Note: I referred several times in this blog post to the idea of entropy "increasing forever", when of course it does no such thing. What I meant to refer to was an inflationary cosmology. I knew I would get some technical details wrong, and worse yet, my other fear -- that this post is redundant -- also seems to be true as well: Carroll tackles a similar scenario just a few pages later in Eternity than where I was when I wrote this. Still, there is some difference: Carroll is arguing that a non-inflationary universe is in contradiction with our observations; whereas I am pointing out that even if, in a misguided attempt to salvage the universe from a future of eternal emptiness, we invoke the anthropic principle to wave away the problematic observations, the universe we find ourselves in is far worse than one which ends with eternal emptiness. Carroll is saying, "This can't be true," while I am saying, "Even though we might fool ourselves into thinking otherwise, we really don't even want this to be true."
Well lookie here, Sean Carroll noticed my preliminary comments about From Eternity to Here, and he blogged about it. I am frankly honored, a bit star-struck even -- though if I'd known this would happen I wish I had put more time into that post! Sean's response in a nutshell seems to be, "Maybe it's a fair cop, but it's difficult to see any way to do better." I think I agree with that. I still think that a reader for whom this book is her first exposure to relativity and quantum mechanics (and logarithms, yeesh) is not going to follow a lot of it... but a lot of the review material is welcome anyway. Good popular science writing is immensely difficult, and Eternity is a truly stellar example of it. I really can't recommend this book enough!
I'm still not quite to the end of the book (I'm a little over 75% of the way through), so perhaps my thinking in this post is wrong-headed, or possibly redundant... but in any case, I think this book has incidentally given me a somewhat more positive view of the heat death of the universe.
Let's face it, the idea that the universe will end not with a bang, not even with a whimper, but with a gradual diffusion into a sea of unstructured particles is downright depressing. Making it worse is the idea of proton decay, a concept that was introduced to me by the light and fun book Death from the Skies. ("Don't be a dick", Phil? Maybe you could start by not telling me the most fucking depressing fact in all of cosmology... dick!)
But I am beginning to think that, if we really take seriously the conclusions of entropy and statistical dynamics, a universe in which we did not expect the arrow of time to point monotonically and irrevocably from the Big Bang towards heat death is even worse.
I am thinking back to what Sean Carroll refers to as the "Boltzmann-Lucretius scenario" (naming it jointly after the brilliant physicist and the renowned poet and philosopher, as each suggested a similar idea about infinite random recurrences of the universe). In this scenario, the universe as we know it, with it's apparent low entropy state, is the result of a random fluctuation from a high entropy state in an eternal universe. The Poincaré recurrence theorem implies that, in an eternal universe of flat spacetime, it is not just possible but inevitable that every possible state will eventually be arrived at by random chance -- including the exact state of the universe in which we find ourselves right now.
Carroll handily disposes of this idea, pointing out that there are all sorts of features we would expect to see in such a random fluctuation which we do not in fact see in our universe; and that, conversely, the features we do see are far more consistent with the idea of our universe having evolved from a low entropy boundary condition.
But hold on there for a moment, let's not just leave it at that. Let's say we have indeed convinced ourselves that the Big Bang really was a low entropy boundary condition, and that this explains the arrow of time (what Carroll calls "the Past Hypothesis"). Yet, having accepted that conclusion -- and therefore having at least nominally disposed of the Boltzmann-Lucretius scenario -- now let's also say that, since we find the idea of the universe dissipating into a uniform quantum soup to be distasteful, we've convinced ourselves that we ain't going out like that. We started out from a low entropy boundary condition called the Big Bang, which defines the arrow of time for us, but we'll eventually settle into a flat universe, where, although the average entropy remains constant, "stuff can still happen". The alternative is too depressing, right?
The second part of that hypothesis may be just wishful thinking, but even still, we ought to be careful what we wish for... because if I'm not mistaken, the consequences of such a universe are epistemologically devastating. Our dear frenemy Poincaré (don't be a dick, Poincaré!) has proven that, even if we accept that there was at one point a nice orderly universe which evolved naturally from a low entropy boundary condition to a state of high entropy, if we don't allow the entropy to keep increasing indefinitely then there would then follow an infinite series of universes that only seemed to have started from a low entropy boundary condition, but really they were merely random departures from equilibrium.
Even if we believed there had been one very nice existentially satisfying Big Bang-bounded universe, the most parsimonious explanation for our current situation would be Last Thursdayism. Sure, it looks like we are living in that very special and orderly "first universe" possessing a nice clear arrow of time leading from a low entropy big bang to a high entropy "future"... but it's far more likely we are in reality in one of the infinite number of "later" universes which happened to randomly fluctuate into a state that just sort of "looked like" it came from a Big Bang.
Except it's even worse than that. Since, in such a universe, all history is an illusion, there is no way to lean on inductive reasoning in order to predict what will happen at any other moment in time. In such a reality, the most parsimonious explanation for the sensations we are experiencing at any given instant in our lives is that we came into being only a picosecond "ago" due to a random fluctuation of the eternal equilibrium end state of the universe, and we will cease to exist a picosecond "later". Sure, we might be in one of the many universes which are evolving from a random low entropy fluctuation that occurred Last Thursday, putting us in a state that approximated a particular Thursday in the "first universe"; but it's inconceivably more likely that we are in a much more local deviation that simply created the illusion of all of that for one infinitesimal moment. It is a nigh certainty that nothing you see is real; with overwhelming probability, you are nothing more than a Boltzmann brain that perceived for an instant the illusion of being in that special "first universe", and then evaporated an instant later.
So yeah, the fact that an expanding universe allows entropy to increase indefinitely sounds depressing... maybe it is a bit depressing... but the alternative is far, far worse. In a universe that will at some point reach a state of eternal thermal equilibrium, with the accompanying random fluctuations into low entropy states, nothing is knowable, nothing can be believed. The heat death of the universe makes me sad, but if it weren't inevitable then the only logically defensible world view would be nihilism.
Nunes said it was a “judgment call”
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