"The Doppler model is currently the only model that fits both size and luminosity data and passes the Tolman test." — Jason Lisle, 2025, in Answers Research Journal.1
"Thus, the 'Doppler Model' of Lisle (2024) is physically indistinguishable from an expanding space model. It is a mere redescription." — Luke Barnes, 2024, replying in the same journal. Barnes is a Christian astrophysicist; the journal is published by Answers in Genesis.2
Summary
Every galaxy outside our own small neighbourhood has its light shifted toward the red end of the spectrum, and the further away the galaxy, the bigger the shift. That is not in dispute. What the shift means is.
There are two live physical pictures. In the first, galaxies sit almost still and the space between them stretches, stretching the light along with it. In the second — the Doppler model — space does not stretch at all, and galaxies are simply flying away from us through it, the way a receding ambulance lowers the pitch of its siren.
In 2024 the young-earth astrophysicist Jason Lisle published a paper in Answers Research Journal arguing that new James Webb Space Telescope data settle this in favour of the second picture, and that the result kills the big bang.3 Later that year Luke Barnes — an astrophysicist, a Christian, and no young-earth creationist — published a reply in the same journal saying the argument fails.2 Lisle answered in 2025.1 That three-paper exchange is the spine of this article.
The short verdict: Lisle is right that the raw data are strange, right that galaxy evolution is used as an adjustable escape hatch, and wrong on the physics that his central claim depends on.
Here is what this article concludes, with the evidence in the sections below.
- "Doppler shift" versus "expanding space" is mostly an argument about words. Within general relativity the two descriptions of the same spacetime are related by a change of coordinates, and standard references on both sides of the creation debate say so. Anyone who tells you that one is obviously right and the other obviously absurd has skipped the literature.45
- What is not an argument about words is the geometry. A universe whose large-scale geometry is static makes different predictions from one whose geometry expands. That is a real, testable difference, and it is what Lisle is actually claiming. This article treats it as a serious claim and tests it.
- Lisle's headline result rests on an error in one equation. His model predicts that surface brightness falls as (1+z)3 while the standard model predicts (1+z)4, and the measured value is near 3. But (1+z)4 dimming is a theorem — Etherington's reciprocity theorem — that holds in any spacetime where light travels on null geodesics and photons are not destroyed. That includes flat, static, non-expanding space. Corrected, the Doppler model predicts (1+z)4 as well, the claimed advantage disappears, and the model then fails badly against supernova data. The two equations in Lisle's paper that produce the (1+z)3 are not even consistent with each other.36
- The Tolman surface-brightness test cannot tell Doppler from expansion at all. What it actually tests is whether the redshift is a metric effect — light following straight paths through a geometry — or something else. It kills tired light decisively, which is exactly what its authors used it for. It has nothing to say about which metric.
- Neither author ran the obvious independent tests. This article runs three of them. Fitting the published Pantheon+ catalogue of 1,371 supernovae, Lisle's distance-redshift law is disfavoured against the standard model, and the corrected version of his own model is excluded outright. Measurements of the temperature of the microwave background at high redshift, and of galaxy-cluster velocities relative to that background, both point the other way by very large factors.
- The Doppler model does not give a young universe. In Lisle's own model the most distant confirmed galaxy is 13.8 billion light years away and receding at 99% of the speed of light. Under the ordinary convention for clock synchronisation its light has been travelling for 13.8 billion years. Barnes made this point; Lisle agreed with it in print. The young universe comes entirely from a separate proposal of Lisle's about the conventionality of simultaneity, and that proposal works — or fails — with the big bang exactly as well as it works with the Doppler model.21
- Quantised redshifts are not real. The nearby-galaxy periodicity claim depends on a tuned reference frame; the quasar periodicity claim was directly tested in two large surveys and failed; and the one measured periodicity in Sloan quasar counts was traced to a telescope filter artefact by John Hartnett, the creationist physicist who had championed the idea.7 If quantisation were real it would wreck the Doppler model too.
- Something genuinely odd is going on with distant galaxy sizes and surface brightnesses, and it is being reported by people with no religious stake in it. A preprint from April 2026 analysing 6,860 JWST galaxies finds "a significant departure from the prediction of the standard cosmological model."8 That is the real anomaly, and it is not settled.
What follows for a reader who doubts the big bang: the honest answer is that this particular argument does not work yet, and that saying so is worth more than another apologetics talking point that a physics graduate student can dismantle in an afternoon.
Four claims, not one
Most of the confusion in this debate comes from treating four separate claims as a package. They are logically independent and the evidence for them is very different.
| Claim | Status | Depends on |
|---|---|---|
| 1. Galaxy redshift increases with distance (Hubble's law) | Measured. Not seriously disputed by anyone. | Nothing but observation |
| 2. The redshift means the galaxies are receding | Very strong, but an inference | Ruling out other causes of a wavelength shift |
| 3. The recession is caused by space itself expanding | A model choice; partly a matter of coordinates | General relativity |
| 4. The expansion began in a hot, dense state 13.8 billion years ago | A further model, with its own separate evidence | Nucleosynthesis, the microwave background, structure formation |
You can accept 1 and 2 and reject 4. Several young-earth astronomers do. Danny Faulkner — a young-earth creationist with a PhD in astronomy — wrote an entire paper in Answers Research Journal urging creationists to accept the Hubble relation, universal expansion, and cosmological quasar redshifts, and warning that "if the universe is expanding, but we reject this, it would be impossible to construct a correct biblical cosmology."9 John Hartnett, also a young-earth creationist, argued the opposite in the same journal.10 This is not a debate between believers and skeptics. It is a live technical disagreement that runs straight through the creationist community.
Why the redshift is almost certainly motion
Before comparing the two motion pictures, it is worth being clear about what has already been eliminated, because this is where the amateur alternatives live.
The shift is uniform. Every wavelength from a given galaxy is stretched by the same factor. A one-nanometre wave becomes a two-nanometre wave and a one-metre radio wave becomes a two-metre radio wave, in exact proportion. No interaction between light and matter does that. Scattering off electrons, dust, or gas is always wavelength-dependent, and it also blurs images. Distant galaxies are not blurred.11
Gravity cannot do it either. A gravitational redshift of the size observed would require the source to sit deep in a potential well. Galaxies are far too diffuse, and their stars orbit thousands of times too slowly, for that.11
Tired light is dead, and it was killed by data, not by consensus. Fritz Zwicky's 1929 proposal was that photons simply lose energy on long journeys.12 It makes two predictions that are now decisively refuted:
- No time dilation. If light only loses energy, a supernova that takes 30 days to rise and fall should still take 30 days when seen from far away. It does not. Supernova light curves and even supernova spectra age more slowly by exactly a factor of (1+z).1314 In 2023 the same (1+z) stretching was finally detected in the variability of 190 quasars monitored for two decades, closing the last loophole; a 2025 reanalysis that allowed for intrinsic scatter still found the cosmological dependence "robust," at n = 1.14 ± 0.34 where relativity predicts 1.1516
- Too little surface-brightness dimming. Tired light predicts surface brightness falling as (1+z)1. Hubble Space Telescope data "rule out the 'tired light' model at a significance level of better than 10 sigma."17
That is a genuine, clean falsification of a named alternative, and creationists should say so plainly. What survives is motion. The question is what kind.
The two pictures, and why the fight is partly about words
Picture A: space is a fixed stage, and galaxies move across it. Picture B: galaxies are pinned to the stage, and the stage itself is being stretched.
Here is the part almost every popular treatment gets wrong. In general relativity there is no way to compare the velocity of a distant object with your own, because there is no global standard of rest — velocity comparison requires bringing two vectors to the same point, and in curved spacetime the answer depends on the path you take. Once you fix a sensible path, the answer falls out. Emory Bunn and David Hogg did exactly that in the American Journal of Physics in 2009 and concluded that "the most natural interpretation of the redshift is as a Doppler shift, or rather as the accumulation of many infinitesimal Doppler shifts."4 Two years earlier Luke Barnes had co-authored the paper defending the other convention, arguing that expanding space is "a completely valid framework for the description of the evolution of the universe."5 Both papers are right, because they are answering different questions with different bookkeeping.
Barnes made the same point to Lisle, citing the standard graduate textbook: "redshifts in all 'expanding space' models (FLRW) can be calculated as an accumulation of small Doppler shifts… the difference between the 'expanding space' picture and the 'Doppler' picture is a mere change in perspective, a coordinate transformation."2
Lisle agreed with that as far as it goes, and then made the move that matters:
I agree with Barnes (and Peacock) that this is the case for expanding space models. But the entire point of my paper is that space might not be expanding. I am hypothesizing that the FLRW metric is not correct, and that the true metric of the universe may be approximately, and perhaps temporarily, static.1
That is the right response, and it converts a semantic dispute into a physical one. A static geometry and an expanding geometry are genuinely different, and they predict different relationships between redshift, apparent size, and apparent brightness. From here on this article treats the question as Lisle poses it: is the large-scale geometry static?
Note
One important piece of background that neither paper mentions. The self-consistent version of "an explosion of galaxies through flat, static space" already has a name in the literature: the Milne model, published by E. A. Milne in 1935. It is an ordinary special-relativistic explosion — every galaxy moving inertially away from a common origin — and it is mathematically identical to an empty expanding-universe solution of Einstein's equations. The same spacetime, written in two coordinate systems. Barnes's "mere redescription" charge is not a rhetorical flourish; for the one fully worked-out version of the Doppler picture, it is a theorem. Lisle's model, as will be shown below, is not the Milne model, and he never says what spacetime it is.
What Lisle's Doppler model actually says
The model is compact enough to state completely. Space is not expanding. A galaxy's redshift is a pure relativistic Doppler shift from its motion, so its recession speed is
v = c [(1+z)2 − 1] / [(1+z)2 + 1]
and its distance is that speed divided by the Hubble constant, taken as 70 km/s per megaparsec:
DD = (c/H0) [(1+z)2 − 1] / [(1+z)2 + 1]
Lisle calls this the Doppler distance, and says it "corresponds to the true distance to a galaxy when the light was emitted."3 Because speed can never reach c, this distance never exceeds c/H0 = 4,283 megaparsecs, or 13.97 billion light years. No galaxy, at any redshift however large, was further away than that when its light left.
Three consequences follow, and all three of Lisle's published numbers reproduce exactly when the equations are recomputed from scratch:
- Angular size flattens out. Because distance saturates, a galaxy of fixed physical size approaches a fixed minimum angular size. For the 4.5 kiloparsec galaxy Lisle adopts, that floor is 0.217 arcseconds — his stated prediction of "just over 0.2 arcseconds" beyond redshift 15.
- No magnification. In the standard model, angular diameter distance peaks at z ≈ 1.6 and then falls, so galaxies beyond that redshift should look bigger the further away they are. Lisle's model has no such turnaround. The predicted ratio between the two models is 5.95 at z = 13, 6.64 at z = 15 and 8.33 at z = 20 — matching his published 5.9, 6.6 and 8.3.
- Slightly fainter galaxies. Relativistic beaming makes a receding source dimmer. Lisle's luminosity distance is DD(1+z)1.5, which makes standard-model absolute magnitudes come out about one magnitude too faint at z = 13.
Set against the JWST deep fields, the fit is visually excellent, and Lisle's summary is not overstated for what he plotted: "all the median values are within one standard deviation, and several are nearly centered on the predicted curve itself. None of the data are within one standard deviation of the ΛCDM curve."3
He then runs the Tolman surface-brightness test, and this is where the argument's weight sits. His model predicts surface brightness falling as (1+z)3; the standard model predicts (1+z)4; the measured value from Lubin and Sandage is near 3. His conclusion: "The Doppler model therefore passes the Tolman test while the standard ΛCDM model and the tired light model do not."3
Barnes's reply, and what it did and did not establish
Barnes's objection is narrow and, on its own terms, correct. Lisle's "standard model" curve assumes galaxies have the same average physical size — 4.5 kiloparsecs — at every redshift. No version of the standard model says that. Barnes ran the publicly available SAGE semi-analytic galaxy-formation model on the MultiDark simulation, computed the predicted angular sizes with real galaxy growth included, and found them consistent with the same JWST data Lisle used. His verdict: "the 'standard model' prediction of Lisle (2024) is both inadequate and inexcusable. It is a straw man."2
He is right that a fixed-size population is not the standard model's prediction, and right that the size growth of dark-matter haloes and their galaxies "is a firm prediction of analytic, N-body and hydrodynamical simulations of galaxy formation."2 He also notes, honestly, that SAGE was published in 2016 and its parameters were never tuned to JWST — so it is a genuine prediction, not a retrofit.
Two things Barnes's reply does not do.
It does not model the survey. Barnes says so himself: he did not include selection criteria, photometric dropouts, or dust. A magnitude-limited survey at z = 12 sees only the brightest handful of galaxies, so comparing a simulated population mean with an observed median of detections is not a like-for-like test in either direction. Neither author does this properly, and it is the single biggest hole in the whole exchange.
It does not answer the mass objection. Lisle's counter-reply is his strongest passage. SAGE, run with Barnes's own parameters, says the average galaxy at z = 12 is about 80 times less massive than a local galaxy. But JWST finds high-redshift galaxies with masses in the local range. If those galaxies are as massive as nearby ones and five to ten times smaller across, they are roughly a thousand times denser, and no simulation predicts that. As Lisle puts it: "no secular model proposes that galaxies grow in size without gaining substantial mass."1
That is a real problem for Barnes's specific rebuttal. It is a weaker problem for the standard model in general, for two reasons Lisle does not weigh. The first is selection again: the JWST-detected objects at z = 12 are the extreme bright tail, not the average, and the mass function's bright end is exactly where a hierarchical model puts its rare massive objects. The second is that the reported high-redshift masses have been falling steadily. Every one of the six "impossible" massive candidates from the 2023 Nature paper that has since been observed spectroscopically came in at a lower redshift or a lower mass than the photometry suggested, and one turned out to be an active galactic nucleus at z = 5.6 rather than a galaxy at z = 8.1.1819
Barnes closes with two claims that go beyond his data. One — that the Doppler model is "physically indistinguishable from an expanding space model" — is defensible and is examined below. The other — "It's another Big Bang model" — is not quite right, and the next section shows why.
Checking the physics: three problems with the Doppler model
Everything to this point is a summary of the published exchange. The rest of this article is independent work: the model's equations recomputed, and tests neither author ran.
Problem one: the surface-brightness claim rests on a broken equation
This is the decisive point, and it is easy to check.
Lisle's luminosity reduction from relativistic beaming appears twice in his paper, and the two versions disagree. His equation (11) gives the reduction as
LR = [(1 − v/c) / (1 + v/c)]3
and his equation (12) states that the same quantity equals 1/(1+z)3. But for a pure Doppler shift, (1 − v/c)/(1 + v/c) is exactly 1/(1+z)2. Cubed, that is 1/(1+z)6, not 1/(1+z)3. The two equations cannot both be true. Everything downstream uses the second one.
More important than the bookkeeping is that the correct answer is neither. For a discrete source receding directly away, the received power is reduced by the fourth power of the Doppler factor, not the third. One power comes from each photon losing energy, one from the reduced arrival rate, and two from relativistic aberration beaming the radiation forward. The third-power version is the formula for a continuous jet whose emitting volume is fixed in the observer's frame — a standing feature of blazar astrophysics, and not what a galaxy is.
There is a much stronger way to see this, which requires no beaming calculation at all. Etherington's reciprocity theorem, proved in 1933, states that luminosity distance and angular diameter distance are always related by
DL = (1 + z)2 DA
The theorem is "valid for all cosmological models based on Riemannian geometry, being dependent neither on Einstein field equations nor the nature of matter-energy content." It requires only that source and observer are joined by light travelling on null geodesics, and that photons are not created or destroyed on the way.62021 Flat, static, non-expanding Minkowski space satisfies both conditions trivially. So does an expanding universe. The relation has been tested directly against data and holds to about 2%.22
Since surface brightness is proportional to (DA/DL)2, the theorem forces surface brightness to dim as (1+z)−4 in every metric theory — expanding, static, Doppler, or otherwise. Tired light escapes only because it is not a metric effect at all: it destroys photon energy along the way, which is precisely why it fails.
The consequences for Lisle's paper are direct. With the reciprocity theorem enforced, his own geometry predicts:
| Quantity | Lisle's published value | Corrected |
|---|---|---|
| Luminosity distance | DD(1+z)1.5 | DD(1+z)2 |
| Surface-brightness exponent | (1+z)−3 | (1+z)−4, same as the standard model |
| Standard-model magnitudes "too faint" at z = 13 | 1.0 magnitudes | 3.9 magnitudes |
| Predicted magnitude slope with redshift | about 0.067 per unit z | about 0.30 per unit z |
| Observed slope (Lisle's own fit) | 0.096 ± 0.038 | 0.096 ± 0.038 |
The claimed victory in the Tolman test evaporates, and the corrected model then fails the brightness test Lisle designed himself, by a factor of three. The (1+z)1.5 is not a detail. It is the load-bearing wall.
An aside on the Tolman test that nobody on either side gets right
Because the (1+z)−4 law is a theorem rather than a model prediction, the Tolman surface-brightness test cannot distinguish an expanding universe from galaxies flying through static space. It never could. What it distinguishes is metric redshifts of any kind from non-metric ones. Sandage's famous summary — "The Tolman prediction is verified. The expansion would seem to be real" — is a correct refutation of tired light and an overstatement about expansion.23
There is a second problem with reading a cosmological exponent off the Lubin and Sandage numbers, and it cuts against Lisle specifically. Their measurement was n = 2.59 ± 0.17 in the rest-frame R band and n = 3.37 ± 0.13 in the rest-frame I band.17 Lisle averages the two to 2.98 ± 0.55 and observes that this matches his predicted 3.3 But a geometric exponent cannot depend on which colour filter you use. The dimming law is the same in every rest-frame passband. A measurement that gives 2.59 in one band and 3.37 in another, with quoted errors of 0.17 and 0.13, is telling you that something band-dependent is present at high significance — which is exactly what stellar-population evolution looks like, since bluer bands change faster as a population ages. Sandage's own follow-up says as much: the data require "a luminosity evolution… of 0.8 mag in Rcape and 0.4 mag in the Icape photometric rest-frame bands."23 Averaging two mutually inconsistent numbers to recover a third is not a measurement of cosmology.
Problem two: the fit has a hidden free parameter
Lisle writes that "the Doppler model has only one adjustable parameter — the Hubble constant."3 It has at least two. The other is the assumed physical diameter of a typical galaxy, and the predicted curve scales directly with it.
He takes it from the Local Group, and states the numbers honestly: of about thirty confirmed members, the mean diameter is around 5,000 parsecs and the median is 1,350 parsecs. He picks 4,500 parsecs, reasoning that dwarf galaxies are under-represented in magnitude-limited surveys — a defensible argument, but a choice, and the range it is chosen from spans a factor of 3.7:
| Assumed galaxy diameter | Doppler-model angular-size floor |
|---|---|
| 1.35 kpc (Local Group median) | 0.065 arcsec |
| 3.0 kpc | 0.145 arcsec |
| 4.5 kpc (Lisle's choice) | 0.217 arcsec |
| 5.0 kpc (Local Group mean) | 0.241 arcsec |
The observed high-redshift medians sit near 0.2 arcseconds. Moving the nuisance parameter within its own stated range moves the prediction across almost the whole gap between the two models. A one-parameter model that fits is impressive; a two-parameter model where the second parameter was chosen after looking at the answer is not.
Problem three: the velocity law is not the self-consistent one, and the fit needs the young universe to work
Lisle assumes the Hubble law is exactly linear in the emission distance, at every redshift. He flags this as an assumption: "let's assume for the sake of hypothesis that the Hubble law is truly linear with respect to velocity even at high redshifts."3 It is a much stronger assumption than it looks.
Take the ordinary picture: galaxies moving inertially through static space, light travelling at c. A galaxy we see at redshift z emitted that light when it was closer than it is now, and how much closer depends on how long the light has been in flight. Working it through gives the emission distance
D = (c/H0) · β / (1 + β)
not (c/H0) · β. That is the Milne result, and it is a factor of (1+β) smaller than Lisle's — approaching a factor of two at high redshift. The angular sizes it predicts are therefore twice Lisle's:
| Redshift | Standard model | Milne (self-consistent kinematic) | Lisle |
|---|---|---|---|
| 1.6 | 0.531" | 0.509" | 0.292" |
| 5 | 0.716" | 0.446" | 0.229" |
| 10 | 1.082" | 0.437" | 0.220" |
| 15 | 1.450" | 0.435" | 0.218" |
| 20 | 1.815" | 0.434" | 0.218" |
Angular diameter of a 4.5 kpc galaxy. Milne's curve is as flat as Lisle's — the "no magnification" claim survives — but it sits at twice the height, in the middle of the gap rather than at the bottom of it.
Why does Lisle's version differ? Because his relation only holds if the light travel time is zero. For a single Hubble constant to describe the velocity field at every emission epoch, either the epochs must all be effectively "now," or the expansion rate must be exactly constant in time, which for freely coasting matter it is not.
This is where the young universe re-enters, and it is not incidental. Lisle's other well-known proposal is the anisotropic synchrony convention (ASC), on which light travelling toward an observer arrives instantaneously, so we see galaxies as they are today rather than as they were.24 Under ASC, "the distance at emission" and "the distance now" are the same thing, and Lisle's velocity law becomes self-consistent — at the price of making the Hubble law a created initial condition with no dynamical explanation. Under the ordinary convention, in a universe old enough for the light to have arrived, the same kinematics give the Milne curve instead.
So the angular-size fit that is presented as independent evidence for a static universe is not independent of the young-universe framework at all. It needs it.
Three tests the exchange never ran
Supernovae: the model can be checked against 1,371 published measurements
Lisle proposes type Ia supernovae as a future test, and says a high-redshift supernova light curve "would be extremely rewarding."3 That test has already been done, many times over. The Pantheon+ compilation contains 1,701 supernovae, and its distance moduli and redshifts are a public download.25
Fitting each model to the 1,371 supernovae above z = 0.023 that are not calibrators, with the absolute-magnitude and Hubble-constant combination marginalised away so that only the shape of the distance-redshift relation is being tested, gives:
| Model | Δχ² versus the standard model |
|---|---|
| Standard model (ΩM = 0.3) | 0 |
| Milne (self-consistent kinematic) | 29 |
| Lisle's Doppler model as published | 126 |
| Lisle's model with reciprocity enforced | 1,785 |
| Tired light | 1,583 |
The ordering is stable when the low-redshift cut is raised to z > 0.1 or z > 0.2, which rules out peculiar-velocity contamination as the cause. These use the diagonal statistical errors only, so they overstate significance somewhat; the published covariance includes correlated systematics that would soften the numbers. But the size of the gap is not in doubt. Lisle's published model is disfavoured, and the physically corrected version of his own model — the one the reciprocity theorem forces — is dead many times over.
The residuals show where the strain is. Against the standard model, Lisle's law is 0.06 magnitudes too bright at z ≈ 0.03 and 0.20 magnitudes too faint at z ≈ 1.8 — a monotonic drift of a quarter of a magnitude across the sample. It is the systematic shape of that drift, not any single point, that the χ² is responding to.
The microwave background temperature at high redshift
In an expanding universe the background radiation cools as the universe grows, so its temperature at redshift z should be T0(1+z). In a static universe with galaxies flying through a fixed radiation bath, it should not.
The prediction has been measured, repeatedly, using molecules in distant gas clouds as thermometers. Carbon monoxide absorption in quasar spectra gives T(z) = (2.725 ± 0.002) × (1+z)(1−β) with β = −0.007 ± 0.027 — the exponent is 1 to within 3%.26 Water absorption in a starburst galaxy puts the background at 16.4–30.2 K at z = 6.34, against 20.0 K predicted.27 Sunyaev-Zel'dovich measurements in hundreds of galaxy clusters agree independently.2829
The Doppler model owes an account of this, and both available answers are bad.
- If the background is a fixed bath in static space, then a cloud at z = 2.4 is ploughing through it at 84% of the speed of light and sees a radiation field that is not a blackbody at all but a violent dipole, twelve times hotter ahead than behind. Every measurement in this literature fits an isotropic blackbody, and they agree with each other across CO, atomic carbon, water and cluster scattering.
- If the background is comoving with the galaxies, then it is expanding and cooling with them — which is the expanding-universe picture Lisle is rejecting.
Galaxy clusters are at rest in the microwave background, and they should not be
This is the sharpest test available, and it is remarkably simple.
When microwave background photons scatter off hot gas in a galaxy cluster that is moving, they pick up a Doppler shift proportional to the cluster's velocity. This is the kinematic Sunyaev-Zel'dovich effect, and it is a direct velocimeter: the temperature shift is roughly the optical depth times v/c. It has been measured. For MACS J0717.5+3745 at z = 0.55 — an extreme triple merger, chosen precisely because it moves fast — the line-of-sight velocity of one sub-cluster is +3,450 ± 900 km/s.30
In Lisle's model that same cluster is receding through static space at 41% of the speed of light: 123,000 km/s. The kinematic signal would be about 11 millikelvin — an order of magnitude larger than the thermal Sunyaev-Zel'dovich decrement of even the most massive clusters, and roughly a hundred times larger than the primary background fluctuations. It is not there, by a factor of about thirty-six in velocity.
The measured cluster velocities are small peculiar motions, exactly what you expect if clusters are essentially at rest relative to the radiation — which is what an expanding universe predicts and what "everything is flying through static space at relativistic speed" cannot accommodate. Again, the only escape is to make the radiation comove with the matter, and that escape is the expanding picture.
A note on Barnes's inversion, corrected
Barnes claimed Lisle's model can be rewritten as an expanding model and is therefore "another Big Bang model." The first half is right and can be carried out explicitly. Setting the standard angular-diameter-distance formula equal to Lisle's Doppler distance and solving for the expansion rate gives a flat expanding universe with
H(z)/H0 = [(1+z)2 + 1]2 / [(1+z)4 + 4(1+z)2 − 1]
This dips to 0.81 H0 around z = 1 and then climbs back toward H0 at high redshift. Because the expansion rate tends to a constant, the model is exponentially expanding in its early history and has no beginning at all — the lookback time to z = 1,000 is 101 billion years and the integral diverges. So the equivalent model is not a big bang model; it is a past-eternal de Sitter-like universe.
Barnes's substantive point survives the correction, though, and it is the one that matters: a static-space Doppler model with a given distance-redshift relation and an expanding model with the same relation make the same observational predictions, because the reciprocity theorem ties luminosity distance to angular diameter distance in both. Two descriptions that agree on everything measurable are not two theories.
Where Lisle is right, and it matters
An article that only listed the problems would be dishonest, because the anomaly he is pointing at is real.
The angular-size turnaround genuinely is not seen in the raw data. The standard model says galaxies beyond z ≈ 1.6 should start looking bigger. Observed sizes keep shrinking. The standard resolution is that intrinsic sizes shrink faster than the magnification grows — and that is a measured effect, with effective radius scaling roughly as (1+z)−1.48 for early-type and (1+z)−0.75 for late-type galaxies out to z = 3.31 But those sizes were themselves derived assuming the standard model's distances. Lisle's complaint about circularity has force, and dismissing it as creationism is not an answer.
Galaxy evolution really is used as an adjustable escape. Lubin and Sandage needed roughly one to one-and-a-half magnitudes of luminosity evolution to reconcile the Tolman measurement with (1+z)4, and said so.17 Pre-launch models of early galaxy formation were revised after JWST found more, brighter galaxies at high redshift than expected. Lisle's rhetorical question — "How many 'epicycles' must be added before we reconsider the underlying paradigm?" — is the right question to keep asking, even when the answer this time is "not yet."3
And the surface-brightness anomaly is being reported by people with no stake in Genesis. A preprint posted on 30 April 2026 analysed 6,860 galaxies with spectroscopic redshifts from the ASTRODEEP-JWST catalogue and reported that mean surface brightness does decrease with distance, but that "the observed trend shows a significant departure from the prediction of the standard cosmological model, which expects the mean surface brightness to decline as (1+z)−4."8 That group has argued for static cosmologies before and should be read with that in mind, and a preprint is not a result. But the honest summary is that the Tolman test in the JWST era is unresolved, and that a young-earth astronomer reading the same tea leaves is not being unreasonable — only premature.
Quantised redshifts: what is real and what is noise
A separate line of argument holds that galaxy redshifts are not smoothly distributed but come in steps. If true it would be revolutionary. It would also, and this is rarely noticed by its creationist advocates, destroy the Doppler model, which needs a smooth, monotonic velocity-distance relation to predict anything at all.
The claims come in three families.
Nearby galaxies, ~37.5 km/s. William Tifft reported redshift steps in the 1970s. Bruce Guthrie and William Napier refined it: a periodicity near 37.5 km/s among spiral galaxies within about 2,600 km/s, and near 71.5 km/s in the Virgo cluster, with claimed chance probabilities below 10−5.32
The problem is not the arithmetic; it is a free parameter. The periodicity appears only after correcting the measured redshifts into a "galactocentric" frame, and the correction vector — the Sun's motion about the galactic centre — is not precisely known. Analyses scanned a range of candidate vectors and reported the strong signal for the one that produced it.33 Scanning a family of transformations and quoting the significance of the best one, without a trials correction, will manufacture a periodicity out of noise reliably. Nothing of this kind has been reproduced in a large, homogeneous modern sample. The dataset that could settle it exists — the ALFALFA survey has about 31,500 hydrogen-line redshifts with the few-km/s precision the test requires, more than a hundred times Guthrie and Napier's sample — and no detection from it has been published.
Quasars, periodic in log(1+z). Karlsson's claimed preferred redshifts (0.06, 0.30, 0.60, 0.96, 1.41, 1.96) are evenly spaced in log(1+z) with a period near 0.089, and Halton Arp built a career on the idea that quasars are ejected from nearby galaxies with intrinsic redshifts.34 This one has been tested head-on and failed twice. Hawkins, Maddox and Merrifield took 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."35 Tang and Zhang repeated the test on Sloan and 2dF data and found none in the high-completeness samples.36 A 2024 revival using singular value decomposition on Sloan quasar-galaxy pairs reports periodicities again, but on a selected, transformed sample and without a look-elsewhere correction.37
Sloan quasar number counts. This is the most instructive case, and the decisive paper was written by a creationist. John Hartnett found apparent periodicities of Δz = 0.258, 0.312, 0.44, 0.63 and 1.1 in Sloan DR6 quasar counts — and then found the same periods in the survey's own redshift-confidence flag. His conclusion, in his own abstract: "these redshift periods must result from some selection effect, as yet undetermined. It does not signal any intrinsic (quantized) redshifts in the quasars."7 The mechanism was later identified. Sloan selects quasars by colour, and strong emission lines crossing the gaps between filter passbands make quasars at certain redshifts harder to detect, imprinting "a periodicity of Δ(z) ~ 0.6… on the redshift-number distribution."38
The verdict. There is no credible evidence for quantised redshifts. There is one real preferred scale in the distribution of galaxies — the baryon acoustic oscillation near 150 megaparsecs — but it is a single broad bump in the two-point correlation function, not a comb of evenly spaced lines, and it is a prediction of the expanding model rather than an embarrassment to it.
The wider lesson is worth stating, because this failure mode recurs across apologetics. A periodicity search over an unspecified range of frequencies, on a small sample, with a tunable coordinate transformation applied first, will find something at 99% confidence essentially every time. Hartnett's 2009 paper is the model of how a scientist with a stake in the answer should handle it.
What this means for the age of the universe
This is the question most readers came for, and the answer is blunt.
The Doppler model does not shorten the age of the universe. Run the numbers in Lisle's own equations. The most distant spectroscopically confirmed galaxy, MoM-z14 at z = 14.44, is receding at 99.2% of the speed of light and sits 13.85 billion light years away.39 Under the ordinary convention for synchronising clocks, its light has been in flight for 13.85 billion years. For comparison, 1/H0 is 13.97 billion years for H0 = 70, and the standard model's age is 13.8 billion years. These are the same number.
Barnes said this plainly: "In both the Doppler Model and the standard model, the finite speed of light will make the universe appear to be billions of years old, so supporting the first while criticising the second does nothing to solve the Starlight and Time problem."2
And Lisle agreed with him, in print. His reply:
Quite right. The Doppler model is not needed to explain distant starlight in a young universe. Rather, it was invoked to explain the angular size and luminosity data in JWST deep fields.1
The young universe in Lisle's framework comes from a different proposal entirely: the anisotropic synchrony convention, on which the one-way speed of light toward an observer is taken to be infinite, so distant events are seen as they happen. Whether that convention is legitimate is a genuine question in the philosophy of relativity — Einstein himself treated the one-way light speed as a matter of definition — and it is disputed inside the same journal, where Phillip Dennis has published two papers arguing the ASC model is internally inconsistent.40 What is not in question is the logic: ASC is what does the young-universe work, and, as Lisle concedes, "the ASC model doesn't assume any particular metric, it is compatible with either the FLRW metric or the Doppler model."1
So the two ideas are separable, and each must stand on its own. The Doppler model is an empirical claim about geometry, and the tests above go against it. ASC is a claim about conventions, and it neither needs nor supports the Doppler model. Presenting them together as a package that yields a young universe from JWST data is the one thing the exchange establishes cannot be done.
Objections and responses
"Redshift only tells you a wavelength changed. Any claim about motion is interpretation." True, and worth insisting on. But the interpretations are not equally supported. A uniform stretch of every wavelength by the same factor, with no blurring, plus a matching (1+z) slowdown of distant clocks measured in both supernovae and quasars, is what motion predicts and what no light-matter interaction produces.
"Superluminal recession proves the standard model is absurd. Galaxies beyond z ≈ 1.5 recede faster than light." They do, in the standard model, and it is not absurd. Special relativity forbids anything from overtaking a light beam locally; it says nothing about the rate at which the distance between two far-apart objects grows in curved spacetime. This is a genuine strength of the Doppler picture rhetorically and no strength at all physically. Note the price: in the Doppler model no light can ever have set out from further than 13.97 billion light years away, no matter how large the redshift, so the visible universe is packed into one Hubble radius and every additional unit of redshift buys almost no additional distance.
"The big bang requires dark matter and dark energy, which nobody has ever detected." A fair complaint about the standard model, and one this site will treat separately. It is not an argument for the Doppler model, which has no account of galaxy rotation curves, cluster masses, gravitational lensing, or the acceleration of the expansion either. Replacing one model's unsolved problems with another model's silence is not progress.
"The Tolman test favours the Doppler model, as Lisle showed." It cannot favour it. The (1+z)−4 dimming law follows from Etherington's reciprocity theorem in any spacetime where photons travel on null geodesics and are conserved, which includes static, flat space. Lisle's (1+z)−3 comes from a beaming exponent that contradicts his own preceding equation.
"JWST found impossibly massive early galaxies, so the standard model is broken." The 2022 headlines have not held up. Of the six massive candidates in the 2023 Nature paper, every one that has since been observed spectroscopically came in lower in redshift or mass, and one was an active galactic nucleus at z = 5.6. The live residual tensions are narrower — the abundance of ultraviolet-bright galaxies at z ≈ 10-14 and the number density of quiescent galaxies at z ≈ 7 — and they are real, but they are not what the popular articles claimed.
"Quantised redshifts prove that redshift is not a distance indicator." The nearby-galaxy claim depends on a tuned reference frame; the quasar claim failed direct tests in 2dF and Sloan; the Sloan number-count periodicity was traced to a filter artefact by the creationist physicist who had promoted it. And if quantisation were real, it would break the Doppler model just as badly as it would break expansion.
"Barnes is an old-earth compromiser, so this is just secular science invading a creationist journal." Barnes is a Christian astrophysicist who published in a young-earth journal at that journal's invitation, and Lisle thanked him for it: "Very few advocates of the big bang are willing to read and interact with creation technical literature. And so, I sincerely wish to thank Luke Barnes for his interest and his constructive criticism."1 That is how the exchange actually went, and treating it as a raid is both false and self-defeating.
What would settle it
Real models make sharp predictions. Lisle's does, to his credit, and they are worth stating so that the question stays open to data rather than to argument.
- Angular sizes beyond z = 15. The Doppler model says the median galaxy diameter should sit just above 0.2 arcseconds and stay flat. The self-consistent kinematic model says about 0.43 arcseconds, also flat. The standard model with galaxy growth predicts sizes that keep falling, so the discriminator there is the level and the slope, not a turnaround — which means this test needs the size and the luminosity measured together on the same objects, not separately. Neither paper does that.
- A type Ia supernova at high redshift. Lisle proposes it as the discriminator. It already exists at moderate redshift and the answer is not encouraging for his model: the Pantheon+ Hubble diagram disfavours his distance law and excludes the corrected version outright. A well-measured supernova beyond z = 3 would close the argument.
- A model-independent Tolman measurement. If the 2026 JWST preprint's departure from (1+z)−4 survives peer review and independent reanalysis, it is a problem for every metric cosmology, including Lisle's, because that exponent is a theorem. That would be far more interesting than anything in this exchange.
- A specified spacetime. Lisle concedes that "the actual metric of the universe cannot be Minkowski because this metric applies to space with negligible mass," and offers no replacement.1 Until the Doppler model names a metric, it cannot predict light bending, cluster dynamics, the acoustic scale in galaxy clustering, or anything else that would let it be tested the way the standard model is tested. That is the largest single gap.
An honest closing
The case for the Doppler model, as published, does not hold. Its central empirical claim depends on an equation that contradicts a neighbouring equation in the same paper and violates a ninety-year-old theorem; its angular-size fit uses a hand-chosen galaxy diameter and a velocity law that only works if light arrives instantly; and it has never been checked against supernovae, the temperature of the microwave background, or cluster velocities, all three of which go against it.
None of that makes the standard model true, and none of it touches the doctrine of creation. It does mean that a Christian who repeats "JWST proved the big bang wrong and the redshifts are just Doppler shifts" is repeating something that a competent astronomer — including a Christian one, in a creationist journal — has already answered in detail.
The most useful thing in the whole exchange is its tone. Barnes wrote a technical reply to a creationist paper and had it published by Answers in Genesis. Lisle answered the argument, conceded the point about starlight travel time, and thanked him. That is worth more to the credibility of creationist science than the paper it was arguing about.
Sources
- 1.
Lisle, Jason. “Sizes of Galaxies in JWST Data and Cosmology — Reply to Barnes.” Answers Research Journal 18:441–447. 2025. Lisle's answer to Barnes's reply, in the same journal. He says he reproduced Barnes's SAGE result with the same simulation and parameters, and that the model Barnes defended was already disproved years ago by galaxy mass and luminosity data from JWST deep fields. The article uses it for Lisle's claim that the Doppler model is currently the only model that passes the Tolman test, which checks how fast the surface brightness of distant galaxies fades with distance, and for his concession that the Doppler model is not needed to explain distant starlight. ↩
- 1a.
Page 446: “So, the Doppler model is currently the only model that fits both size and luminosity data and passes the Tolman test.” ↩
- 1b.
Page 444: “To my knowledge, no secular model proposes that galaxies grow in size without gaining substantial mass.” ↩
- 1c.
Page 446: “I agree with Barnes (and Peacock) that this is the case for expanding space models. But the entire point of my paper is that space might not be expanding (Lisle 2024). I am hypothesizing that the FLRW metric is not correct, and that the true metric of the universe may be approximately, and perhaps temporarily, static.” ↩
- 1d.
Page 442: “Of course, the actual metric of the universe cannot be Minkowski because this metric applies to space with negligible mass. But it is an example of a non-expanding metric in contrast to the FLRW metric.” ↩
- 1e.
Page 446: “Quite right. The Doppler model is not needed to explain distant starlight in a young universe. Rather, it was invoked to explain the angular size and luminosity data in JWST deep fields.” ↩ ↩
- 1f.
Page 447: “And since the ASC model doesn't assume any particular metric, it is compatible with either the FLRW metric or the Doppler model.” ↩
- 1g.
Page 447: “Very few advocates of the big bang are willing to read and interact with creation technical literature. And so, I sincerely wish to thank Luke Barnes for his interest and his constructive criticism.” ↩
- 1a.
- 2.
Barnes, Luke A. “Size of Galaxies in JWST Data and Cosmology — Reply to Lisle.” Answers Research Journal 17:785–789. 2024. A reply to Lisle in the same journal, written by Luke A. Barnes of Sydney, Australia. Barnes ran a standard galaxy-formation simulation (the SAGE model, run through the free TAO web tool) and found that its predicted galaxy sizes are consistent with the JWST data, including data above redshift z = 7. He says the apparent conflict comes from Lisle's own model, which gives every galaxy one size at all times, and the article uses it for Barnes's claim that Lisle's Doppler model is the same as an expanding-space model described in other coordinates, and for his point that the Doppler model gives no young universe. ↩
- 2a.
Page 787: “In light of these resources, the 'standard model' prediction of Lisle (2024) is both inadequate and inexcusable. It is a straw man.” ↩
- 2b.
Page 787: “The increase in masses and physical sizes of haloes and their associated galaxies with time is a firm prediction of analytic, N-body and hydrodynamical simulations of galaxy formation. These models are no secret.” ↩
- 2c.
Page 788: “As explained in Peacock (1999, 87), redshifts in all 'expanding space' models (FLRW) can be calculated as an accumulation of small Doppler shifts, caused as light travels between neighbouring comoving observers. In other words, the difference between the 'expanding space' picture and the 'Doppler' picture is a mere change in perspective, a coordinate transformation. General Relativity is founded on coordinate-independence.” ↩
- 2d.
Page 788: “Thus, the 'Doppler Model' of Lisle (2024) is physically indistinguishable from an expanding space model. It is a mere redescription. The only difference is a change of coordinates, which aren't physically observable.” ↩
- 2e.
Page 788: “In both the Doppler Model and the standard model, the finite speed of light will make the universe appear to be billions of years old, so supporting the first while criticising the second does nothing to solve the Starlight and Time problem.” ↩ ↩
- 2a.
- 3.
Lisle, Jason. “Sizes of Galaxies in JWST Data Suggest New Cosmology.” Answers Research Journal 17:445–457. 2024. A paper by the young-earth creationist Jason Lisle in a journal of Answers in Genesis. It takes the apparent sizes of galaxies in JWST deep-field images and tests them against a model in which galaxies recede through space that does not expand, so that redshift is a Doppler shift. It reports that the data fit that model and fail the standard expanding-universe model, and the article uses it as the creationist case that the new JWST data favour the Doppler model; the three-paper exchange starts here. ↩
- 3a.
Page 448: “This 'Doppler distance' (DD) is shown in blue in fig. 2. It corresponds to the true distance to a galaxy when the light was emitted assuming redshifts are entirely due to the Doppler effect.” ↩
- 3b.
Page 449: Equation (11): “LR = [(1 − v/c)/(1 + v/c)]3”. and equation (12): “LR = 1/(z + 1)3”. For a relativistic Doppler shift, (1 − v/c)/(1 + v/c) = (1 + z)−2 exactly, so the cube of equation (11) is (1 + z)−6, not (1 + z)−3. Equation (13), the luminosity distance DD(1 + z)1.5, follows from equation (12). ↩
- 3c.
Page 450: “Clearly the data are remarkably consistent with the Doppler model; all the median values are within one standard deviation, and several are nearly centered on the predicted curve itself. None of the data are within one standard deviation of the ΛCDM curve.” ↩
- 3d.
Page 454: “The Doppler model therefore passes the Tolman test while the standard ΛCDM model and the tired light model do not.” ↩
- 3e.
Page 454: “The average of these two exponents is 2.98 ± 0.55, consistent with the Doppler model prediction of 3, but well below the standard model's prediction of 4.” ↩
- 3f.
Page 455: “Furthermore, the Doppler model has only one adjustable parameter — the Hubble constant (H0). Yet, it fits the data better than the standard model which has three adjustable parameters.” ↩
- 3g.
Page 448: “Furthermore, let's assume for the sake of hypothesis that the Hubble law is truly linear with respect to velocity even at high redshifts as shown in equation (3).” ↩
- 3h.
Page 456: “Determining the light curve of a high redshift supernova would require multiple JWST observations. But the results would be extremely rewarding.” ↩
- 3i.
Page 455: “How many 'epicycles' must be added before we reconsider the underlying paradigm?” ↩
- 3a.
- 4.
Bunn, Emory F., and David W. Hogg. “The Kinematic Origin of the Cosmological Redshift.” American Journal of Physics 77(8):688–694. 2009. A 2009 paper that works out how to compare the speeds of distant objects in general relativity, where there is no global standard of rest, and concludes that the redshift is best read as many small Doppler shifts added together. The article cites it for the point that the Doppler and expanding-space descriptions are related by a change of coordinates. ↩
- 4a.
Section abstract: “The most natural interpretation of the redshift is as a Doppler shift, or rather as the accumulation of many infinitesimal Doppler shifts.” ↩
- 4a.
- 5.
Francis, Matthew J. et al. “Expanding Space: the Root of All Evil?” Publications of the Astronomical Society of Australia 24(2):95–102. 2007. A paper by four authors, in the journal of the Astronomical Society of Australia, that defends the idea of expanding space against its critics. The article cites it with Bunn and Hogg for the point that the Doppler and expanding-space descriptions are related by a change of coordinates. ↩
- 5a.
Section abstract: The paper argues that expanding space provides. “a completely valid framework for the description of the evolution of the universe,”. and that critiques of the concept fail because they attribute to it properties general relativity does not predict. ↩
- 5a.
- 6.
Etherington, I. M. H. “On the Definition of Distance in General Relativity.” Philosophical Magazine 15:761–773. 1933. The 1933 paper that states the reciprocity theorem: DL = (1 + z)2 DA in any Riemannian spacetime with light on null geodesics and conserved photon number. Riemannian spacetime is the curved-space geometry used in general relativity. The article relies on this theorem for its claim that surface brightness falls as (1+z)4 in any such spacetime, including a static one. ↩ ↩
- 7.
Hartnett, John G. “Unknown Selection Effect Simulates Redshift Periodicity in Quasar Number Counts from Sloan Digital Sky Survey.” Astrophysics and Space Science 324:13–16. 2009. A short paper by a physicist who had championed quantized redshifts, on quasar counts in Sloan Digital Sky Survey data, which finds that an apparent periodicity is a selection effect. The article cites it as the decisive paper, and its author is a creationist. Mirror: arXiv
- 7a.
Section Abstract: “However the same periods are found in the mean of the zConf parameter used to flag the reliability of the spectroscopic measurements. It follows that these redshift periods must result from some selection effect, as yet undetermined. It does not signal any intrinsic (quantized) redshifts in the quasars.” ↩ ↩
- 7a.
- 8.
Tsymbal, V. V. et al. Cosmological Observational Tests in the JWST Era. II: The Tolman Test. Apr 30, 2026. A preprint, not peer reviewed at the time of writing, that tests the Tolman surface-brightness prediction on 6 860 JWST galaxies with spectroscopic redshifts. The article notes that this group has argued for static cosmologies before, and that a preprint is not a result.
- 8a.
Section abstract: “We analyzed 6 860 galaxies with reliably determined spectroscopic redshifts from the ASTRODEEP-JWST photometric catalogue. We find that (a) the mean surface brightness of galaxies indeed decreases with increasing distance, and (b) the observed trend shows a significant departure from the prediction of the standard cosmological model, which expects the mean surface brightness to decline as ~ (1 + z)-4.” ↩ ↩
- 8a.
- 9.
Faulkner, Danny R. “The Case for Cosmological Redshifts.” Answers Research Journal 11:31–47. 2018. A paper in an Answers in Genesis journal by a young-earth creationist astronomer, urging creationists to accept that the universe is expanding and that the redshifts of galaxies are cosmological. The article uses it as its clearest example of a young-earth astronomer who accepts the expansion.
- 9a.
Page 46: “This short-cut way of undermining the big bang model could be a huge mistake, for if the universe is expanding, but we reject this, it would be impossible to construct a correct biblical cosmology.” Section abstract: The abstract's own summary is milder: “Rejection of cosmological redshifts could stifle development of a true biblical cosmology.” ↩
- 9a.
- 10.
Hartnett, John G. “Expansion of Space — A Dark Science.” Answers Research Journal 7:453–459. 2014. A paper by a young-earth creationist in an Answers in Genesis journal, which the article gives as the opposing young-earth view to Faulkner's on whether to accept cosmological redshifts. ↩
- 11.
Barnes, Luke A., and Geraint F. Lewis. The Cosmic Revolutionary's Handbook (Or: How to Beat the Big Bang). Cambridge University Press. 2020. A popular book by two astronomers arguing that the redshift of galaxies is not caused by matter stretching light or by unseen matter. The article quotes it on two points: that no matter can stretch light uniformly, and that galaxies' stars orbit too slowly for gravity to explain the redshift.
- 11a.
Chapter 3: “There just isn't a way to make a uniform light stretcher out of matter.” ↩
- 11b.
Chapter 3: “We can measure the Doppler shifts of the stars in galaxies. They orbit the centre of their galaxies, but at speeds that are thousands of times too slow. This precludes the possibility that the redshift is caused by an enormous amount of unseen matter.” ↩
- 11a.
- 12.
Zwicky, F. “On the Red Shift of Spectral Lines through Interstellar Space.” Proceedings of the National Academy of Sciences 15(10):773–779. 1929. The 1929 paper that proposed that photons simply lose energy on long journeys, the idea now called tired light. The article uses it as the proposal it tests, and says that the proposal makes two predictions now decisively refuted. ↩
- 13.
Goldhaber, G. et al. “Timescale Stretch Parameterization of Type Ia Supernova B-Band Light Curves.” The Astrophysical Journal 558(1):359–368. 2001. A paper on the timescale stretch of Type Ia supernova light curves in B-band (blue) light. The article cites it for light curves that run slower by a factor of (1 + z) at high redshift. ↩
- 14.
Blondin, S. et al. “Time Dilation in Type Ia Supernova Spectra at High Redshift.” The Astrophysical Journal 682:724–736. 2008. A study of 13 high-redshift Type Ia supernovae, each observed in spectra at several epochs, that measures how fast their spectra age. The aging rate matches the 1/(1 + z) factor expected in an expanding universe, and the authors say it rules out tired light, a model with no time dilation. Spectral ageing, not just photometric, confirms the (1 + z) factor, and the article cites it for that. Mirror: arXiv ↩
- 15.
Lewis, Geraint F., and Brendon J. Brewer. “Detection of the Cosmological Time Dilation of High-Redshift Quasars.” Nature Astronomy 7:1265. 2023. “Here we present the identification of cosmic time dilation in a sample of 190 quasars monitored for over two decades in multiple wavebands.” A 2023 paper reporting cosmic time dilation in the brightness changes of 190 quasars monitored for over two decades. The article cites it as the detection that closes the last loophole for the (1 + z) stretch in quasars. Mirror: arXiv ↩
- 16.
Brewer, Brendon J. et al. “Revisiting the Cosmological Time Dilation of Distant Quasars: Influence of Source Properties and Evolution.” Monthly Notices of the Royal Astronomical Society 537(2):809–816. 2025. A 2025 reanalysis of the quasar time-dilation test by two authors of the 2023 paper, which allows for intrinsic scatter (extra spread between quasars beyond measurement error). The authors find n = 1.14 ± 0.34 with intrinsic scatter of 0.288 dex, a dex being one power of ten, against the value of 1 that relativity predicts. The article cites it as a reanalysis that still found the dependence robust. ↩
- 17.
Lubin, Lori M., and Allan Sandage. “The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies.” The Astronomical Journal 122(3):1084–1103. 2001. A 2001 measurement of how the surface brightness of distant early-type galaxies, the smooth elliptical kind, dims with distance, which is the Tolman test, and of how much those galaxies brightened over time. The article uses its numbers for two points: the measured exponent differs between two colour bands, and the authors needed galaxy evolution to make the result fit the expected exponent of 4.
- 17a.
Section abstract: “Expressed as the exponent, n, in 2.5 log (1 + z)n mag, the value of n for all three clusters is n = 2.59 +/- 0.17 in the R band and 3.37 +/- 0.13 in the I band for a qo = 1/2 model.” ↩
- 17b.
Section abstract: “For a true Tolman signal with n = 4, the luminosity evolution in the look-back time… must then be between 1.72 to 1.19 in the R band and 0.94 to 0.45 in the I band. We show that this is precisely the range expected from the evolutionary models of Bruzual & Charlot.” ↩
- 17c.
Section abstract: “The HST data rule out the 'tired light' model at a significance level of better than 10 sigma.” ↩
- 17a.
- 18.
Kocevski, Dale D. et al. Hidden Little Monsters: Spectroscopic Identification of Low-Mass, Broad-Line AGN at z > 5 with CEERS. 2023. A JWST spectroscopy paper on low-mass, broad-line active galactic nuclei (AGN, black holes that are actively feeding) at redshift above 5, in the CEERS survey. Its spectra show broad H-alpha emission from two such objects, and it identifies one of the six Labbé massive candidates, CEERS 3210 at z = 5.624, as a heavily obscured broad-line AGN. The article cites it for the candidate that turned out to be an active galactic nucleus. Mirror: arXiv ↩
- 19.
Wang, Bingjie et al. RUBIES: Evolved Stellar Populations with Extended Formation Histories at z ~ 7-9 in Candidate Massive Galaxies Identified with JWST/NIRCam. 2024. A spectroscopic follow-up of three candidate massive galaxies at redshift 6.7 to 8.4. Their spectra show Balmer breaks, which show that starlight dominates at that wavelength, but their stellar masses remain highly uncertain, spanning about 10^9 to 10^11 solar masses. The article cites it among the spectroscopic follow-ups that revised the candidates' masses. Mirror: arXiv ↩
- 20.
Holanda, R. F. L. et al. “Testing the Distance-Duality Relation with Galaxy Clusters and Type Ia Supernovae.” Astrophysical Journal Letters 722:L233–L237. 2010. Section 1: Stated immediately after the relation is written out. “This equation is completely general, valid for all cosmological models based on Riemannian geometry, being dependent neither on Einstein field equations nor the nature of matter-energy content.” This is the source of the sentence the article quotes. A 2010 test of the distance-duality relation, the Etherington reciprocity theorem, that compares distances from Type Ia supernovae with distances from galaxy clusters. It finds the relation only marginally compatible with one cluster sample and clearly incompatible with another. The article uses it for the exact wording of the theorem's conditions. ↩
- 21.
Renzi, Fabrizio et al. “The Resilience of the Etherington-Hubble Relation.” Monthly Notices of the Royal Astronomical Society 513(3):4004–4014. 2022. A 2022 consistency check of the Etherington relation against late-time data, allowing only small departures from it, measured by a parameter called epsilon. Its joint fit gives that parameter as 0.001, with errors of +0.023 and −0.026. The article cites it with Etherington and Holanda, and its introduction states the conditions the relation needs: photons travelling on null geodesics and photon number conserved. ↩
- 22.
“Tests of the cosmic distance duality relation using DESI 2024 baryon acoustic oscillation measurements combined with supernovae.” The Astrophysical Journal. 2025. A 2025 study that pairs DESI 2024 measurements of baryon acoustic oscillations, a regular pattern in the spacing of galaxies used as a standard ruler, with supernova data. Its deviation parameter is consistent with zero at the ~2% level. The article cites it for the claim that the relation has been tested directly against data and holds to about 2%. ↩
- 23.
Sandage, Allan. “The Tolman Surface Brightness Test for the Reality of the Expansion. V. Provenance of the Test and a New Representation of the Data for Three Remote HST Galaxy Clusters.” The Astronomical Journal 139(2):728. 2010. A 2010 reanalysis of Hubble Space Telescope photometry of elliptical galaxies in three clusters near redshift 0.85, looking for the Tolman signal of surface-brightness dimming. The author finds a highly significant signal, blurred by luminosity evolution of the galaxies over look-back time, and concludes that the expansion is real. The article quotes its summary and argues that the Tolman test cannot by itself separate expansion from galaxies flying through static space.
- 23a.
Quoted by Barnes from the body of the paper: “the Tolman test… has not been quite as easily done as I set out… in 1974. It has required many developments not yet made at the time. However, the test seems to have been successful. The Tolman prediction is verified. The expansion would seem to be real.” ↩
- 23b.
Section abstract: “The expansion is real and a luminosity evolution exists at the mean redshift of the HST clusters of 0.8 mag in Rcape and 0.4 mag in the Icape photometric rest-frame bands, consistent with the evolution models of Bruzual and Charlot.” ↩
- 23a.
- 24.
Lisle, Jason. “Anisotropic Synchrony Convention — A Solution to the Distant Starlight Problem.” Answers Research Journal 3:191–207. 2010. A 2010 article by Jason Lisle of Answers in Genesis proposing a new rule for which distant clocks count as simultaneous, which he calls the anisotropic synchrony convention. Under that rule, light travelling toward the observer takes no time, so distant starlight reaches Earth within a few thousand years and everything in the universe appears to be a few thousand years old. The article uses it to show that the young-universe claim rests on this convention, not on the Doppler model. ↩
- 25.
Scolnic, Dan et al. “The Pantheon+ Analysis: The Full Data Set and Light-Curve Release.” The Astrophysical Journal 938:113. 2022. The full data set and light-curve release for Pantheon+, a large collection of Type Ia supernovae. The article's fits use 1,371 of them, those above z = 0.023, with diagonal (uncorrelated) statistical errors and the absolute-magnitude offset marginalised analytically, meaning averaged out mathematically. The article uses it as the test Lisle proposed for Type Ia supernovae, since its distances and redshifts are a public download. ↩
- 26.
Noterdaeme, P. et al. “The Evolution of the Cosmic Microwave Background Temperature: Measurements of TCMB at High Redshift from Carbon Monoxide Excitation.” Astronomy & Astrophysics 526:L7. 2011. A paper that measures the cosmic microwave background temperature at high redshift from how carbon monoxide molecules in distant gas clouds are excited, using them as thermometers. The article cites it as a measured confirmation that the temperature rises with (1 + z), with the exponent close to 1. Mirror: arXiv
- 26a.
Section Abstract: “Combining our precise measurements with previous constraints, we obtain TCMB(z) = (2.725 +/- 0.002) x (1+z)(1-beta) K with beta = -0.007 +/- 0.027, a more than two-fold improvement in precision.” ↩
- 26a.
- 27.
Riechers, Dominik A. et al. “Microwave Background Temperature at a Redshift of 6.34 from H2O Absorption.” Nature 602:58–62. 2022. A measurement of the microwave background temperature at redshift 6.34, read from water absorption in a starburst galaxy. It gives 16.4-30.2 K (1σ, one standard deviation) against the 20.0 K predicted, and the article cites it as one of the molecular measurements of the temperature at high redshift. ↩
- 28.
Hurier, G. et al. “Measurement of the TCMB Evolution from the Sunyaev-Zel'dovich Effect.” Astronomy & Astrophysics 561:A143. 2014. A measurement of how the microwave background temperature changes with redshift, made with the Sunyaev-Zel'dovich effect, in which hot gas in galaxy clusters distorts the background light. The article cites it among the cluster measurements that agree independently with the prediction. ↩
- 29.
de Martino, I. et al. “Constraining the Redshift Evolution of the Cosmic Microwave Background Blackbody Temperature with PLANCK Data.” The Astrophysical Journal 808:128. 2015. A test of how the microwave background temperature changes with redshift, using data from the Planck satellite. Joint constraints with the Hurier sample give a deviation parameter α = −0.001 ± 0.012, a measure of how far the change departs from the prediction, and the article cites it for that agreement. ↩
- 30.
Sayers, Jack et al. “A Measurement of the Kinetic Sunyaev-Zel'dovich Signal Toward MACS J0717.5+3745.” The Astrophysical Journal 778(1):52. 2013. A measurement of the kinetic Sunyaev-Zel'dovich effect, the Doppler-type shift that hot gas in a moving galaxy cluster gives the microwave background, toward the cluster MACS J0717.5+3745. The best-fit line-of-sight velocity for sub-cluster B is +3,450 ± 900 km/s, and the article uses it as a direct measure of the speed of a fast-moving merging cluster. Mirror: arXiv ↩
- 31.
van der Wel, A. et al. “3D-HST+CANDELS: The Evolution of the Galaxy Size-Mass Distribution since z = 3.” The Astrophysical Journal 788(1):28. 2014. A survey of how galaxy sizes change from z = 0 to z = 3, using spectroscopic and photometric redshifts from the 3D-HST survey with structural measurements from Hubble imaging in the CANDELS survey. It finds early-type galaxies are smaller than late-type galaxies at every redshift, with effective radius scaling as (1 + z)−1.48 for early types and (1 + z)−0.75 for late types, and the article cites those rates as the measured size evolution. Mirror: arXiv ↩
- 32.
Napier, W. M., and B. N. G. Guthrie. “Quantized Redshifts: A Status Report.” Journal of Astrophysics and Astronomy 18:455–463. 1997. A status report on the claim that galaxy redshifts come in quantized steps, reporting periodicities near 37.5 km/s among field spirals and 71.5 km/s in the Virgo cluster, in the galactocentric frame (a frame centred on the Milky Way's centre). The article cites it as the refinement of William Tifft's redshift-step claims from the 1970s. ↩
- 33.
Bajan, K. et al. “On the Investigations of Galaxy Redshift Periodicity.” Physics of Particles and Nuclei Letters 4:5–10. 2007. “weak effects of redshift periodisation”. A sympathetic review of the galaxy redshift periodicity claim that nonetheless finds the effects weak, and documents that the signal depends on the assumed solar motion correction vector. The article cites it for that dependence: a strong signal appears only for the correction vector that produced it. Mirror: arXiv ↩
- 34.
Arp, H. et al. Periodicities of Quasar Redshifts in Large Area Surveys. 2005. A reanalysis of quasar redshifts in the 2dF and SDSS surveys, written in reply to Hawkins et al. (2002). The authors argue that the redshifts fit Karlsson's formula very exactly and confirm preferred values, and the article cites it as a recent test that supports Halton Arp's idea that quasars are ejected from nearby galaxies with intrinsic redshifts. Mirror: arXiv ↩
- 35.
Hawkins, E. et al. “No Periodicities in 2dF Redshift Survey Data.” Monthly Notices of the Royal Astronomical Society 336:L13. 2002. A test of a claimed periodicity in quasar redshifts, run on the 2dF Galaxy Redshift Survey and 2dF QSO Redshift Survey data. Bill Napier, who had made the claim, gave the instructions for the analysis and took no part in running it. The article cites it as the first of two head-on tests that failed. Mirror: arXiv
- 35a.
Section Abstract: The analysis of 1,647 quasar-galaxy pairs found. “no evidence for a periodicity at the predicted frequency in log(1+z), or at any other frequency.” ↩
- 35a.
- 36.
Tang, Su Min, and Shuang Nan Zhang. “Critical Examinations of QSO Redshift Periodicities and Associations with Galaxies in Sloan Digital Sky Survey Data.” The Astrophysical Journal 633(1):41. 2005. A test of two models that say quasars are ejected from galaxies with periodic non-cosmological redshifts, Karlsson's log(1 + z) model and Bell's decreasing intrinsic redshift model, using Sloan and 2dF quasar data. It finds no evidence for a periodicity in four sets of quasar-galaxy pairs, and none in high-completeness samples of quasar redshifts, and the article cites it as the second failed test of the Karlsson periodicity. Mirror: arXiv ↩
- 37.
Mal, Arindam et al. “Quantized Redshift and its Significance for Recent Observation.” Research in Astronomy and Astrophysics 24(9):095014. 2024. A 2024 analysis of quasar-galaxy pair redshifts from SDSS and 2dF, using singular value decomposition, a method for finding periodic signals in noisy data. The authors report periodicities of 0.077 and 0.089 in log scale, and the article cites it as the 2024 revival of the Karlsson periodicity. Mirror: arXiv ↩
- 38.
Bell, M. B., and S. P. Comeau. “Selection Effects in the SDSS Quasar Sample: The Filter Gap Footprint.” Astrophysics and Space Science 326:11–17. 2010. Section Abstract: “It is shown here that a periodicity of Delta(z)~0.6 is imprinted on the redshift-number distribution by this selection effect.” A paper showing that a selection effect called the filter gap footprint imprints a periodicity of about 0.6 in redshift on the SDSS quasar sample. The article cites it for the mechanism behind Hartnett's periods: strong emission lines crossing the gaps between the survey's colour filters. Mirror: arXiv ↩
- 39.
Naidu, Rohan P. et al. “A Cosmic Miracle: A Remarkably Luminous Galaxy at zspec = 14.44 Confirmed with JWST.” The Open Journal of Astrophysics. 2026. An observational paper confirming the redshift of MoM-z14, a luminous galaxy, from a sharp Lyman-α break in JWST NIRSpec spectra, a drop in its ultraviolet light caused by hydrogen absorption. The article cites it as the most distant spectroscopically confirmed galaxy, at redshift 14.44, and uses that redshift in its check of Lisle's own equations for the age of the universe. Mirror: arXiv ↩
- 40.
Dennis, Phillip W. “An Internal Contradiction of Lisle's Anisotropic Synchrony Convention (ASC) Model.” Answers Research Journal 17:427–433. Jul 10, 2024. A 2024 paper by an independent researcher arguing that Lisle's ASC model, a clock-setting convention that lets light from far away arrive at any chosen speed, contradicts the special relativity it relies on. The article uses it to show that the convention is disputed inside the same journal. A second paper by Dennis, 'A Refutation of Lisle's 'Refutation' of Dennis (2024)', followed in the same journal (volume 17) on 20 November 2024. ↩