The laws of physics are, in general, time-reversible*, and the only thing that creates our apparent arrow of time is the direction of increasing entropy. This, for human experience and cosmic evolution, anyway, is because all the processes by which we experience the passage of time—our movement, our growth, our aging, the laying down of memories in our brains and our computers and our books, as well as the formation and evolution of galaxies, stars, planets, and the like—all depend upon, and are driven by, the increase in overall entropy via the exchange of energy from areas of local concentration. dispersing into less organized, less useful energy, usually in the form of “heat”. Thus, the prediction of the “heat death” of the universe, when, in the fullness of time, entropy overall throughout our universe is in its maximal state, at which point, the notion of time—or at least of its passage—will become nonsensical.
Time, however, in General and Special Relativity, is not just a thing that we experience passing, whether in one direction or another. It is, in fact, a real dimension, the fourth dimension of spacetime, and according to Relativity, the very sense of the passage of time is in fact an illusion, though—as Einstein noted—it is a persistent one. All of time is already and still in existence, so to speak. (I’ve discussed this notion playfully before.)
The only reason we experience an evolving cosmos at all is that 13.8 billion years ago (or thereabouts), something produced a state of universal low entropy—this was possibly an inflaton field that spontaneously changed phase and dropped to a lower energy level, converting all its stored energy into the various types of particles and energy that eventually became everything we see around us.
But if spacetime is a block—with a time dimension that doesn’t have any inherent directionality, any more than do length, width, and height (they all go on forever in both directions)—then that seems to imply that, from whatever region of spacetime this low-entropy state occurred, the universe should have evolved in both directions in time, so to speak. There’s no reason to think that the entropy would decrease only in our direction, as it were. After all, the predictions of thermodynamics state that any relatively low-entropy region should increase in entropy both going “forward” and going “backward” in time, since the increase in entropy is a description of probabilistic tendencies, and is born of some fundamental mathematics, as well as physics.
If this is the case, then on the other side of inflation—and of whatever caused it, if it happened—there should be another universe, a mirror universe of sorts…though there’s no reason to suspect that it would be a mirror of ours in any literal sense. It might even, for all we know, have different specific constants of nature, though obviously, the fundamental laws of physics—whatever those might be—would of necessity be the same (If they weren’t it would have nothing to do with our universe in any sense). But there should be, on that other “side” of the Big Bang, a cosmos evolving in the “other” direction of time, though any inhabitants and processes within it would just experience it as being time’s forward direction, since that perception is born of the direction of increasing entropy. Some inhabitants there might even wonder about the possibility of another universe on the other side of the Big Bang from them, experiencing the “flow” of time in the opposite direction.
This raises questions about what it might mean for the probability of “future” universes being born long after the heat death of our universe, when random statistical fluctuations bring about a Planck scale existence of inflaton field (assuming that inflationary cosmology is correct), and thus leading to a new universe. Why would such a universe propagate only forward in time? Why would it not propagate backward, “toward” us, as it were? But would it be constrained because of previously existing spacetime, if such a notion has any meaning? Might that inflaton field lead to a universe going in the other direction from us in time, but in our very far distant “future” as it were? Would it “overwrite” parts of our future block of spacetime? Or would it be forced to develop, in a sense, orthogonally to or next to our direction of the “flow” of spacetime? The laws of Relativity allow for stranger warping of spacetime than this, and I’ve read of descriptions of inflationary cosmologies that suggest that such new inflaton fields would pinch off from our spacetime into a new, localized spacetime. Why not? There’s no certainty that time itself only has one dimension. But if it doesn’t pinch off, and future inflation is “constrained” if you will, by the existence of our configuration of spacetime, like growing ice-crystals in supercooled water encountering another front of growing ice crystals, then maybe this is another way in which a kind of “cyclic cosmology” could occur: In the very far distant future, our universe could become the far future of a yet more distant future universe, pointing in the opposite direction in “time”, and if it were possible to travel against that current, continuing in our own “direction”**, one would encounter a seemingly backward-running universe, a rewinding universe—from our point of view—as we would be a rewinding universe from their point of view. This is really no more inconceivable then the fact that a person going out of their driveway onto a street can turn right or left and be going forward to them no matter which direction they choose. I suspect that time would make for a one-lane road, and that universes could not “pass each other on the right” or the left, so to speak…though, again, if time has sideways dimensions and whatnot, or the geometry of spacetime has certain characteristics, this may indeed be possible.
And, of course, if one continued along in that (to us) rewinding universe, one would arrive finally at that new instantiation of the inflaton field, and if one were able to get past it—which I doubt could be done, but we’re imagining a lot of things here—one would find, on the other side of it, a new area of increasing entropy, with time once again going in what we would, from our current point of view, perceive as the “forward” direction. And then, once that local area of low entropy evolved toward its own heat death, perhaps the process would repeat. To be fair, if it can repeat, it would repeat, given endless chances. And it would repeat infinitely many times. Whether such universes abut each other at the outer borders of their heat deaths, or whether each new instance of inflation creates a new, separate “layer” of time, if you will, it could still continue infinitely. I can see no reason to think it would stop.
We’re a long way from knowing with reasonable certainty that inflation even happened—though it’s apparently the best candidate we have for explaining the “bang” part of our Big Bang. But, of course, one doesn’t need inflation specifically, just some source of an “initial”, low-entropy state of our universe, that led to the arrow of time as we experience it. No matter what the cause, there’s no obvious reason (to me) that the increase in entropy could increase in only one direction in time.
It’s an interesting thought, and it can at least help keep all the local, absurd and idiotic events in the human world in perspective. After all, in a hundred Brahma Years, who’s gonna care?
*With the possible exception of the W and Z particles of the weak force and the production of antimatter versus matter, but I’m not well-versed enough in these specific theories to know whether this is enough of a change to make a difference, since my understanding is that, when combined, charge, parity, and time are symmetric.
**I suspect that it would not be possible, as one would be attempting to travel in a direction of what would be, to us, one of decreasing entropy, which would tend to undo our very processes of experience. But I very much doubt there will be anyone around to try it.