What the Equations Allow, and What the Universe Actually Did

Einstein’s field equations do not distinguish between forward and backward. Take any solution, replace time with its negative, and what comes out is another perfectly valid solution. Do that to a black hole and you get a white hole: a region nothing can fall into and everything must eventually leave, with its singularity in the past instead of the future.

So white holes are allowed. Nothing in general relativity forbids one.

There is still no white hole anywhere anyone has looked, and there are two independent reasons to expect there is none to find. The distance between the equations permit this and this happens is the whole subject here — and it is not a technicality. It is where the difference between past and future actually lives.

Where this came from

Three proposals, arrived at in sequence, which turn out to be one proposal.

The first: a white hole is just a black hole in reverse time, and since Einstein’s equations are indifferent to the direction of time, the white hole is not merely permitted but is literally happening simultaneously with the black hole. Not two objects sitting side by side — one object. An observer outside the history, scrolling it one way, sees a black hole; scrolling the other way, sees a white hole. Same footage, opposite playback.

The second: our universe might be sitting in the middle of the Hawking radiation of a really, really big black hole. Hawking radiation is random, so it would produce a random and evenly distributed cloud of matter — a fair description of how the early universe looked, and so possibly what began it.

The fourth: time is the fourth dimension and we are creatures trapped inside it, so a higher-dimensional being would stand above time — seeing all of it at once and existing permanently. That would explain how the universe manages to have no start and no end, and matter may itself be of a higher-dimensional nature, unlike our memory-forming consciousness.

The third: that smoothness is the reversed direction’s natural end state. Matter moving apart eventually spreads until it is spread evenly, while matter that attracts eventually crumples into a ball. Our beginning is where the reversed reading finishes, which would make the Big Bang’s evenness an equilibrium rather than a fine-tuned accident.

The position, stated in full

Worth setting out at its strongest before anything is done to it, because the parts support one another.

1. The premise. Time is reversible. The laws governing matter carry no preferred direction. If a sequence of events is a legal way for matter to move, that same sequence run backwards is equally legal.

2. What reversal produces. Reverse time and matter behaves in the opposite way from how it behaved before. That reversed behaviour is not an artifact or an approximation — it is a valid way for matter to move, with the same standing as the original.

3. What a white hole is. A black hole is a region matter falls into and cannot leave. Reversed, it is a region matter leaves and cannot enter — a white hole. Not a separate exotic object requiring its own justification, but what a black hole is, read the other way.

4. Why they are simultaneous. Because the reversal is a reading direction, there are not two objects but one. An observer outside the history, scrolling it: scroll right, black hole; scroll left, white hole. Same footage. Both descriptions are true of the same thing at once.

5. Why the mathematics carries both. This is the explanation for why Einstein’s equations hold black hole and white hole solutions — not two separate discoveries that happen to coexist, but one solution read two ways.

6. The observers reverse too. The objection that beings on the other side would notice something wrong — remembering the future, seeing effects before causes — fails, because everything reverses, including them. They do not make memories the way we do; the memorisation process reverses along with the rest. Memory cannot be used to break the tie, because memory pointing the other way is forgetting: the terms themselves flip. Every asymmetry offered as proof that our direction is the real one reverses along with everything else.

7. Why we see no white holes. The theory explains the absence rather than being embarrassed by it. We do not observe white holes because we are on the black hole side — our universe is the black hole reading. That is the prediction, not a coincidence. And for the guys living in the other direction, the very objects we call black holes are white holes. Their universe is full of them, and it is the same universe.

8. The antiparticle case. The pattern already shows up in matter itself. Antiparticles exist because reversing time makes particles behave in the anti way — the same particles, acting oppositely.

9. The smoothness. In the reversed direction matter moves apart until it is spread evenly, which is what the early universe looked like; in ours everything attracts and eventually crumples together. The Big Bang’s evenness is therefore the reversed reading’s end state rather than a fine-tuned accident.

10. Standing above time. We are third-dimensional creatures limited inside our own dimensions, unable to do anything about time. A higher-dimensional creature exists above time and therefore permanently — which is how the universe can have no start and no end. Matter may be of a higher-dimensional nature, rather than the three-dimensional nature of memory-forming consciousness.

The load-bearing commitment. Nothing in the contents of the universe privileges one reading over the other. Every apparent asymmetry is an artifact of which reading is being performed, and reverses when the reading switches. Everything above rests on this.

Where the article goes

The sections that follow take these in order: what reversal actually changes and what it leaves alone; where the scrolling picture is exact and where it stops; whether the other direction can be occupied at all; what “the equations allow it” buys; the antiparticle case, which is the one place the reversal is real and observed; then the Hawking-radiation proposal; then the smoothness proposal.

The time-reverse of a black hole really is a white hole

This part is exactly right, and it is the standard way the objects are introduced.

The Schwarzschild solution — the geometry around any non-rotating, uncharged black hole — contains time only as a squared quantity. Flipping the sign of time changes nothing in it whatsoever. The geometry is not merely unchanging over time; it is unchanged by reversing time. That is what makes the black hole’s mirror image a legitimate solution rather than a curiosity.

The mirror image is the white hole. Where a black hole horizon is a surface you can cross inward and never back out, a white hole horizon is a surface you can cross outward and never back in. Same geometry, same mass, same gravitational pull at every distance. From far away, a white hole of a given mass and a black hole of the same mass are indistinguishable — identical orbits, identical light-bending, identical everything. The only difference is which way things are permitted to cross the horizon.

For a spinning black hole the reversal takes one extra step: the time-reverse of a rotating black hole is a white hole rotating the other way. The symmetry holds, it just carries the spin along with it.

What reversal changes, and what it leaves alone

Worth being precise about this early, because a great deal downstream depends on it.

When you reverse time, the laws do not change. That is not a side remark — it is the entire content of time-reversal invariance, and it is the reason the reversed motion counts as a valid solution at all. If the laws flipped under reversal, the reversed process would be obeying different laws and would not be a solution of the original ones. “Reverse time and the reversed behaviour is legal” and “reverse time and the laws flip” cannot both hold. The first is the one that does.

What reverses is the trajectory, not the rulebook. Velocities flip, because velocity is a first derivative of position with respect to time. Accelerations do not, because acceleration is a second derivative and the two sign flips cancel. Forces enter the equations as accelerations, so forces are untouched.

The test that settles it

Film an apple falling from a tree, then run the film backwards.

Forward: the apple starts at rest, picks up speed downward, hits the ground. Backwards: the apple leaves the ground moving fast, slows down as it rises, and comes to rest at the branch.

Now ask what a repulsive Earth would do to that apple. It would push it away — speeding it up as it climbed. The reversed film shows the exact opposite: the apple decelerating the whole way up, as though something were pulling it back down. Something is. The reversed film is a film of a thrown apple, and a thrown apple is under ordinary attractive gravity.

Orbits make the point with nothing left to interpret. Reverse a film of the Earth going around the Sun and you see the Earth going around the other way — still in orbit, still bound, still held by an inward pull. If reversal turned gravity into repulsion, the reversed Earth would fly off immediately. It does not. Every orbit in the solar system runs backwards as an orbit.

The intuition that misfires here identifies moving apart with being repelled. Those are different. Moving apart is a statement about velocity; being repelled is a statement about acceleration. A thrown ball moves apart from the Earth the entire time the Earth is attracting it. Reversal flips the first and leaves the second alone.

As for why different behaviour does not imply a different law: falling and throwing are already the same law, differing only in the velocity they start with. Reversal changes the starting velocity. That is a change of state, not of rulebook.

Why a flipped-law reading is self-defeating

There is a decisive reason to prefer this beyond the mechanics.

“Reverse time and the reversed motion is a valid way for matter to move” means the reversed motion satisfies our equations. That is what validity is, and it is the entire basis for saying Einstein’s equations contain white hole solutions.

If the laws flipped under reversal, the reversed motion would satisfy some other set of equations and would not be a solution of ours — which would mean white holes are not solutions of Einstein’s equations at all. The flipped-law reading removes the conclusion it was brought in to support.

Only one of the two can be held, and the one that yields white holes is the one where the laws stay put.

Each row below is a place where the intuition reaches for something to flip and nothing does:

That last row is where the intuition is right, and it is the deepest of them. T on its own is not a symmetry of the weak interaction; the exact symmetry is CPT. So making a reversed process genuinely legal does require flipping something — but what flips is charge and parity, turning particles into antiparticles. Not the gravitational force law, and not the direction in which anything is experienced.

Scrolling the history in both directions

The strongest form of the reverse-time claim is not about two objects coexisting somewhere. It is this: take the whole four-dimensional spacetime as a finished block, and let something outside it read the block in either direction. Read one way, matter falls in and never returns — a black hole. Read the other way, matter emerges and can never get back in — a white hole. One object. The label depends on which way you scan.

For the eternal black hole this is not an analogy. It is literally true, and it is provable.

Write the eternal Schwarzschild geometry in coordinates chosen so light always travels at forty-five degrees on the page. Flip the sign of the time coordinate and the metric comes back identical — not similar, not physically equivalent, but the same geometry point for point. That is a genuine symmetry of the spacetime, an isometry. And it does something specific: it exchanges the black hole region with the white hole region, leaving everything else where it was.

So for the eternal solution, which one you call “the hole” is a choice of time orientation rather than a fact about the object. The black hole and the white hole are related by a symmetry the geometry already possesses. The scrolling picture holds exactly.

Where the two regions sit

Drawn in those coordinates, the spacetime is a square cut by two crossing diagonals — a large X — into four wedges:

The time-flip is the reflection that swaps top and bottom. And within the block, the geometry orders these two regions on its own: every event in the bottom wedge lies in the causal past of every event in the top one, for every observer, with no exceptions. To be in the top wedge a point must sit higher above the crossing than it sits sideways from center; to be in the bottom, lower below than sideways. So any line joining a bottom point to a top point covers more vertical than horizontal — steeper than a light ray, and therefore strictly ordered in time.

That ordering is worth noticing, because it is a fact about the block’s contents rather than about how anyone reads it. Scanning direction decides which end you call earlier. It does not decide the internal structure.

Where the picture stops working

Every black hole that exists formed from something, and a spacetime with a collapsing star in it is not time-symmetric.

Reverse it and you do still get a white hole — that much is fully general, and it is the part of the original claim that survives all the way down. The time-reverse of any black hole solution is a white hole solution. But it is a different spacetime, not the same one read backwards. The eternal solution maps onto itself under the flip, which is what licenses the scrolling picture. A collapse spacetime maps onto a distinct solution: a white hole that disgorges a star, which then flies apart. Two solutions, not one object with two readings.

Both are legal. Both satisfy the field equations exactly. The universe contains an enormous number of the first and, as far as anyone can tell, none of the second.

So the simultaneity claim holds precisely where the object is idealized enough to be time-symmetric, and fails precisely where it is real. The eternal black hole is a vacuum solution with no formation history, no matter anywhere, existing unchanged for infinite time in both directions. Its time-symmetry is a property of that idealization. Nothing in nature has it — because everything in nature has a past.

The observer who scrolls

The natural completion of the scrolling picture is that the observers reverse too. Beings living in the other direction do not remember things the way we do — their memorization process runs backwards along with everything else. Nothing is privileged about our side; we simply happen to be on it.

The part about mechanisms is correct. Reverse the block and every process in it reverses, memory included. But that does not deliver observers who experience the other direction, for a reason that has nothing to do with mechanisms.

A memory is not a process. It is a correlation — a physical record in one place that matches an event elsewhere in time. And a correlation is a fact about the block’s contents, not about the direction anyone reads them. In our spacetime, brain states at any moment correlate with events on the low-entropy side and with nothing on the high-entropy side. Flipping the reading direction does not move that correlation; it stays exactly where it was.

So reversing a memory mechanism does not produce a mechanism that remembers the other way. It produces a mechanism that forgets — records dissolving rather than forming.

That word cannot be leaned on, though. “Forgetting” is itself defined by an arrow, so calling the reversed process forgetting is a relabeling rather than an argument; from the other side, our remembering is their forgetting. The fact that does the work is not the direction the process runs. It is which end the correlations point at.

“Records correlate with earlier events” is arrow-relative and says nothing. “Records correlate with the smooth end” is not arrow-relative at all — the smooth end can be picked out by inspecting the contents of the block, with no direction of time assumed.

And there is a mechanism forcing the second one. Making a record requires a low-entropy ready state: a blank page, an unexposed film, a neuron that has not yet fired. Ready states have to be paid for out of the entropy budget, and in our universe that budget has exactly one source. So any record-bearing structure anywhere in the block, running in whichever direction, carries records of the smooth end. Scan the reversed being’s brain at any moment and the traces in it correlate with the Big Bang side — fixed by the block’s contents, not by who reads them.

Whatever such a being knows about, it knows about the smooth end. And what you hold records of is what you call your past.

The symmetric reply would be that in their universe records point at their low-entropy end, which is our high-entropy end. That needs a universe with a smooth end in both directions. Ours has one; a universe with two is the subject of section 6.

The time-reverse of our universe, lived in, is our universe

This is the result that settles it, and it takes only a few lines to check.

Take the entire four-dimensional solution describing our universe and flip the sign of time. In the new labeling, entropy decreases as the coordinate advances, and every black hole reads as a white hole — matter streaming out of horizons nothing can enter. That is a perfectly legal solution, and it looks like exactly the mirror world the picture calls for.

Now put an observer in it. Their arrow is set by the entropy gradient, and in the flipped solution that gradient points toward decreasing coordinate time. So they live the flipped solution in the direction we would label backwards — which is our original solution, unchanged. And in that direction, matter falls into horizons and cannot get back out.

They see black holes. The same ones we see, doing the same thing ours do.

The flip is a relabeling of the paper the solution is written on. It changes no observation, because it carries the observers’ arrow along with everything else. Reversal cannot manufacture a vantage point from which our black holes look like white holes, because reversal takes the observers with it.

The two ends are not alike

There is a blunter version of the same point.

If the direction of time were only a matter of which way the block is read, the two ends of our universe would have to look the same. They do not. One end is smooth, hot, dense, and simple enough to describe in a paragraph. The other is cold, lumpy, and full of black holes. That asymmetry sits in the contents. No choice of reading direction creates it and none removes it.

So there are not two sides with people on each. There is a gradient with one low end, and everything capable of observing anything sits somewhere along it, facing the same way.

Where beings in the other direction are taken seriously

Separating the experiences of the two directions is not an unreasonable move, and it is worth saying plainly what it would take rather than leaving it as a flat refusal. It requires an entropy minimum with matter on both sides of it. Our universe appears to have its minimum at one end, which leaves only one side to stand on. Put the minimum in the middle instead and there are genuinely two populations, each with its own experienced arrow, each regarding the other as reversed — and that is a serious proposal rather than a thought experiment.

The idea is not fringe, and it has been pursued by people who knew exactly what they were doing. It just needs a different shape of universe than ours appears to be.

Gold’s reversing universe. Thomas Gold proposed that if cosmic expansion halts and reverses, the thermodynamic arrow flips at the turnaround, so the contracting phase runs backwards relative to us. This is the closest thing in the literature to the claim that our black holes are somebody’s white holes, and it was argued over seriously. It was refuted — by Penrose, and by Zeldovich and Novikov. The core failure: a recontracting universe does not retrace its smooth beginning in reverse. It collapses into a lumpy, black-hole-riddled state, so entropy climbs straight through the turnaround instead of flipping. Tolman had already undercut the premise that entropy tracks the size of the universe at all.

Two arrows from a middle. Sean Carroll and Jennifer Chen proposed a spacetime shaped like an hourglass, with our Big Bang at the narrow neck as the point of lowest entropy and entropy increasing outward in both directions. Julian Barbour, Tim Koslowski and Flavio Mercati arrived at a structurally similar picture from gravitational dynamics: their “Janus point” is a configuration of minimum size from which two oppositely directed arrows emerge. In both, observers can exist on both sides, each experiencing time as running away from the middle, each regarding the other as reversed.

That is genuinely people living in the other direction, and it is live physics rather than a thought experiment. It still does not produce white holes. Those observers sit on the far side of an entropy minimum, in their own stretch of spacetime, with their own arrow — and along that arrow, matter falls in. They have black holes too. Two branches, two arrows, black holes in both.

What “the equations allow it” actually buys

Less than it sounds like, and this is the load-bearing point of the whole article.

A physical theory has two independent parts: the equations, and the state you feed them. The equations say which evolutions are legal. The state says which one is happening. Time-symmetric equations are entirely compatible with a universe where one direction looks nothing like the other, because the asymmetry can live in the state rather than the law.

Everyday life is saturated with this. Newtonian mechanics is time-symmetric, so a film of a glass shattering and a film of shards reassembling are both legal evolutions. Only one of them ever plays. Nothing in the laws picks the winner; the initial condition does. “Einstein’s equations permit white holes” is a statement of exactly this kind — true, and silent about whether any exist.

One caveat on the symmetry itself

Time-reversal invariance is not quite universal among the laws, which is worth stating because the argument above leans on it.

Gravity and electromagnetism are exactly time-symmetric. The weak interaction is not. T violation has been measured directly — the BaBar collaboration observed it in 2012 in the neutral B meson system, comparing transition rates that can only be related to one another by a time-reversal transformation, and found them unequal. The exact symmetry of nature appears to be CPT: reverse time, mirror space, and swap every particle for its antiparticle, and only then does the reversed process become a genuine solution.

For black holes none of this matters. General relativity is exactly T-symmetric, the weak interaction plays no role in the geometry, and the reversed solution is a solution in the full sense. But “reverse time and the reversed motion is legal” is a statement about specific laws rather than about time as such, and it happens to be false for one of the four forces.

And a white hole would not survive being made

Suppose one existed anyway. It would not last.

A white hole is violently unstable. Douglas Eardley showed in 1974 that anything falling toward one — even the faintest ambient radiation — piles up on the past horizon with unboundedly growing energy, and the gravitational effect of that accumulating material converts the white hole into an ordinary black hole. The instability grows exponentially. Later work refined the mechanism, disputing whether the primary cause is the blueshift itself or the gravity of the accreted material, but not the conclusion.

So the case against macroscopic white holes has two independent legs. Nothing known makes one, and if something did, it would promptly turn into a black hole.

Where the reversal is real, and observed

There is one place where “reverse it and you get the anti version” is not an analogy but the standard working formalism of physics. Setting it beside the black hole case is instructive in both directions.

An antiparticle is a particle propagating backwards in time. This is the Stückelberg–Feynman interpretation, and it is not a picturesque gloss on the mathematics — it is the mathematics. Stückelberg found that the negative-energy solutions of the relativistic electron equation become sensible when read as propagating backward, which immediately explains why the partner object carries identical mass and spin and opposite charge. Feynman built that reading into his diagram technique, where an antiparticle line is drawn literally as a particle line pointing the other way through time — and that technique is how amplitudes are computed in quantum field theory today. A positron is an electron going the other way.

The formalism does not merely permit this, it requires it

T alone is not an exact symmetry of nature. The exact one is CPT: reverse time, mirror space, and exchange every particle for its antiparticle.

The C in that expression is precisely the particle–antiparticle swap, and it is there because reversing time by itself does not hand back a solution. To make the reversed process legal you must also turn everything into its opposite. So the demand that things become their anti versions when time runs backwards is not a fact discovered about antiparticles afterwards — it is written into the deepest symmetry theorem in physics, and it is why the C sits next to the T.

Antiparticles are also not an optional extra. Charge conjugation only has meaning inside Lorentz symmetry; antiparticles are a consequence of special relativity, and a particle and its antiparticle occupy the same irreducible representation of the Poincaré group. In the formal sense that matters, they are one object.

Wheeler’s one electron

The most extreme version of this idea came from John Wheeler, in a phone call to Feynman in 1940: every electron in the universe is the same electron, threading forward and backward through time, with the backward-running segments being what we detect as positrons. Cut the tangle with a plane of constant time and you see many particles, half of them going each way.

Feynman found it could be made mathematically consistent and gave it its famous airing in his 1965 Nobel lecture. He also supplied the objection: we observe vastly more electrons than positrons, so the tangle does not balance. Wheeler’s patch — that the missing positrons are hiding inside protons — did not survive.

What the comparison shows

This is where the antiparticle case and the black hole case come apart, and the difference is the informative part.

Positrons are here. They exist in our universe, moving forward along our arrow, produced in accelerators and in certain radioactive decays, used routinely in medical imaging. The backwards-in-time reading is how the propagator is written; the object it describes is an ordinary forward-moving thing in our world, sitting alongside its partner.

So if a black hole and a white hole stood in the relation an electron and a positron stand in, white holes would be predicted right here — observable, in the same universe, along the same arrow as black holes. Followed through, the analogy points at our own sky rather than at the far side of a reversal.

And then the parallel resumes exactly, at the level that matters most:

Both are cases where the laws barely distinguish the two options and the universe is overwhelmingly one-sided. In both, the asymmetry is not produced by the laws — it traces back to conditions in the early universe. The matter side of it is called baryogenesis, and Andrei Sakharov’s conditions for it are baryon number violation, C and CP violation, and departure from thermal equilibrium — a thermodynamic condition on the early universe, from the same family as the low-entropy past this article keeps returning to. It is also unsolved: the CP violation available in the Standard Model falls far short of accounting for the matter we see, and something beyond it is required.

So the antiparticle case is a second instance of the same structure rather than an exception to it. Symmetric laws, one-sided contents, the asymmetry deposited by the early universe, and the reason still unknown.

The second proposal: the universe as somebody’s Hawking radiation

Now the harder question, which has a genuinely good observation inside it.

Black holes are not perfectly black. Hawking showed they radiate, with a spectrum that is thermal — random, featureless, characterized by nothing but a temperature. And the early universe was, in fact, an extraordinarily uniform hot bath. The cosmic microwave background is the most perfect blackbody spectrum ever measured, matching the ideal curve to within fifty parts per million, and it is the same brightness in every direction to about one part in a hundred thousand.

So the observation that thermal, random, evenly-distributed radiation resembles the early universe is not a bad observation. It is very nearly a description of the cosmic microwave background. The proposal fails on where that radiation could have come from.

The dial that runs the wrong way

The Hawking temperature of a black hole is inversely proportional to its mass. Bigger means colder, without exception.

The scale is brutal:

Read that table in the direction the proposal needs and the problem is immediate. To supply a universe’s worth of matter, the black hole must be enormous. To be hot enough to be a Big Bang, it must be tiny. These are the same dial turned in opposite directions.

Put a number on the gap. To radiate at even nucleosynthesis temperatures — the modest early-universe milestone where hydrogen fuses into helium, far cooler than the Big Bang’s opening act — the black hole would have to weigh about 10¹⁴ kilograms, roughly a large asteroid. That is short of the observable universe’s matter content by about thirty-nine orders of magnitude. And a black hole actually holding a universe’s worth of matter radiates at 10⁻³⁰ K: colder than today’s microwave background by a factor of 10³⁰, and colder than the early universe by vastly more.

A “really, really big” black hole is the coldest object the laws of physics describe.

A trickle spread over 10¹³⁵ years

The temperature is only half the problem. The other half is that Hawking radiation is not an event.

Evaporation time scales as the cube of the mass. A solar-mass black hole takes about 2 × 10⁶⁷ years to evaporate. One holding the observable universe’s matter would take on the order of 10¹³⁵ years — around 10¹²⁵ times the current age of the universe. The radiation does not arrive; it seeps, over a span for which the word “slow” has no useful meaning.

There is also a prior obstacle. A black hole colder than its surroundings absorbs more than it emits, so a hole at 10⁻³⁰ K does not evaporate at all until its environment has cooled below that — which, in a universe like ours, takes something like a trillion years of expansion before evaporation can even begin. That particular constraint depends on assumptions about the parent universe, so it is a complication rather than a refutation, but it points the same way as everything else.

The natural rescue is to note that evaporation does end in a hot flash: as the hole shrinks its temperature climbs, and the final moments are genuinely violent. But that only makes the last microgram hot. By then the other 10⁵³ kilograms left long ago, cold, and have been spreading outward for 10¹³⁵ years — smeared across a region 10¹²⁵ times wider than everything we can see. There is no moment at which the mass is both hot and gathered. A Big Bang requires it to be both.

Why “random and even” is the hardest thing to make

This is where the second proposal fails in the interesting way, and it is the same failure as the first.

The intuition that even distribution equals randomness equals high entropy is correct for a gas in a box. Open a perfume bottle and the molecules spread until they are everywhere; that spread-out state is overwhelmingly the most likely one, which is exactly why it happens on its own and never reverses.

Gravity inverts this completely. Gravity only attracts — there is no negative mass to cancel it the way opposite charges cancel electric forces — so a self-gravitating system does not spread out. It clumps. Matter falls together, forms stars, forms galaxies, and in the limit forms black holes. For matter with gravity, smooth is the low-entropy state and lumpy is the high-entropy one. The clumpiness we see around us is not order emerging from chaos; it is the universe running downhill, exactly as thermodynamics requires.

Which reverses the meaning of the observation the proposal is built on. The early universe’s near-perfect smoothness is not evidence that something random made it. It is the single most fine-tuned fact about our universe.

The numbers are stark. The cosmic microwave background carries about 2 × 10⁸⁹ units of entropy. The observable universe today holds about 3 × 10¹⁰⁴, dominated by the supermassive black holes at galactic centers. And the maximum available — everything collapsed into one black hole — is around 10¹²³, the figure Penrose used to argue that the initial state of the universe was selected to a precision of one part in 10^(10^123).

So the early universe began roughly thirty-four orders of magnitude below the entropy it could have had. That gap is the entire budget from which every subsequent event has been paid: every star that ignited, every galaxy that assembled, every living thing, every thought anyone has had.

Hawking radiation sits at the wrong end of that scale. It is exactly thermal — maximum entropy for its energy, carrying essentially no information about whatever fell in. It is what a system looks like when its budget is spent. Starting a universe with it is asking for a 13.8-billion-year history to be financed from an empty account.

There is an observational version of this argument too. The temperature ripples in the microwave background are not random noise; they form a specific pattern of peaks at specific angular scales, which requires all the ripples to have started oscillating in phase, at the same moment, from a common origin. Models that generate fluctuations continuously and randomly as the universe evolves — cosmic strings and other topological defects were the serious candidates — produce incoherent ripples that smear those peaks out. That mismatch is what ruled those models out. A randomly-radiating source has the same problem.

A source would leave a direction

One more check, simpler than the rest. Hawking radiation comes from a place. It streams outward from a hole, into a space that already exists, with a definable center and an outer edge.

The Big Bang was not like that. It did not happen at a location and expand into surrounding space; space itself expanded, everywhere at once, with no center and no outside. These are not two descriptions of one thing — they make different predictions.

If we sat inside an expanding shell of radiation from a central source, the sky would show it: a systematic gradient, a strong preferred direction. What the sky actually shows, once our own motion through the microwave background is subtracted, is uniformity to about ten parts per million. There is no center to be found because there is no center.

The third proposal: repulsion as the reason for a smooth start

The two halves of this article combine into something sharper than either. Section 13 established that a smooth spread of matter is the low-entropy state once gravity is in play, which makes the Big Bang’s smoothness the most fine-tuned fact about our universe rather than its most natural one. The proposal is that reversal dissolves that puzzle: in the reversed reading gravity repels rather than attracts, and matter that repels pushes itself apart until it is spread evenly. Smoothness stops being a fine-tuned starting condition and becomes an equilibrium — the state the reversed dynamics relaxes into on its own. Our beginning is the reverse universe’s end.

For a repulsive force the reasoning is correct. Repulsion does drive matter toward an even spread, and that spread is a genuine attractor rather than a coincidence.

Time reversal does not produce a repulsive force. Per section 3, forces are accelerations and accelerations survive the flip untouched; only velocities reverse. Gravity attracts just as hard in either reading.

The concrete version: the time-reverse of falling is throwing, not repelling. Film a dropped ball, run it backwards, and you see a ball moving away from the Earth while slowing down — pulled downward the entire way. That is a thrown ball. Nothing in the reversed film shows repulsion.

The same holds at cosmic scale. Reverse a collapsing universe and you get an expanding one decelerating under its own gravity, not a universe in which gravity pushes. So the reversed reading of our history is not a repelling universe relaxing toward smoothness — it is a contracting universe whose matter un-clumps, every particle moving in precisely the coordinated way needed to undo structure. That is not an equilibrium being approached. It is the original fine-tuning wearing a different label.

If “repel” only means that things move apart

There is a second reading, and it needs its own answer: not that gravity’s sign flips, but simply that in the reversed direction matter does separate and does end up evenly spread.

Read that way it is straightforwardly true. Our universe ran smooth to clumpy, so the reversed reading runs clumpy to smooth, with matter moving apart the whole way. Nothing to dispute.

What the reading costs is the explanation.

Genuine repulsion would explain an even spread because the even spread is an attractor: start almost anywhere, run the dynamics, arrive there. That robustness is what makes it explanatory. Perturb the starting configuration and you still finish smooth.

Reversed attraction has no such property. Take the reversed universe and jiggle one particle’s velocity slightly. It does not still finish smooth — it finishes clumpy, because gravity is still attractive and clumping is what attractive gravity does to nearly any configuration handed to it. The smooth outcome survives only for velocities tuned to undo one specific history exactly, and any perturbation destroys it.

A shattered glass makes this concrete. In the reversed film the shards really do move together and really do end as an intact glass. Entirely true, and it explains nothing about why intact glasses exist — because reassembly is not a tendency of shards. It requires every shard, and every air molecule, carrying precisely the right velocity. “Moving together” describes the reversed film; it is not a force that makes glasses.

Underneath sits a circularity. Why does matter spread evenly in the reversed reading? Because our universe began smooth and grew clumpy. The reversed direction’s apparent tendency toward evenness is not an independent dynamical fact — it is our own history, read backwards. Using it to explain why that history started smooth is explaining the thing with itself.

So the proposal meets a fork, and both branches are covered:

• Repulsion as a force. Genuinely explanatory, because an even spread really is a robust attractor. But reversal does not deliver a force flip — the apple and the orbits settle that.
• Repulsion as description. Reversal does deliver this, and it is true. But it is our own history read backwards, so it cannot explain that history.

Either way the explanatory work goes undone. That is not a defeat of the instinct behind it: the link between dispersal and evenness is real, and the subsection below is where it actually cashes out. Dark energy is a genuine repulsion, it genuinely drives the universe toward smoothness, and it does so robustly.

Repulsive gravity does exist, though

Cosmic expansion is exactly the right thing to raise here, and it leads somewhere better than a counterpoint.

Repulsive gravity is real and we are living in it. In general relativity what sources gravitational attraction is not density alone but ρ + 3p — energy density plus three times pressure. Dark energy carries pressure close to −ρc², which makes that combination negative: one attractive energy against three repulsive pressures, netting repulsion. It is roughly two-thirds of the universe’s energy budget, and it is why cosmic expansion stopped decelerating and began speeding up.

And it does precisely what the proposal says repulsion should do. Under accelerating expansion the far future is de Sitter space — everything unbound driven beyond every horizon, leaving a universe empty, cold, and perfectly smooth.

Why that still does not give a Big Bang

Both ends of our universe are smooth, and their entropies differ by about thirty-four orders of magnitude. The early universe carried roughly 10⁸⁹ units against a ceiling near 10¹²³. The de Sitter future sits essentially at that ceiling; the cosmic event horizon alone accounts for about 10¹²².

Smoothness by itself does not fix entropy. Density does. Smooth and dense is a low-entropy state, because an enormous amount of clumping is available and none of it has been spent. Smooth and empty is a high-entropy state, because there is nothing left to clump. The Big Bang was the first kind; the de Sitter future is the second.

So repulsion delivers smoothness of the spent variety, not the loaded variety. Run the empty smooth state backwards and you do not recover a hot dense beginning — you recover a de Sitter space, which is where you began.

One correction in passing: with dark energy in the picture our universe does not end by crumpling into a ball either. Bound structures stay bound and collapse locally, but everything unbound recedes forever. The far future is isolated islands drifting apart, not a single sphere. Crumpling was the standard expectation until the supernova measurements of 1998.

The target is right, and it is being pursued

What the proposal reaches for — making the smooth state dynamically natural rather than fine-tuned — is a serious research programme, and it does not need repulsion to get there.

Barbour, Koslowski and Mercati studied the Newtonian N-body problem at zero total energy and angular momentum: plain attractive gravity, with no box around it. Their claim is that no special initial conditions have to be imposed on a time-symmetric law for its solutions to display an arrow of time. In an unconfined system there is no equilibrium to relax into at all, so the usual entropy reasoning does not even apply. The quantity governing the dynamics is complexity, a measure of clustering, and it has a minimum — a uniform configuration the system simply passes through, with clustering growing in both directions away from it.

That uniform state is not an improbable fluctuation. It is a dynamical waypoint. Which is exactly the status the proposal wants for the Big Bang’s smoothness — obtained with attraction alone, and with no reversal required.

The fourth proposal: standing above time

We are already four-dimensional

The premise needs one correction, and it makes the picture stronger rather than weaker.

In relativity we are not three-dimensional creatures carried through a fourth dimension. We are four-dimensional objects outright. A person is a worldtube — a shape extended through time as genuinely as through space — and what anyone calls “themselves right now” is a three-dimensional slice across it. The whole shape is there. What is confined to the slice is perception, not existence — and existing is accordingly a spacetime-level affair rather than a moment-by-moment one. A thing’s existence is its entire worldtube.

So the limitation is real. It is just not a shortage of dimensions.

Extra dimensions buy no freedom in time

This is the step that fails, and it fails on the structure of spacetime rather than on anything exotic.

The reason nobody can move around in time is not a missing dimension. It is the minus sign. Spacetime’s geometry treats time with the opposite sign from the three spatial directions, and that one difference is what produces light cones and separates timelike paths from spacelike ones. Moving sideways through time would mean following a spacelike path — travelling faster than light.

That constraint has nothing to do with how many spatial dimensions anyone has. A creature with ten spatial dimensions is bound by the same light cones and moves through time exactly as helplessly as we do. Adding room to the space part of spacetime buys nothing at all in the time part.

What would buy it is a second time dimension, and that has been examined. The results are discouraging. With two timelike directions there is a closed timelike curve joining any two points whatsoever, so causality collapses completely — and worse, a light cone with its origin removed no longer falls into two separate pieces, meaning there is no future/past distinction left to have. Extra time dimensions also bring ghost fields of negative norm, negative probabilities, and an ill-posed initial value problem. Itzhak Bars has built a two-time physics in which a (d+2)-dimensional description projects holographically down to ordinary one-time physics, but the extra time is gauged away in every observable sector — which is precisely not a vantage point above time.

There is no established outside to stand in

The Flatland picture assumes our spacetime sits inside a larger space that a higher being could look down from. General relativity requires no such thing, and this is not a technicality.

Gauss proved that the curvature of a surface can be determined from measurements made entirely inside it, with no reference to any surrounding space — the Theorema Egregium. Riemann generalised intrinsic curvature to any number of dimensions, and Einstein built gravity on that generalisation. Spacetime curves intrinsically, not into anything. A two-dimensional being on a sphere can establish that the sphere is curved without knowing three-dimensional space exists.

There is no observational evidence that our spacetime is embedded in a higher-dimensional one, and the theory does not need it to be. The balcony this proposal wants to stand on is not something physics supplies.

”Permanently” is a temporal word

Worth separating out. If a being genuinely stands outside time, then saying it exists permanently applies a temporal predicate to something atemporal. Permanent means “at all times”, and for such a being there are no times. It would not exist for a very long while. It would exist timelessly, which is a different and stranger claim.

Whether the universe has a start

Genuinely open, and worth reporting rather than settling.

The block-universe view does make “what brought the universe into existence” a possibly malformed question. If the whole four-dimensional object simply is, there is no moment at which it was produced, and asking what preceded the earliest moment may be like asking what lies north of the north pole. That is a respectable position, and the Hartle–Hawking no-boundary proposal formalises a version of it: a past that is finite and yet has no edge, the way a sphere’s surface is finite without a rim.

Pulling the other way is the Borde–Guth–Vilenkin theorem, which shows that any spacetime whose average expansion has been positive is geodesically incomplete toward the past. It assumes nothing about energy conditions, which is what makes it hard to evade, and on it an inflating universe cannot be past-eternal and must have a prior boundary of some kind. It is not the last word — recent work presents inflationary solutions claimed to be smooth and geodesically complete into the past. The question is live.

What a higher-dimensional vantage does not do is settle it. If the block has a boundary in one time direction then it has one, and standing outside changes nothing about whether it does. A viewpoint is not a modification of the thing viewed.

Matter, consciousness, and which one is confined

The last piece contains something real and locates its cause in the wrong place.

Matter is four-dimensional, exactly as proposed. A particle is a worldline, an atom a worldtube; the full existence of any material thing is its entire shape in spacetime rather than the momentary cross-section we meet.

But brains are four-dimensional on precisely the same terms. There is no dimensional gap between matter and the consciousness it supports — both are worldtubes.

The asymmetry being sensed is real all the same. Matter’s worldline is present in its entirety while awareness is confined to a travelling slice. The cause is the one this article keeps arriving at: at every slice a brain holds records correlating with the smooth end of the block and none correlating with the other. Confinement to the slice follows from the record structure, which follows from the entropy gradient. Thermodynamic, not dimensional.

There is, though, a real physical model in which different things get different numbers of dimensions. In Randall–Sundrum braneworlds our universe is a brane sitting in a higher-dimensional bulk, Standard Model matter and forces are confined to the brane, and gravity propagates through the full bulk. So the split exists in serious physics — with gravity as the higher-dimensional participant and matter as the confined one, which is the reverse of the arrangement proposed here.

What a higher-dimensional perspective would actually be like

Two rules generate nearly all of this, and they are worth having before the examples.

Rule one: you perceive one dimension fewer than you inhabit. A creature living on a line sees points. A creature on a plane sees lines. We live in three spatial dimensions and see surfaces — the retina is a two-dimensional sheet, and every visual experience anyone has ever had is a two-dimensional projection. Nobody has ever seen a volume. We infer volumes by moving around, by having two eyes set slightly apart, by memory. A four-dimensional creature would see volumes as directly as we see surfaces.

Rule two: anything sealed in N dimensions is wide open from N + 1. A line segment imprisons a creature on a line, and anyone with a second dimension simply steps over it. A drawn circle imprisons a creature on a plane, and we reach in from above without crossing the line at all. A locked safe imprisons us; a four-dimensional creature lifts the contents out without the safe ever being opened.

Climbing the ladder

On a plane, a Flatlander sees other shapes as line segments. It cannot see inside a circle, cannot see its own insides, and to learn the shape of a square it has to travel around the square and assemble the answer from memory.

Now let a sphere pass through the Flatlander’s plane. What the Flatlander experiences is a point appearing out of nowhere, swelling into a circle, shrinking back to a point, and vanishing. Nothing in that resembles a sphere. The sphere was there the whole time, entire; the Flatlander only ever met its cross-sections, one at a time.

Everything else follows by moving one rung up.

So a four-dimensional creature could see every one of your organs at once, in full, with your skin nowhere in the way — and could touch your heart without breaking that skin, exactly as a surgeon from our world could operate on a Flatlander’s stomach by reaching in from above, leaving the outline of their body unbroken.

It could also pick up your left glove, rotate it through the fourth direction, and hand it back as a right glove. That sounds like a conjuring trick, and it is precisely the trick we perform on flat things constantly: a letter b printed on a page can never be slid across the page into a d, but lift it off, flip it, set it down, and a d is what you have. Left and right hands are the same object viewed from opposite sides of a dimension we do not possess.

And a four-dimensional object passing through our space would look to us the way the sphere looked to the Flatlander — something appearing from nowhere as a point, swelling into a full solid shape, changing, shrinking, and vanishing.

The version where the extra dimension is time

That ladder was built entirely out of space. The version this article is really about is different.

Our spacetime is three of space and one of time. A being that treated time the way we treat a spatial direction would not see you as a body at all. It would see your whole life at once as a single object: a long tapering shape with an infant at one end and a corpse at the other and every intermediate moment present along its length. Your worldtube.

It would not watch you age, because watching requires a sequence and it has none. It would examine your life the way we examine a sculpture — any part, in any order, the whole thing simply there. There would be no now for it, in the same way there is no privileged inch on a sculpture.

That picture is coherent, and it is the honest visual form of the block universe. Where it stops being physics is the point made above: moving about in time that way requires a second time dimension, and second time dimensions bring closed timelike curves between every pair of points and abolish the distinction between future and past.

Five, six, and the honest limit

Past this point imagination outruns physics, and it is better to say so than to supply a confident scheme.

Mathematically a fifth dimension is nothing more exotic than a fifth independent direction — one that no combination of the other four can reach. By rule one, a five-dimensional being would see four-dimensional images. That is genuinely all that can be said with confidence.

If you want the time-flavoured version, the usual imaginative move is that a fifth direction lets you travel between whole spacetimes: not merely your entire life at once, but every possible version of it laid side by side, with freedom to move among them. A sixth would be another such direction. That is imaginable, and it is not established physics — the widely circulated schemes assigning specific meanings to the fifth, sixth and seventh dimensions (possibility, choice, and so on) are invention rather than results, and are worth treating as such.

What extra dimensions actually are in physics is more modest and more surprising. String theory’s ten or eleven dimensions are nine or ten of space and exactly one of time, the extra spatial ones curled so small that nothing moves through them appreciably. Braneworld models allow one large extra spatial dimension, but only gravity reaches into it. Across all of it the count of time dimensions stays at one. Nobody in serious physics is proposing a being that steps outside time. They are proposing extra room in space.

Every proposal here was about the arrow of time

Strip away the specifics and every proposal here is one proposal. Each tries to source the difference between past and future from somewhere other than the contents of our universe — from the time-symmetry of the field equations, from the randomness of thermal radiation, from a force reversing sign, or from a vantage point above the whole thing.

Four routes, one wall. A four-dimensional being looking down at our spacetime would see one smooth end and one lumpy end, and black holes forming toward the lumpy one. The asymmetry is in what is being looked at, not in the looking, and no change of vantage alters it. And it is not there. Symmetric laws cannot produce an asymmetry, and randomness cannot produce the most special initial condition in the universe.

The arrow of time lives in the boundary condition. The universe began in an extraordinarily low-entropy state, and everything that distinguishes the past from the future — why eggs break and never unbreak, why black holes form and white holes do not, why the universe grew lumpy rather than smooth — is that one fact being spent down.

That is also why white holes are not, strictly speaking, forbidden. No law prohibits one. They are excluded the same way an unbreaking egg is excluded: nothing in the dynamics rules it out, and everything about how our universe actually started means it does not happen.

There is a genuine irony at the end of this. The one event in the history of the universe that does look like matter pouring out of a singularity — a past singularity, with everything emerging from it and nothing able to enter — is the Big Bang itself. It is not a white hole in the technical sense; its singularity has a different geometric character, spread across all of space rather than sitting at a point in it. But the reason white holes are impossible everywhere else is the low-entropy past, and the low-entropy past is the Big Bang. The thing that rules them out is the closest thing to one that ever existed.

What this leaves open

• Why the initial condition was low-entropy at all. This is unsolved, and it is the actual frontier both questions were circling. Inflation explains how a small smooth patch becomes a large smooth universe, but Penrose and others argue it presupposes rather than explains the low-entropy starting point, since inflation itself requires special initial conditions to begin. There is no consensus.
• Whether the record asymmetry is fully explained. The argument that an observer’s memories must point toward the low-entropy end rests on the Past Hypothesis — the posit that the universe began in a very low-entropy macrostate — combined with assumptions about the initial probability distribution. David Albert and Barry Loewer’s development of this is the standard account, and it is not universally accepted. If it is wrong, the question of which directions can host observers reopens.
• Being inside a black hole, rather than downstream of one. Nikodem Popławski’s work proposes that torsion — a twisting of spacetime sourced by the spin of matter — halts gravitational collapse before a singularity forms and produces a bounce, so that the interior of every black hole is a new expanding universe. This is a live idea and it is close to the second proposal in spirit, but the mechanism is different in a way that matters: the matter comes from the collapse, arriving hot and dense, not from the radiation, arriving cold and dispersed.
• The end of one universe as the beginning of the next. Penrose’s Conformal Cyclic Cosmology takes the far future — every black hole evaporated, nothing left but massless radiation — and identifies it, after a rescaling of size, with the Big Bang of a new aeon. This is the closest serious version of “Hawking radiation becomes a universe.” It remains a minority position; how to fix the rescaling uniquely is an unsolved problem, and its claimed observational signatures are contested.
• White holes at the Planck scale. Carlo Rovelli, Francesca Vidotto and collaborators argue that quantum gravity may let a black hole tunnel into a white hole at the end of evaporation, and that the resulting remnants — stabilized at around the Planck mass, below which loop quantum gravity permits no hole at all — could constitute part of dark matter. If that is right, white holes exist after all, just nothing like the macroscopic ones the classical equations describe.
• Whether Hawking radiation is exactly thermal. The entropy argument above leans on it being featureless. The black hole information paradox is precisely the question of whether that is literally true, and it is not settled.

Sources

• Death of White Holes in the Early Universe — Eardley, Phys. Rev. Lett. 33, 442 (1974) — the exponential instability converting white holes into black holes
• Death of white holes — Blau, Phys. Rev. D 47, 2383 (1993) — refinement attributing the death to accreting material rather than the blueshift divergence
• Maximal extension of the Schwarzschild metric (arXiv:2005.14211) — the four Kruskal–Szekeres regions, and that no gravitational process realizes regions III and IV
• Hawking temperature and evaporation time references — the inverse-mass temperature relation and the cubic evaporation lifetime
• The Cosmic Microwave Background Spectrum from the Full COBE FIRAS Data Set and COBE — Scholarpedia — blackbody fit to 50 parts per million, isotropy to 10 parts per million after removing our motion
• A Larger Estimate of the Entropy of the Universe — Egan & Lineweaver (arXiv:0909.3983) — CMB entropy 2.03 × 10⁸⁹, observable-universe total 3.1 × 10¹⁰⁴ dominated by supermassive black holes, cosmic event horizon 2.6 × 10¹²²
• On the Weyl Curvature Hypothesis (arXiv:1203.3382) — why low initial entropy must come from geometry, since the matter fields began in thermal equilibrium
• Topological Defects in Cosmology (arXiv:astro-ph/0110285) and Power Spectra in Global Defect Theories (arXiv:astro-ph/9704165) — coherence of the acoustic peaks, and why incoherent random sources are excluded
• The Universe is Not a Black Hole — Sean Carroll — why the observable universe’s mass having a Schwarzschild radius near its own size is a restatement of spatial flatness, not evidence of anything
• Gravitational Collapse with Torsion and Universe in a Black Hole (arXiv:2307.12190) — Popławski’s torsion bounce
• The Physics of Conformal Cyclic Cosmology (arXiv:2503.24263) and Toward fixing a framework for conformal cyclic cosmology — CCC and its unresolved conformal-factor problem
• White-hole dark matter and the origin of past low-entropy — Vidotto (arXiv:1804.04147) and Planck stars, White Holes, Remnants (arXiv:2407.09584) — black-to-white-hole tunneling and Planck-mass remnants as dark matter
• Janus Points and Arrows of Time — Barbour, Koslowski & Mercati (arXiv:1604.03956) — two oppositely directed arrows emerging from a configuration of minimum size
• 2 Futures Can Explain Time’s Mysterious Past — Scientific American — the Carroll–Chen hourglass, with entropy increasing outward in both directions and observers possible on both sides
• Thermodynamic Asymmetry in Time — Stanford Encyclopedia of Philosophy — Gold’s reversing universe, its refutation by Penrose, Zeldovich and Novikov, and Tolman’s earlier objection to the premise
• Time and Chance — Albert, and the record asymmetry literature — why records and memories are anchored to the low-entropy end rather than to a direction of reading
• Observation of Time Reversal Violation in the B0 Meson System — BaBar (arXiv:1207.5832) — direct measurement of T violation in the weak interaction, and why CPT rather than T is the exact symmetry
• Stückelberg–Feynman interpretation of antiparticles — antiparticles as particles propagating backward in time, and its role in the Feynman diagram technique
• CPT symmetry and The genesis of the CPT theorem — why C accompanies T, and why CPT rather than any of its parts is the exact symmetry
• One-electron universe and Feynman’s 1965 Nobel Lecture — Wheeler’s proposal and the electron/positron counting objection
• The Matter-Antimatter Asymmetry of the Universe (arXiv:hep-ph/0207323) and Matter over Antimatter: The Sakharov Conditions After 50 Years — the three conditions for baryogenesis and why Standard Model CP violation is insufficient
• Dark Energy: Mystery of the Millennium (arXiv:astro-ph/0603114) and Dark Energy Antigravity — Perivolaropoulos — why ρ + 3p rather than ρ sources gravitational acceleration, and how negative pressure produces repulsion
• Identification of a Gravitational Arrow of Time (arXiv:1409.0917) and Arrows of time in unconfined systems (arXiv:1602.08019) — complexity as the governing quantity, and arrows arising without special initial conditions
• Gauss’s Theorema Egregium and Riemann’s non-Euclidean geometry — curvature as intrinsic, requiring no higher-dimensional embedding
• Multiple time dimensions and Physics With Two Time Dimensions (arXiv:1001.2485) — closed timelike curves everywhere, ghosts, and the loss of any future/past split
• A Two-Time Universe? — USC Dornsife — Bars’s two-time physics and the gauging away of the extra time
• Brane-World Gravity — Living Reviews in Relativity — matter confined to the brane while gravity propagates in the bulk
• Inflationary Spacetimes Are Incomplete in Past Directions — Borde, Guth & Vilenkin and Geodesic Completeness in General Cosmological Scenarios (arXiv:2604.20809) — the past-incompleteness result and recent challenges to it