The Expanding Universe

"From a discussion of available data, we adopt R'/R = 0·68 × 10⁻²⁷ cm.⁻¹" — the whole of Georges Lemaître's derivation of the expansion rate, as it appeared in the 1931 English translation.  The French original of 1927 gives the galaxies, the distances, the velocities, the number 625 km/s per megaparsec, and Lemaître's own warning that the correlation was weak.¹

Summary

This article is the case file for one claim:  distant galaxies are receding from us.  It is a child of the standard model overview, which treats the same ground in a page.

Most arguments about the expanding universe fail because they run four separate claims together.  Separate them and the evidence sorts itself out.

• Claim 1 — redshift grows with distance — is measured, and nobody disputes it. The distance is measured without reference to the redshift — by Cepheid variables, the tip of the red giant branch, Type Ia supernovae, the geometry of water masers, and gravitational-wave sirens — and the two measurements track each other out past redshift 1.
• Claim 2 — the redshift means recession — is very strong, but it is an inference. It requires ruling out every other way of reddening light. Two facts do most of the ruling out. The shift is uniform: every wavelength from a given galaxy is stretched by the same factor, and radio and ultraviolet measurements of the same gas agree to one part in 100,000. And distant galaxies are sharp: no scattering mechanism can shift light without also blurring the image. Gravitational redshift is out by five orders of magnitude.
• The measurement that settles it is time dilation. A supernova at redshift 1 rises and fades twice as slowly as an identical supernova nearby. This has been measured three ways: in light curves, in the ageing of the spectra themselves, and since 2023 in the variability of 190 quasars watched for two decades. Tired light predicts no stretching at all and dies here. It is a clean, dated falsification of a named alternative, and creationists should say so plainly.
• Claim 3 — that space itself expands rather than galaxies moving through it — is largely a choice of coordinates, and the two sides of that argument are both right. Inside general relativity there is no observation that separates them, because there is no global standard of rest to measure a distant velocity against. What is physical, and testable, is whether the large-scale geometry is static. That question is treated at length in the sister article on the Doppler model.
• The Tolman surface-brightness test does not do what almost everyone says it does. Etherington proved in 1933 that luminosity distance equals (1 + z)² times angular-diameter distance in any spacetime with Riemannian geometry, light on null geodesics and conserved photons — including flat, static, non-expanding space. So the (1 + z)⁻⁴ dimming of galaxies is a theorem, not a prediction of expansion. It kills tired light. It cannot tell expansion from motion through static space. Both sides of the creation debate have misused it.
• Claim 4 — that the expansion began in a hot dense state 13.8 billion years ago — is a further model resting on separate evidence. A reader can accept claims 1 and 2 and reject claim 4. Several young-earth astronomers do exactly that, and one of them, Danny Faulkner, argues in print that creationists should.
• Two Christian uses of the expansion, tested. The "stretching out the heavens" verses (Isaiah 40:22 and others) are compatible with an expanding universe but do not predict it; the young-earth physicists John Hartnett and Russell Humphreys, who once read them that way, both withdrew that reading by 2014. The argument from a beginning is stronger: the Borde-Guth-Vilenkin theorem needs only average expansion, not the hot big bang, to show the classical past is incomplete. Its own authors say it does not prove a unique beginning or say anything about God, and it gives no age.
• The history is not the textbook story. Vesto Slipher measured the velocities and is barely remembered. Lemaître published the velocity-distance law with a numerical rate two years before Hubble, then deleted that derivation himself from his own English translation. Hubble never endorsed an expanding universe; in 1929 he preferred de Sitter's static, empty model.
• One live anomaly, honestly flagged. An April 2026 preprint measuring surface brightness for 6,860 JWST galaxies reports "a significant departure from the prediction of the standard cosmological model." It is a preprint, from a group that has argued for static cosmologies before, and it is not settled either way.

Four claims, not one

Almost every bad argument about the expanding universe — on either side — comes from treating these four statements as a single package.  They are logically independent, they rest on different evidence, and they can fail separately.

A reader can accept 1 and 2 and reject 4 without contradiction.  Several young-earth astronomers do.  Danny Faulkner, who holds a PhD in astronomy, wrote a whole paper in Answers Research Journal urging creationists to accept the Hubble relation, universal expansion, and cosmological quasar redshifts.  His reason is worth reading, because it is not a concession:  "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."²  He goes further, arguing that denying the Hubble relation as an expansion "amounts to a denial of general relativity" — which most of the creationists denying it do not intend.²

John Hartnett, also a young-earth creationist and a physicist, argued the opposite in the same journal.³  This is not believers against skeptics.  It is a live technical argument that runs through the middle of the creationist community, and the rest of this article treats it that way.

Claim 1: redshift rises with distance

What is actually measured

A galaxy's spectrum carries dark absorption lines and bright emission lines at wavelengths fixed by atomic physics.  Calcium H and K, the hydrogen Balmer series, the sodium D doublet, the 21-centimetre line of neutral hydrogen — all of them sit where laboratory measurement says they sit.  In a distant galaxy the whole pattern appears at longer wavelengths.  The redshift z is defined by how much longer:  the observed wavelength divided by the rest wavelength, minus one.

Two things are worth noticing about that definition before any interpretation is attached to it.

First, it is a ratio, not a shift.  Every line moves by the same fraction, not the same number of nanometres.  Vesto Slipher checked this in his very first measurement, in 1912, and said why:  he noted "that the shift at the violet end of the spectrum was fully twice that at the blue end, which should be the case if it were due to velocity."⁴  That is the single most important empirical fact in the whole subject, and it was established before anyone knew the nebulae were other galaxies.

Second, the redshift is measured with no reference to distance at all.  Distance comes from something else entirely — Cepheid variables, the tip of the red giant branch, Type Ia supernovae, surface-brightness fluctuations, gravitational-wave sirens, water-maser geometry.  The Hubble relation is the empirical finding that two independent measurements track each other.

Slipher measured the velocities, and got almost no credit

In 1912 Vesto Slipher, working at the Lowell Observatory in Flagstaff, Arizona, aimed a spectrograph bolted to a 24-inch refractor at the Andromeda Nebula.  His exposures ran six to fifty hours.  Four plates over three months gave −284, −296, −308 and −301 km/s, a mean of −300.⁴  Nothing in the sky had ever been clocked that fast.  Slipher's own comment is a model of how to state a result:

The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at the present no other interpretation for it.⁴

By April 1917 he had between forty and fifty spectrograms of 25 spiral nebulae.  Twenty-one were receding.  Four were approaching, and three of those four — NGC 221, 224 and 598 — are the Andromeda system and the Triangulum galaxy, our own nearest neighbours.  The arithmetic mean of the speeds was 570 km/s, about thirty times the average stellar velocity.⁵

And Slipher did not conclude that the universe was expanding.  He could not:  the nebulae with positive velocities were clustered near right ascension twelve hours, and a general expansion should show no such direction preference.  His actual proposal was that the Sun's own system is drifting:  "A preliminary solution of the material at present available indicates that we are moving in the direction of right-ascension 22 hours and declination −22° with a velocity of about 700 km."⁵  He was wrong, but he was wrong for a good reason — his 25 objects were badly distributed on the sky, and he said so.

Slipher's velocities are the raw material for everything that follows.  Hubble's 1929 paper uses them, with four re-measurements by Milton Humason.  Slipher is not thanked in Hubble's paper, is not mentioned in Jan Oort's 1931 summary of the discovery, and does not have the law named after him.

Lemaître published the law first, with a number

Georges Lemaître was a Belgian Catholic priest and a trained astronomer.  In 1927 he published, in French, in the Annales de la Société Scientifique de Bruxelles, a paper that did three things at once:  it gave an expanding solution of Einstein's equations, it derived a proportionality between a nebula's velocity and its distance, and it put a number on the constant.  On printed page 56:

Utilisant les 42 nébuleuses figurant dans les listes de Hubble et de Strömberg, et tenant compte de la vitesse propre du soleil (300 Km. dans la direction α = 315°, δ = 62°), on trouve une distance moyenne de 0,95 millions de parsecs et une vitesse radiale de 600 Km./sec, soit 625 Km./sec à 10⁶ parsecs.⁶

That is Hubble's law with a measured constant, two years before Hubble's paper.  Lemaître's equation (24) turns it into the expansion rate 0.68 × 10⁻²⁷ cm⁻¹.

And Lemaître deleted the whole passage from his own English translation.  When Monthly Notices of the Royal Astronomical Society published the translation in 1931, the galaxies, the distances, the velocities, the 625 and the derivation all vanish, replaced by one sentence:  "From a discussion of available data, we adopt R'/R = 0·68 × 10⁻²⁷ cm.⁻¹"¹  For decades this looked like censorship, and it was written up that way.  It was not.  Jean-Pierre Luminet found the letter:  on 9 March 1931, Lemaître wrote to the MNRAS editor W. H. Smart, "I did not find advisable to reprint the provisional discussion of radial velocities which is clearly of no actual interest."⁷  By 1931 Hubble's better data existed, and Lemaître thought his own 1927 numbers had been superseded.

What was cut with them is the part this article cares about most.  Lemaître's own footnote on that page says the data barely support the relation:

Certains auteurs ont cherché à mettre en évidence la relation entre v et r et n'ont obtenu qu'une très faible corrélation entre ces deux grandeurs… il semble donc que ces résultats négatifs ne sont ni pour ni contre l'interprétation relativistique de l'effet Doppler.⁶

"A very weak correlation."  "Neither for nor against the relativistic interpretation of the Doppler effect."  The same footnote gives an unweighted alternative — 670 km/s at 1.16 million parsecs, which is 575 km/s per million parsecs — so his own constant moves by 8 percent depending on how he groups the data.  Lemaître in 1927 was more candid about the weakness of the evidence than most textbooks are about it today.

Hubble measured the distances, and never endorsed expansion

Edwin Hubble's 1929 paper is three pages long.⁸  Its contribution is distances, not velocities:  "Radial velocities of 46 extra-galactic nebulae are now available, but individual distances are estimated for only 24."  He got those 24 distances from Cepheid variables where he could resolve them and from the brightest stars where he could not, and he was honest that the second method carries "considerable probable errors."

His result was two fits.  Twenty-four objects individually gave K = 465 ± 50 km/s per million parsecs.  The same objects binned into nine groups gave 513 ± 60.  He then rounded:  "let A = 277°, D = +36°… V₀ = 280 km./sec., K = +500 km./sec. per million parsecs."⁸  That number is about 7.3 times the modern value, because his Cepheid calibration was wrong.  His whole data set spans two million parsecs — the Virgo cluster — and tops out at 1,090 km/s.

Two things about the paper are usually left out.

Hubble said his own linear law was provisional.  His closing sentence:  "it may be emphasized that the linear relation found in the present discussion is a first approximation representing a restricted range in distance."⁸

Hubble did not propose an expanding universe.  His preferred reading was Willem de Sitter's static, empty model, in which the redshift is not simply a velocity:  "In the de Sitter cosmology, displacements of the spectra arise from two sources, an apparent slowing down of atomic vibrations and a general tendency of material particles to scatter."⁸  He stayed cautious about this for the rest of his life.

That caution is a favourite creationist quotation mine, and it should not be.  Faulkner devoted a paper in Answers Research Journal to showing that the line usually quoted — "the unwelcome supposition of a favoured location must be avoided at all costs" — is Hubble stating a hypothesis that he goes on to reject two sentences later.⁹  Do not use it.

Who deserves the credit

One more name belongs on that list for the opposite reason.  Gustaf Strömberg, working from the same 1924 data, concluded that "we have found no sufficient reason to believe that there exists any dependence of radial motion upon distance."¹⁰  The relation was not obvious in the data of the 1920s.  It became obvious when the distances got better.

In 2018 the International Astronomical Union passed Resolution B4, "on a suggested renaming of the Hubble Law," resolving "to recommend that from now on the expansion of the universe be referred to as the 'Hubble-Lemaître law'."  The resolution's own reasoning is worth reading, because it settles the deletion question in the historical record:  Lemaître translated his 1927 paper "deliberately omitting the section in which he derived the rate of expansion because he did not find advisable to reprint the [his] provisional discussion of radial velocities."¹¹

Gerald Shaviv, who worked through the primary papers, put the honest verdict on Hubble this way:  "Hubble who found the data used by others had no reason to plagiarize and did better and more accurately than others.  He proved for the first time what other tried to prove or assumed."¹⁰

What the measurement looks like now

Hubble had 24 galaxies out to 2 megaparsecs.  The modern relation holds over a range roughly a thousand times larger, and the distances come from several methods:  Cepheid variables, the tip of the red giant branch, Type Ia supernovae, surface-brightness fluctuations, the geometry of the water-maser disc in NGC 4258, and — completely independent of all of them — gravitational-wave sirens.  Some of those are rungs on a common ladder and share calibration;  the maser geometry and the sirens are not, and they agree.  The spread among the best current measurements of the constant is the well-known "Hubble tension" — roughly 67 to 74 km/s per megaparsec depending on method — and that argument is about a 9 percent disagreement in the slope, not about whether the slope exists.¹²

The relevant point for this article is smaller and more useful.  A young-earth reader looking for a place to attack should not attack claim 1.  It is not a model-dependent inference.  It is two measurements agreeing.

Claim 2: the redshift means recession

Redshift is a measurement.  Recession is an interpretation.  Getting from one to the other means eliminating everything else that can lengthen a wavelength.  There are only four candidates, and three of them fail on evidence that has nothing to do with cosmology.

The shift is a pure ratio, and that is very hard to fake

Every spectral line from a given galaxy is stretched by the same factor.  Not the same number of nanometres — the same fraction.  This is not an assumption built into the analysis;  it is the thing that makes a redshift measurable at all, because the pattern of lines has to still look like the pattern of lines after the shift.

How far does the uniformity hold?  Further than most readers expect.  The same absorbing gas cloud in front of a quasar can be seen in the 21-centimetre line of neutral hydrogen and in ultraviolet metal lines around 100 to 300 nanometres.  Those two rest wavelengths differ by a factor of roughly a million.  Tzanavaris and colleagues compared the two redshifts in absorbers between z = 0.24 and z = 2.04 and found them equal to about one part in 10⁵, with the small residual — about 6 km/s — attributable to the radio and ultraviolet lines sampling slightly different parcels of gas rather than to any wavelength dependence in the shift itself.¹³  Their purpose was to constrain drift in the fine-structure constant.  The by-product is the tightest test anyone has run of whether redshift depends on wavelength.  It does not.

No material can do that.  Luke Barnes and Geraint Lewis give the argument in a form a high schooler can check.  To affect light at all, a substance has to contain electric charge.  But charged parts interact with each other:  electrons are bound to nuclei, atoms are bound into molecules, molecules into lattices.  Every real substance therefore has a personality — it responds strongly to some wavelengths and ignores others.  That is why tinted glass reddens visible light while radio waves pass straight through it.  A substance that shifted every wavelength by the same factor would have to have no internal structure of its own to imprint, which is exactly what charged matter cannot be:

There just isn't a way to make a uniform light stretcher out of matter.¹⁴

This eliminates dust, gas, plasma, and every "intergalactic medium reddens the light" proposal in one move — provided the shift really is uniform, which is why the Tzanavaris measurement matters.

Distant objects are sharp, and scattering blurs

Any process that takes momentum from a photon also changes its direction.  A little, over a very long path, adds up:  images would be smeared, in the way distant hills are smeared by fog.  They are not.  Hubble and Webb images of quasars at z > 5 show diffraction-limited point sources — Airy patterns, the sharpest a telescope can physically produce.  Eric Steinbring's search for even the smallest possible blurring, from hypothetical Planck-scale spacetime foam, opens by conceding what was already known:  "Blurring this dramatic has already been observationally ruled out by images from Hubble Space Telescope."¹⁵

The most useful person to quote here is a critic of the standard model, not a defender of it.  Martín López-Corredoira's 2017 review is the most thorough catalogue of the big bang's problems in print, and he is not neutral about wanting alternatives to work.  On the classic energy-loss mechanisms he writes that there are "two problems":  first, that "all images of distant objects would look blurred if intergalactic space produced scattering, something that is incompatible with present-day observations";  second, that "the scattering effect and the consequent loss of energy would be frequency dependent, which is again incompatible with what we observe in galaxies."¹⁶  He then spends four pages describing the exotic mechanisms invented to dodge both problems, which is a fair description of the state of that literature.

Gravitational redshift is out by five or six orders of magnitude

Light climbing out of a gravitational well loses energy, and the shift is uniform across wavelengths, so gravity is not disqualified by the argument above.  It is disqualified by size.

The effect is real and measured.  Light leaving the Sun's surface is redshifted by about 633 metres per second in velocity units — a fractional shift of 2.1 × 10⁻⁶.  A 2020 measurement of 97 iron lines in sunlight reflected off the Moon, calibrated against a laser frequency comb, gives 638 ± 6 m/s.¹⁷  That is the whole Sun, and it is a redshift of two parts in a million.

For a galaxy the number is no better, because a galaxy's gravitational redshift is set by how tightly its mass is packed, and the packing is measurable.  For a system held together by gravity, the redshift is roughly the square of the internal velocity divided by the square of the speed of light.  Stars in a big spiral orbit at about 200 km/s, which gives 4 × 10⁻⁷.  The most massive elliptical galaxies reach velocity dispersions near 400 km/s, which gives 2 × 10⁻⁶.  A galaxy at redshift 0.1 — utterly ordinary, in every survey — needs 250,000 times more than a spiral supplies.  A galaxy at redshift 1 needs two and a half million times more.

Barnes and Lewis put the same point geometrically.  To make its own light redshift by a factor of two, a galaxy's entire stellar mass would have to sit "perilously close" to the event horizon of a black hole, compressed into a region "about 1% of the distance from the Sun to our nearest star."  And then:  "we can see the galaxy.  We can see how big it appears, and because we know how far away it is, we can calculate that it's millions of times too big."¹⁴

There is a structural objection as well, and it is the stronger one.  A gravitational redshift depends on the source's compactness, not on its distance.  For it to produce Hubble's law, distant galaxies would have to be systematically more compact than nearby ones in exactly the proportion required — a coincidence with no mechanism, and one that the measured internal velocities of those galaxies directly contradict.

What is left

Three of the four candidates are gone.  What remains is motion, geometry, or some process that removes energy from photons in flight without scattering them and without caring about their wavelength.  That last one is tired light, and it has its own article on this site.  Here it matters only because two measurements kill it, and those two measurements are the subject of the next two sections.

The measurement that decides it: distant events run slow

This is the single most important test in the subject, and it is the one popular treatments skip.

Here is the logic.  A moving source, or a stretching geometry, does not only lengthen the waves — it lengthens the interval between anything the source does.  If a galaxy's light is stretched by a factor of two, then a clock in that galaxy appears to us to tick twice as slowly.  An energy-loss mechanism does not do that.  Tired light of any kind takes energy out of each photon individually;  it has no way to change how often the photons arrive.  So there is a clean, quantitative split:

The universe supplies clocks:  supernovae, which rise and fade on a schedule set by radioactive decay, and quasars, which flicker.  All that is needed is to watch a distant one and time it.

Light curves: Goldhaber 2001

Type Ia supernovae brighten and fade over a few weeks.  They are not identical — a brighter one fades more slowly, the "stretch" relation that makes them usable as distance indicators in the first place — so the test is statistical.  Fit a width to every supernova's light curve, and ask whether the widths of high-redshift supernovae are systematically larger by (1 + z).

Gerson Goldhaber and the Supernova Cosmology Project did this with roughly 1,300 brightness measurements from high-redshift supernovae and about 300 from 18 nearby Calán/Tololo supernovae at z < 0.11.  Fitted with a free time-axis width factor w = s(1 + z), the intrinsic stretch s came out independent of redshift while the (1 + z) factor was required.  Their own summary:  "We also demonstrate the 1+z light-curve time-axis broadening expected from cosmological expansion.  This argues strongly against alternative explanations, such as tired light, for the redshift of distant objects."¹⁸

The honest weakness of this version:  it assumes the intrinsic width distribution of supernovae does not itself change with redshift.  If distant supernovae were intrinsically slower for some astrophysical reason, and if a magnitude-limited survey preferentially found the slow bright ones, part of the effect could be mimicked.  That is not a hypothetical objection — it is exactly what the next paper set out to remove.

Spectra: Blondin 2008, and why it is the stronger test

A supernova's spectrum changes as it ages.  Different elements dominate on different days;  the absorption features move as the ejecta thin out.  That progression is a clock that does not depend on how bright the supernova is, and it cannot be mimicked by an intrinsically wide light curve.

Stéphane Blondin and 31 co-authors took 35 spectra of 13 high-redshift Type Ia supernovae between z = 0.28 and z = 0.62, used pattern-matching against a library of nearby supernova spectra to read off each one's age in its own rest frame, and compared that with the elapsed time an Earth clock recorded between the observations.  The ratio is the time-dilation factor, measured directly.

The numbers are decisive.  Fitting an aging rate of 1/(1 + z)^b gives b = 0.97 ± 0.10 for the whole sample and 0.95 ± 0.10 for the high-redshift objects alone.  Relativity predicts exactly 1.  A no-time-dilation model gives χ² = 150.3 for 35 degrees of freedom — a goodness of fit of 0.0 percent — against χ² = 27.0 for the same 35 degrees of freedom for the (1 + z) prediction.¹⁹

Blondin's paper says plainly why it supersedes the light-curve version:  "previous use of SN Ia light curves to test this hypothesis (Leibundgut et al. 1996; Goldhaber et al. 2001) are prone to the spread in intrinsic light-curve widths and its possible variation with redshift."  And on the result:  "This hypothesis is favored beyond doubt over models that predict no time dilation."¹⁹

Quasars: the loophole that stayed open until 2023

Until recently a critic had a real reply available:  supernovae are one class of object, and quasar variability had failed to show the expected stretching in several published analyses.  López-Corredoira's 2017 review listed that failure among the standard model's problems, and he was right to.

It closed in 2023.  Geraint Lewis and Brendon Brewer analysed 190 quasars monitored for over two decades in multiple wavebands, using a Bayesian model comparison rather than a simple structure-function fit, and detected the (1 + z) stretching.  Their abstract states the point without hedging:  "This detection counters previous claims that observed quasar variability lacked the expected redshift-dependent time dilation."²⁰

A 2025 follow-up by the same authors plus Yuan Li did the sceptic's job on their own result.  Quasar variability timescales depend on luminosity and on the rest-frame wavelength observed, and the quasar population evolves;  all three could in principle counterfeit a redshift dependence.  Allowing for an intrinsic scatter of 0.288 ± 0.021 dex that the earlier work had not modelled, they refitted (1 + z)ⁿ and got n = 1.14 ± 0.34, consistent with the predicted 1.  The most telling line in the paper is not that number but what happened in the model comparison:  "The only exception was a model that assumes n = 1, which outperformed the main model."²¹  The free parameter did not earn its keep.  The prediction fit better than the fit.

The one place the test is still weak: gamma-ray bursts

Honesty requires flagging the item on López-Corredoira's list that has not closed.  Gamma-ray bursts should be time-dilated too, and the signal has been hard to pull out.  Amitesh Singh and Shantanu Desai revisited it with 247 Swift bursts, measuring durations in a fixed rest-frame energy band and fitting duration ∝ (1 + z)^B, where B should equal 1.  Their opening sentence is the fair summary of the field:  "the cosmological time dilation signature for GRBs has not been unequivocally demonstrated."  Their own result is mixed — binned analyses come out consistent with B = 1 within 1σ, while unbinned analyses show intrinsic scatter above 100 percent and "no definitive conclusion... can be inferred."²²

That is a genuine loose end, and it should be reported as one.  It is also a much weaker loose end than it looks, because gamma-ray burst durations vary intrinsically by three orders of magnitude, while supernova light curves vary by tens of percent.  A test whose intrinsic scatter swamps the signal is uninformative, not contrary.

What time dilation does not settle

Tired light is dead.  Not out of favour, not unfashionable — measured and excluded, three independent ways, over thirty years.  A creationist writing about cosmology should retire it and say why.

But time dilation does not distinguish motion from expansion.  Both predict exactly (1 + z).  Jason Lisle is entirely correct that his static-space Doppler model passes this test, and any argument that uses supernova time dilation against a Doppler model is confused.  What the test does is eliminate the one remaining non-kinematic option.  It closes the door on tired light and leaves the room with two people in it.

The Tolman surface-brightness test, told correctly

This test is misused by nearly everyone who cites it, in both directions.  Getting it right takes one theorem and one paragraph of algebra, and it changes what the test is worth.

What Tolman proposed

Richard Tolman noticed in 1930 that surface brightness — light received per unit area of a galaxy's image on the sky — behaves very differently in an expanding universe than in a static one.  Allan Sandage, who spent thirty-five years on the measurement, states Tolman's result exactly:

Tolman (1930, 1934) discovered the effect that the surface brightness of a "standard" radiating object that is receding with redshift z will be fainter than a similar stationary "standard" object at rest by (1 + z)⁴.  However, if the manifold is stationary but nevertheless has a redshift due to an "unknown law of nature", the factor is only (1 + z).²³

Read that carefully, because it is the whole argument.  Sandage's contrast is between an object receding and an object at rest whose redshift comes from an unknown law of nature.  It is not a contrast between expanding space and motion through static space.  Tolman's test was built to catch a non-kinematic redshift.  That is what it catches.

The reason surface brightness is such a good discriminator is that distance cancels out of it.  A galaxy twice as far away delivers a quarter of the light — but it also covers a quarter of the sky.  In a static, Euclidean, non-expanding universe with no redshift at all, surface brightness does not depend on distance.  Every effect that survives the cancellation is therefore a direct probe of the geometry and of what happens to photons in flight.

Why (1 + z)⁻⁴ is a theorem, not a prediction

The dimming has two standard derivations, and both make clear that it carries almost no cosmological content.

The bookkeeping version.  Four factors of (1 + z) show up.  Each photon arrives with its energy reduced by (1 + z).  Photons arrive less often, by another (1 + z) — that is the time dilation of the previous section.  The remaining two come from the relation between the two ways of measuring distance:  the luminosity distance D_L, defined by how faint an object of known brightness looks, and the angular-diameter distance D_A, defined by how small an object of known size looks.  Surface brightness is flux divided by solid angle, which works out to (D_A/D_L)² times the intrinsic value.

The deep version.  Photons in vacuum obey Liouville's theorem:  the density of photons in phase space is conserved along a ray.  That forces the specific intensity divided by the cube of the frequency to be an invariant, and so bolometric surface brightness scales as the fourth power of the frequency ratio — that is, as (1 + z)⁻⁴.  Nothing in that argument mentions expansion, or Einstein's equations, or what the universe is made of.  It only requires that photons travel freely and are not destroyed.

The formal statement is Etherington's reciprocity theorem, proved in 1933:

D_L = (1 + z)² D_A

Holanda, Lima and Ribeiro state its scope as plainly as anyone has:

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.  It only requires that source and observer are connected by null geodesics in a Riemannian spacetime and that the number of photons are conserved.²⁴

Renzi, Hogg and Giarè, who tested it against data, give the same three conditions in the negative:  deviations "would appear if photons did not propagate on null geodesics (i.e. were not massless), if photon number was not conserved… or if the spacetime was not described by a pseudo-Riemannian manifold."²⁵  Their joint fit to late-time data gives a deviation parameter ε = 0.001, with an uncertainty of about 0.025 — consistent with zero at the couple-of-percent level.²⁵

Flat, static, non-expanding Minkowski space satisfies all three conditions trivially.  So does an expanding FLRW universe.  So does Jason Lisle's static Doppler model, whatever metric it turns out to have.  All of them predict (1 + z)⁻⁴.

Why tired light fails it, and what that shows

Tired light escapes the theorem by violating its premises.  It removes energy from photons in transit, so photon number and energy are not conserved along the ray, and the redshift is not a property of the geometry at all.

Lubin and Sandage put the problem in the sharpest possible form when they tried to compute a tired-light prediction:

In contrast with the standard model with the Mattig equations, there is no metric theory of how distances and magnitudes are measured in a "tired light" model.  Therefore, we must guess at a reasonable equation for distance.²⁶

That sentence is worth more to a sceptical reader than any of the numbers.  Tired light is not a rival cosmology.  It is a proposal about photons with no geometry attached, which is why it has to be hand-fitted at every step and why it fails so badly when it is.

With a Euclidean static geometry and no time dilation, the surface-brightness exponent comes out to 1 instead of 4.  Measured against Hubble Space Telescope photometry of three galaxy clusters near z = 0.85, Lubin and Sandage report:  "The HST data rule out the 'tired light' model at a significance level of better than 10 σ."²⁶

The measurement, and the problem with it

Here is where the honesty is due, because the Tolman measurement is much messier than either side admits.

The exponent has to be extracted from real galaxies, whose intrinsic surface brightness is not known and changes as their stars age.  Lubin and Sandage's result for three HST clusters was:

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 q_o = 1/2 model.²⁶

Neither number is 4.  The gap is attributed to luminosity evolution — the galaxies were younger and brighter then — and the required amount, "between 1.72 to 1.19 in the R band and 0.94 to 0.45 in the I band," is what stellar-population models independently predict.²⁶  Sandage's 2010 reanalysis, using fixed radius bins instead of calibrating out the size dependence, lands in the same place:  "The expansion is real and a luminosity evolution exists at the mean redshift of the HST clusters of 0.8 mag in R_cape and 0.4 mag in the I_cape photometric rest-frame bands, consistent with the evolution models of Bruzual and Charlot."²³

The band dependence is the tell, and it cuts both ways.  A geometric dimming exponent cannot depend on which colour filter you use.  The dimming law is identical in every rest-frame passband.  A measurement giving 2.59 in one band and 3.37 in another, with quoted errors of 0.17 and 0.13, is announcing at high significance that something band-dependent is present.  That something is stellar evolution, and bluer bands change faster as a population ages, which is exactly the sign observed.

This is why Lisle's use of the same numbers does not work.  He averages the two exponents to 2.98 ± 0.55 and observes that it matches his model's predicted 3.²⁷  But averaging two mutually inconsistent numbers to recover a third is not a measurement of cosmology, and his own model — once Etherington is enforced — predicts 4 anyway.  That argument is worked through in full in the article on the Doppler model, and is not repeated here.

Sandage's own verdict, and the overstatement in it

Sandage closed the fifty-year programme like this:

The solution of the Tolman test given by LS01c and differently here has not been quite as easily done as I set out at the planning meeting for the LST 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.²³

The first three sentences are exactly right.  The last one goes beyond what the test can deliver, for the reason given above:  a static-space Doppler model predicts the same (1 + z)⁻⁴ and would pass the same test.

Barnes and Lewis, who accept the standard model, give the fair summary from the other side:  the big bang "survives the surface brightness test.  It doesn't fail… But it doesn't pass with flying colours either."  They add, drily, "Cosmologists aren't exactly enthusiastic about the surface brightness (Tolman) test."¹⁴

Neither side should be leaning on this test.  It is a decisive refutation of tired light and a weak, evolution-contaminated confirmation of everything else.

Claim 3: is space "really" expanding?

This is the question everybody asks and almost nobody answers carefully.  It has three layers, and they need separating before anything sensible can be said.

Layer one: a distant galaxy's velocity is not a well-defined number

In special relativity, comparing two velocities is easy.  In general relativity it is not, and the reason is geometric rather than philosophical.  A velocity is a vector.  To compare two vectors you must bring them to the same point.  In curved spacetime, carrying a vector from one place to another changes it, and how it changes depends on the route you take.  There is no global standard of rest, so "how fast is that galaxy moving away from us" has no answer until you specify a rule for the comparison.

Different rules give different answers, and none of them is wrong.

Layer two: the two conventions, and why both papers are correct

Emory Bunn and David Hogg took the most natural rule — carry the comparison along the path the light actually travelled — and worked out the consequence in the American Journal of Physics in 2009.  Their conclusion:  "The most natural interpretation of the redshift is as a Doppler shift, or rather as the accumulation of many infinitesimal Doppler shifts."²⁸

Two years earlier, Matthew Francis, Luke Barnes, Berian James and Geraint Lewis had defended the other convention in Publications of the Astronomical Society of Australia, arguing that expanding space is "a completely valid framework for the description of the evolution of the universe," and that most attacks on the idea fail because they attribute to it properties general relativity does not actually predict.²⁹

Both papers are right, and they know it.  They are answering different questions with different bookkeeping on the same spacetime.  A reader who has been told that one picture is obviously correct and the other obviously absurd has been reading popularisation, not literature.

The cleanest demonstration that the two pictures can be literally identical is the Milne model, published by E. A. Milne in 1935.  It describes galaxies flying apart from a common origin through flat, empty, static space — an ordinary special-relativistic explosion.  It is also exactly an empty expanding-universe solution of Einstein's equations.  Same spacetime, two coordinate systems.  Neither description is more real than the other, and no measurement can prefer one.

Luke Barnes made this point to Jason Lisle directly, citing the standard graduate text:

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.³⁰

Layer three: the part that is not a matter of words

Lisle's reply is the right one, and it converts the argument into physics:

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.³¹

That is a real, testable claim, and it is not the same claim as "the redshift is a Doppler shift."  A static large-scale geometry predicts different relationships among redshift, apparent size, apparent brightness and number counts than an expanding one.  Those are observations.  The full test is carried out in the sister article on the Doppler model, which finds the specific static model fails;  what belongs here is the general point that the question has a physical form and a verbal form, and only the physical form is worth arguing about.

What is observable and what is not

Two results that do bear on the physical version

Supernova magnitudes.  Tamara Davis and Charles Lineweaver fitted a purely special-relativistic reading of Hubble's law — recession velocity from the relativistic Doppler formula, distance from v = HD — against the 1999 Supernova Cosmology Project data, and found it "23σ from the general relativistic ΛCDM model."³²  That number should be handled with care, and this article will not hide the caveat:  they held the supernova absolute magnitude fixed at M_B = −3.45 rather than marginalising over it, and they used D_L = D(1 + z), which is neither what Etherington requires for a metric static model nor what Lisle's paper uses.  An independent fit to the much larger Pantheon+ catalogue with the magnitude offset marginalised — reported in the Doppler model article — gives a smaller but still adverse result.  The direction of the answer is robust;  the "23σ" is not.

Cluster velocities.  If the redshift is real motion through a static space filled with a static radiation bath, then a cluster at z = 0.55 is physically moving at about 123,000 km/s, and that motion would leave an enormous imprint on the microwave background photons scattering through its hot gas.  The measured value for the best-studied case, sub-cluster B of MACS J0717.5+3745, is +3,450 ± 900 km/s — roughly thirty-six times too small.³³  Clusters are essentially at rest in the microwave background frame.  That is what expansion predicts and what wholesale motion through a static bath forbids.

One thing "expanding space" does not mean

Space expanding does not stretch atoms, planets, people, or the solar system.  Gravitationally and electromagnetically bound systems are held together by forces far stronger than the cosmological effect, and they simply do not participate.  The Andromeda galaxy is moving toward the Milky Way at 109 ± 4 km/s, measured from Hubble Space Telescope proper motions, which is not a paradox³⁴ — local gravity beats the Hubble flow on local scales, and the expansion only dominates once the galaxies are far enough apart that gravity between them has become negligible.  Any argument that begins "if space were expanding, rulers would expand too, so we could not measure it" has misunderstood what the claim is.

Claim 4: the hot dense beginning is a separate question

Everything above is about whether the galaxies are receding.  None of it says the recession began in a hot dense state 13.8 billion years ago.  That is a further claim, and it rests on a different body of evidence:  the abundances of the light elements, the microwave background and its acoustic peaks, the growth of structure, and stellar ages.  Each has its own article on this site — big bang nucleosynthesis, the cosmic microwave background, large-scale structure — and the overview that ties them together is the standard model article.

One test does sit on the boundary, and it belongs here because it is the point where "the galaxies are receding" starts to force "and the past was different."

The microwave background must have been hotter in the past.  If it is relic radiation cooling as the universe expands, its temperature at redshift z must be exactly (1 + z) times its temperature now.  This is measurable, because gas clouds in front of distant quasars are excited by that radiation, and the excitation depends on the temperature.  Carbon monoxide and neutral carbon absorption give T_CMB(z) = (2.725 ± 0.002) × (1 + z)^(1−β) with β = −0.007 ± 0.027 — the predicted scaling, to about 3 percent.³⁵  A water-absorption measurement at z = 6.34 gives 16.4 to 30.2 K against a predicted 20.0 K.³⁶

The most valuable witness on this is again López-Corredoira, because he is spending a 64-page review looking for holes:

The CMBR temperature measured from the rotational excitation of some molecules as a function of redshift has been quite successful in proving expansion:  the results of Noterdaeme et al. with the exact expected dependence on T = T₀(1 + z) are impressive… one can say with almost total confidence that a local origin of the CMBR in a static Universe is excluded.¹⁶

Note the exact scope of that concession.  It excludes a static origin for the background.  It does not by itself establish a hot dense state at redshift 1,100, which is a further inference from the blackbody spectrum and the acoustic peaks.

Why a young-earth reader should care about the difference.  Danny Faulkner's argument in Answers Research Journal is that the expansion is the part creationists should keep, not the part they should attack, because a biblical cosmology has to be built inside a correct description of the universe's geometry.²  Whether he is right about the theology, he is right about the logic:  claims 1 and 2 are strongly supported, claim 3 is largely semantic, and the argument worth having is over claim 4.  An apologetic that spends its ammunition on claims 1 and 2 arrives at claim 4 with an empty magazine and a damaged reputation.

Two Christian uses of the expansion, tested

Christians use the expansion in two ways.  One of them holds up and the other does not.

"He stretches out the heavens" is not a description of the Hubble expansion.  Isaiah 40:22 says God "stretches out the heavens like a curtain, and spreads them like a tent to dwell in," and the same picture recurs in Job 9:8, Psalm 104:2, Isaiah 42:5, 44:24 and 45:12, Jeremiah 10:12 and Zechariah 12:1.  Creationists have often read these verses as the Bible describing cosmological expansion long before Hubble.³⁷  Russell Humphreys built that reading into his white-hole cosmology.  In Starlight and Time (1994) he listed the verses and concluded that they "imply that God stretched out space itself at some time in the past."  He did not mean the expansion astronomers measure today, though.  He suggested the stretching "stopped on or before the sixth day" of creation week.³⁸

The two physicists who built young-earth cosmologies on general relativity have both since dropped the claim that these verses describe space stretching by a large factor.  John Hartnett reviewed the passages in Journal of Creation in 2011.  The Hebrew verb natah is the one used when "Moses stretched forth his hand toward heaven" (Exodus 10:22), and the images are a curtain and a tent, fabrics that are put up and then stay the same size.  His verdict is that reading cosmological expansion into these texts "is not justifiable and is pure eisegesis."³⁷  Humphreys agreed.  In an email of 24 April 2014, which Hartnett published with his permission, Humphreys wrote that when Hartnett raised the point in early 2011 "I realized he was absolutely right," because the fabrics of Bible times stretch by only a few percent, "not nearly large enough to give the sevenfold or more increase in size that we would need to explain the redshifts we observe."³⁹  The stretched-sky image is also older than Israel:  in Enuma Elish Marduk stretches Tiamat's skin to make the heavens, as the sister article on ancient cosmology and Genesis documents from the tablets.

So the verses are compatible with an expanding universe, as they would be with a static one, but they are not a fulfilled scientific prediction.  A skeptic who calls the expansion reading hindsight is right, and the young-earth cosmologists who first made it now say the same.  The claim that survives is narrower:  the Bible describes heavens that God made and spread out, and nothing in the measured expansion contradicts that.

The expansion does point to a beginning, but it proves less than apologists often claim.  In 2003 Arvind Borde, Alan Guth and Alexander Vilenkin proved that "a cosmological model which is inflating – or just expanding sufficiently fast – must be incomplete in null and timelike past directions."⁴⁰  Their condition is only that "the average expansion rate in the past is greater than zero."⁴⁰  That makes the theorem a claim-2 result, not a claim-4 result.  It needs the galaxies to have been receding on average, which this article finds very strong.  It needs nothing about a hot dense state, the light elements, the microwave background or 13.8 billion years.  Vilenkin's own summary is that the answer to "Did the universe have a beginning?" is "It probably did."⁴¹

Three limits travel with the theorem, and an apologist who drops them will be caught.  First, "incomplete" means the classical description runs out at a past boundary, not that a creation event has been observed:  the authors' own conclusion is that "some new physics is necessary in order to determine the correct conditions at the boundary."⁴⁰  Second, Guth denies that it proves a single start:  "There is of course no conclusion that an eternally inflating model must have a unique beginning."⁴²  Third, Vilenkin writes that "the theorem does not tell us anything about the existence of God."⁴¹  So the theorem supports the premise "the universe began to exist," not the conclusion "God made it";  that further step is philosophy, which the physics does not take.  And the theorem gives no age.  It fits a universe 6,000 years old as well as one 13.8 billion years old, so it neither helps nor hurts the young-earth timeline.

The live anomaly: JWST galaxy sizes and surface brightness

Something is genuinely odd in the deep James Webb Space Telescope fields, and the people reporting it are not creationists.

The size problem.  In an expanding universe, angular-diameter distance peaks at z ≈ 1.6 and then decreases, so a galaxy of fixed physical size should look bigger the further away it is beyond that redshift.  That turnaround is not seen in raw observed sizes.  The standard resolution is that galaxies were genuinely smaller in the past — measured size evolution goes as (1 + z)^−1.48 for early-type and (1 + z)^−0.75 for late-type galaxies out to z = 3.⁴³  This is real physics and it is independently motivated by galaxy-formation models.  It is also circular in an uncomfortable way, because those intrinsic sizes were derived assuming standard-model distances.  López-Corredoira makes the same complaint from outside the creationist world:  the angular-size data show "a dependence θ ~ z⁻¹, a static Euclidean effect over all scales," reconcilable with the standard model "unless we assume a strong evolution of galactic radii."¹⁶  He then adds his own caveat, which should travel with the quotation:  "we must be cautious with this interpretation, because of the uncertainty in the galaxy size evolution."

The surface-brightness preprint.  In April 2026, V. V. Tsymbal, A. A. Raikov and N. Yu. Lovyagin posted an analysis of 6,860 galaxies with spectroscopic redshifts from the ASTRODEEP-JWST catalogue.  Their abstract:

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)⁻⁴.⁴⁴

Three things must be said about it, and all three matter.

First, it is a preprint.  It has not been through peer review.  Preprints in observational cosmology have a substantial failure rate, and a departure from a prediction found in one catalogue with one selection function is not a result yet.

Second, the group has a prior position.  Lovyagin is a co-author of Lovyagin et al. 2022, which argues for static cosmologies, and which is Lisle's own source for the tired-light curve in his 2024 paper.  That does not make the analysis wrong — a scientist's motivations are not evidence about the universe — but a reader deserves to know it, and this article says so plainly for the same reason it flags creationist authorship elsewhere.

Third, and most important, it does not help a young-earth cosmology even if it holds up.  Any measured departure from (1 + z)⁻⁴ is a departure from Etherington's theorem, and Etherington's theorem holds in static Doppler models too.  A confirmed anomaly here would be a problem for the whole class of metric cosmologies, not a win for one of them.  It would most likely be traced to selection effects, to intrinsic evolution in galaxy surface brightness, or to the morphological k-correction — sizes at z ≈ 10 are measured in rest-frame ultraviolet light while sizes at z ≈ 1 are rest-frame optical, and neither the Lisle-Barnes exchange nor the ASTRODEEP preprint handles that mismatch.

The honest verdict:  unresolved, watch it, do not build on it.

What would falsify the expansion

A claim worth believing has to be able to fail.  Here is what would do it.

Redshift drift, and it is nearly here.  If the universe is expanding, the redshift of any individual galaxy is changing, very slowly, as the expansion rate evolves.  Allan Sandage worked out the size of the effect in 1962:

dz/dt₀ = H₀(1 + z) − H_em³²

The magnitude is about one part in 10¹³ per day — hopeless for 1962 instruments, which is why Sandage published it as a thought experiment.  It was revived by Abraham Loeb in the late 1990s and is now called the Sandage-Loeb test.¹⁴  The reference feasibility study, by Jan Liske and colleagues, finds that "a 42-m telescope is capable of unambiguously detecting the redshift drift over a period of ~20 yr using 4000 h of observing time," using the Lyman-alpha forest between z = 2 and z = 5.⁴⁵  The Extremely Large Telescope, now under construction, is 39 metres.

This is the cleanest possible test in the subject, and it has three properties nothing else has.  It needs no standard candle, no standard ruler, no assumption about galaxy evolution, and no cosmological model to interpret it.  It measures the expansion rate directly, at two epochs, on the same objects.  A static universe — Doppler, tired light, or anything else — predicts zero drift.  An expanding one predicts a specific non-zero number that depends on the matter and dark-energy content.

If the drift comes out zero, the expanding universe is dead, and this article is wrong.  That is a real risk and it will be settled by measurement, probably within twenty years.  Any young-earth cosmologist looking for a decisive experiment to bet on should bet on this one.

Other things that would do it.

• A distance indicator independent of redshift that disagrees with the Hubble relation. Gravitational-wave "standard sirens" are exactly that: the distance comes straight out of the waveform, with no rungs on a ladder and no calibration to anything. The first one, the neutron-star merger GW170817, gave H₀ = 70 (+12, −8) km/s per megaparsec.⁴⁶ That is consistent with the ladder and with the microwave background — and also far too imprecise to choose between them. It is a genuine independent confirmation of the relation and no help at all on its slope.
• A measured surface-brightness exponent that is robustly not 4 after evolution and selection are modelled properly. This is what the ASTRODEEP preprint claims, which is why it deserves following.
• A time-dilation exponent robustly different from 1. Blondin measured 0.97 ± 0.10 and Brewer 1.14 ± 0.34. A future measurement landing at, say, 0.5 ± 0.05 would break everything.
• A measured T(z) exponent departing from 1. Current constraints are β = −0.007 ± 0.027.
• Galaxy clusters found to be moving at the speeds a static-space model requires. Kinematic Sunyaev-Zel'dovich measurements say they are not, by a factor of about thirty-six.

Objections and responses

"Redshift could just be light getting tired on the long journey."

It could have been, and Fritz Zwicky proposed exactly that in 1929, in the same year Hubble's paper appeared.  It is not a stupid idea and it was not rejected for being unfashionable.  It was measured and excluded.  Tired light removes energy from photons one at a time;  it has no way to change how often they arrive.  So it predicts that a supernova at redshift 0.5 rises and fades on the same schedule as one next door.  It does not.  Blondin and colleagues measured the ageing rate directly from supernova spectra and got an exponent of 0.97 ± 0.10 where tired light needs 0;  the no-dilation model fits with χ² = 150.3 for 35 degrees of freedom, a goodness of fit of zero percent.¹⁹  Add to that the surface-brightness exponent — tired light predicts 1, the data give roughly 3, and Lubin and Sandage rule the model out "at a significance level of better than 10 σ."²⁶  This is a clean falsification of a named alternative and creationists should stop citing it.

"Even Hubble didn't believe the universe was expanding."

True, and irrelevant, and the quotation usually deployed to prove it is doctored.  Hubble preferred de Sitter's static model in 1929 and stayed cautious for decades — but for a reason that has since evaporated:  as Sandage explains, Hubble used a redshift-distance formula, D = cz/H₀, that is simply wrong in relativistic cosmology, and the correct one was not published until Mattig in 1958.²³  The truncated Hubble quote about "the unwelcome supposition of a favoured location" reverses his meaning;  a young-earth astronomer, Danny Faulkner, wrote a whole paper documenting the misuse.⁹  An argument that depends on a 1929 astronomer's provisional opinion, misquoted, is not an argument.

"The redshift is a Doppler shift, not expanding space, and that kills the big bang."

The first half is defensible and the second half does not follow.  Within general relativity, "Doppler shift" and "expanding space" are two coordinate descriptions of the same spacetime, and standard references defend each.²⁹²⁸  What would be a real difference is a static large-scale geometry, and that is a testable claim rather than a verbal one.  It is tested — and found wanting — in the Doppler model article.  More to the point, Jason Lisle, who proposed the leading young-earth version, agrees in print that it does not deliver a young universe:  "Quite right.  The Doppler model is not needed to explain distant starlight in a young universe."³¹

"The Tolman surface-brightness test proves the expansion is real."

It does not, and Sandage's own summary overstates what his data can support.  The (1 + z)⁻⁴ law follows from Etherington's reciprocity theorem, which holds in any spacetime with Riemannian geometry, light on null geodesics and conserved photons — flat static Minkowski space included.²⁴  What the test really separates is metric redshifts from non-metric ones.  It kills tired light and says nothing about which metric.

"The Tolman test proves the standard model is wrong, because the measured exponent is 3, not 4."

This is the mirror-image error and it appears in Answers Research Journal.  The measured exponent is not one number:  Lubin and Sandage got 2.59 ± 0.17 in the R band and 3.37 ± 0.13 in the I band.²⁶  A geometric exponent cannot depend on the filter, so that split is a high-significance detection of something else — stellar population evolution, which independently predicts corrections of the observed size and sign.  Averaging the two to 2.98 and matching it to a predicted 3 averages two mutually inconsistent measurements.

"If space is expanding, wouldn't our rulers expand too, so we could never notice?"

No.  Bound systems do not expand.  Atoms are held together by electromagnetism and galaxies by gravity, both overwhelmingly stronger on those scales than the cosmological effect.  The Andromeda galaxy is approaching us at 109 ± 4 km/s.³⁴  Expansion only dominates on scales where nothing else is holding things together.

"Redshifts are quantised, which means they are not velocities at all."

They are not quantised.  The nearby-galaxy periodicity near 37.5 km/s appears only after a galactocentric correction whose reference vector was scanned, and a sympathetic review found only "weak effects."  The quasar periodicity in log(1 + z) was directly tested against 1,647 quasar-galaxy pairs and found absent "at the predicted frequency… or at any other frequency."  And the one measured periodicity in Sloan quasar number counts was traced to a telescope artefact by John Hartnett, the young-earth physicist who had championed it:  "It does not signal any intrinsic (quantized) redshifts in the quasars."⁴⁷  Note also that quantisation, if real, would break the Doppler model too, since that needs a smooth monotonic velocity-distance law.  The full account is in the Doppler model article.

"Nobody has ever seen a galaxy move.  This is all inference."

Correct, and the same is true of continental drift, plate tectonics and the age of a tree from its rings.  What makes an inference strong is that it is over-determined:  several measurements that could have disagreed do not.  Here the redshift-distance relation, supernova time dilation, spectral ageing, quasar variability, surface-brightness dimming, the background temperature at high redshift, and cluster velocities in the background frame all point the same way, and each of them could have come out differently.  If the answer were wrong, all seven would have to be wrong together, in the same direction, for unrelated reasons.

"Fine — but does the expansion prove the universe is 13.8 billion years old?"

No, and this is the distinction the article exists to make.  The expansion is claim 2.  The age is claim 4.  The age comes from a model of the expansion history — the Hubble constant plus the matter and dark-energy content — and from independent clocks:  the oldest globular clusters, the light-element abundances, radioactive dating of the elements.  Those clocks agree with each other to within a billion years or so, which is a genuine and non-trivial concordance.  Attacking that concordance is a real argument.  Attacking the redshift-distance relation is not.

Sources