales are ubiquitous and substantial, with long-range distortions varying between typically ±200 m s⁻¹ per 1000 Å."¹⁶

And what those distortions do to the α results:

"The spurious deviations in α produced by the model closely match important aspects of the VLT–UVES quasar results at all redshifts and partially explain the HIRES results, though not self-consistently at all redshifts.  That is, the apparent ubiquity, size and general characteristics of the distortions are capable of significantly weakening the evidence for variations in α from quasar absorption lines."¹⁶

Read the second sentence carefully.  It does not say the variation is disproved.  It says an instrumental effect that is definitely present, in both telescopes, over twenty years of archival data, produces a spurious signal that looks like the reported one.  That is the same category of problem as unweighted least squares:  an artefact of the measuring apparatus that mimics the effect being claimed.

Every measurement made with the systematic under control has come out consistent with zero.  Once the calibration problem was understood, the field moved to measurements where it could be corrected.

• 2017. Kotus, Murphy and Carswell took the brightest southern quasar above z = 1, HE 0515−4414, built a spectrum with signal-to-noise around 250 per pixel, and corrected the UVES wavelength scale using HARPS observations of the same object. Result: Δα/α = −1.42 ± 0.55(stat) ± 0.65(sys) parts per million — "the most precise measurement of Δα/α from a single absorption system to date," from one absorber, with a precision "comparable with the precision from previous, large samples of ~150 absorbers."¹⁷
• 2020. Wilczynska and colleagues, including Webb himself, pushed to z = 7.1 using the X-SHOOTER near-infrared spectrograph — the universe at 0.8 billion years on the standard model. Result: Δα/α = (−2.18 ± 7.27) × 10⁻⁵. Their own words: "we find no evidence for a temporal change from the 4 new very high redshift measurements." Combined with the older sample, they report spatial variation "marginally preferred over a no-variation model at the 3.7σ level."¹⁸
• 2022. Murphy and colleagues used ESPRESSO on the VLT with a laser frequency comb — a calibration source good enough that the old distortions simply do not arise. One absorber gave Δα/α = 1.3 ± 1.3(stat) ± 0.4(sys) ppm. Combining it with 28 other well-calibrated measurements gives a weighted mean of −0.5 ± 0.5(stat) ± 0.4(sys) ppm over redshifts 0.6 to 2.4.¹⁹

The honest summary is this.  A variation in α has been claimed, repeatedly, by a serious group using a sound method.  It has not been confirmed by other groups or by better-calibrated instruments, a systematic effect capable of producing it has been demonstrated to exist, and every measurement made since that systematic was brought under control is consistent with no variation at all.  The dipole claim is not dead — Wilczynska 2020 still prefers it at 3.7σ — but it is not established, and the best current numbers are consistent with zero.

The Oklo reactor, and the caveat that belongs with it

There is a second, completely independent route, and it is worth explaining because it is one of the strangest experiments in physics.

About two billion years ago on the standard geological timescale, in what is now Gabon, groundwater seeping through a rich uranium ore body moderated enough neutrons to start a self-sustaining fission chain reaction.  It was discovered in 1972 because the uranium mined from it was measurably short of ²³⁵U — it had been burned.

The isotopic wreckage is still in the rock, and one isotope is a superb probe of α.  Samarium-149 captures thermal neutrons through a nuclear resonance sitting only 97.3 millielectronvolts above threshold.²⁰  That is an extraordinarily fine balance:  nuclear energy levels are set by strong-interaction scales millions of times larger, so a resonance perched a fraction of an electronvolt above threshold is a knife edge.  Move α even slightly and the resonance shifts off the thermal neutron energies, the capture cross-section changes by a large factor, and the surviving ratio of ¹⁴⁹Sm to ¹⁴⁷Sm comes out different.  It does not come out different.

Thibault Damour and Freeman Dyson's 1996 reanalysis is the careful one:  they reworked a large selection of the published rare-earth data, took seriously "the very large uncertainty of the temperature at which the reactors operated," and connected the resonance shift to α using isotope-shift measurements.²¹  Yasunori Fujii's group used new samples chosen to minimise contamination and got a compatible answer, while noting honestly that "another range of the resonance energy shift indicating a nonzero time variation of the constants" also fits, and can only be excluded by bringing in the gadolinium data.²⁰  Yuri Petrov's group rebuilt reactor zone RZ2 as a full Monte Carlo model with two independent codes and found "no evidence for the change of the fine structure constant in the past."²²

Now the caveat, and it must be stated because this article is written for readers on both sides.

The rate limits assume the reactor ran two billion years ago.  A young-earth reader does not accept that, and is entitled to say the 10⁻¹⁷ per year numbers are conditional on a date they reject.  That is correct.

The fractional-shift limit does not depend on the date at all.  Damour and Dyson's bound — that α at Oklo differed from α now by less than about one part in ten million — is a statement about the physics operating in that ore body while it was critical.  It follows from the isotope ratios in the rock and the neutron physics that produced them.  Whenever the reactor ran, α was then what it is now, to one part in ten million.  For the c-decay hypothesis, which needs α's constituent parts to be reshuffled by factors of millions, that is the relevant number and it is unaffected by the geological date.

A creationist physicist has contested these limits, and it should be said who and on what grounds.  Eugene Chaffin — the same man who killed Setterfield's Rømer anchor — argued in 1990 that the published Oklo limits are "more imaginary than real," on the grounds that the reactor's operating temperature and neutron spectrum are poorly known and that different assumptions all fit the data:

"However, from the fact that various assumptions satisfy the data, we must conclude that the Oklo data are insufficient to decide whether the Sm-149 cross section has varied, and therefore whether the strength of the nuclear force has varied with respect to the Coulomb force."²³²³

That objection was reasonable in 1990 and it is much weaker now, because the three papers above are precisely responses to it.  Damour and Dyson's central methodological point was the reactor temperature, which they treat as an explicit uncertainty spanning hundreds of degrees rather than a fixed number.  Petrov's group replaced the assumed Maxwellian neutron spectrum — the thing Chaffin objected to — with a computed reactor spectrum from two independent Monte Carlo codes, and found that it changes the answer:  "The averaged cross section of ¹⁴⁹Sm and its dependence on the shift of resonance position…are significantly different from previous results."²²  The limit survived the correction.

Chaffin's broader methodological point still stands, though, and it is a good one:  "It is easy to assume that the laws of physics should be written in the usual form, then to allow the constants to vary in these equations, and to do various derivations to show that inconsistencies result.  But the larger question is whether the laws and equations may be altered in a way that is consistent with observation and experiment."²³  A constraint derived inside a framework only constrains theories inside that framework.  What it does not do is give a varying-constants model a free pass:  the alternative framework has to be written down and shown to fit the isotope ratios too, and nobody has done that for Oklo.

The laboratory limit, and the size of the gap

The third route is to stop looking at the sky and put two clocks side by side.

Different atomic transitions depend on α to different powers.  Compare two optical clocks built on different transitions, keep comparing them for years, and any drift in α shows up as a drift in their frequency ratio.  In 2021 a team at the Physikalisch-Technische Bundesanstalt in Braunschweig did exactly this with two transitions in the same ion, ytterbium-171, measured repeatedly over several years:

"We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant α to 1.0(1.1) × 10⁻¹⁸/yr and of the proton-to-electron mass ratio μ to −8(36) × 10⁻¹⁸/yr."²⁴

One part in 10¹⁸ per year, consistent with zero.  Run that for six thousand years and the total permitted drift in α is about one part in 10¹⁴.

Put all of it in one place:

The last row is not in the same units as the others, and that is the point.  Every real constraint is a fractional limit at the level of parts per million or better.  Setterfield's model needs a change of seven orders of magnitude.  Even granting his scheme in which the dimensionless numbers are all preserved by compensating changes, there is no measurement anywhere in this literature that leaves room for anything of that size, and the compensating-change scheme is precisely the manoeuvre that makes the model unfalsifiable.

What else would have to be true

Setterfield never claimed that only c changed.  He could not, and the report says why:  the speed of light appears inside so many other physical relationships that moving it drags a long chain behind it.  This section lays out what the chain contains, what Setterfield said about each link, and what the observations say.

The chain

The report derives its scaling laws from conservation of energy.  It gives, among others:

The scalings are quoted from the report;  the third column is arithmetic.¹

On rest mass the report is explicit:

"Chemical and nuclear reactions obey the standard equation E = mc² which O'Rahilly has demonstrated can be derived non-relativistically and without any assumptions about c behavior.  For energy E to be conserved in all chemical and nuclear reactions requires that m ~ 1/c²."¹

An electron with 10⁻¹⁴ of its present mass is not an electron with a small correction.  It is a different particle in a different atom, with different orbital radii, different binding energies and different spectral lines.  Faulkner's version of this objection, without the algebra:

"One problem is that the speed of light is not an arbitrary constant.  Its value depends upon two fundamental constants of nature, constants that govern the strength of electrical and magnetic forces.  These forces play important roles in the structure of matter.  If the speed of light were changed even a small amount, it would greatly change the structure of matter.  There is no evidence that this has ever happened."¹¹

The immunity clause

Setterfield's answer is that everything changes together, so nothing changes.  Faulkner records the exchange fairly:

"Opponents point out that any significant change in the speed of light would alter the structure of matter that ought to be visible in distant objects.  Supporters agree, but argue that other factors have changed to compensate for this."²⁵²⁵

The report's own statement of this is the sentence quoted earlier — "the atom sees no change in c!" — and it is applied to the energy budget too.  If radioactive decay ran ten million times faster during creation week, the Earth should have been sterilised.  Setterfield's reply:

"For example, if the speed of light was 10 times its present value at some stage in the past, then radioactive decay would have occurred 10 times more quickly.  However, although 10 times as much radioactive decay was occurring in a given interval, the intensity of radiation from each decaying atom was only 1/10th of today's value.  Accordingly, the total observed intensity would only be the same as today's level.  In a word, radioactive decay was far safer and much less of a problem in the past with higher c than it is today."¹

The same move covers stellar luminosity:

"Although stellar and radioactive processes were more vigorous in the past, proportional to c, the net radiation intensity remained unchanged with temperatures unaffected.  The latter follows since thermal conductivity is proportional to c."¹

Take these at face value and count what is left.  Every observable consequence of a ten-million-fold change in the speed of light has been cancelled by a compensating change in something else.  The heat is cancelled.  The stellar structure is cancelled.  The atomic spectra are cancelled.  Holt saw where this ends in 1988:  "One could imagine everything changing with the speed of light in such a way that it would not be detectable, but there would be no way to prove this type of a decay."⁹

Except that it is not fully cancelled, and Aardsma found the leak

Two things do not cancel, and both are fatal.

Radiocarbon.  If decay constants scaled with c, then a radiocarbon measurement does not date an object in ordinary years;  it dates it in "atomic" years that have to be rescaled.  Aardsma ran the conversion on an object whose age is known independently.  The Dead Sea Scrolls have a radiocarbon date around 20 BC ± 200 years and a palaeographic and archaeological date between about 135 BC and AD 68.  Under Setterfield's rescaling, that radiocarbon date converts to a "true" date of about AD 800.⁵  The scrolls were in a cave near Qumran that was abandoned in AD 68.

This is why Aardsma's abstract puts radioactivity alongside the statistics:  "The implications of the hypothesis for radioactivity and radiocarbon dating are shown to be unacceptable."⁵  His conclusion says it twice over:  "the implications of the theory are unacceptable for radioactive decay, in general, and radiocarbon dating, in particular."⁵

Rotation.  Holt's pulsar analysis found the second leak.  For the model to survive pulsar timing, the rotation rate of a spinning body must have scaled as 1/c — and the Earth is a spinning body.  A thousand years ago the day would have been twelve hours long and the year would have had 730 days.⁹  Every civilisation that kept a calendar would have noticed.

The direct check, and the answer Setterfield gives to it

There is an observation that tests the whole package at once.

Supernova 1987A exploded in the Large Magellanic Cloud, whose distance is pinned geometrically by the light echo off its circumstellar ring.  Its late-time energy output comes from the decay of radioactive titanium-44 made in the explosion.  In 2012 the INTEGRAL satellite detected the two hard X-ray escape lines of ⁴⁴Ti from the remnant, at 67.9 and 78.4 keV.²⁶

Those are the laboratory energies.  Nuclear energy levels depend on the same constants a changing c would move, and they came out of a star 168,000 light years away with the values they have on Earth.  On any young-earth model that light left within the last few thousand years — inside the era in which Setterfield's curve is still dropping steeply.

Setterfield has an answer, and it is the same answer as before.  Writing in 2015 about the cobalt decay that powers the supernova's light curve:

"So what is happening when we see SN1987A and other supermova is that we are indeed seeing the process in slow motion, since the half-life of Cobalt isotopes was proportionally shorter when the explosion occurred.  In a word, the slowing of light exactly counteracts the faster decay rate, so we see it from earth in the same elapsed time as would normally occur."²⁷²⁷

And on the light echo off the ring, which times the geometry:

"Critics have stated that if the speed of light was then ten times what it is now, the light should have illuminated the sheets and formed the rings in only 1/10 of the time we see it happening now.  However, what has been ignored in that criticism is that the light is being received at only 1/10th of the rate the original events occurred.  So we see events which nonetheless are in accord with a value for c equal to c now.  It is therefore impossible to deal with the speed of light issue in this fashion, as the slow-motion effect will always match the faster speed."²⁷

Take that at face value.  Setterfield is saying, in his own words, that no observation of a distant object can ever bear on the question, because the compensation is exact by construction.  That is not a defence of the hypothesis.  It is a statement that the hypothesis has no observational consequences, which is what Holt said in 1988 and what Duff's argument implies in general.

The redshift claim fails a separate test, and this one Setterfield does not neutralise, because it is a claim he makes rather than a claim made against him.  The 1987 report proposed that the cosmological redshift is caused by wavelengths stretching in transit as c falls.¹  Any mechanism that changes a photon's wavelength without changing the geometry predicts that distant clocks tick at the normal rate.  They do not.  Type Ia supernova light curves — and their spectra, which is the harder test — age more slowly by exactly a factor of (1+z).²⁸²⁹  The general case is worked through in The Doppler Model of Galaxy Redshifts.  Setterfield withdrew this part of the 1987 model in 2001, as the next section describes.

The third leg: Van Flandern's clocks, and what happened to them

The historical c measurements were one leg of the report's tripod.  The atomic-constant tables were the second.  The third was Thomas Van Flandern's claim that atomic clocks and gravitational clocks were drifting apart, and it is the one that carried the most weight, because it was a modern measurement rather than a reworking of seventeenth-century observations.

Van Flandern was an astronomer at the U.S. Naval Observatory.  In 1981 he compared the Moon's observed orbital acceleration with the part attributable to ocean tides, and found a leftover.  His interpretation:

"Macroscopic physical phenomena which are uniform with respect to a dynamical time scale are speeding up with respect to an atomic time scale;  i.e., the number of cesium transitions in the dynamical time second is becoming fewer with time. …  While the universe has an 'age' of about 10¹⁰ years of atomic time, its 'age' in dynamical time must be much greater, and perhaps infinite."³⁰³⁰

Read in the framework of Canuto and Hsieh's scalar-covariant cosmology, his number was:

Ġ/G = (−6.4 ± 2.2) × 10⁻¹¹ per year

That is a three-sigma result, and it is why Setterfield could write that the two clocks "do run at different rates."¹

Van Flandern also did something that deserves respect:  he named, in the same paper, the measurement that would kill his result.

"Any future determination which sets an upper limit of less than 2 × 10⁻¹¹/yr in ṅ/n would tend to disprove those theories, and to support the view that Ġ/G is actually zero.  That is definitely not the present situation."³⁰

It became the situation.  Lunar laser ranging — bouncing laser pulses off the retroreflectors left on the Moon by Apollo and Lunokhod — has been measuring the lunar orbit continuously since 1969, and the data set is now more than fifty years long.

Van Flandern's claimed effect, 6.4 × 10⁻¹¹ per year, is more than six thousand times larger than the entire present-day uncertainty of 9.6 × 10⁻¹⁵ — and the present-day central value is consistent with zero.³¹  Every step of that tightening happened after 1987.  The measurement that supplied the third leg of Setterfield's tripod no longer exists, by the standard Van Flandern himself set.

This matters more than the statistics arguments, because it is the only place where the model had a genuine dimensionless observable — the ratio of an atomic clock's rate to a gravitational one.  Duff's argument says that ratio is the only thing a "changing c" could ever have meant.  It has been measured to fifteen decimal places per year, and it is not changing.

What a real varying-constant theory has to do

Physics does not forbid constants from changing.  What it does is impose requirements on anyone who proposes a change, and those requirements are the standard against which Setterfield's proposal should be judged — the same standard by which mainstream varying-speed-of-light cosmologies have been judged and found wanting.

George Ellis and Jean-Philippe Uzan set it out in the American Journal of Physics in 2005, aimed at the varying-speed-of-light cosmologies of Moffat, Albrecht, Magueijo and Barrow.  Setterfield is never mentioned, which makes the argument more useful here, not less:  it is not an anti-creationist objection.  Their starting point is Duff's:

"It is however well known that only the variation of dimensionless quantities can be determined, mainly because measuring a physical quantity reduces to comparison with a physical system that is chosen as reference. …  However, while only variation of dimensionless constants is meaningful, one can implement a theory in which such dimensionless constants are varying by assuming that a dimensional constant is varying while specifying clearly what other quantities are being kept fixed."³²³²

That last clause is a real escape route.  You may build a theory in which c varies — provided you say exactly what is held fixed while it does.  Their worked example is Dirac's large-numbers hypothesis, described as a theory "resulting from atomic clocks varying relative to gravitational clocks," which is Setterfield's framing exactly.³²

They then point out that "the speed of light" is not one thing.  There is the electromagnetic constant, c_EM² ≡ 1/(ε₀μ₀), which appears in Maxwell's equations.  There is the spacetime constant, c_ST, which appears in the Lorentz transformations and in E = mc_ST².  Their coincidence is an experimental result, not a definition:

"The speed of light c_EM agrees with the universal speed, c_ST, only to within the experimental precision of Michelson-Morley type experiments (or put differently, the photon has zero mass only within some accuracy) and the causal cone need not coincide with the light cone."³²

And so their requirement:

"These different facets have to be distinguished if one wants to construct a theory in which it is supposed to vary.  In particular if it is the electromagnetic speed that is supposed to vary, we should be shown how Maxwell's equations are to be changed;  if it is the causal speed that is to vary we should be shown how the spacetime metric tensor structure and interpretation is altered."³²

Then comes the sentence that describes the 1987 report's method exactly, though it was not written about it:

"As we emphasized, letting a constant vary implies replacing it by a dynamical field consistently.  Letting it vary in equations derived under the assumption it is a constant leads to incorrect results, as the example of a scalar tensor theory clearly shows.  One needs to go back to a Lagrangian that allows one to determine the degrees of freedom of the theory and to check if it is well defined."³²

That is what The Atomic Constants, Light, and Time does throughout.  It takes standard formulae for Planck's constant, electron mass, radioactive decay constants and gravitation — every one of them derived on the assumption that c is constant — and lets c slide inside them, then reads off the scalings.  Ellis and Uzan's verdict on the mainstream VSL papers that do the same thing is blunt:  "it cannot be taken seriously, according to usual theoretical standards, as a proposal for the speed of light to vary."³²

Uzan's 2011 review in Living Reviews in Relativity states the positive requirement, and it is the constructive half of the answer:

"Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter.  This will induce a violation of the universality of free fall.  It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy."³³

So a genuine varying-constant theory has three obligations.  Name the field.  Write the Lagrangian.  Predict the equivalence-principle violation, so somebody can go and look for it.  Torsion-balance and lunar-laser-ranging tests of the equivalence principle are precisely where this gets checked, and nothing has turned up.

And a warning against the opposite error, from the same paper, which this article should carry:

"It follows that any variation of constants that will let these numbers unaffected is actually just a redefinition of units."³³

Setterfield's scheme is explicitly designed so that the dimensionless numbers are unaffected.

Setterfield's later work, and his answer to the critics

Setterfield did not stop in 1988, and reporting only the 1987 report would misrepresent him.

The reply that was not a reply

The nearest thing to a published Setterfield response to Aardsma is a rebuttal he wrote in August 2000 to a skeptic's critique.  It is a delegation rather than an argument:

"Aardsma's incorrect methodology was pointed out to him by several individuals before he even published the article.  He arguments were also effectively rebutted by Trevor Norman, who was in the Math Dept. of Flinders University.  Norman's rebuttal was based on a superior statistical approach recommended by the then Professor of Statistics in his Department.  Aardsma never fully addressed the issues raised by Norman, and neither did several other statistical detractors.  Furthermore, following an extensive series of analyses, Alan Montgomery presented two articles, one at a Creationist Conference (ICC 1994 Proceedings), the other in Galilean Electrodynamics (Vol.4 No.5 [1993] p93 and following), that effectively silenced all statistical criticism of the c-decay proposition.  Montgomery's two articles have never been refuted."³⁴³⁴

Three observations, offered plainly.

First, Setterfield does not engage the weighting argument himself, anywhere in that piece.  He asserts that Norman answered it.  Norman's rebuttal was not located while writing this article, so it cannot be assessed.

Second, "never been refuted" is not the same as "correct."  Galilean Electrodynamics is a fringe journal devoted to challenging relativity, and papers published there are not widely read;  going unrefuted in that venue is close to automatic.  Montgomery's two papers were not obtained here either, so this article takes no position on their contents beyond noting that neither is cited in the mainstream varying-constants literature.

Third, and most importantly, the four CRSQ papers of 1988 are not mentioned at all — not Humphreys' four minimum standards, not Brown's recomputation, not Holt's pulsar constraint.

The zero-point-energy model

The substantial development is that Setterfield replaced the mechanism.  A page on his site, dated 2 October 2001 and updated in February 2012, lists the changes, and it is more candid than the 1987 report:

"As a result of this extension, some of the conclusions reached in the 1987 Report require modification."³⁵³⁵

The new proposal is that space was invested with energy when it was stretched out, that this energy — the quantum vacuum's zero-point energy — has been increasing ever since, and that a rising zero-point energy is what slows light and slows atomic clocks.³⁵  Atomic energy levels then rise in discrete jumps when the zero-point energy crosses a threshold, which is offered as an explanation of William Tifft's claimed quantised galaxy redshifts.

Three of the changes matter for this article.

The redshift treatment in the 1987 report is withdrawn.  "This means that the treatment of the redshift and the Doppler formula in the 1987 Report has been superseded."³⁵

The historical measurements are no longer the primary evidence.  In the new model the curve of c against time is read off the redshift-distance relation instead:  "the standard graph of redshift plotted against distance is equivalent to a graph of the speed of light plotted against time.  It is the same graph with re-scaled axes."³⁵  That is a substantial retreat.  The 163 historical measurements were the whole empirical case in 1987.  They are now a footnote to a curve derived from something else.

And c may now be rising.  "This oscillation means that the minimum value attained for c around 1970 may be followed by a slight increase or, alternatively, may be followed by further decay after this stationary period has ended. …  However, evidence is accumulating that a slight rise in c has occurred."³⁵

Faulkner's asymmetry test applies here with some force.  A model whose central claim is that light has been slowing down, and which now allows that light may be speeding up, has stopped constraining anything.

The mature version of the model was set out in a 2003 paper with Daniel Dzimano, "The Redshift and the Zero Point Energy," and in a 463-page monograph, Cosmology and the Zero Point Energy, published by the Natural Philosophy Alliance in 2013.³⁶³⁷  The 2003 paper's headline claim is that a rising zero-point energy "predicts that light emitted from distant galaxies should have a basic redshift quantization of 2.671 km/s, which is in good agreement with Tifft's basic quantum of 2.667 km/s," and that the redshift-distance relation follows from vacuum physics rather than from expansion or motion.³⁶  The historical c measurements are still cited, but the 2003 paper calls them exactly what they have become:  "This confirmatory evidence was a topic of discussion by important physicists in key journals."³⁶  The data set has also grown, from 163 values by 16 methods to "638 measurements by 41 methods."³⁶

Two caveats belong with that.  The Natural Philosophy Alliance was an organisation of scientists who rejected relativity and Big Bang cosmology;  Setterfield describes the monograph as having "underwent peer review," and that phrase should not be read as it would be for a mainstream journal.²⁷  And the quantised redshifts the model is built on have been tested directly and failed.  Michael Hawkins, Stephen Maddox and Michael Merrifield examined 1,647 quasar-galaxy pairs from the 2dF survey and found "no evidence for a periodicity at the predicted frequency in log(1+z), or at any other frequency."³⁸  The redshift-quantisation literature is worked through in The Doppler Model of Galaxy Redshifts.

Setterfield's own answer on the fine-structure constant

The most important thing Setterfield has published since 1987 is his answer to the objection this article's middle section makes:  that only a dimensionless quantity can be said to have changed, and that the dimensionless quantity in question is α.

His answer, from 2015, is that α is built from four quantities and that they move in pairs that cancel:

"The data analysis in the Report showed that as c was dropping, h was increasing.  Indeed, the combination hc is an absolute constant, as suggested in the Report, and subsequently proven.  As one went up, the other went down in inverse proportion. …  Likewise, subsequent to the Report, it was demonstrated that the quantity e²/P, which also appears in the fine structure constant, is invariant as well.  In each case, this invariance comes about because of the properties of the vacuum are controlled by the ZPE.

Since Alpha is made up of two sets of invariant combinations of constants, the final result is that Alpha will never register any change, no matter how the speed of light or the other three quantities vary."²⁷

This is the pivot of the whole case, and it is worth being scrupulous about what it does and does not concede.

Setterfield is not denying that α is constant.  He is asserting it, and asserting that his model requires it.  "Alpha will never register any change, no matter how the speed of light or the other three quantities vary" is a strong claim, and it is the claim Duff, Dirac, Ellis and Uzan were all making.  Uzan states the consequence in one sentence:  "any variation of constants that will let these numbers unaffected is actually just a redefinition of units."³³

So the answer to the objection is not a rebuttal.  It is the objection, restated as the model's central feature.  Setterfield has built a scheme in which every dimensionless quantity is preserved — and a scheme in which every dimensionless quantity is preserved is, by the standard the physics literature uses, a change of units and not a change in the world.

He applies the same cancellation to mass-energy — "in the famous equation, E = mc², it is E that remains constant as c changes"²⁷ — and to supernova timing, as quoted earlier.  Each application is internally consistent.  Together they leave the model with no observational consequence anywhere, which is what "no operational meaning" means.

One point of fairness, and one correction

Setterfield's own account of why creationist organisations rejected his work is that it was not about the science:

"Through the years, since 1987, Barry Setterfield's work has been declared invalid by a number of major creationist organizations in both the United States and Australia.  Two reasons have been given for this, which are quite interesting:  1. Barry does not have a university degree and 2. The United States creationist organizations would not have the direction of creation science dictated to them by a 'foreigner.'  Barry is Australian."²⁷

The documentary record does not support that.  It is true that Setterfield had no university degree, and Humphreys says so in print — "a non-degreed researcher who has been studying the velocity of light since 1980."⁷  But what Humphreys, Aardsma, Holt, Brown and Chaffin published were detailed technical critiques:  a weighted least-squares refit, a recomputation of every significance claim, a pulsar-timing constraint, and a from-scratch redetermination of Rømer's value with the author's own telescope as a control.  Humphreys stated in the same paper that he wanted the hypothesis to be true and would have welcomed the book.  Those are not the actions of people dismissing a foreigner without a degree.

Setterfield's own statement of where he stands is worth quoting, because it is honest and because it is the right note on which to close a section about him:

"As a Christian I do accept God's Word, or Scripture, as authoritative on the issues it addresses.  Thus it is reasonable that I would be interested in pursuing an area of research which addresses some of these matters.  I am not infallible and do not claim to have all the facts here."³⁴

The verdict, and who reached it

The verdict on c decay was reached by creationists, published in creationist journals, and is now the stated position of the two largest creation-science organisations.

Andrew Repp's 2022 survey of fifty-seven years of creationist astronomy, in the Creation Research Society Quarterly, records the outcome in one sentence:

"Others, most notably Setterfield (Norman and Setterfield, 1987), proposed a decay extending to modern times, discernable by careful analysis of historical measurements.  However, a general consensus has emerged (see e.g., Chaffin, 1992) that the purported evidence for such decay is artifactual in nature."³⁹³⁹

Note the reference Repp reaches for:  Chaffin 1992, the paper that killed the Rømer anchor.

Creation Ministries International lists the argument under the heading "What arguments are doubtful, hence inadvisable to use?":

"'The speed of light has decreased over time' (c decay).  Although most of the evolutionary counter-arguments have been proven to be fallacious, there are still a number of problems, many of which were raised by creationists, which we believe have not been satisfactorily answered."⁴⁰⁴⁰

Read that last clause again:  "many of which were raised by creationists."  That is an accurate summary of everything above.  The refutation is:

Not one row of that table is an atheist, an old-earth creationist, or a critic of Genesis.  Every one is a young-earth creationist publishing in a young-earth venue.  Humphreys says outright that he wanted the result to be true.  Chaffin retracted his own earlier paper to get there.  Aardsma closes his by quoting Matthew 7 against his own side:  "it will hardly do to point out slivers of this nature in the anti-creationists' eyes, if we are content to have logs in our own eyes."⁵

A movement that does this in print, at cost, deserves to be read on the arguments it has kept.

Verdict:  refuted, and ill-posed besides.  The historical data show no trend once they are weighted.  The largest single lever in the data set was an unpublished figure that turned out not to be real.  The claim as normally stated is about units rather than about the world.  The dimensionless version of the claim is constrained to parts per million where seven orders of magnitude were needed.  The observational anchor the model rested on has been superseded by a measurement thousands of times tighter that finds nothing.  And the model's own author has replaced the mechanism, withdrawn the redshift treatment, demoted the historical data, and allowed that the speed of light may now be rising.

The distant-starlight problem is real, and it is not solved this way.  The other seven answers are graded in Young-Universe Cosmologies.

Objections and responses

"The historical measurements really do decline.  You can see it in the graph."  They do, and that is the honest starting point.  The question is what causes the decline.  Two candidates fit:  a real change in c, or measurements getting better while experimenters are anchored on the previous published value.  The second one predicts something the first does not — that the decline should be steepest inside each measurement technique as it matures, and should flatten as precision improves, which is exactly what the data do.  Humphreys made that point in 1988 and noted that Norman and Setterfield "offered no alternative explanation for the flattening trend."⁷  Faulkner made it again in 2021 and drew a horizontal line through every error bar.¹¹

"Aardsma's weighting was arbitrary — he could have chosen error bars that gave any answer he liked."  He published his rule and it is objective:  for the twenty-eight points with no stated uncertainty, use the scatter of three to eight neighbouring measurements made by the same method within twenty years.⁵  He also showed the result is insensitive to getting those error bars wrong by a factor of two or three, which it must be, because the weights in this data set span fifteen orders of magnitude.⁵  And the single most important finding does not involve weighting at all:  removing one mishandled 1693 point takes the unweighted answer from 38 ± 8 to 11 ± 6 km/s per year.⁵

"The modern laser measurements are so precise that a weighted fit is forced to be flat.  Of course you find no decay."  Aardsma anticipated this and threw the post-1972 laser values out.  The refit gives 0.0101 ± 0.0068 km/s/year — still consistent with zero, and still 3,700 times smaller than the claimed rate.⁵

"Setterfield says other constants changed to compensate, so of course no experiment detects it."  That is exactly the problem, and it is the model's own words:  "the atom sees no change in c!"¹  If every dimensionless quantity is preserved, nothing observable follows from the change, and the hypothesis has bought immunity from testing at the price of content.  Holt put it plainly in 1988:  "If something cannot be detected and measured, it is not subject to the scientific method."⁹

"Webb's group has reported a varying fine-structure constant.  Doesn't that vindicate the idea?"  No, and the scale is why.  Webb's largest claimed effect is about one part in 100,000.¹⁴  The best current measurements are consistent with zero at the level of parts per million,¹⁹ and the best laboratory limit is one part in 10¹⁸ per year.²⁴  Setterfield's model needs a change of about ten million-fold.  A claimed anomaly at 10⁻⁵ does not license a hypothesis at 10⁷.  It is also worth noting that the α-variation claim has been weakened by the discovery of a wavelength-calibration systematic capable of faking it — found by one of Webb's own co-authors.¹⁶

"The Oklo constraint assumes the reactor ran two billion years ago, which a young-earth creationist rejects."  Correct, for the rate limits.  Fujii's and Petrov's 10⁻¹⁷ per year figures divide a measured shift by an assumed 2-Gyr interval, and a reader who rejects the interval may reject the rate.  But Damour and Dyson's limit is on the fractional shift itself — α while the reactor ran differed from α now by less than about one part in ten million — and that follows from the isotope ratios and the neutron physics regardless of when the reactor operated.²¹  For c decay, the fractional shift is the relevant number.

"Eugene Chaffin argued that the Oklo limits are illusory."  He did, in 1990, and his objection was that the reactor's operating temperature and neutron spectrum were poorly known.²³  Both objections were then addressed:  Damour and Dyson treated the temperature as an explicit large uncertainty rather than a fixed number, and Petrov's group replaced the assumed Maxwellian neutron spectrum with one computed by two independent Monte Carlo reactor codes — and reported that this changes the cross-sections significantly, yet leaves the limit standing.²²  Chaffin is also the man whose 1992 paper destroyed Setterfield's Rømer anchor, so he is not being cited selectively here.

"This is just secular physicists ruling out a creationist idea."  It is not, and that is the most important thing in this article.  Every stage of the refutation was carried out by young-earth creationists publishing in young-earth journals:  Aardsma and Humphreys in June 1988, Holt and Brown in September 1988, Chaffin in 1992, Faulkner in 2021, Repp recording the consensus in 2022.  The secular physics — Duff, Ellis and Uzan, the quasar spectroscopists, the lunar laser rangers — arrives afterwards and independently, and agrees.

"So what does solve the distant-starlight problem?"  Nothing yet, and that should be said plainly.  Seven other answers have been published, and the honest audit of all of them is in Young-Universe Cosmologies.  Several are dead.  The surviving ones reproduce standard observational cosmology exactly, by construction, which is why none has been refuted and why none has predicted anything.  The problem is open.  A retired argument is not a substitute for a working one, and pretending otherwise is what got this argument into print in the first place.

Sources