Cosmic Invariance

If the universe is truly cyclic in nature, does that mean its evolution is as well? In cyclic cosmologies, the universe expands from a singularity and evolves, mostly according to Newton's laws of motion (let's leave quantum effects out of the picture for now). From the starting singularity, there's a burst of energy and expansion. As particles expand outward, they come into contact with one another - they trade energies, repel, coalesce with new momentum and continue on their way. In this respect, the analogy of a game of pool is very apt. Think of the starting singularity as the initial break and the subsequent motions and interactions all under the control and guidance of Newtonian mechanics. If you knew the exact position and momentum of each and every particle, you could figure out where any one would be and what it would be doing a billion or one hundred billion years from now. In short, the universe is deterministic and clockwork for the most part. Furthermore, and more to the point of this post, the universe appears to be a closed system like a box of gas or a pool table with balls in motion on it.

Henri Poincaré. Note the spiffy glasses and awesome beard.
Why did I shave?

In the late nineteenth century, mathematician Henri Poincaré, as part of an attempt to solve the infamous "three body problem" (in short, how three objects would move under the influence of mutual gravitational pull) stumbled upon something he called the Recurrence Theorem. This was the heyday of statistical mechanics and Boltzmann's descriptions of entropic forces and the evolution of closed systems was in many ways the central focus of physics. What Poincaré discovered, put simply, was that if you started a closed system (one free of outside physical influence) in any particular configuration and let it evolve according to Newton's laws of dynamics (motion), and if you had an infinite amount of time to wait and observe, that system would eventually return to its initial configuration, not just once, but over and over again. The fewer the components you have the shorter the recurrence time would be and the more you add, the longer you'd have to wait. The universe is home to more particles than can possibly be imagined, so the recurrence time would be huge - but if the universe is really eternal (and closed), it is virtually guaranteed to return to its initial state and evolve precisely along the same lines all over again.

Think about what that means for a moment. Every single event in the history of your life, in the history of the universe, would be bound to repeat itself, over and over and over again - with no variation within those particular evolutions. How long would we have to wait for one recurrence time for the universe? A box with sixty particles in it has a recurrence time of the present age of the universe. In other words, it would take a box of sixty particles nearly 14.7 billion years to return to its initial configuration, statistically speaking of course. By comparison, a typical macroscopic object, made up of much, much more than sixty measly particles, has a recurrence time would be 10^{1,000,000,000,000,000,000,000,000} seconds. (Carroll, 205-206).

The idea of recurrence seems much more profound than mere fate. A typical determinist may look at the universe and say, "Well, it's all in motion like a train and cannot be stopped." Life unfolds, the universe evolves and there's no tampering with it. It's almost like a movie playing itself out, but that analogy isn't quite right because it's as if we, the observers are part of the movie too. Our reactions to it, indeed, even whether we recognize it as such, has already been determined as part of the story. But if Poincaré is correct, and he is mathematically, if not physically, then it's a movie on repeat - a disc stuck in a dvd player, but you'd never recognize it as such. If a cyclic cosmology is correct and the universe indeed goes through expansion and contraction phases infinitely into the future with a sort of bounce in between, then certainly some, though probably not all, of the expansions may create histories that look exactly like our own, given we wait long enough. The life you experience now may be the very first of a series of repetitions you can do nothing about or control - or, it could be the 1,000,913,456th. It may happen all over again in the very next cycle the universe goes through, or it may take another ninety evolutions, but here you'd be all over again - with the same joys and frustrations, accomplishments and failures.

Even more interesting: in an endlessly cycling universe there are bound to be cycles where the history or evolution is dramatically different. Ones in which no sentient life forms exist or evolve at all, for example. Or, it could have evolutions that are quite similar, but subtly different (from a cosmic perspective at least). There could be alternate histories and evolutions where Hitler was never born (a favorite for alternative history science fiction fodder), or where you were born in another country, to another set of parents (but would it still be you?). All it would take is the subtle displacement of a single hydrogen atom or a change in vector of a single electron to change the whole subsequent history of the universe, giving birth to different realities and different histories each time the universe expands anew.

Could you be born into a family of Wookies because an electron
zigs instead of zags in the next expansion cycle of the
universe?

Is it true? Are we doomed (or blessed) to live the lives we have now forever? For truly any other evolution, no matter how slightly different, would result in an us that is not us and therefore different. This reality is all that we have. Well, there's a couple of snags that complicate Poincaré's picture:

1. What we know of quantum mechanics seems to suggest that there is an inherent level, not of randomness, but probability to reality itself. Virtual particles pop into and out of existence, leaving their mark, no matter how subtle in a myriad ways - causing black holes to evaporate or contributing to mysterious macroscopic behaviors like the Casimir Effect. In short, ephemeral instability and unpredictability have a subtle effect on macroscopic objects and their motion or movement. If such events truly are part of the fabric of reality, they would perpetually disturb the motion of electrons and other subatomic particles and alter the history of each subsequent expansion or history. Would it still be possible for the same evolution to occur, down to the same perturbations? Maybe. Probably, given that you had an infinite amount of time to sit around and wait, but the recurrence time would be even more monstrously huge.

2. On a more concrete level, we know that the universe is expanding. Leave aside whether or not the universe is indeed closed or open, or if we're one pocket universe nestled in a multiverse of other universes - cosmologists know that objects in the universe are moving away from one another. Not only that, but they're doing so at an accelerating rate. In short, that's bad news for cyclic cosmologies. When is contraction going to occur? By what means? It seems like expansion will continue into the future unchecked, stretching the particulate matter of the universe into a thin gruel spread over even more unimaginable distances. It's hard to imagine a spontaneous contraction that would reverse then start the cycle all over again. It seems far more likely that the universe will suffer entropic heat death and it'll all end in a Big Freeze.

3. Even more basically, cyclic cosmologies may be inherently incorrect, the reason stated in point #2 being just one flaw of such theories (see earlier posts).

4. Even among those who embrace cyclic cosmologies, like Roger Penrose, there are those (again, like Penrose) who believe that events in one expansion cycle effect events in the next. Penrose believes that events in the previous cycle have left imprints on the Cosmic Microwave Background that are visible today. Those imprints, speculated to be caused by supermassive black holes near the end of the contraction of a previous cycle, surely would affect the motion of particles in this expansionary phase. In short, there is no repetitive, or recurring cycle as events in one cycle have specific effects on the next.

Granted, I'm no expert, but I tend to think that while recurrence is a pretty thought-provoking and amazing idea to think about, it has no strong scientific backing. Poincaré's math is solid. If you really did have a closed system and we only considered Newtonian physics, recurrence would occur. Unfortunately (or fortunately), I don't think the universe is quite as neat or simple as a box of gas.

Carroll, Sean. From Eternity to Here: The Quest for the Ultimate Theory of Time. London: Plume Books, 2010.