Halton Arp and Discordant Redshifts

Summary

• Halton Arp was a first-rate observer who made a real discovery and then read it wrongly. He spent twenty-nine years as a staff astronomer at the Mount Wilson and Palomar Observatories, and his Atlas of Peculiar Galaxies (1966) is still in use sixty years later. His claim was that some quasars are not far away at all, that nearby galaxies eject them, and that their large redshifts are intrinsic rather than a measure of distance.
• Arp did not deny the expanding universe, and creationists who recruit him for that are misreading him. Danny Faulkner, a young-earth astronomer, states it flatly: "Arp and other astronomers who questioned whether quasars had cosmological redshifts never doubted that the universe was expanding."¹ Arp held that most redshifts were cosmological, with exceptions. He was defending the steady-state model, which requires expansion.
• His flagship case has been resolved against him. Arp's 1971 four-hour Palomar plate of NGC 4319 and Markarian 205 showed what he called "a narrow, luminous connection."² In 1992 the Hubble Space Telescope found magnesium absorption in the spectrum of Markarian 205 at the galaxy's velocity, 1265 ± 55 km/s.³ Light from the quasar passes through NGC 4319's gas. The quasar is behind the galaxy.
• The one testable prediction the school made was tested twice, by agreement, and failed. Karlsson's preferred quasar redshifts (0.06, 0.30, 0.60, 0.96, 1.41, 1.96) form a geometric series in 1+z with ratio 1.227, which is a period of 0.089 in log(1+z).⁴ William Napier specified the test in advance and handed it to three astronomers with no stake in the answer. On 1,647 quasar-galaxy pairs from the 2dF surveys they found "no evidence for a periodicity at the predicted frequency in log(1+z), or at any other frequency."⁵ Tang and Zhang repeated it on Sloan and 2dF and found none in the high-completeness samples.⁶
• The statistical case never worked, and the reason is worth learning. Arp found his pairs by eye, in images chosen because they looked striking, and then computed the probability that such an alignment would occur by chance. That number is meaningless. A probability has to be attached to a hypothesis stated before the data are seen. Faulkner puts it in one line: "This sort of statistical argument works only if one specifies the outcome prior to investigating the outcome."¹
• Three independent lines of evidence now place quasars at their redshift distance. Foreground galaxies gravitationally lens quasars into multiple images, which requires the quasar to be behind. Quasar host galaxies are resolved, and they sit at the quasar's own redshift. Quasar spectra carry a forest of hydrogen absorption lines at every redshift between zero and the quasar's, which requires a long path through intervening gas.
• The excess of quasars near bright galaxies is real, and it has a standard-cosmology explanation. Foreground mass magnifies background quasars and pushes faint ones over the survey's detection limit. Sloan measured this "cosmic magnification" on 200,000 quasars and 13 million galaxies at about 8σ, with the predicted sign flip between bright and faint quasars.⁷ Arp saw a genuine correlation. He read the wrong cause into it.
• Answers in Genesis contradicts itself on this in public and has not fixed it. It hosts Faulkner's 2018 paper taking Arp apart, and it also still hosts, unannotated, his 2004 chapter endorsing Arp and calling redshift quantisation a live problem. That chapter also says "As the first data from COBE were assembled in the early 1990s, we found that the CBR was perfectly smooth."⁸ That statement is false. COBE detected the anisotropies, and the detection won the 2006 Nobel Prize.
• A 2024 paper revives the periodicity claim and should be read carefully rather than waved away. Mal and colleagues apply singular value decomposition to Sloan quasar-galaxy pairs and report peaks near the Karlsson values.⁹ But the sample is selected, the data are transformed before the search, and no look-elsewhere correction is reported. Those are the same three moves that produced the original signal.
• The honest verdict has two halves and both are true. Arp was treated badly: Palomar and NOAO cut off his telescope time for the subject he had given his life to, which is a bad way to settle a scientific question.¹ And he was wrong anyway. Neither half cancels the other, and neither should be dropped.

This article is the case file for one specific claim.  For the wider argument about what redshift measures, see the Doppler-model article and tired light.  For the standard model those claims attack, see the Big Bang overview.

Who Arp was, and why he earned a hearing

Halton Christian Arp (1927-2013) was not a crank, and the case against him fails if it starts by pretending otherwise.

He was a staff astronomer at the Mount Wilson and Palomar Observatories for twenty-nine years, which for most of that period meant regular access to the 200-inch Hale Telescope, then the largest in the world.¹⁰  His first major project was the one Edwin Hubble and Walter Baade wanted done and could not do themselves:  a nightly nova patrol of the Andromeda galaxy.  Arp observed on 290 nights between June 1953 and January 1955, found 30 novae, and wrote that the study "is in great part due to Baade's and Hubble's efforts to realize this program."¹¹  In 1960 the American Astronomical Society gave him its Helen B. Warner Prize, the year after it went to Geoffrey and Margaret Burbidge, who would become his closest collaborators.¹²  He was, in Faulkner's own words, "a keen observer, a veritable giant in the field of observational astronomy."¹

His lasting work is the Atlas of Peculiar Galaxies, published by Caltech in 1966.  It is a catalogue of 338 entries that do not fit the ordinary spiral-elliptical classification:  galaxies with tails, bridges, jets, distorted arms and close companions.  Arp assembled it from his own 200-inch plates.  Sixty years later the Arp numbers are still the standard way to name these objects, and NASA's Extragalactic Database hosts the whole atlas online.¹³  His stated purpose was diagnostic:  "The peculiarities of the galaxies pictured in this Atlas represent perturbations, deformations, and interactions which should enable us to analyze the nature of the real galaxies which we observe and which are too remote to experiment on directly."¹³  Most of the objects turned out to be interacting and merging galaxies.  That was not Arp's own reading in 1966.  His preface proposes magnetic fields and "viscosity-like forces" instead.¹³  Arp found the phenomenon.  Others explained it.

That is the right frame for what followed.  Arp had a genuine talent for seeing structure in photographic plates that other people missed.  The question is whether that talent, pointed at a different problem, produced another discovery or produced an artifact.

What Arp actually claimed

Arp's claim is narrower than either his admirers or his opponents usually state it.

He accepted the Hubble relation.  He accepted that the universe is expanding.  He accepted that most extragalactic redshifts are cosmological, meaning that they measure distance.  What he denied is that all of them do.  His position was that a class of compact, active objects, quasars and Seyfert nuclei, are ejected from the cores of ordinary nearby galaxies, and carry a large redshift that is intrinsic to the object rather than a measure of its distance.

Faulkner, writing as a young-earth creationist to other creationists, is blunt about how badly this gets garbled:

Furthermore, contrary to common misconception among recent creationists, Arp and other astronomers who questioned whether quasars had cosmological redshifts never doubted that the universe was expanding.  Indeed, Arp and his colleagues clung to the steady state model long after nearly everyone else had abandoned it.  The steady state model is not possible if the universe is not expanding, so it would have made no sense for Arp and his colleagues to have doubted universal expansion.¹

That last point is the key to Arp's motive, and it is not a hostile reading.  The steady-state cosmology of Hoyle, Bondi and Gold requires an expanding universe in which new matter is continuously created, so that the average density never changes.  Arp's suggestion was that quasars are where the new matter appears.  Young, compact, high-redshift objects, spat out of galaxy nuclei.  His collaborators were Geoffrey and Margaret Burbidge, Fred Hoyle, and Jayant Narlikar, all steady-state men.

This matters for creationist use of Arp in two ways.  First, an argument that quotes Arp against the expansion of the universe is quoting him against a position he held.  Second, the cosmology Arp was defending is eternal, a universe with no beginning at all.  It is an odd ally for a doctrine of creation.

Arp's own summary, at the end of his 1971 paper on NGC 4319, states his conclusion at its narrowest and most careful:

In summary, Markarian 205 appears to be a bonafide quasi-stellar object, which is connected to the nucleus of a larger, lower-redshift galaxy.  Evidence that compact objects with intrinsic, non-velocity redshifts are ejected from galaxies has been presented elsewhere.²

"Intrinsic, non-velocity redshifts."  That is the claim, and it is a physical claim about a class of objects, not a claim about cosmology as a whole.

The case Arp built

Arp's argument had three legs:  individual objects that appear physically connected but have wildly different redshifts, a statistical excess of quasars near bright nearby galaxies, and a claimed periodicity in the quasar redshifts themselves.  Each is worth stating at its strongest before it is answered.

NGC 4319 and Markarian 205

This was the flagship, and Arp knew it.  A highly processed image of the pair is on the dust jacket of his 1987 book.¹

The setup:  NGC 4319 is a barred spiral galaxy in Draco.  Markarian 205 is a compact, star-like ultraviolet-bright object sitting about 40 arcseconds south of the galaxy's nucleus, projected inside the galaxy's spiral arms.  Daniel Weedman measured its spectrum in 1970 and found a Seyfert-type redshift of z = 0.070.¹⁴  Arp had Maarten Schmidt take two spectra of the galaxy itself, which had never been measured, and got 1700 ± 100 km/s, roughly z = 0.006.²  A factor of ten apart.  If both redshifts are distances, one object is ten times farther away than the other, and their apparent closeness is an accident of projection.

Arp went after the accident.  On 29 June 1970 he took twenty- and thirty-minute plates with the 200-inch and saw nothing between the two objects.  He waited nine months for good seeing.  On 28 March 1971 he took a four-hour exposure on baked IIIa-J plates, which reached more than a magnitude fainter, and something appeared:

This plate reached more than one magnitude fainter than the standard ones and revealed a luminous, linear feature originating at the Markarian object and running north into the over-exposed central portion of NGC 4319.²

Two months later, with time given him by Wallace Sargent, he took narrow-band plates through an H-alpha filter with an image-intensifier tube.  This is where the case became striking:

But on the Hα plates, a narrow, luminous connection could be seen linearly traversing the whole distance between Markarian 205 and the nucleus of NGC 4319.²

Note what he had done.  He did not just find a smudge on a deep continuum plate.  He tuned an 80-Ångström filter to the galaxy's redshift.  He says so explicitly, putting the half-transmission points "close to a redshift of 2100 km/sec."²  The bridge showed up brighter in that narrow band than in white light.  That is what you would expect if the bridge is hydrogen gas belonging to NGC 4319, excited by something passing through it.  Arp's proposed mechanism was exactly that:

Possibly the passage of the Markarian 205 object from the nucleus of NGC 4319 out through the disk has caused the hydrogen in the disk of the spiral to become excited and to radiate hydrogen emission lines.²

This is a real argument, made by a competent observer, with a physical mechanism and a testable consequence.  It deserved the attention it got.

The quasar excess near bright galaxies

Arp's second leg was statistical.  He compiled lists of quasars found close on the sky to bright, low-redshift galaxies, and argued that there were far more of them than random projection allows.  In a 1981 study, as López-Corredoira and Gutiérrez summarise it, he examined every non-elliptical galaxy brighter than magnitude 12.8 that had an apparent companion, and found that 13 of the 34 candidate companions had a higher-redshift quasar nearby.  Taking the chance probability as under 0.01 per galaxy, the combined odds come out near 10⁻¹⁷.¹⁵

He also argued that the quasars are not scattered randomly around the parent galaxies but lie along axes, in pairs on opposite sides.  That is what an ejection model predicts and a chance-projection model does not.

NGC 7603: the case that is still hardest to dismiss

The best modern version of Arp's argument is not Arp's.  It belongs to two secular astronomers who took the question seriously and did the observations properly.

NGC 7603 is a Seyfert galaxy at z = 0.029.  A luminous filament runs from it to a companion, NGC 7603B, at z = 0.057.  Arp published the pair in 1971, and it is entry 92 in his own atlas.¹⁶  In 2002 Martín López-Corredoira and Carlos Gutiérrez took spectra of two faint compact objects sitting inside that filament and found redshifts of z = 0.243 and z = 0.391.¹⁶  Four objects, four different redshifts, strung out along one thin line of light.

They followed it up in 2004 with imaging, photometry over two years, and archival Hubble images, and did the statistics carefully.  Their headline number:  the probability of three background galaxies of the observed brightnesses landing by chance on a filament of that area, in front of a galaxy like NGC 7603, is about 3 × 10⁻⁹.¹⁵

They then did something Arp rarely did:  they corrected for the fact that they had not searched a defined sample.

We have found this extraneous combination of circumstances (if we adopt the hypothesis of cosmological redshifts) by accident.  We did not sistematically analyze all the Seyfert galaxies like NGC 7603 in order to find something like this.¹⁵

Applying a trials factor over the 3,655 galaxies in SIMBAD brighter than B = 14, they arrive at a corrected probability near 10⁻⁵, still low, and they conclude "it is justified to talk about 'anomaly'."¹⁵

Anyone who wants to argue that Arp's whole programme was worthless has to deal with this paper.  It remains the strongest single case, and it is not closed.

But notice where the strength of the case actually sits, because it decides everything.  López-Corredoira and Gutiérrez ran the calculation a second way, ignoring the filament and asking only how strange it is to find four objects of those magnitudes inside a 59-arcsecond square somewhere on the sky.  Their own answer:  about 1.1 × 10⁻², a one-percent coincidence, over the whole sky.¹⁵  A one-percent coincidence somewhere on the whole sky is not an anomaly at all.  It is Tuesday.

So the entire weight of the strongest surviving Arp case rests on one judgement:  that the filament is a real physical structure and that the two faint objects are in it rather than merely projected on it.  That judgement is made by eye, from an image.  Which brings up the problem that runs through this whole subject.

The selection-effect problem, explained slowly

This is the heart of the matter, and it is not a technicality.  It is the reason a pile of individually impressive coincidences adds up to nothing.

Start with a fair coin.  The chance of flipping five heads in a row is one in thirty-two.  Now flip a coin five hundred times and write down the results.  Somewhere in that run there will almost certainly be a stretch of five heads.  If you circle that stretch and announce that you have found a one-in-thirty-two event, you have said nothing.  The probability was computed for a run specified in advance.  You specified it afterward, by looking.

Faulkner uses exactly this example, and then a sharper one:

Given the way genetic material is shuffled during reproduction, the total possible number of unique children that any couple can have is staggering.  Yet, human couples can have only a very small number of children.  Therefore, one could conclude that the probability of any one of us existing is vanishingly small, yet here we are.  Of course, the resolution to this paradox is that each one of us happened, so the probability that each one of us happened is one.  This sort of statistical argument works only if one specifies the outcome prior to investigating the outcome.  Asking the probability after the outcome is determined is meaningless.¹

Now apply it to the sky.

The whole sky is about 41,000 square degrees, and quasars are not rare on it:  Faulkner puts the surface density at 5 to 10 per square degree down to magnitude 20, levelling off near 50 per square degree at magnitude 21.¹  That is something like two million quasars bright enough to be catalogued, sitting behind millions of catalogued galaxies.  And neither population is spread like paint;  both are clustered.  In a sky that large, with both populations clustered, some galaxies will happen to have quasars projected right on top of them.  Some galaxies will happen to have two quasars on opposite sides.  Some will happen to have a faint filament pointing at one.  Not "might."  Will, in large numbers, from chance alone.

Faulkner draws the conclusion that a young-earth creationist ought to find uncomfortable and states anyway:

Arp and his colleagues have unintentionally biased their searches toward finding clumping of quasars with galaxies.  This amounts to cherry-picking data.  If both quasars and galaxies are somewhat randomly distributed in space, then it would be amazing if there were no clumping found.¹

And in his summing-up, the sentence that names the deeper problem:

However, there are far more examples of physically connected galaxies with the same redshift.  For instance, many entries in Arp's Atlas of Peculiar Galaxies appear to be interacting galaxies, yet they have similar redshifts.  Therefore, it appears that Arp cherry-picked many of his examples of supposedly interacting objects with discordant redshifts.  Again, Arp believed that most redshifts were cosmological, but that there were exceptions.  Who was to decide what the exceptions were?  Well, of course, Arp decided.¹

That last question is the one with no good answer.  Arp's own atlas is mostly full of interacting pairs at matching redshifts.  Those are the successes of the cosmological interpretation, catalogued by Arp himself.  He treated them as the normal case and the mismatches as the informative case.  But the criterion for calling a pair "physically connected" was visual, and it was applied by the person who already believed some of them would be anomalous.  There is no way to compute a probability out of that, because there is no defined sample and no stated trials factor.

Two further points, because this failure mode is subtler than it looks.

Post-hoc probability is not fixed by making the number smaller.  The instinct is to say that 10⁻¹⁷ is so extreme that no amount of selection could account for it.  That instinct is wrong, and the reason is that selection does not shave a factor off the probability.  It invalidates the calculation.  A number computed from an unspecified search over an unspecified sample has no interpretation at all.  It is not a small probability.  It is not a probability.

The proponents saw this too, and the good ones said so.  López-Corredoira and Gutiérrez raise the objection against themselves, using the constellation Orion:  compute the probability that Orion's stars fall in exactly that pattern and you get zero, "but the calculation of this probability is worthless because we have selected a particular configuration which has been observed a priori."¹⁵  Their answer is that their configuration is not arbitrary.  A line of objects is what an ejection model specifically predicts, so a filament is a physically motivated shape rather than a shape picked for being pretty.  That is a real answer and it is the right kind of answer.  It is also why their case survives while most of Arp's do not.

And there is a failure mode on the analysis side too.  Any search for a periodic signal in a finite dataset has to contend with the fact that the dataset has edges.  Hawkins, Maddox and Merrifield show it directly:  a uniform random distribution truncated sharply at both ends produces a power spectrum full of "seemingly-periodic features," nothing like the flat spectrum a true random infinite sample would give.⁵  Smooth the edges, which statisticians call apodization, and the artifacts go away.  So does most of the claimed signal, as the next section shows.

Redshift quantisation: the one testable prediction

Everything above is about individual objects, and individual objects are hard to argue about.  The quantisation claim is different.  It is a sharp, numerical, falsifiable prediction, and it was tested.

What Karlsson claimed

In 1971 K. G. Karlsson at Uppsala took the 166 quasar redshifts then known and noticed that the peaks in their distribution were not randomly spaced.  Writing 1+z rather than z, the peaks formed a geometric series with a constant ratio:

It is very remarkable that the quantities (1 + z_i), where i = 1 for the peak at z = 1.956, can be described as a geometrical series with a ratio (1 + z_i)/(1 + z_i+1) = 1.227.⁴

Run that ratio down from z = 1.956 and you get the famous list.  Taking logarithms turns a geometric series into an evenly spaced one, so the prediction is a comb of equally spaced lines in log(1+z).  Karlsson states the spacing himself:  "The expected period in x is 0.089," where x = log(1+z).⁴

The fourth column drops by 0.0888 at every step, which is log₁₀(1.227).  Karlsson's published list is the last column.⁴  That is the whole claim, and it is admirably concrete.  Karlsson's own significance estimate was cautious but firm:  the probability of a period this well defined arising by chance is "definitely below 1%, and is probably far smaller than this."⁴

Why would quasar redshifts come in steps at all?  On the ejection model they should.  If a quasar is born inside a galaxy with a large intrinsic redshift that decays as the object ages, and if the decay goes through discrete stages, then quasars caught at different stages will show preferred redshift values.  The peaks are the stages.  This is the reasoning behind Arp's version, and it is why the periodicity and the ejection claim stand or fall together.

There is one wrinkle that has to be handled correctly, and both sides agree on it.  If quasars are ejected from parent galaxies, the intrinsic redshift is measured in the parent galaxy's frame, not ours.  So before looking for the comb you must divide out the parent's redshift:

1 + z_intrinsic = (1 + z_quasar) / (1 + z_galaxy)

Every serious test of the claim, on both sides, does this.

The 2dF test: a prediction registered in advance

In 2002 something unusual happened, and it is a model of how a contested claim should be settled.

William Napier, one of the leading proponents of redshift periodicity, went to three astronomers at Nottingham who had no stake in the question, Edward Hawkins, Steve Maddox and Michael Merrifield, and asked them to run the test.  He specified it in advance and then stepped back.  Hawkins and colleagues describe the arrangement in their own paper:

Napier recognized the importance of the study being carried out independent from any of the researchers with vested interests one way or the other.  He therefore gave clear instructions as to what analysis should be performed and what periodic effect should be seen if the phenomenon is real, but chose to take no part in the subsequent analysis.⁵

Napier's instructions were specific:  take every galaxy in the 2dF Galaxy Redshift Survey, find every quasar in the 2dF QSO Redshift Survey projected within 200 kiloparsecs of it, transform the quasar redshifts into the galaxies' frame, and look for a periodicity at P ≈ 0.09 in log(1+z).  That yielded 1,647 quasar-galaxy pairs, nearly eight times the sample size of the previous positive detection.⁵

Two results came back.

First, on the old data.  Reanalysing the 116 quasar redshifts from Karlsson's 1990 sample, the raw power spectrum does show the P ≈ 0.09 peak.  It also shows a peak at P ≈ 0.07, which the proponents themselves had already attributed to the window function, the artifact from the dataset's sharp edges.  When Hawkins and colleagues smoothed those edges, the acknowledged artifact dropped to about 1.5σ, and the "real" signal dropped further, to about 1σ.⁵  The claimed detection was mostly an edge effect.

Second, on the new data.  The abstract is one sentence long:

There is no evidence for a periodicity at the predicted frequency in log(1 + z), or at any other frequency.⁵

They add:  "Given that there are almost eight times as many data points in this sample as in the previous analysis by Burbidge & Napier (2001), we must conclude that the previous detection of a periodic signal arose from the combination of noise and the effects of the window function."⁵

And their acknowledgement, which does Napier credit:  "We are most grateful to Bill Napier for suggesting that we undertake this study, and for setting up such a fair test of this hypothesis."⁵

The Sloan test

Three years later Su Min Tang and Shuang Nan Zhang repeated the exercise independently, on both the Sloan Digital Sky Survey and the 2dF quasar survey, and tested two versions of the claim:  Karlsson's log(1+z) periods and Morley Bell's "decreasing intrinsic redshift" model.  They built four different sets of quasar-galaxy pairs using four different selection criteria, so that the answer could not turn on one arbitrary choice.  Their finding:

First, using different criteria, we generate four sets of QSO-galaxy pairs and find there is no evidence for a periodicity at the predicted frequency in log(1 + z), or at any other frequency… We also analyze the periodicity in redshifts of QSOs, and no periodicity is found in high completeness samples, contrary to the DIR model.  These results support that QSOs are not ejected from active galaxies.⁶

They also tested the spatial half of the claim directly, and it failed the same way:  "the distribution of projected distance between high redshift QSOs and nearby active galaxies and the distribution of redshifts of those active galaxies are consistent with a distribution of simulated random pairs."⁶

Arp's answer, and why it does not work

Arp did not accept the 2dF result.  With Christopher Fulton and David Roscoe he published a reply in 2005 arguing that the periodicity is "indeed strongly present" when the data are analysed correctly.¹⁷

Read what "correctly" means in their own paper, because they state it plainly.

They concede that the whole-survey analysis does not work:

However, it is also clear from these contour plots that even selecting a bright subsample that was sufficiently large to include all four bright-end spikes (typically, Bmag < 19.6) would not produce a sample that was sufficiently clean that a simple technique like power spectrum analysis would detect the periodicity signal implied by the A, B, C, D spikes.¹⁷

They concede that the signal disappears at faint magnitudes:

For much fainter apparent magnitude quasars the parent galaxies would have a much wider range in redshift and the raw quasar redshifts would be expected to approach a smooth distribution as is, in fact, born out by the contours at faintest apparent magnitudes in Figs. 1, 2 and 3.¹⁷

They therefore propose that the analyst must look at the images and decide which quasar belongs to which parent galaxy before the test is run:  "there would seem to be no substitute for actually looking at the fields which are being tested."¹⁷

And they say what follows from that:

Consequently if we had just done what was done in the highly publicized Hawkins et al paper, then a negative result would most certainly have been obtained.¹⁷

That sentence is an admission, and it is fatal.  It concedes that a blind, pre-specified test yields nothing, and asks instead for a test whose input depends on the analyst's judgement about which objects go together.  That judgement is made by the same person who expects the periodicity.

The showcase field makes it worse.  Their Sloan example is the region around NGC 622, and they explain how it was picked:

…given that the field was chosen because one of us (Arp) has already considered the same field many years ago when it contained only two quasars, we can see that this is a result having an extremely low probability of being a chance result.¹⁷

The field was chosen because Arp had already found it interesting.  A probability computed on a field chosen that way measures nothing.

The 2024 revival, read carefully

The claim has not gone away.  In 2024 Arindam Mal, Sarbani Palit, Christopher Fulton and Sisir Roy published a new analysis in Research in Astronomy and Astrophysics, using singular value decomposition instead of a Fourier power spectrum, on the grounds that SVD handles noisy data with multiple harmonics better.  They report periodicities again.⁹

This deserves to be engaged rather than waved off, so here is what their own results table says.

Four problems, in order of severity.

The confidence intervals swallow the result.  The Sloan pair measurement, 0.0884, is close to Karlsson's 0.089.  Its 95% interval runs from 0.018 to 0.090, a factor of five.  An interval that wide is consistent with a period at almost any value, and with no period at all.  A number is not a detection because its central value lands where you hoped.

The two methods disagree with each other on the same data.  On the 2dF pairs, SVR1 gives 0.0770 and SVR2 gives 0.0462.  Those are not the same answer.  If the signal were a real feature of the data, two implementations of the same technique would not differ by 40%.

The method finds periods in galaxy redshifts too.  The paper reports periodicities of 0.0040, 0.0140, 0.0150, 0.0159, 0.0220, 0.0430 and 0.0797 in various galaxy samples, and treats this as confirmation.⁹  Nobody, on any side of this argument, claims that ordinary galaxy redshifts are quantised at seven mutually inconsistent values.  A tool that reports a period in every dataset you feed it is reporting the properties of the tool.

There is no look-elsewhere correction.  The base period is chosen by the analyst:  "A peak location is selected as the base period if peaks are also observed at integral multiples of that peak location."⁹  Bin widths differ between datasets.  No trials factor is reported anywhere in the paper.  Selected sample, tuned transformation, uncorrected significance.  These are the same three moves that produced the original signal in 1971.

The one honest quantisation result came from a creationist

The most instructive episode in this whole story was not written by a critic of Arp.

John Hartnett is a young-earth creationist physicist who had argued in print that quantised quasar redshifts support a galactocentric cosmology.  In 2009 he analysed the Sloan DR6 quasar number counts and found apparent periodicities at Δz = 0.258, 0.312, 0.44, 0.63 and 1.1.  Then he checked whether the same periods appeared in something that could not possibly be physical, the survey's own confidence flag for its redshift measurements.  They did.  His 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.¹⁸

The mechanism was identified the following year.  Sloan finds quasars by colour.  Strong emission lines moving across the gaps between the survey's filter passbands make quasars at certain redshifts systematically harder to detect, which stamps "a periodicity of Δ(z) ~ 0.6" onto the redshift-number distribution.¹⁹

Hartnett had every incentive to publish the positive result and stop.  He did the control test instead, found his own effect was an artifact, and said so in the abstract.  That is what the method looks like when it is working, and it is worth more to this article than any number of refutations from the other side.

What settled it observationally

Statistics can be argued about forever.  What ended the debate was a set of measurements that each independently require the quasar to be far away, and that have nothing to do with counting coincidences.

Absorption lines from the foreground galaxy

The cleanest test of a claimed pair is direct.  If the quasar really is behind the galaxy, its light has crossed the galaxy's gas, and the gas will stamp absorption lines on the quasar's spectrum at the galaxy's redshift.  If the quasar is in front, or beside, or ejected from the nucleus, no such lines appear.

This test was run on Arp's flagship case, by the man Arp had debated in public.  On 30 December 1972 Arp and John Bahcall had squared off in a live debate, published the following year as The Redshift Controversy.¹⁰  Nineteen years later Bahcall pointed the Hubble Space Telescope's Faint Object Spectrograph at Markarian 205 and took a near-ultraviolet spectrum at resolution R = 1300.

Fifteen absorption lines came out.  Thirteen were from gas in our own Milky Way.  Two were not:

Two of the absorption lines, the Mg II resonant doublet, are produced by gas in the intervening galaxy NGC 4319.  This is the first detection of absorption due to intervening gas in this famous quasar-galaxy pair.³

The measured heliocentric velocity of that absorbing gas was 1265 ± 55 km/s.³  NGC 4319's own velocity is about 1405 km/s.  Arp himself measured it at 1700 ± 100 km/s.  The absorbing material moves with the galaxy, which is what it means for light to have passed through it.

Their conclusion:

We have detected absorption in the spectrum of the bright AGN Mrk 205 that is produced by Mg II ions in the intervening barred spiral galaxy NGC 4319.  This result is consistent with the cosmological interpretation of the redshifts of both Mrk 205 and of NGC 4319, according to which the two objects are accidentally projected close to each other on the sky and the light from Mrk 205 passes through the disk and the halo of NGC 4319 on its way to the observer.³

The bridge, meanwhile, did not survive better imaging.  Photographic plates were replaced by CCDs;  the pair has been imaged from above the atmosphere;  and the Hubble image shows no luminous bridge between them.¹

One caution, and Faulkner is the one who raises it.  The absorption test is decisive only in the direction that came out.  Had no absorption been found, the ejection camp would have claimed a win.  But when absorption is found, the ejection model can absorb that too, by placing the ejected quasar just beyond the galaxy's disk.  Faulkner's comment on a later case:

Notice carefully what is going on here.  If there were no absorption from gas in the galaxy in the spectrum of the quasar, that would be evidence for Arp's contention.  But if there is absorption, then that can be explained by Arp's contention too.  Therefore, Arp's contention can account for evidence either way.  That is, Arp's hypothesis makes no testable prediction in this matter.  However, the conventional understanding, that the quasar is a background object, makes a very specific prediction that was tested, and it passed that test.¹

That is the correct scoring.  The absorption result is not a knockout on its own.  It is a prediction that the standard picture made and the rival did not, and the standard picture won it.

Gravitational lensing

This is the one Arp's model cannot survive, and the reason is geometric rather than statistical.  A foreground mass bends the light of a background source and can produce two or more images of it.  This requires the source to be behind the lens.  There is no configuration in which a nearby ejected object gets multiply imaged by the galaxy it was ejected from.

The first case was found in 1979.  Dennis Walsh, Robert Carswell and Ray Weymann reported two seventeenth-magnitude quasars 5.7 arcseconds apart with the same redshift, 1.405, and near-identical spectra:  "Difficulties arise in describing them as two distinct objects and the possibility that they are two images of the same object formed by a gravitational lens is discussed."²⁰

The case that matters most for Arp came six years later, because it is an Arp configuration.  John Huchra and colleagues found a quasar at z = 1.695 sitting almost exactly on the nucleus of a fifteenth-magnitude spiral galaxy at z = 0.0394, a redshift ratio of forty-three, with the quasar's centroid "within approximately 0″3 of the center of the galaxy."²¹  On Arp's model this is the perfect example:  a high-redshift compact object at the very core of a low-redshift spiral.

It is not.  At higher resolution the quasar resolves into four images arranged around the galaxy's nucleus.²²  It is called the Einstein Cross.  The lens model that Huchra's team sketched in the discovery paper accounts for the geometry, and the system has since been used as a natural telescope to measure the size of the quasar's X-ray emitting region.

A single object ejected from a nucleus does not appear four times.

Quasar host galaxies

If a quasar is a small object thrown out of a nearby galaxy, it should have no galaxy of its own.  If it is a supermassive black hole accreting at the centre of a distant galaxy, it should sit in one, and the host should be at the quasar's redshift, with the size and brightness of a real galaxy at that distance.

Bahcall, Kirhakos, Saxe and Schneider imaged twenty luminous quasars with z < 0.30 using the repaired Hubble Space Telescope.  They found hosts, and they found ordinary ones:  ellipticals, spirals with H II regions, and interacting systems.  The quasars sit dead centre in them:

The quasar host galaxies are centered on the quasar to the accuracy of our measurements, 400 pc.²³

The hosts are luminous, on average 2.2 magnitudes brighter than a typical field galaxy.²³  That number only makes sense at the quasar's own distance.  Put the quasar ten times closer, as the ejection model requires, and the "host" becomes a hundred times fainter and ten times smaller:  not a galaxy at all, but a puff of nebulosity of a kind that has no counterpart anywhere.

The Lyman-alpha forest

This is the argument Faulkner calls "one of the major arguments for quasar redshift being cosmological," and it is the hardest to escape.¹

Neutral hydrogen absorbs ultraviolet light sharply at 121.6 nanometres.  If a beam of light from a quasar crosses many clouds of cool hydrogen on its way here, each cloud is at a different distance, so each cloud's absorption line lands at a different observed wavelength.  The result is a dense thicket of absorption lines blueward of the quasar's own hydrogen emission line.

Roger Lynds found it in 1971, in the spectrum of the then-record-holding quasar 4C 05.34 at z = 2.877:

Evidence is found for five separate absorption-line redshifts, all of which are less than the emission-line value.  The distribution of absorption lines is striking in that essentially all unidentified lines are located on the short-wavelength side of the Lα emission line.²⁴

Three features of the forest are fatal to the ejection model.

The absorption redshifts are always less than the emission redshift, never more.  That is exactly what a beam travelling toward us through a foreground of gas produces.  There is no reason for an ejected object with an intrinsic redshift to acquire a forest, and no reason for that forest to be one-sided.

The clouds cannot be near the quasar.  A quasar's ultraviolet output would ionise nearby hydrogen and strip it of the ground-state electrons the absorption requires.  So the absorbers must be far from the quasar, along the line of sight to us.¹

The forest gets thicker with the quasar's redshift, and at high enough redshift it goes black.  Robert Becker and colleagues took Keck spectra of a quasar at z = 6.28 and found the transmitted flux in the Lyman-alpha region had dropped to 0.0038 ± 0.0026 of the continuum, consistent with zero, a factor of more than 150 below the level at lower redshift.²⁵  This is the Gunn-Peterson trough, and it means the beam has crossed so much neutral hydrogen that essentially no light gets through.  A beam that has travelled a few tens of millions of light years out of a nearby galaxy does not cross that much gas.

Time dilation in quasar light curves

If a quasar is far away in an expanding universe, its variations should appear stretched by a factor of (1+z).  For years this was a genuine problem:  studies of quasar variability failed to find the stretch, and that failure was used against the cosmological interpretation.

It was resolved in 2023.  Geraint Lewis and Brendon Brewer took 190 quasars monitored for over two decades in several wavebands and did a Bayesian analysis:

Here we present the identification of cosmic time dilation in a sample of 190 quasars monitored for over two decades in multiple wavebands by assessing various hypotheses through Bayesian analysis.  This detection counters previous claims that observed quasar variability lacked the expected redshift-dependent time dilation.²⁶

This is worth flagging as an example of the honest scoring this article is trying to do.  For roughly two decades the absence of quasar time dilation was a real anomaly and a fair argument against the standard picture.  It stopped being one in 2023.

The excess of quasars near galaxies is real, and it is lensing

Here is the part where Arp turns out to have found something.

There genuinely are more quasars close to bright foreground galaxies than a uniform random distribution predicts.  Arp measured it.  The standard model predicts it too, for a reason that has nothing to do with ejection:  the foreground mass magnifies the background quasar.  Magnification does two competing things.  It brightens each quasar, pushing faint ones over the survey's detection limit.  It also stretches the sky area, which dilutes the surface density.  Which effect wins depends on the slope of the quasar number counts.  For steep counts you see an excess;  for shallow counts you see a deficit.  This is called magnification bias, and the sign flip is a sharp, falsifiable prediction.

Ryan Scranton and twelve colleagues measured it in the Sloan survey:

We present an 8σ detection of cosmic magnification measured by the variation of quasar density due to gravitational lensing by foreground large scale structure.  To make this measurement we used 3800 square degrees of photometric observations from the Sloan Digital Sky Survey (SDSS) containing ∼ 200,000 quasars and 13 million galaxies.  Our measurement of the galaxy-quasar cross-correlation function exhibits the amplitude, angular dependence and change in sign as a function of the slope of the observed quasar number counts that is expected from magnification bias due to weak gravitational lensing.⁷

Amplitude, angular dependence, and the predicted change of sign.  All three, at 8σ, on scales from 60 kiloparsecs to 10 megaparsecs, in agreement with the standard cosmology.

This is the right way to close out Arp.  The correlation he spent decades documenting is real.  It has a cause.  The cause is that the quasars are behind the galaxies, which is the opposite of what he concluded.

How creationists have handled Arp, scored honestly

Arp was not a creationist.  He was a steady-state cosmologist defending an eternal universe.  That has not stopped creationist organisations from adopting him, and the record deserves to be told straight.

Answers in Genesis publishes both sides and has not resolved it

Answers in Genesis hosts Danny Faulkner's 2018 paper The Case for Cosmological Redshifts, which takes Arp apart on statistical grounds, points out that Arp never doubted expansion, and warns creationists that rejecting the Hubble relation "amounts to a denial of general relativity."¹

It restated the case in plainer language on its main site two years later.  Faulkner's 2020 piece Common Big Bang Cosmology Misconceptions answers the question "Doesn't Arp's Work Disprove the Expansion of the Universe?" with a flat no:  "Arp thought that the universe is expanding, and so he thought that most galaxy redshifts are cosmological and thus could be used to find distance."²⁷  It reports the Hubble result on the flagship case in one line, "There was no luminous bridge."²⁷  And it explains Arp's motive as this article does.  A steady-state universe cannot have young galaxies far away and mature ones nearby.²⁷

It also still hosts, as current content, chapter 4 of Faulkner's own 2004 book Universe by Design, republished on the AiG website on 11 June 2013.⁸  That chapter presents Arp's case as open.  "The question really comes down to whether you believe what the redshifts tell us or if you believe what the images seem to tell us," it says.⁸  And it treats redshift quantisation as a live problem for the Big Bang:

While most cosmologists doubt that quantization is real, no one has been able to discredit it… It could develop into a major problem for the big-bang theory.⁸

That sentence was already false when AiG republished it in 2013.  Hawkins, Maddox and Merrifield had discredited the quasar version in 2002.  Tang and Zhang had confirmed the null in 2005.  Hartnett had traced the Sloan number-count periodicity to a selection effect in 2009, and Bell and Comeau had identified the mechanism in 2010.

The same chapter contains a plainly false statement about a different subject:

As the first data from COBE were assembled in the early 1990s, we found that the CBR was perfectly smooth.⁸

COBE did not find the microwave background perfectly smooth.  Its Differential Microwave Radiometer detected the temperature anisotropies, at the level the theory required, and John Mather and George Smoot shared the 2006 Nobel Prize in Physics for that work and for the blackbody spectrum measurement.  The chapter's own next sentence concedes the detection while framing it as a statistical artefact.

Neither the 2004 chapter nor the two later Faulkner pieces carries a note pointing to the others.  A reader arriving at the AiG site from a search engine can read either one and never learn that the organisation's own astronomer published the opposite conclusion.  Publishing both is not the problem;  publishing both without an editorial note is.

Creation Ministries International, and a harder case

Creation Ministries International published an obituary of Arp on 29 December 2013, written by John Hartnett, headed "Big bang critic passes away."²⁸  It calls Arp's publications "legendary," presents the ejection model as well supported, and cites Fulton and Arp's 2012 claim of a correlation at greater than 50σ.²⁸

Two things have to be said about this, and they pull in opposite directions.

The first is that this is the same John Hartnett who, four years earlier, had published the single most honest paper in the entire quantisation literature, the one that found his own signal in the survey's reliability flag and reported it.  His 2009 paper and his 2013 obituary are not a flat contradiction, because they are about different claims:  the 2009 paper concerns periodicity in Sloan quasar number counts, and the obituary concerns the ejection-plus-Karlsson correlation.  But the methodological lesson of 2009 applies directly to the 2012 result he cites, and it is not applied.

The second is a factual error that a fact-checker should have caught.  The obituary says the quasar found by Galianni and colleagues lies "only 8 arc minutes" from the nucleus of NGC 7319.²⁸  The discovery paper, on which Arp is an author, says 8 arcseconds.²⁹  That is a factor of sixty, and it matters, because the whole force of the case is that the quasar is inside the galaxy's visible body.  Eight arcminutes would put it well outside.

Where the creationist argument goes wrong at the root

The deepest problem is not any single error.  It is that the argument was recruited for a job it cannot do.

Suppose Arp had been right in every particular.  Suppose quasar redshifts are intrinsic and quasars sit a few tens of millions of light years away.  The universe would not become younger or smaller by one light year.  The galaxy distance ladder does not run through quasars.  Cepheids, tip-of-the-red-giant-branch stars, surface-brightness fluctuations and type Ia supernovae all work on ordinary galaxies, whose redshifts Arp accepted as cosmological.  See the cosmic distance ladder for how those rungs are calibrated.

Faulkner makes this point to his own side and it is worth repeating in full force:  the man creationists cite against cosmological redshifts held that most redshifts are cosmological, held that the universe expands, and was defending a cosmology with no beginning.  Recruiting him is not merely unhelpful.  It attaches a young-earth argument to an eternal-universe model.

Scorecard: the individual cases

Objections and responses

"Arp was silenced.  That is why the question was never settled." The first half is close to true and the second half is false.  The directors of Palomar and the National Optical Astronomy Observatory jointly told Arp he would not receive telescope time to pursue this work, and he left the United States over it.¹  That was a bad way to handle a scientific dispute:  it removes the evidence-gathering that could settle the question and replaces it with an administrative decision, and it made a martyr of a claim that deserved to be beaten on the data.  But the question was settled afterwards, and settled with instruments Arp never had:  the Hubble Space Telescope, the 2dF and Sloan surveys, Chandra, Keck.  Arp himself continued publishing from Garching for another thirty years, including the 2005 paper answered above.  His case did not die of neglect.

"Small-probability alignments cannot all be coincidence." They can, and the reason is that the probability is not what it seems.  A probability is a statement about a hypothesis specified before the data are examined.  Arp specified his cases by looking at plates and picking the striking ones.  Faulkner's summary is exact:  "Asking the probability after the outcome is determined is meaningless."¹  The one way to escape this is to state the test in advance and let someone else run it.  That was done, in 2002, at Napier's own suggestion, and the answer came back null.

"The quantisation is still being reported.  See the 2024 paper." It is, and the 2024 paper should be read rather than dismissed.  Read, it reports a period of 0.0884 with a 95% interval of 0.018 to 0.090;  two implementations of its own method disagreeing by 40% on the same data;  claimed periodicities in ordinary galaxy redshifts at seven mutually inconsistent values;  and no trials correction anywhere.⁹  Those are not the marks of a detection.

"Gravitational lensing is a theory-laden interpretation, not an observation." Lensing makes checkable predictions that nothing else does.  Multiple images of one source have the same redshift and near-identical spectra, as Walsh, Carswell and Weymann found.  Their brightness varies in the same pattern with a measurable time delay between images.  The image geometry follows from a mass model of the lens that can be cross-checked against the lens galaxy's own starlight and dynamics.  And the magnification-bias signal changes sign with the slope of the number counts, exactly as predicted, at 8σ.⁷  A framework that gets all of that right is not an interpretation laid over the data.

"If quasars are close, the Big Bang collapses." No.  The Big Bang's main supports are the microwave background's blackbody spectrum and acoustic peaks, the light-element abundances, and the growth of large-scale structure.  Quasar distances are not among them.  This is worth stating because it also runs the other way:  if a creationist stakes the case against an old universe on Arp, and Arp is wrong, the case goes with him.  See the Big Bang overview and large-scale structure.

"Even the critics admit NGC 7603 is unexplained." They do, and this article says so.  López-Corredoira and Gutiérrez put the corrected probability near 10⁻⁵ and call it an anomaly.¹⁵  Two things follow.  One unexplained system out of the many that have been examined is what a large sky produces;  a 10⁻⁵ event that occurs once in a survey of thousands of galaxies is not surprising.  And an unexplained configuration is not a mechanism.  Nobody has proposed a physical process that gives a compact object a redshift of 0.39 without moving it, and no such process has ever been seen in a laboratory or anywhere else.

"Redshift quantisation would prove we are at the centre of the universe." This is Russell Humphreys' argument, and it should be separated from Arp's.  Humphreys wrote that "redshift quantization is evidence (1) against the big bang theory, and (2) for a galactocentric cosmology," reasoning that quantised distances mean concentric shells and that we must be near their centre.³⁰  Two problems.  First, the nearby-galaxy quantisation he relies on appears only after transforming redshifts into a "galactocentric" frame whose correction vector is itself uncertain, and scanning a family of transformations and quoting the best one will manufacture a periodicity from noise;  see the Doppler-model article.  Second, as Faulkner points out, creationists who reject cosmic expansion while embracing the galactocentric reading of quantised redshifts are holding two incompatible positions:  the shell argument only works if redshift is distance.¹  Faulkner also answers the shell argument directly on Answers in Genesis's own site:  galaxies are not spread evenly but strung into sheets and filaments, so looking outward through several sheets produces apparent clumping in redshift, and "it is likely that any observer anywhere in the universe would see the same thing."²⁷

What to take from this

Two things are true at once, and the temptation in every direction is to drop one of them.

Arp was treated badly.  A working astronomer with a first-rate observational record was denied the instrument he needed to pursue a question he had made his life's work, by an administrative decision rather than by an experiment.  That is not how a scientific dispute should end.  It gave the appearance of suppression, and appearances of suppression are expensive:  they are still being cashed, forty years later, by people who have never read the papers.

Arp was also wrong.  Not wrong in a way that requires charity or hindsight, but wrong by tests he lived to see and answered badly.  His flagship object turned out to have foreground absorption at the galaxy's velocity.  His statistics could not survive being specified in advance.  His most striking configuration type turned out to be produced by a physical process, gravitational lensing, whose sign he had backwards.

There is a lesson in this that a Christian apologist has a particular reason to learn, because the failure mode is the same one that produces bad apologetics.  Arp's error was not dishonesty and it was not incompetence.  It was the natural human habit of noticing what confirms and skipping past what does not, formalised into a research programme, and then defended by moving the goalposts to wherever the analyst's judgement had to enter.  When Arp and his colleagues wrote that "if we had just done what was done in the highly publicized Hawkins et al paper, then a negative result would most certainly have been obtained,"¹⁷ they were describing an argument that had stopped being able to lose.

An argument that cannot lose cannot win either.  Truth is not served by evidence that would have been claimed as support whichever way it came out.  The right response to a striking coincidence is to state in advance what would count against it, hand the test to someone with no stake in the answer, and then live with what comes back.  Napier did that in 2002 and it cost him his claim.  Hartnett did it in 2009 and it cost him his result.  Both of them did the honourable thing, and the encyclopaedia should say so as loudly as it says the rest.

Sources