Humphreys' White Hole Cosmology

Summary

• The proposal. D. Russell Humphreys, a PhD physicist who spent twenty-two years at Sandia National Laboratories, argued in Starlight and Time (1994) that the matter of the universe is a finite ball with empty space beyond it. A finite ball has a centre. Clocks near the centre of a mass concentration run slow. Put the earth near that centre, start the ball small enough that it lies inside its own event horizon, and the horizon shrinks past the earth during creation week. On the day it passes, "billions of years worth of physical processes take place in the distant cosmos" while one ordinary day passes here.
• The physics it uses is real. Gravitational time dilation is measured to fifteen decimal places, at heights of a third of a metre. It is not a creationist invention. A bounded matter distribution really does have a centre in a way an unbounded one does not, and Humphreys was right that this is a genuine difference between his cosmos and the standard one.
• The technical objection came from a first-rate relativist, and it is the heart of the case. Don Page worked with Stephen Hawking on black hole radiation. With Samuel Conner he argued in 1998 that "physical clocks located on Earth and on distant galaxies behave identically in bounded and unbounded Universes which have identical interior matter distributions." If that is right the boundary does no work at all, and the model is "a trivial variant of the Big Bang model."
• Why they say that. Gravitational time dilation depends on the difference in gravitational potential between two places, and the potential difference between two points is set by the matter between and around them. In Newtonian terms, adding a uniform shell of matter outside both points shifts both potentials by the same constant. A constant shift cancels out of a clock ratio. Deleting the matter outside a radius is what "bounding" the universe does, and it leaves the interior clock rates unchanged.
• Humphreys did not concede, and he caught a real error in their argument. Conner and Page derived the field in an unbounded cosmos using the shell theorem, which needs spherical symmetry about a point, so their own construction quietly assumed a centre. That catch is correct. It does not, however, rescue the mechanism, because the shell-cancellation result can be derived without the disputed step.
• The bigger problem is that Humphreys' own numbers say a bounded universe is not enough. He wrote in 1994 that if the observed matter is all there is, "our clocks are ticking only a few percent slower than clocks near the edge. This is not enough to solve the problem." The billions of years come from the event horizon, not from the boundary. That relocates the dispute onto whether the horizon behaves as he says.
• The replacement mechanism was checked and it failed. Humphreys' 1998 answer was that the Klein metric contains a "timeless zone" of Euclidean signature that the critics' metric could not show. Samuel Conner showed in 1999 that the sign changes cancel, so "there are no timeless regions in the Klein metric." Edward Fackerell and Colin McIntosh, the two general relativists who had refereed the 1998 exchange, published the same finding in 2000: the claim "is false, and in fact is due to his uncritical use of an unphysical coordinate." Conner and Page added the argument that settles it even if the physics is granted: a signature change happens at one cosmic time everywhere, so it produces no differential ageing at all.
• The 2008 revision replaced the mechanism rather than defending it. Humphreys introduced "achronicity," a state in which time stops throughout a volume rather than only at a surface, and built a Day Four scenario in which a timeless zone expands at exactly the speed of light and then contracts at exactly minus the speed of light. He labelled it "a speculative light transit-time scenario." The revision does not answer the 1998 objection. It abandons the ground the objection was fought on.
• Its motivating observation disappeared, and he said in print what he would do about it. Humphreys derived the 2007 metric behind the revision to explain the Pioneer anomaly, and wrote that "the Pioneer effect supports the essentials of several creationist cosmologies." In 2012 Slava Turyshev's team modelled the spacecraft's own waste heat and found that "once the thermal recoil force is properly accounted for, no anomalous acceleration remains." Humphreys answered in 2013 that he was waiting for the detailed thermal model, and committed himself: "If it doesn't materialize in a year or so … I'll re-visit the issue in print. If it does materialize, I'll go over it carefully and submit an update." An independent group published exactly that model in 2014 and confirmed the result. He has published nothing on the Pioneer anomaly since.
• Two young-earth astronomers report that Humphreys abandoned the model, independently. Jason Lisle in 2020: "Even Humphreys has abandoned this model, along with a subsequent model." Danny Faulkner in 2021: "Many supporters of the white hole cosmology don't know that Humphreys has since abandoned his model." Humphreys himself never published a retraction, and the abandonment rests on their reports, which this article treats as reports. What he did publish is a series of partial withdrawals, ending with a 2014 paper that gives up the reading of Scripture the 1994 model was built on and a 2017 paper that argues against a rival cosmology from end-times prophecy.
• A problem nobody in the young-earth literature has worked: isotropy. Any bounded, centred cosmos with a radial gradient produces a microwave dipole of order the fractional off-centre displacement. The observed dipole is fully accounted for by the sun's 370 km/s motion. That looks like a severe constraint, but every published numerical exclusion of this type was built against void models for cosmic acceleration, and nobody has run one against Humphreys' metric. The scaling transfers; the numbers do not. This article states the gap instead of inventing a bound.
• A defect in the secondary record, stated as fact and not as accusation. Humphreys' 1998 reproductions of his own 1994 book insert bracketed glosses that are not in the book, and his reproduction of Conner and Page's key sentence splices the word "standard" from their abstract into a sentence from their introduction. Anyone quoting either side should quote it from the original.
• The verdict. A competent physicist built a serious general-relativistic model, the decisive objection came from inside the technical literature rather than from hostile outsiders, the author revised rather than answered, and the revision's one empirical support evaporated. The white hole cosmology is not a live solution to the distant starlight problem, and presenting it as one in 2026 is out of date.

This article is the case file on one model.  The other seven answers, and how they compare, are in Young-Universe Cosmologies.

The problem it was built to solve

Light travels about 300,000 kilometres per second.  The galaxy NGC 4993 is about 130 million light years away.  If light left it 130 million years ago and has been travelling ever since, the universe is at least that old.  Multiply by the most distant objects and the number reaches billions.  That is the distant starlight problem, and it is the hardest single argument against a 6,000-year universe.

Before 1994 young-earth creationists had three answers and none of them worked well.  One was to shrink the universe, which fails on parallax alone;  Gaia measures parallaxes below 0.1 milliarcseconds, so even the Milky Way does not fit inside 6,000 light years.  Another was to speed up light in the past, which Barry Setterfield's own community refuted:  Gerald Aardsma's weighted refit of Setterfield's data gave a decay rate of 0.0000140 ± 0.0000596 km/s per year, consistent with zero.¹  The third was to say God created the beams already in flight, which most young-earth astronomers abandoned because the beams would then record events that never happened.  Each of those has its own article:  The Cosmic Distance Ladder, A Decaying Speed of Light, and Light Created in Transit.

Humphreys' book was different, and that is why it landed.  It did not deny the distances, deny the physics, or invoke a miracle without a mechanism.  It proposed that general relativity, taken seriously and applied to a matter distribution the standard model does not use, gives billions of years out there and days here.  Danny Faulkner, an astronomer who does not hold the model, describes its reception:²  "Right away, the white hole cosmology gained many adherents among creationists.  The appeal was that it was the first rigorously scientific approach to the light travel time problem."²

Who Humphreys is, and why the credential matters here

D. Russell Humphreys took a BS in physics from Duke University in 1963 and a PhD in physics from Louisiana State University in 1972.  He worked as a physicist at Sandia National Laboratories in Albuquerque for twenty-two years, retiring in 2001, and the biography printed with the 1998 paper adds a detail worth keeping:  "The Laboratories have not supported this work."³  After Sandia he was an associate professor of physics at the Institute for Creation Research, and from 2008 a speaker and writer for Creation Ministries International.⁴  He is not a populariser writing about physics from outside it.  Starlight and Time contains a technical appendix with the field equations, the Klein metric, embedding diagrams and worked integrals.  His 1998 reply to critics runs eighteen journal pages and argues about metric signature, geodesics and Birkhoff's theorem.

That matters for how the case is read.  When a model like this fails, it does not fail because its author could not do the mathematics.  It fails at a specific technical joint, and locating that joint is the only useful thing an encyclopedia article can do.

The physics the model borrows, which is real

Two pieces of established physics do the work in Humphreys' argument, and neither is controversial.

Clocks deep in a gravitational well run slow.  This is gravitational time dilation, and it is one of the best-measured effects in physics.  A clock raised by height Δh near Earth's surface runs fast by Δf/f₀ = gΔh/c², about 1.1 parts in 10¹⁶ per metre.  In 2010 a team at the National Institute of Standards and Technology compared two aluminium-ion optical clocks and then raised one of them by 33 centimetres.  The measured fractional frequency change was (4.1 ± 1.6) × 10⁻¹⁷, which read as a height difference gives 37 ± 15 cm against a known 33 cm.⁵  In 2022 a strontium lattice clock resolved the redshift gradient inside a single millimetre-tall sample of atoms, at a fractional measurement uncertainty of 7.6 × 10⁻²¹.⁶  Nobody has to take gravitational time dilation on authority.

A bounded matter distribution has a centre, and an unbounded one does not.  This is also true, and Humphreys was right to insist on it.  The standard cosmological models assume the cosmological principle:  matter is spread smoothly and without limit, so no point is special.  A finite ball of galaxies surrounded by empty space is a different object.  It has a centre of mass.  Humphreys made this the pivot of his whole case:  "A centre of mass is essential to my theory."³

Those two facts are the raw material.  The dispute is entirely about whether putting them together produces the effect he claimed.

What the model claims

The setup

In Starlight and Time Humphreys proposes that the matter of the universe is a finite ball⁷ with empty space beyond it, and that the Earth is near the middle.  Run the expansion backwards and the ball was once small enough that all of it lay inside its own Schwarzschild radius, which is the radius at which the escape speed reaches the speed of light.  Matter inside that radius and moving outward is a white hole, the time reverse of a black hole.  As matter crosses the boundary and leaves, the boundary shrinks.

He names it and states the payoff in the same sentence:

"I call it a 'White Hole' cosmology for reasons to become clearer shortly — and it just happens to solve the problem of the starlight travel-time rather neatly."⁷

The mechanism, in his own words

The horizon sweeps inward and reaches the Earth on Day Four:

"The shrinking event horizon reaches earth early on the morning of the fourth day.  During this ordinary day as measured on earth, billions of years worth of physical processes take place in the distant cosmos."⁷

And the summary he gives at the end of the book:

"I propose that the critical moment arrived on earth during the fourth day of creation.  During that day, billions of years would elapse in the distant sky, allowing light from galaxies to reach the earth within one ordinary day of earth's time.  This theory also explains the red shifts of galaxies and the cosmic microwave background.  As measured by clocks on earth, the age of the universe today could be as small as the face-value biblical age of about 6000 years."⁷

It is a young-earth, old-universe model

Read that carefully.  The distant galaxies really did live through billions of years of their own time.  Stars really did burn through their lives.  Only Earth's clock reads 6,000 years.  Faulkner points out that most of the model's supporters never noticed:  "Few creationists realized that, while the white hole cosmology was young earth, it was an old universe theory."²

This is worth stating plainly to a skeptical reader.  The white hole cosmology concedes that the distant universe is billions of years old.  It is a proposal about whose clock counts, not about whether the history happened.

Humphreys' own numbers say the boundary alone is not enough

One point in the 1994 book is decisive for everything that follows, and both sides tend to skip it.  A bounded universe the size of the one we observe does not produce anything like the required dilation:

"For a given amount of matter, the bigger the radius in which it is contained, the less the effect of gravitational time dilation.  If we assume that the matter we can observe with telescopes is all there is (i.e., the edge of matter is closer than, say, 20 billion light-years), then our clocks are ticking only a few percent slower than clocks near the edge.  This is not enough to solve the problem."⁷

A few percent.  Not a factor of a million.  The billions of years therefore do not come from the boundary at all.  They come from the event horizon, at which the ratio between Earth's clock and a distant clock is supposed to blow up.  The boundary's job is only to make the horizon exist, because an unbounded universe has no exterior for light to fail to escape to.

What the model requires

The Conner and Page critique

Who wrote it

The critique appeared in 1998 in the same journal issue in which Humphreys replied, so both papers can be read side by side.⁸³  Its second author is Don N. Page, a general relativist who worked alongside Stephen Hawking in Cambridge and co-authored with him the 1976 Astrophysical Journal paper on gamma rays from primordial black holes.⁹  Humphreys records that Hugh Ross, an old-earth astronomer whose organisation Humphreys had been arguing with, commissioned the critique in 1995.³  That is worth knowing and it changes nothing about the physics.

Their charge is in their title.  Starlight and Time is the Big Bang.

"An accurate treatment of the physics indicates that this model is actually a trivial variant of the standard Big Bang model, with its attendant implications for the age of the Universe and the Earth time required for light to travel from distant galaxies to the Earth."⁸

The gravitational argument, which is the one that matters

Their central claim is a statement about general relativity that can be checked without reference to anything else in the dispute:

"In fact, physical clocks located on Earth and on distant galaxies behave identically in bounded and unbounded Universes which have identical interior matter distributions."⁸

The qualifying clause at the end is the whole argument.  Take a bounded universe:  a ball of galaxies of radius R, empty outside.  Now build an unbounded universe by keeping that ball exactly as it is and adding more of the same matter outside, out to infinity.  The two universes differ by one thing, a spherically symmetric shell of matter lying entirely outside R.

What does that shell do to the inside?  Nothing.  Newton's shell theorem settles it:  the gravitational field inside a hollow spherically symmetric shell vanishes everywhere, and the potential inside it is constant.  A constant added to the potential cancels out of every clock-rate ratio, because a clock rate depends on the difference of potential between two places.  Conner and Page spell out the split explicitly, writing the field at a point inside as the sum of an interior contribution and an exterior contribution, then showing the exterior term is zero.⁸

They then check the result in general relativity rather than leaving it Newtonian, and they quote the corollary of Birkhoff's theorem from Weinberg's textbook:

"the metric inside an empty spherical cavity at the center of a spherically symmetric system must be equivalent to the flat-space Minkowski metric ηαβ . . . Its importance arises from the fact that the Birkhoff theorem is a local theorem, not depending on any conditions on the metric for → ∞ (aside from spherical symmetry), so that space must be flat in a spherical cavity at the center of a spherically symmetric system, even if the system is infinite — even, in fact, if the system is the whole universe."⁸

Their conclusion is blunt:

"The imposition of a spherical boundary to the matter of the Universe has no effect on the gravitational and clock time-keeping properties in the interior of such a boundary."⁸

If that is right, the load-bearing beam of the 1994 book is not there.  Humphreys' picture has a pattern of gravitational force pointing inward in the bounded case and no such pattern in the unbounded case.  Conner and Page say both cases have the same pattern, and that Humphreys' claim of zero field in the unbounded case would imply an unbounded universe expands without decelerating, which is false.⁸

The time argument

The second half of the critique is about which clock counts, and it is the part a lay reader can follow all the way down.

In relativity, the time a clock records between two events is the proper time along its path.  Proper time is computed from the metric and it is a scalar invariant, which means every coordinate system gives the same answer for the same physical clock.  Conner and Page state the rule and its consequence:

"The time elapsed on a physical clock is determined by the clock's trajectory through space-time, not by the coordinate system used to describe the trajectory.  This means that there is something incorrect in the appeal, in Starlight and Time, to a different coordinate system to argue against physical results which are derived from the standard comoving coordinate system of cosmology theory."⁸

Then they do the calculation.  For an observer riding along with a galaxy, the comoving spatial coordinates are constant, so the metric collapses to dτ = dτ_c.  The proper time on any galaxy's clock equals the cosmic time, and the observer's position drops out of the equation entirely.⁸  Every galactic clock in a locally homogeneous universe, bounded or not, records the same elapsed time as the universe expands from one size to another.

Humphreys' answer is to use a different time coordinate, Schwarzschild time, in which clocks at different radii do run at different rates.  Conner and Page point out that he stated the correct rule himself in his own book, and they quote him doing it:

"The 'cosmic' time τ[ τc in equation (3)] in the Robertson-Walker metric is same [sic] as the proper time or 'natural' time in eq. (1).  It is the time measured by a set of clocks throughout the universe, each one riding with a galaxy as it moves with the expansion of space."⁸

So the model's own foundation says the physical clocks are the comoving ones, and the comoving ones agree.

The event horizon argument

The third piece is the sharpest, because the event horizon is where the 1994 book gets its billions of years.

Conner and Page work out where the horizon actually is.  A past event horizon in an expanding bounded universe is the set of inward-travelling radial light rays that leave the surface at the moment the surface expands through its Schwarzschild radius.  It is a light-like surface, and the arrival of the horizon at an observer is simply the arrival of one light ray:

"The light ray arrives at the comoving observer and passes on toward the centre.  That is the event horizon, as seen by such an observer.  This light trajectory manifestly has no effect on the passage of time for this observer.  His comoving clock continues to tick in concert with the expansion of the Universe and in synchrony with every other comoving clock on his constant a surface."⁸

They also correct a technical error.  Humphreys locates the horizon where the time-time component of the metric vanishes, g_tt = 0.  That works for a static geometry like Schwarzschild's, where the horizon does not move.  It does not work for a dynamic geometry, because a moving horizon must be a null surface, and g_tt = 0 and the null condition are incompatible unless the radial component happens to vanish at the same place, which in the Klein metric it does not.⁸  Their Figure 4 plots the two curves and they do not coincide.

Humphreys later accepted this.  More on that below, because it is the most important admission in the exchange and almost nobody cites it.

The observational tests

The last section of Conner and Page is the one that gets least attention and it deserves more, because it does not depend on the metric dispute at all.  Any young-universe model that gets its light here by rapid cosmic expansion has to expand the universe by a large factor in a short time as measured on Earth.  That has consequences you can look for.

Redshift drift.  In an expanding universe a galaxy's redshift changes slowly with time, at a rate set by the Hubble parameter.  In the standard model the rate is around 10⁻¹⁰ per year, far below detection.  In a 6,000-year expansion the Hubble parameter must have been enormous, and Conner and Page derive a lower bound on the present drift rate of 3 × 10⁻⁴ per year.  For the expansion factor Starlight and Time actually calls for, about 10¹⁰ in six days, they get a present drift of about −1400 per year, which they call "a manifestly absurd prediction."⁸  Nothing of the kind is seen.  Their Figure 7 collects the most precise measurements available in 1998 and reports that "The observed limits on dZ/dτ are 100 to 1000 times too small to be compatible with the young-Universe scenario."⁸

They also close the obvious escape route.  If the expansion happened in discrete jerks with static intervals between them, the jerks would still have to sum to a total expansion factor of six since light left a redshift-5 quasar, and the astronomical literature holds thousands of pairs of redshift measurements separated by years to decades whose emission times "would densely blanket a 6,000-year expansion history."⁸

An upper bound on distance from the light travel time.  Their second test is a short proof.  In any on-average homogeneous expanding universe, the angular diameter distance of an object divides by the speed of light to give a lower bound on the Earth proper time the light spent in transit.  Turn it around and the light travel time bounds the distance:  if the light has been in flight for 6,000 years of Earth time, nothing visible can have an angular diameter distance greater than 6,000 light years.  They note the obvious problem.  The centre of our own galaxy is about four times that far.⁸

Their verdict

"The bounded cosmology approach of Starlight and Time leads to cosmological models which are identical to the standard Big Bang model in their time-scale implications.  It should not be promoted in the Church as a scientifically sound young-Universe alternative to Big Bang cosmology."⁸

Humphreys' reply, and what it gave away

Humphreys answered in the same issue, at eighteen pages.³  The reply is not a retreat.  It is a counter-attack with a new technical claim at its centre, and reading it carefully is the only way to see where the model actually stood after 1998.

The new defence: a timeless zone with Euclidean signature

Humphreys concedes nothing about proper time.  Instead he argues that Conner and Page used the wrong metric.  They analysed his cosmos with the Robertson-Walker metric of standard cosmology.  He says his cosmos is described by the Klein metric, a 1961 solution for a contracting or expanding cloud of dust, and that the Klein metric contains a feature the Robertson-Walker metric cannot show.

The feature is a change of signature.  The signature of a metric is the pattern of plus and minus signs among its diagonal components.  Ordinary spacetime has one time direction and three space directions.  Humphreys claims that in the early stages of the expansion the Klein metric has a region in which all four components carry the same sign, so there are four space directions and no time direction at all.  He quotes a relativist's summary of such a region:  "there is no time there."³  He calls it the timeless zone, and states his priority claim:  "As far as I know, this is the first time anyone has pointed out this unusual feature of the Klein metric."³

He grounds the possibility in real literature.  George Ellis and three co-authors published a 1992 paper in Classical and Quantum Gravity arguing that classical solutions of Einstein's equations are not obliged to keep one signature, and Humphreys quotes them:

"At first one's reaction is, certainly not, all solutions maintain the same signature.  However this is true in the usual solutions not because it is demanded by the field equations, but rather because it is a condition we normally impose on the metric before we start looking for solutions."³

His summary of the defence is that the critique missed the mechanism entirely:  "the Conner-Page critique suffers throughout from a fatal defect — unawareness of the timeless Euclidean zone."³

The catch he landed, which is real

One part of Humphreys' reply is correct and should be recorded, because getting it wrong would be unfair to him.

Conner and Page's Newtonian argument comes with a figure showing an unbounded cosmos with arrows of gravitational force converging on a dot.  Humphreys points out that this is incoherent.  An unbounded cosmos obeying the cosmological principle cannot have a special point, and their own derivation smuggles one in, because the shell theorem they invoke requires spherical symmetry about a point.  His two-line statement of the problem:  "an unbounded cosmos can have no centre," and "a centre contradicts the Copernican principle, which they are trying to uphold."³

He is right about the figure, and he is right about a real subtlety.  In an infinite uniform dust the Newtonian field integral is only conditionally convergent, so the answer depends on how the limit is taken, and any point can be made to look like the centre.  This has been known since the nineteenth century and it is why Newtonian cosmology is written in terms of relative accelerations rather than absolute fields.

But the catch does not rescue the mechanism, for two reasons that the article states in its own voice because nobody in this exchange stated them.

First, the sphere in the argument is not arbitrary.  Conner and Page restrict attention to universes "which are spherically symmetric about Earth," and the comparison is between Humphreys' bounded ball and an unbounded distribution built by extending that same ball outward.  The exterior matter is therefore a spherically symmetric shell centred on the ball's own centre.  That symmetry is not an extra assumption smuggled in by the critics.  It is Humphreys' own hypothesis, and the shell theorem applies to it exactly.

Second, the Newtonian step is not the argument.  Conner and Page give the general relativistic version immediately afterward, using the corollary of Birkhoff's theorem quoted above, and that corollary makes no reference to a centre of the exterior matter.  It says that a spherical cavity inside a spherically symmetric system is flat, whatever the system is, "even if the system is infinite."  Deleting the disputed diagram leaves the conclusion standing.

The admission almost nobody cites

Buried in section 10 of the reply is a retraction of the 1994 book's mechanism.  Humphreys writes that Conner and Page attacked the wrong horizon, and then explains why they cannot be blamed:

"But it is I who am responsible — inadvertently — for misleading them.  The misleading happened because I myself did not understand the meaning of the Euclidean zone when I published my book in 1994.  At that time I knew nothing of the newly-generated literature on classical signature change.  I was aware of the time-stopping effects at the centre, as in equation (12), but I wrongly attributed that to the arrival of the event horizon and the fact that the Earth was not comoving with the expansion."³

He goes further and withdraws a figure from the book:  "the lines to the left of the cusps in Figure 10 (page 118) of my book should not be in the figure at all."³

Take the measure of that.  The popular version of the white hole cosmology, the one repeated in ministry articles and in seminar talks to this day, is the shrinking event horizon sweeping past the Earth on Day Four.  Its author said in 1998 that he had misidentified the mechanism, and that the time dilation he needs happens somewhere else, at a surface of signature change that his book never described.  The 1994 story was disowned by its author four years after publication, ten years before the 2008 revision, and twenty-three years before Faulkner reported that the model had been abandoned.

The concession that ends the argument

Conner and Page's observational tests are answered in section 11, and the answer is the most consequential sentence in the whole exchange.  Humphreys says the tests target a model he does not hold, because the "rapid" expansion is rapid only by Earth clocks that were stopped.  Then he states what his model predicts:

"During the billions of years, space would have expanded by the same factor as suggested by conventional cosmologies, so the amount of redshift would be the same as in such cosmologies.  The travel distance and redshift being the same, the Hubble constant would then be the same."³

And on the distance bound:

"Since in my cosmology the distances travelled are the same as in the conventional cosmologies, the observed angular diameters with which this section is much exercised should be the same."³

That is a complete answer to the observational tests, and it concedes the title of the paper he is rebutting.  Every observable quantity in the white hole cosmology matches standard cosmology by construction.  Redshift, distance, Hubble constant, angular size.  The model differs from the big bang in exactly one respect:  the amount of Earth proper time assigned to the process, and Earth proper time during creation week is not a quantity anybody can measure.

This is not a peculiarity of Humphreys.  It is the pattern across every surviving young-universe cosmology, and each author says it in his own words.  John Hartnett on his bounded Carmelian solution:¹⁰  "The new solution though is identical with the unbounded solution."¹⁰  Jason Lisle on the anisotropic synchrony convention:¹¹  "the difference between ESC and ASC is one of coordinates, leaving the underlying geometry and measurable observations unaffected."¹¹  Phillip Dennis on his own coordinate construction:¹²  "There can be no unprejudiced objection to this solution."¹²  The parent article, Young-Universe Cosmologies, works through why this keeps happening.

The signature-change claim was checked, and it failed

The Euclidean zone is the load-bearing part of Humphreys' 1998 defence.  It is also the part most accounts of this dispute stop before reaching, which is unfortunate, because it was answered three times in print between 1999 and 2000, by a fourth critic a year before Conner and Page even published, and the four answers converge.

First, what the mainstream literature on signature change actually says

Humphreys leans on two papers by George Ellis and co-workers.  Both are real, both are worth reading, and neither says what a reader of the 1998 paper would assume.

The 1997 paper Humphreys cites for support is a construction, not a discovery.¹³  Charles Hellaby, Adam Sumeruk and Ellis take a Schwarzschild black hole and glue a Euclidean region into it by hand to see whether the singularity can be avoided:  "We investigate the process of re-birth of Schwarzschild type black holes, modelling it as a double signature change, joining two universes of Lorentzian signature through a Euclidean region which provides a 'bounce'."¹³  When they come to the Schwarzschild metric itself they say plainly that its sign interchange at R = 2M is a relabelling, and that to get a real signature change they have to insert two extra sign factors that the solution does not supply:  the interchange leads "to reinterpertaion of the roles of R and T," so "it is not clear which sign we should change to introduce the signature change."¹³

The same paper gives the test that decides Humphreys' claim:

"Even though the metric signature is invisible to the Einstein Field Equations, it should be noted that a change of signature is not, either g00 goes through zero, in which case the metric is degenerate and g⁰⁰ singular there, or both g00 and g⁰⁰ jump from positive to negative values, in which case the metric is discontinuous.  In either case, the Einstein Field equations cannot be defined in the usual way at the signature change."¹³

Tevian Dray, Ellis, Hellaby and Corinne Manogue put the same rule more compactly a year earlier:  "Signature-changing metrics must be either degenerate (vanishing determinant) or discontinuous, but Einstein's equations implicitly assume that the metric is nondegenerate and at least continuous."¹⁴

A genuine classical signature change needs the metric to degenerate or to jump.  Components swapping signs in a chart is not enough.  The reason is a theorem of linear algebra, Sylvester's law of inertia, which says the counts of plus and minus signs in a real quadratic form do not depend on the basis you write it in.  The Schwarzschild horizon is the standard illustration.  There g_tt and g_rr both flip, the determinant stays finite, and the signature does not change.  Humphreys states that case correctly himself, two paragraphs before he introduces the Euclidean zone.³

And the people who developed classical signature change say in Physical Review D that it is not established physics.  Hellaby and Dray, comparing the rival formulations:¹⁵  "There is (as yet) no rigorous derivation of appropriate distributional field equations," and "None of them can claim to have any experimental or observational support."¹⁵

Second, Conner answered in 1999

Samuel Conner replied in the next volume of the same journal.¹⁶  His argument is short.  In the Klein metric, the quantity Humphreys says goes negative and the squared Schwarzschild time interval go negative together, so their product stays positive.  He traces the Earth's trajectory through the alleged region and generalises:

"This simple analysis for the spacetime trajectory of Earth through the Euclidean signature region of the Klein metric can be easily repeated for any other comoving trajectory (that is, any non-zero value of η).  The outcome is the same:  β(a,η) and dt²_Schwarz, comoving clock always have the same sign, so that their product is always positive."¹⁶

His verdict, and it is one sentence:  "In other words, there are no timeless regions in the Klein metric."¹⁶  His footnote adds the diagnosis:  "The divergence and vanishing of β are artefacts of the Klein coordinate system and have no physical consequences for physical observers inside the matter sphere."¹⁶

Humphreys replied in the same issue.¹⁷  His technical answer is a single move:  Klein's integral for Schwarzschild time is valid only for real values of the integration variable, so Conner's starting equation does not hold in the region where he needs it.¹⁷  He then invites the reader to skip the physics:  "You, the reader, do not need to make a technical judgment about the correctness of my assertion.  All you need to do is notice that Conner never dealt with my comment."¹⁷  Most of the reply is about Conner's association with Hugh Ross and about Don Page's missing by-line:  "Is that because, after my article had pinpointed the mistake, Page was embarrassed?"¹⁷

Third, two professional relativists settled it in 2000

Edward Fackerell of the University of Sydney and Colin McIntosh of Monash University published "Errors in Humphreys' cosmological model" in the same journal in 2000.¹⁸  Two facts about them matter for how much weight the paper carries.  They are evangelical Christians, and they were the referees of the 1998 exchange.¹⁸  They state their qualifications rather than assert authority:

"We wish to point out that both of us are evangelical Christians who not only have graduate-level training in general relativity but actually wrote our PhDs specifically in general relativity and went on to lengthy international research careers in general relativity based at Monash University and at the University of Sydney."¹⁸

On the Euclidean zone their finding is flat:

"One of these is his claim in the CEN Tech. J. paper that he has discovered a region of signature change in the Klein metric solution given in his book.  However, as we now show, this claim is false, and in fact is due to his uncritical use of an unphysical coordinate, namely, the Schwarzschild time."¹⁸

The reason is the one Conner had reached independently the year before, and they spell it out:

"The first consequence of this is that dt is pure imaginary in precisely those regions where δ is negative (if it weren't, we would not have a solution of the Einstein field equations in these regions).  Hence, instead of being positive, dt² < 0 in precisely those parts where δ is negative since i² = –1, and so Lorentzian signature is preserved everywhere ('minus times minus = plus'). … One might have expected this, since a mere change of coordinates cannot alter the signature of the metric.  Furthermore, since the lapse function in the Friedmann metric from which the Klein metric is derived has no zero, it is impossible to obtain a change in signature in the Klein metric."¹⁸

They also correct the event-horizon criterion with a counterexample, which is the cleanest way to settle it.  Humphreys locates horizons where g_tt = 0.  In the Kerr solution for a rotating black hole, g_tt = 0 gives the static limit, and the outer event horizon sits at a radius where g_tt is not zero.¹⁸  Their diagnosis of the root error is the same one Conner and Page made in 1998:

"The principal reason for Humphreys making this error is his unfounded belief that the Schwarzschild t coordinate is somehow fundamental.  When one looks at the statements in his book, pages 110–113, one sees immediately that Humphreys is unaware of the fact that inside r = 2M, the Schwarzschild t direction is no longer timelike but in fact spacelike, so that there is no way that the Schwarzschild t can be used as a time coordinate inside the horizon of the Schwarzschild geometry."¹⁸

And their verdict:

"For these reasons, based only on the proper analysis of the mathematics and fundamental physics of light-cones and clocks in general relativity, our conclusion is that Humphreys' attempt to reconcile general relativity with a young-earth viewpoint is flawed."¹⁸

Humphreys' one-page answer¹⁹ restates the Klein-integral move, complains that they ignored his 1999 reply, and dismisses their central equations:  "Their thirteenth and fourteenth equations, and the words around them, simply reassert — without proof — their view that there is no Euclidean zone.  Assertions without proof require no further rebuttal."¹⁹  He also denies the event-horizon criterion is his:  "Yet in their reference 19 (my book Starlight and Time, pages 117 and 119), I can find no such claim.  Moreover, I never intended to make such a claim."¹⁹

Fourth, Conner and Page came back, with Page's name on it

In the same 2000 issue, Conner and Page published a joint reply.²⁰  Page's by-line is on it, which answers Humphreys' 1999 taunt.  Three of their points matter.

On the "acentric" catch Humphreys had scored in 1998, they concede the wording and deny the conclusion:

"Such universes are not acentric, as claimed by Humphreys, but rather have infinitely many centres of spherical symmetry.  The centres of spherical symmetry are not unique, but that does not mean that they do not exist at all."²⁰

On the appeal to Ellis and co-workers:

"First, Humphreys fails to note the speculative character of this literature.  No one knows at present whether, and, if so, under what physical conditions classical signature change may occur.  This literature certainly does not establish Humphreys' claims (and, in any event, Humphreys' model does not undergo the signature change described in this literature;  the sign change in Humphreys' model is the consequence of the imaginary character of the Klein time coordinate)."²⁰

And the argument that settles the matter even if every one of Humphreys' technical claims is granted:

"if one were to adopt such an unusual description of the expansion dynamics and impose a hypothetical signature change surface at some point in the past, this still would not solve the light travel problem, for such a signature change would occur simultaneously (that is, at the same value of a and t) throughout the universe, so that there would be no differential ageing of different parts of the universe."²⁰

"If the location of a hypothetical signature change surface were adjusted to provide only 6,000 years of proper time since the beginning of the universe, as proposed by Humphreys, the particle horizon would be only about 6,000 light years distant, making all objects more distant than this invisible to observers on Earth."²⁰

That is the whole case in two sentences.  A signature change happens at one cosmic time everywhere, so it cannot make one place older than another;  and if it is placed so as to leave 6,000 years of proper time, nothing further than 6,000 light years is visible.  Their endnote states the diagnosis as compactly as anyone has:

"In Humphreys' coordinate-artefact-induced metric sign change, there is both a metric sign change and a Wick rotation of the time coordinate, and the two cancel each other, leaving the intrinsic signature of spacetime unchanged. … Humphreys' coordinate-artefact-induced sign change is not a physical process at all, but simply an artefact of the particular coordinate system he prefers to use, the Klein coordinate system."²⁰

What John Byl had already shown in 1997

The earliest technical objection came from a creationist mathematician, John Byl of Trinity Western University, a year before Conner and Page published.²¹  His argument is the same one, reached from a different direction.  In comoving coordinates the Klein metric is the Robertson-Walker metric, and there "dτ = dt (i.e., the proper time equals the coordinate time) and there is no gravitational time dilation.  All galactic clocks tick at the same rate."²¹  He explains where Humphreys' dilation comes from:  the transformation to exterior Schwarzschild coordinates, which is the right thing to do when a human observer watches a star collapse from outside, and which "serves no purpose" when every observer is inside the universe.²¹

Byl also lands the item that hurts most, and it involves Oskar Klein himself.  Humphreys built on Klein's 1961 analysis of a collapsing star.  Byl points out that Klein went on to do Humphreys' cosmology, and got a different answer:

"In a later paper Klein (1971) himself studied a cosmological model identical to that of Humphreys:  a bounded, finite universe of constant density which has a definite center and a gravitational potential gradient. … Yet he analyzed all observations using the interior metric (equation 3).  For example, Klein finds that the frequency shift we should observe from a distant source within the universe depends only on the fractional change in the scale factor R during the light travel time.  There is no further change due to differences in gravitational potential, implying that there is no time dilation."²¹

Byl's own conclusion is worth quoting because he is a young-earth creationist writing in a young-earth journal:  "In summary, neither special nor general relativity appear to lend much support to the time dilation hypothesis."²¹  And the concession that closes his paper is the one a skeptical reader should notice:  even if the model worked, it would not help nearby stars.  "Certainly not for the Sun, where the cosmic gravitational potential — and hence the clock rate — is essentially the same as at the earth."²¹

The state of the record

So the answer to "was it ever checked" is yes, and by four sets of people whose findings agree.  Byl reached the underlying diagnosis in 1997, from inside the movement, before the Euclidean zone had been proposed:  the dilation is an artefact of transforming to exterior Schwarzschild coordinates.  Conner applied that diagnosis to the Euclidean zone itself in 1999.  Fackerell and McIntosh, who had refereed the exchange and hold doctorates in general relativity, reached the same result independently in 2000.  Conner and Page added the argument from simultaneity in the same year.  Humphreys answered each of them, disputed the starting equation each time, and never published a derivation meeting the standard Fackerell and McIntosh set out:  separate coordinate patches for the collapsing dust, the exterior vacuum, the expanding dust and its exterior, with a proof that the junction conditions hold across each boundary.¹⁸

One creationist reader drew the obvious conclusion in print in 2001.  Bill Worraker of Didcot, Oxfordshire, writing to the same journal:  "we cannot yet claim to have a possible solution to the distant starlight problem," and he says he is writing "partly to correct the impression given by recent creationist advertising that the distant starlight problem has been solved."²²

The 2008 revision: achronicity

What changed

Nine years later Humphreys published a different model.⁴  It rests on a metric he derived in 2007 for the interior of an expanding spherical shell of mass, which he identifies with "the waters that are above the heavens" of Psalm 148:4.²³  The shell's total mass he puts at more than 8.8 × 10⁵² kg, more than twenty times the mass of all the stars the Hubble Space Telescope can see, spread so thinly over so large an area that its areal density is under half a kilogram per square metre.⁴

The new effect he calls achronicity.  Inside a spherical shell the gravitational potential is uniform, Φ = −GM/R.  His time dilation formula for a motionless clock is the standard one, dτ/dt = √(1 + 2Φ/c²).  When Φ falls below a critical value Φ_c = −½c², the expression under the square root goes negative and the proper time interval becomes imaginary.  Humphreys reads that as time stopping:

"That means dτ is a mathematically imaginary number.  This suggests that in this region, physical clocks would stop completely.  Time would no longer exist.  Regions of space below the critical gravitational potential would be achronous."⁴

The advertised advantage over the old model is scope.  Ordinary gravitational time dilation stops clocks only at a surface.  Achronicity stops them throughout a volume:  "Achronicity is more extensive than the more familiar kind of time dilation, because the former stops time not in a very narrow region … but throughout possibly vast regions of space."⁴

And he states outright that this is a different model, not a repair of the old one:  "The cosmology this paper outlines is a new one that does not stem from the Klein metric."⁴

The Day Four scenario

The scenario built on it is intricate and Humphreys labels it as speculation before he begins:  "In this section I outline a speculative light transit-time scenario during Day 4.  Other scenarios are possible, so you should take this as only an example of the possibilities that achronicity opens up."⁴

The steps are these.  God creates the star masses in a pattern that dents the otherwise flat potential of space, pushing the central region containing the Earth below the critical potential, so a growing sphere of timelessness appears around the Earth.  The critical potential itself depends on the speed of light, which Humphreys ties to a tension in "the fabric of space" that God can adjust.  Lowering the tension raises the critical level and expands the timeless sphere.  He then asks God to tune three quantities so that the sphere's boundary sweeps outward at exactly the speed of light, freezing each galaxy as it passes.  Then the tension is reversed and the boundary contracts at exactly minus the speed of light.  Each galaxy thaws, resumes emitting, and the inbound light rides just behind the shrinking boundary:

"When the sphere reaches zero radius and disappears, the Earth emerges, and immediately the light that has been following the sphere will reach earth, even light that started billions of light years away."⁴

There is a second, smaller episode during the Flood year, which yields the one dated prediction in the paper:  "if Noah could have seen the night sky, its appearance would have changed suddenly.  With a suitable telescope, he would have seen the galaxies suddenly look roughly 500 Ma older (i.e. spiral galaxies would be more wound up, etc.)."⁴  He offers this as the explanation of why distant galaxies do not look younger than nearby ones.

Does the revision answer the 1998 objection, or move it?

It moves it, and there is a prior problem with the metric that has to be dealt with first.

Humphreys' interior metric, his equation (2), is

ds² = c²(1 + 2Φ/c²)dt² − (1 + 2Φ/c²)⁻¹ dw²

with Φ = −GM/R(t) uniform in space and varying only with time as the shell radius R changes, and dw² = dx² + dy² + dz².  He asserts that this is exact:  "The radius R can depend on time, making Φ depend on time, and yet metric (2) will still be an exact solution of Einstein's gravitational field equations."⁴

Write A(t) = 1 + 2Φ/c² and define a new time coordinate by dT = √A dt.  The metric becomes

ds² = c²dT² − a(T)² dw²,   with a = A^(−1/2)

which is a spatially flat Friedmann-Lemaître-Robertson-Walker metric, the same family standard cosmology uses, with a scale factor that changes whenever Φ changes.  For that metric the Einstein tensor is not zero.  Its time-time component is 3(ȧ/a)², which by Einstein's equations equals 8πGρ.  A region of that shape is empty only if the scale factor is constant, and the scale factor is constant only if Φ is constant.

So metric (2) with a time-varying potential is an exact solution of Einstein's equations for a region containing matter, not for an empty cavity.  This is Birkhoff's theorem doing its work again:  the vacuum interior of a spherically symmetric shell is flat and static, whatever the shell is doing outside.  The same theorem Conner and Page used against the 1994 model applies to the 2007 metric.

Humphreys saw the conflict and claimed an exemption.  He writes in the 2007 paper that a time-dependent interior coefficient is "contrary to a common interpretation of a well-known theorem by Birkhoff," and his appendix argues that the metric coefficients must be continuous across a shell only about 40 metres thick, so the interior inherits the exterior's time dependence.²³²³  The step that carries the argument is his claim that the radial derivatives of the metric coefficients "are at a maximum just outside the shell," which lets him bound the change across the shell by its fractional thickness, of order 10⁻²⁵.  That bound is computed in the vacuum region outside the shell, and it is applied across the region that contains all of the mass.  Inside the shell material the mass function climbs from zero to M, and the derivatives are set by that climb rather than by the vacuum solution.  This article records that as the point at which the 2007 appendix should be checked.  No relativist has published a check, and neither has any creationist.

Set that aside and take the metric on its own terms.  The potential Φ in his time-dilation formula is uniform inside the shell.  It is the conversion factor between a clock inside and a clock at infinity, where Φ = 0.  It is the same for every clock inside.  So a uniform interior potential, however deep, cannot by itself make a distant galaxy age faster than the Earth when both are inside the same shell.

Humphreys is aware of this and his scenario supplies the missing gradient by hand.  God creates star masses "in a way that would create a linearly-dented perturbation in the otherwise flat potential."⁴  The dilation therefore does not come from the shell, and it does not come from a boundary, and it does not come from an event horizon.  It comes from a potential shape that God is asked to design, together with a speed of light that God is asked to vary, tuned so that a boundary moves at exactly +c and then exactly −c.  Humphreys names the three quantities that have to be adjusted and says so:  "let's say that God designs or adjusts these three factors so that the expansion speed vt of the timeless zone surface is exactly c continuously."⁴

The 1998 objection therefore survives the revision intact.  Conner and Page's point was that a clock's reading is fixed by its path through spacetime and not by a coordinate label.  In the 2008 model the claim "time stops" is the claim that a coordinate ratio dτ/dt goes imaginary, where t is the time kept by a distant clock outside the shell.  Unless the signature really changes, the interior is flat, a good local time coordinate exists everywhere in it, and nothing stops.

Humphreys knows that mainstream relativity rejects the reading and he says why he thinks it does:

"However, most relativists think it is impossible for an object to have zero velocity inside the event horizon, partly because they want to avoid the possibility of the spacetime interval ds being imaginary, (i.e. achronicity)."⁴

That attributes a preference to relativists where there is a theorem.  Inside a Schwarzschild horizon the radial coordinate is timelike, so a worldline at constant r is spacelike, and a massive particle cannot follow it.  Nobody is avoiding an uncomfortable possibility.  The trajectory is not available.

The observation the revision was built on has gone

The 2007 metric was not derived to solve the starlight problem.  It was derived to explain the Pioneer anomaly, a small unexplained sunward acceleration of (8.74 ± 1.33) × 10⁻¹⁰ m/s² in the tracking data of Pioneer 10 and 11.  Humphreys presented that explanation as support for creationist cosmology in general:

"Thus the Pioneer effect supports the essentials of several creationist cosmologies:  a centre of mass, expansion of space and recent time dilation.  Big bang theorists, whose cosmology does not have a centre of mass, cannot use this explanation.  As yet, they have no alternative theory upon which they agree."²³

In 2012 Slava Turyshev and colleagues at the Jet Propulsion Laboratory settled it.²⁴  They built a finite-element thermal model of both spacecraft from the original design drawings, drove it with the actual flight telemetry, and computed the recoil from heat radiating asymmetrically off the vehicles.  Their conclusion:

"We find no statistically significant difference between the two estimates and conclude that once the thermal recoil force is properly accounted for, no anomalous acceleration remains."²⁴

Be precise about what this does and does not do.  It is not a refutation of Humphreys' metric, which is a valid solution of the field equations for the situation it describes.  It removes the one measurement he offered as evidence that the metric describes the real world.  A model whose motivating anomaly has been explained by spacecraft engineering needs a new reason to be believed, and no such reason has been published.

What became of the model

The author never published a retraction

This has to be stated carefully, because "the author abandoned his own model" is a strong claim and the evidence for it is indirect.

Humphreys has never published a paper saying he was wrong.  What he has published is a series of partial withdrawals.  In 1998 he withdrew the 1994 book's mechanism, saying he had misattributed the time dilation to the event horizon.  In 2008 he announced a replacement:  "The cosmology this paper outlines is a new one that does not stem from the Klein metric."⁴  In 2014 he withdrew the reading of Scripture that put a large cosmic expansion in the 1994 model at all.²⁵  Each step leaves less of Starlight and Time standing, and none of them is a retraction of its conclusion.

The abandonment is reported by two other young-earth astronomers, independently, and both reports should be read as reports.

Jason Lisle, 2020, in a series on distant starlight:²⁶  "So the gravitational time dilation model seems to be eliminated on the basis of both theoretical computations and observations.  Even Humphreys has abandoned this model, along with a subsequent model.  The last time I chatted with him, Dr. Humphreys was working on a third cosmological model.  Although the original model did not pan out, it was a brilliant attempt and helped to advance study on this topic by including the effects of the physics of Einstein — an extremely important consideration."²⁶

Danny Faulkner, 2021, in a survey of all the proposed solutions:  "Many supporters of the white hole cosmology don't know that Humphreys has since abandoned his model.  For several years, Humphreys has been pursuing a different approach, again relying upon general relativity.  Humphreys now believes an expansion early in the creation week produced what he calls a 'timeless zone,' which again allowed much time to elapse in part of the universe but not everywhere.  He is still refining this model."²

Lisle's report is the stronger of the two, because it is first-hand and it counts models.  He says Humphreys abandoned the white hole cosmology and the model that replaced it, and had moved to a third.  Faulkner, writing a year later, describes the second model as still being refined.  The two reports are not in conflict on the main point and they differ on how far the process has gone.

What he did publish after 2008, and what it gave up

Two more cosmology papers appeared, and they matter for the question of whether the white hole is alive.

2014, in the Journal of Creation.²⁵  Humphreys proposes a picture of gravity in which space is a membrane accelerating in a fourth spatial dimension, and uses the Unruh effect to explain the cosmic microwave background.  The opening paragraph is the important part, because it withdraws the reading of Scripture the 1994 model was built on:

"In my 1994 book, Starlight and Time, I interpreted scriptures mentioning a stretching-out of the heavens as supporting a large expansion of the universe.  But in 2011 John Hartnett pointed out a scriptural reason why that interpretation is probably incorrect.  He suggested that the red shifts of light from distant galaxies may have a different cause than expansion.  My 2008 cosmology allows for a different cause:  a slow increase of gravitational potential."²⁵

Note what moved him.  Not an observation.  A scriptural argument from another creationist.  The paper ends with two more promises:  "In one or two future papers I plan to apply this new view of gravity to (1) galaxy redshifts, and (2) the Pioneer anomaly and recent developments about it."²⁵  Neither paper appeared.

2017, in the Creation Research Society Quarterly.²⁷  This one is not physics.  It argues from prophecy that Lisle's anisotropic synchrony convention must be wrong, because Revelation 6:13, Matthew 24:29 and Isaiah 34:4 have all the stars falling at the end of the age, and those stars will by then be much older than we now see them.  His conclusion:  "None of the stars or galaxies seen at the end of the age would appear to have aged more than 6,000 years, contrary to the star-aging verses above.  Thus, those verses are evidence against the ASC cosmology."²⁷  Whatever one makes of the exegesis, it is worth noticing that by 2017 Humphreys' published cosmological argument was an argument from eschatology, and that his own reference list cites nothing of his own on cosmology later than the 2014 gravity paper.

Beyond those two there is nothing.  The 2008 paper's promised sequel on achronicity at high velocity, "the interesting and possibly useful effects of achronicity for non-negligible particle velocities," never appeared.⁴  He contributed no cosmology paper to the International Conference on Creationism in 2013, 2018 or 2023;  his only 2023 paper there is about carbon-14.

The Pioneer answer he promised and never wrote

Humphreys did answer Turyshev, once, in a reader-feedback item on the Creation Ministries International site dated 22 April 2013.²⁸  He names the Physical Review Letters paper by its URL, so there is no doubt what he is answering.  His objections are four:  his own back-of-envelope estimates make the heat unlikely;  the residual acceleration in their own graph levels out at a value close to the Hubble constant times the speed of light, and "To have 'heat' accidentally give a number with such cosmic significance seems highly unlikely to me";  Galileo and Ulysses showed a similar deceleration with quite different structures;  and the paper "offered no details on the simulation itself … yet it is crucial to the result they claim."  He reports that Turyshev e-mailed him in September 2012 saying a paper with the thermal simulation details was in preparation.²⁸

Then he set himself a test, in public, with a deadline:

"I'm waiting to see the alleged detailed thermal analysis from Turyshev et al.  If it doesn't materialize in a year or so, that will tell me they found a flaw in their analysis, and I'll re-visit the issue in print.  If it does materialize, I'll go over it carefully and submit an update, possibly a letter, to Journal of Creation."²⁸

Both branches fired.  Turyshev published nothing further on the Pioneer anomaly.  And in November 2013, seven months after the feedback item, Dario Modenini and Paolo Tortora submitted exactly the analysis Humphreys had asked for:  an independent finite-element thermal model of the spacecraft with a sensitivity analysis and a formal uncertainty, run through NASA's own orbit determination program.  Their result:  "orbital solutions may be achieved that do not require the addition of any 'unknown' acceleration other than the one of thermal origin."²⁹  Humphreys has published nothing on the Pioneer anomaly since 22 April 2013.

The popular article in which he bet against the thermal explanation is also still on the site, unamended.  Writing in Creation magazine in 2008, before the Turyshev result, he said of the heat-radiation explanations that "the required coincidences stretch my credulity a bit," and concluded that "the big bang model has been unable to explain the anomalous Pioneer acceleration."³⁰  The footnote to that passage cites Turyshev's own conference abstract, so he saw the work coming.  The page as served in 2026 still carries a last-modified date of March 2010.

Lisle's own objections

Lisle is worth quoting at length because he is a young-earth astrophysicist arguing against a young-earth model on physics grounds, which is the kind of witness a skeptical reader should weigh most heavily.  He gives three objections.²⁶

The first is that the model rests on an untested assumption, "the model only works if the galaxies in the universe are indeed finite in number and distributed in a roughly spherical pattern centered around our solar system.  There is currently no proof of this;  however, neither is there evidence for the contrary."

The second is quantitative and it repeats Humphreys' own 1994 concession from the other side.  Using the estimated mass of all the galaxies including dark matter, "the amount of time dilation experienced on earth relative to the distant universe is very small."  Lisle works a number:  if Earth clocks ran 2 percent slow relative to the most distant galaxies, light from a galaxy 10 billion light years away would take 9.98 billion years by Earth clocks instead of 10 billion.

The third is observational and it is the one worth thinking about:

"Secondly, if the gravitational time dilation were strong enough to slow the passage of time on earth by a sufficient amount to solve the starlight problem, it would produce observable effects.  Not the least of these would be a universal blueshift.  Since processes in galaxies at tremendous distance from earth would happen much faster than processes on earth, light from these galaxies would have a much higher frequency — millions of times higher.  We would therefore observe a blueshift proportional to distance.  This is not observed.  In fact, we observe the opposite — a universal redshift."²⁶

State the reply that Humphreys has available, because the objection is not airtight.  In both of Humphreys' models the dilation is episodic.  It happens on Day Four, and in the 2008 version again during the Flood year, and it is over.  Light arriving today is emitted and received under nearly equal potentials, so on his account it carries the ordinary cosmological redshift and no blueshift.  His 2008 redshift formula makes exactly that point:  the potential ratio between emission and reception drops out when the potentials are equal, and "eq. (21) reduces to the big bang result."⁴  Lisle's objection lands squarely on any model with ongoing dilation and glances off an episodic one.  Nobody has worked this through in print in either direction.

Hartnett's objection, which has never been answered

John Hartnett, who built a competing young-earth cosmology and then retracted it, raised a mechanical problem in 2003 and restated it in 2019:³¹

"In 2003, I pointed out that there is a problem of the light-travel time within the Milky Way galaxy with white-hole gravitational-well ESC-based time-dilation cosmologies.  They cannot provide sufficient time-dilation.  That problem has not been solved, though Russ Humphreys has developed a much better model since his first ones.  I suspect though that his current model is somewhat ad hoc in the details to get it all to work."³¹

The point is simple and it is the same one Conner and Page made with angular diameter distances.  A model that manufactures billions of years at cosmological distance still has to get light across 100,000 light years of our own galaxy, and across 4.3 light years from Alpha Centauri, inside creation week.  Gradients that are enormous at the edge of the universe are negligible within the Milky Way.

The isotropy problem, and the gap in the literature

Every version of this model needs the Earth near the centre of a spherically symmetric matter distribution.  Humphreys is explicit that the centre is load-bearing.  He later argued the position outright,³² calculating from redshift quantisation that our galaxy sits within about 1.6 million light years of the centre of a 20-billion-light-year cosmos, a probability of "less than one out of a trillion" by chance.³²  The redshift quantisation that argument rests on has since been traced to a selection effect in the survey data, by Hartnett among others, so the argument is dead;  the requirement it was meant to satisfy is not.

There is an obvious observational test and it has not been run.

The cosmic microwave background is smooth to about one part in 10⁵ after the dipole is removed.  The dipole itself, 3362.08 ± 0.99 μK, is fully accounted for by the solar system's motion at 369.82 ± 0.11 km/s.³³³³  Now suppose the universe really is a ball with a radial structure, and the Earth sits off-centre by a fraction a/R of the radius.  Looking one way you see deeper into the structure than the other.  For a shell-boundary or radial-gradient model with redshift roughly proportional to distance, the resulting temperature dipole is of order a/R.  Setting that below the whole observed dipole gives a/R ≲ 1.234 × 10⁻³, which is a volume fraction of about 1.9 × 10⁻⁹.  For a 20-billion-light-year radius that is a position accurate to within about 7.6 megaparsecs.

Two things have to be said about that number and the second matters more than the first.

The scaling is standard.  It comes out of the literature on inhomogeneous void models, where an off-centre observer's microwave dipole grows in proportion to the displacement.  Håvard Alnes and Morad Amarzguioui computed it for a specific void model³⁴ and found the observer confined to d_obs ≲ 15 Mpc inside a structure about 1,500 Mpc across, "roughly a chance of 1 to 10⁶" for a random position.³⁴  Later work tightened the constraints on void models sharply.  Pengjie Zhang and Albert Stebbins used the kinetic Sunyaev-Zel'dovich effect³⁵ to show that such models predict small-scale microwave power two orders of magnitude above the South Pole Telescope and Atacama Cosmology Telescope limits.³⁵

But none of that was computed for Humphreys' cosmos, and the numerical exclusion does not transfer.  Every published constraint of this kind targets Lemaître-Tolman-Bondi void models built to mimic cosmic acceleration without dark energy.  Those models have a specific density profile, a specific expansion history, and a specific relation between redshift and distance.  Humphreys' bounded ball with an optically thick boundary is a different object with a different microwave background story;  he explains the microwave background as relict light from Day One, not as a last-scattering surface.³⁶

So the honest statement is this.  The dipole scaling transfers and it is a real constraint in form.  The numerical bound above is this article's own arithmetic from the Planck dipole and a scaling argument, not a result anybody has published.  Nobody in the young-earth literature has run an isotropy calculation for a bounded, centred cosmology, and nobody in the mainstream literature has run one either, because nobody outside the movement takes the model seriously enough to model it.  The model owes that calculation.  Until someone does it, "the microwave background rules this out" is a claim nobody has earned, and so is "the microwave background is consistent with it."

Andrew Repp, writing in the Creation Research Society Quarterly,³⁶ makes the same complaint from inside about the microwave background anisotropies:  "there has been little if any attempt to explain them within a creation framework."³⁶  That article has more on the microwave background:  The Cosmic Microwave Background.

The record, and two defects in it

Two problems in how this dispute has been transmitted are worth stating as facts, because anyone re-checking the sources will hit them.  Neither is an accusation of bad faith.  Both change what a reader takes away.

Humphreys' reproduction of Conner and Page splices two sentences.  In his 1998 reply he quotes their charge as:  "The model of Starlight and Time is in fact a trivial variant of the standard Big Bang model," and attributes it to their section 1.³  Their section 1 says:  "The model of Starlight and Time is in fact a trivial variant of the Big Bang model."  There is no "standard" in it.  The word comes from their abstract, in a different sentence:  "this model is actually a trivial variant of the standard Big Bang model, with its attendant implications…"  The splice makes the charge narrower than it is.  Conner and Page's point is that his model is a variant of the big bang, full stop, not of one particular version of it.  Quote them from their own paper.

In the same passage Humphreys truncates their clocks sentence to "physical clocks located on Earth and on distant galaxies behave identically in bounded and unbounded Universes ..." with the ellipsis marked.³  What the ellipsis removes is "which have identical interior matter distributions," and that clause is the argument.  Their claim is conditional and the condition is what makes it true.  Marking an ellipsis is honest practice, but a reader who never sees the full sentence will not know what was being claimed.

Humphreys' 1998 reproductions of his own 1994 book add bracketed glosses that are not in the book.  Where the reply quotes his earlier text, it inserts explanatory phrases in square brackets, for example "[that is, within the three dimensions we can perceive]."³  These are the 1998 author clarifying the 1994 author.  The brackets signal an insertion, which is proper, but the effect is that his 1994 position reads as more carefully qualified than it was.  Anyone quoting Starlight and Time should quote it from the book.

There is a third item, and it is a matter of currency rather than accuracy.  The Creation Ministries International page listing arguments creationists should not use³⁷ still says, in the paragraph that retires the decaying speed of light, that "CMI currently believes that both Dr Russell Humphreys' and Dr John Hartnett's cosmologies (both involving relativistic time dilation) provide viable solutions for the distant starlight problem."³⁷  Hartnett retracted his in writing in 2019 and again in 2021.  Humphreys replaced his in 2008 and, on two independent reports, abandoned that replacement too.

The two models side by side

Timeline

Objections and responses

"Gravitational time dilation is a real effect, so the model is on solid ground."  The effect is real and the model is not on solid ground, and the gap between those two statements is the entire case.  Gravitational time dilation depends on differences in potential.  The question is whether drawing a boundary around the matter of the universe produces the differences Humphreys needs, and the answer, by Newton's shell theorem and by the corollary of Birkhoff's theorem, is that it does not.  Humphreys himself conceded that a bounded universe of the observed size gives "only a few percent."

"Conner and Page refuted it, so young-earth cosmology is finished."  Overstated in the other direction.  Humphreys replied, disputed the metric they used, and caught a genuine incoherence in one of their figures.  What his critics then did was answer him again, in 1999 and twice in 2000, and on the Euclidean zone they converge from three independent starting points.  The narrower claim is what this article defends:  the white hole cosmology failed.  Young-earth cosmology as a project did not stand or fall with it, and two of the people who refuted it, Byl and Worraker, are young-earth creationists who said so in young-earth journals.

"Don Page was commissioned by Hugh Ross, an old-earth apologist, so the critique is motivated."  True and irrelevant.  The shell theorem does not care who paid for the paper.  The Newtonian argument, the Birkhoff corollary and the proper-time calculation can each be checked by anyone with a general relativity textbook, and the strongest single objection to the model came later from a young-earth astronomer, Lisle, with no such motive.

"The whole exchange happened in a creationist journal, so this is not real peer review."  Half right, and the half that is wrong is the interesting half.  CEN Technical Journal is not the Physical Review, and this dispute was never adjudicated by the wider physics community, which has never heard of it.  But the exchange was refereed, and by the right people:  Edward Fackerell and Colin McIntosh, who refereed the 1998 papers, hold doctorates in general relativity and spent their careers in it, and when they published their own assessment in 2000 they reached the same conclusion as Conner and Page.  The claim was checked by people competent to check it.  It failed.

"The model does have an event horizon.  Standard cosmology has none.  That is a real difference."  Conner and Page grant it.  Their answer is that the horizon exists for the reason Humphreys did not give:  it exists because there is an outside for light to fail to reach, not because of any pattern of gravitational force inside.  And they show what its passage does to a comoving observer, which is nothing.  The horizon is an inward-travelling light ray.  It arrives, it passes, and the observer's clock keeps ticking with every other comoving clock.  Humphreys accepted this in 1998 and moved his mechanism elsewhere.

"Classical signature change is real physics.  George Ellis published on it."  He did, and that was the strongest card in Humphreys' 1998 reply.  Three things travel with it.  The Hellaby, Sumeruk and Ellis construction inserts a Euclidean region into Schwarzschild by hand, using sign factors the solution does not supply, and its authors say in Physical Review D that no formulation of signature change has "any experimental or observational support."¹⁵  The criterion those authors give for a real signature change, degeneracy or discontinuity of the metric, is not met by components swapping signs in a chart.  And Conner and Page point out that Humphreys' model does not undergo the process Ellis describes at all:  the sign change in the Klein metric "is the consequence of the imaginary character of the Klein time coordinate."²⁰  Ellis publishing that signature change is possible was never Ellis endorsing that the Klein metric has one.

"The distant universe really is billions of years old on this model, so it concedes the whole argument."  That is a fair description and Humphreys would not deny it.  The white hole cosmology is a young-earth, old-universe model.  What it claims is that the Genesis days are Earth days, measured by Earth clocks, and that general relativity permits distant clocks to have run much further.  Whether that satisfies the text of Genesis is an exegetical question rather than a physical one.  Faulkner notes that most of its supporters never realised what they were signing up for.

"None of this is testable either way, so the argument is a stalemate."  Not quite.  Conner and Page derived two tests that do not depend on the metric dispute:  present-day redshift drift, and an upper bound on angular diameter distance from the light travel time.  Both fail for a rapidly expanding young universe.  Humphreys' answer is that Earth clocks were stopped, so those tests measure something else.  That answer works, and the price of it is that the model's only distinguishing quantity is the amount of Earth proper time elapsed during creation week, which no instrument reaches.  That is the same structure as light created in transit:  unfalsifiable, and unfalsifiable for the same reason.

"Creation ministries still present this as a working solution, so it must be alive."  Some do, and they are out of date.  The Creation Ministries International page on arguments not to use still lists both Humphreys' and Hartnett's cosmologies as viable.  Hartnett retracted his in writing.  Humphreys replaced his and, on two independent reports, moved past the replacement as well.

Verdict

The white hole cosmology is not a live solution to the distant starlight problem, and the reasons are internal to the physics rather than imported from outside it.

The 1994 mechanism was withdrawn by its own author in 1998.  The Euclidean zone that replaced it was shown to be a coordinate artefact by Conner in 1999, by two professional relativists in 2000, and by Conner and Page again in 2000, and Humphreys' answer to all three was that their starting equation did not apply.  The 2008 model rests on an interior metric whose exactness for a time-varying potential runs against Birkhoff's theorem, on a scenario with several quantities God is asked to tune, and on an observation that turned out to be spacecraft waste heat.  In 2013 Humphreys promised in print to revisit that observation either way, and did not.  In 2014 he withdrew the reading of Scripture that put the expansion in the model at all.  Two young-earth astronomers report that he has moved on, and his last cosmology paper, in 2017, argues from end-times prophecy rather than from a metric.

What remains standing is Conner and Page's central result, which is the part a reader can check independently:  adding or removing matter outside a spherical boundary changes nothing about clocks inside it.  If that is right, the boundary that gives the model its name does no work, and the argument moves to whether an event horizon or a signature change supplies what the boundary cannot.  Humphreys' own answer to the observational tests concedes the rest.  His model's redshifts, distances, Hubble constant and angular sizes are those of standard cosmology, by construction.

There is a general lesson here and it is worth stating in the article's own voice, because it is not the lesson either side usually draws.

A competent physicist with a real doctorate and a real career built a serious model out of real general relativity.  Every criticism that mattered came from inside the small world that cared about the answer.  A creationist mathematician found the central error first, in 1997.  A relativist who had co-authored with Hawking published the full critique in a creationist journal in 1998.  The two men who refereed that exchange, both evangelical Christians with doctorates in general relativity, published their own refutation in the same journal in 2000.  A creationist reader wrote in 2001 that the problem was not solved and that his own side's advertising had said otherwise.  A young-earth astrophysicist supplied the quantitative objection in 2020 and reported that the author had abandoned the model.  Nobody outside the movement had to do anything, and as far as the wider physics community is concerned, none of this ever happened.

That is what a working intellectual community looks like, and this one is small enough that the same names appear on both sides of the argument.  It also shows what the movement's cosmology has not yet produced:  a model that predicts an observation standard cosmology does not.  Humphreys came closest, because his 1994 model made claims that could be checked, and when they were checked he answered by making the model observationally identical to the theory it was meant to replace.  Every surviving young-universe cosmology has done the same thing since.  The parent article, Young-Universe Cosmologies, traces that pattern across all eight of them, and the two answers still defended are the anisotropic synchrony convention and light created in transit.

Sources