I had planned to write this follow-up to this thread, and drafted some of it, before I knew Roger Penrose was nominated for the Nobel Prize for Physics. There's some overlap, and I had cited some of his work, which is fortuitous.

In the above thread, I laid out a defence of determinism against Copenhagenists based on the following:

• most fundamental processes are reversible
• the universe of special relativity should properly be thought of as a 4D space
• relativistic wave equations have both retarded and advanced solutions
• the proper boundary conditions for a particle are its creation and annihilation
• only the conjugations of retarded and advanced wavefunctions are (quite literally) real (the transactional interpretation of QM)
• while the trajectories of a single body treated this way are numerous, the rest of the universe will generally act to eliminate them (self-consistent histories)

The above really only applies to the electromagnetic universe. There are some phenomena, such as some nuclear decays, that are irreversible. These I won't treat here. I don't actually have any clue about how I'd go about that, and I'm not particularly averse to the universe being only mostly time-symmetric, which it is in the standard model.

Thermodynamics and cosmology are more interesting because we associate an arrow of time to them: entropy increases with time; the universe expands with time. Penrose is one of many theorists who have concluded that they are the same arrow of time. A steady state universe in thermal equilibrium everywhere would have neither arrow; if that universe suddenly expanded, it would have both arrows aligned.

Just a quick point on thermodynamics specifically: all of the laws of thermodynamics are derivable from standard quantum mechanics. (Indeed, this is how we learned statistical mechanics at my university.) And all of standard QM deal with reversible processes as described in my previous thread (creation, annihilation, and movement). So the fundamental mechanics involved in thermodynamics have no such arrow of time, rather it is the starting conditions of systems that drives entropy increase.

The ultimate ordered starting condition is the singularity at the big bang, wherein all matter now in the universe was contained in a single point. As the universe expanded (the cosmological arrow of time), the distribution of matter expanded with it (the thermodynamic arrow of time).

There is a similar but backwards event in the universe: the black hole. A black hole is also a singularity, but all of matter is drawn in toward it rather than expands away from it when viewed in the normal way. The big question of black hole thermodynamics is: what happens to entropy? Bringing distributed matter to a single point is an ordering process: it decreases entropy! However, any entropy-increasing byproduct of this ordering process also cannot escape the black hole. Some options:

• black holes reduce the amount of matter in the universe, therefore increase the number of possible configurations of matter in the universe by increasing the volume to density ratio;
• black holes retain the matter they order, but increase the total entropy of the universe as it does so;
• black holes pay the entropy back in the future;
• black holes reverse the arrow of time.

The first would breach a lot of conservation laws. Hawking put forward the idea that black holes obey conservation laws over multiverses, not individual universes. I put this in for completeness.

Hawking radiation and the holographic principle might implement the second. As the mass of the black hole increases, the event horizon gets larger, and the amount it radiates also increases. The event horizon is considered a measure of the entropy of the black hole, while radiating energy through work is also an entropy-increasing process. However, the amount of Hawking radiation expected from even a supermassive black hole (SMBH) is extremely small: it is estimated it would take $10^{106}$ years for the largest (super-duper-massive?) black holes (SDMBH) to radiate to nothing. Further, entropy is effectively being redefined here: it is the sum of standard entropy plus this additional event-horizon--dependent term that is increasing with time, which isn't compelling cookery.

Penrose proposes the third. He is an apostle of the conformal cyclic cosmology in which every aeon of a universe that begins with a big bang ends with a SDMBH which then radiates into a new aeon. I btw am not, but the mad bastard has a Nobel prize now and I haven't got mine yet. I'm no cosmologist (shoulda opened with that really) and won't claim to completely understand it, but as far as I can tell it does not locally increase classical entropy either. Instead, entropy is increased as the SDMBH Hawking radiates in the form of photons and, due to the fact that the proper time of photons is zero, no matter how long this takes this energy is essentially focused onto a single future event: the next big bang, at which point there's a massive entropy increase.





I'm going to argue for the fourth. On the face of it, entropy decreases near a black hole, and simply finding something that increases, multiplying it by stuff that yields the right units (which is what Hawking did) and adding it to entropy isn't going to change that.

This means that, near a black hole: 1) the distance between matter decreases, and 2) entropy decreases, which looks like a time-reversed big bang.

Indeed, early cosmological models for the big bang used black hole models with a minus sign: a white hole. White-hole--like (WHL) big bangs haven't been much in favour for a while, although seem to be making a bit of a comeback, and part of the reason is good ol' empiricism. Black holes exert tidal forces which make their mark on the matter around them. The cosmic microwave background (CMB) on the other hand is quite homogeneous (although Penrose believes he has found remnants of older WHL big bangs in the CMB).

Standard models of the big bang also differ from white holes in their event horizon. From outside the event horizon of a black hole, all worldlines terminate at that event horizon (time slows to a standstill), while inside the event horizon all worldlines converge without every meeting (time goes on forever).



This means that, for a white hole, outside the event horizon, all worldlines originate at the event horizon while, inside, all worldlines have origins infinitely far in the past. The standard cosmological model is quite different, in which all worldlines originate from a common event a finite distance back in our past. The event horizon of the standard big bang model also gets smaller as it contains a denser distribution of mass, unlike a black hole whose event horizon increases with density.


(Image from https://www.sciencedirect.com/science/article/pii/S1631070515001310 )
(edited for traceability)

The lack of evidence of tidal forces from a WHL bang is based on the assumption that the universe isn't much larger than the observable universe, and therefore if there was any large-scale structure to the CMB, we would have seen it.



A perfectly straightforward counterargument, then, is that this is not necessarily the case. In fact, there is some debate about whether large-scale anomalies to the homogeneity have already been found (see above). There are no periodic features like this, but if we were looking at only a small portion of the sky, we wouldn't expect to see any. Annoyingly, the only way to know is to wait until the observable universe gets larger, and our past light cone encompasses more of the entire universe from the past.

A fairly recent paper makes the case that, not only should white holes exist in nature, we have already seen them.

A super-duper massive white hole (SDMWH) model of the big bang was by Hellaby in 1987, based on the now-outdated Tolman model describing the now-outdated big crunch terminus. Here, the universe began with a chain of white holes exploding independently and merging to create a single universe. Roger Penrose's latest paper suggests that the afterglow of multiple previous big bangs is evident to 99.98% certainty in the CMB as six hot spots with characteristic angles; in his model, these are each a big bang from a previous aeon, but it's not difficult to see that they might also fit Hellaby's model. There is also a nice time-reversal here of Penrose's idea that the universe will end with one or more SDMBH black holes.

As I said, though, I don't buy Penrose's view of the universe. General relativity is in itself time-reversible, and one expects that to manifest itself in nature. Putting all of the pieces together:

• the cosmological arrow of time is given locally by whether space expands or contracts, i.e. whether it is dominated by big-bang-- or black-hole--like objects;
• the thermodynamic arrow of time is reversible, such that entropy will decrease in the vicinity of a black hole;
• black holes and their time-reversals, white holes, exist, likewise supermassive black and white holes exist;
• the big bang was a super-duper-massive white hole;
• worldlines start at the event horizon of white hole and terminate at the event horizon of a black hole;
• this loosely describes the large-scale structure of the universe.

The above gives a flavour of what a truly reversible universe might look like, and the question must be: is it consistent with empirical evidence. From our point of view (and the only points of view possible in this local part of the graph are those with the same arrow of time as us), the singularity behind us (and to our right) is our big bang: space and time expand from this singularity, matter forms, stars form, black holes form, SMBHs form, galaxies form, SDMBHs form. The latter, a la Penrose, gobble up most of everything in their local region of the universe: we do not need a single SDMBH at the end of time as Penrose does, which is a bit of an ask from the universe.

However, they gobble up more than that which emerges from our big bang (see worldline above either neighbouring SDMBH). To understand how, we switch direction in time. Reversed, our big bang is a SDMBH, and each neighbouring SDMBH is now a SDMWH -- a big bang! Multiple big bangs, in fact, each completely independent of each other, each with worldlines that never meet except at the terminus of a SDMBH they share (our big bang).

These big bangs form SDMBHs, one of which is our big bang, others having worldlines that never meet any worldline in our universe. One might think that these additional SDMBHs in the time-reversed frame will therefore be SDMWHs in our frame of reference, but this isn't really justifiable. Our arrow of time need not be parallel to theirs. Indeed, from Where We Are, it isn't necessary for the arrow of time heading toward a terminal SDMBH to be parallel to ours. From our frame, all worldlines terminate at the event horizon from all possible directions, thus a unique arrow of time is not given... Time stops at the event horizon, not the singularity, hence the worldlines of each singularity lie outside of time in our frame.

What of Penrose's afterglows from previous big bangs? Consistent with general relativity, other black and white holes that are not large enough to destroy or create universes are possible. Black holes have been discovered, and perhaps Penrose's hot spots are previously undiscovered white holes.

The number of terminals is open. Worldlines originate at one singularity and end at another; they are not affected by any other singularity. As such, one could have an infinite number of singularities. Large, small, or infinite, such an arrangement satisfies the condition for the universe to be much larger than the observable universe to allow for WHL big bangs.

Don't take the above image too literally; it is merely an illustration of a principal, not an argument for a particular structure of the universe, or, as it effectively is, the multiverse. The real point of this post is to extend the principle of reversibility to cosmology and thermodynamics.

Is this empirically justified? No, not as is. Recently, astronomers found six entire galaxies trapped by a SMBH. We can consider the time-reversal of this and ask if this is what we expect to see of a white hole, and the answer is obviously not. A white hole, for instance, still has mass and ought to attract matter from outside. But by definition nothing can go beyond its event horizon. And we certainly wouldn't expect a WHL big bang to just quickly spew out galaxies the way this black hole is apparently gobbling them up. One needs to address at least the fact that a true white hole must essentially be an anti-gravity well (or gravity barrier), the opposite to a black hole which is a gravity well.

A more recent paper has argued for a spacetime metric that exhibits this reversal precisely, yielding a gravity that is repulsive for white hole scales and attractive thereafter. As a side note, this is an example of 5D general relativity, another of which is Kaluza Klein theory, my favourite mystery of unproven physical theory in which Maxwell's equations fall out for free, in addition to Einstein's GR equations. Alas the paper says nothing about this.

Gravitational repulsion is an idea that comes up a lot in cosmology, and one empirical observation that may be explained by it is the predominance of matter over antimatter in the universe. This paper argues that this is due to matter and antimatter having opposite stress-energy tensors. After the big bang, which created matter and antimatter in equal measure, the gravitational repulsion between them forced them as far away from each other as possible, resulting in a local, observable universe dominated by one and not the other. In principle, it doesn't seem obvious that this is necessary. Our observations of galaxy clusters are electromagnetic, and galaxy clusters of antimatter would appear identical to galaxy clusters of matter. (For instance, an anti-hydrogen atom consisting of an anti-proton and a positron will have the same photon spectrum as a hydrogen atom.)

Such a self-organisation would lead to net repulsion between matter and antimatter galaxy clusters, which would be a contributor, but not the sole contributor, of the current expansion of the universe (e.g. a dark energy candidate: full article here https://iopscience.iop.org/article/10.1209/0295-5075/94/20001/pdf).

This potentially solves the asymmetry between observed black holes and our big bang. Smaller and super-massive black holes tend to form inside galaxies and galaxy clusters, i.e. they are made of matter or antimatter. Their time-reversed equivalents would not just be white holes but anti-gravity white holes which repel the kind of matter they are emitting from their event horizons. An antimatter white hole (a time-reversed matter black hole) would only be gravitationally attractive to matter and vice-versa. Any white hole that is attractive to matter such as constitutes our galaxy cluster would be an antimatter emitter. In equilibrium, such a hole would be its own anti-hole, similar to that described by Hawking: it would absorb only matter and emit only antimatter.

On the other hand, our WHL big bang (SDMWH) is both a matter and antimatter emitter, just as Penrose's ultimate SDMBH at the end of time must be a matter and antimatter (and black-hole and anti--black-hole) absorber. This obeys the above anti-symmetry: a matter SDMBH would be attractive to matter and repulsive to antimatter but attractive to antimatter white holes (in the same way that an antimatter white hole would be repulsive to antimatter but attractive to matter) and vice versa. Ultimately, whatever is being emitted, there's something that will eat it.



Again, this is not a putative model of how things are so much as an illustration of what the theory says is possible with empirical data in mind. Nor is this anything like a representation of standard models. Cosmology is a problematic field with much dispute around the fundamentals and with notable figures (like Penrose) and notable institutions with open ears (such as phys.org) who are standing or entertaining ideas well outside of the mainstream. It feels like everything is still up for grabs, and so we should be wary of prematurely subscribing to a particular model when the gold standard is so rapidly varying. The news that the universe's expansion is accelerating came not that long ago, and ideas such as anti-gravity, white-hole--like big bangs, periodic or non-repeating boundary conditions, the relationships between arrows of time, matter and antimatter dominance, etc., etc. are still very much on the table in on-going research.

My current inclination, as is probably obvious, is something like the above that both obeys and manifests the time-symmetry of our fundamental theories: general relativity and relativistic quantum mechanics. However, the odds of happening upon an accurate cosmological model, especially one with as many freedoms as above, is slight. It is more the underlying concepts that attract me, ones that do not rely on by-hand introduction of arrows of time into our universe when our best theoretical frameworks demand no such thing.