The Sciences

The First Quantum Cosmologist

Cosmic VarianceBy Sean CarrollAug 21, 2008 3:20 PM


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Many of you scoffed last week when I mentioned that Lucretius had been a pioneer in statistical mechanics. (Not out loud, but inwardly, there was scoffing.) But it's true. Check out this passage from De Rerum Natura, in which Lucretius proposes that the universe arises as a quantum fluctuation:

For surely the atoms did not hold council, assigning order to each, flexing their keen minds with questions of place and motion and who goes where. But shuffled and jumbled in many ways, in the course of endless time they are buffeted, driven along, chancing upon all motions, combinations. At last they fall into such an arrangement as would create this universe...

Lucretius, along with Democritus and Epicurus, was an early champion of atomism -- the idea that the tremendous variety of substances we see around us arise from different combinations of a few kinds of underlying particles. He was also a materialist, believing that the atoms obeyed laws, not that they received external guidance. So a problem arose: how could all of that regular atomic motion give rise to the complexity we see around us? In response, Lucretius (actually Epicurus -- see below) invented the "swerve" -- an occasional, unpredictable deviation from regular atomic behavior. And then, he points out, if you wait long enough you will swerve your way into the universe. It's a good idea, and one that has been re-invented since then. Boltzmann, another famous atomist, hit upon the same basic scenario. Here is Boltzmann in 1897:

There must then be in the universe, which is in thermal equilibrium as a whole and therefore dead, here and there relatively small regions of the size of our galaxy (which we call worlds), which during the relatively short time of eons deviate significantly from thermal equilibrium. Among these worlds the state probability increases as often as it decreases. For the universe as a whole the two directions of time are indistinguishable, just as in space there is no up or down. However, just as at a certain place on the earth's surface we can call "down'' the direction toward the centre of the earth, so a living being that finds itself in such a world at a certain period of time can define the time direction as going from less probable to more probable states (the former will be the "past'' and the latter the "future'') and by virtue of this definition he will find that this small region, isolated from the rest of the universe, is "initially'' always in an improbable state.

Boltzmann imagines the universe as a whole (or what we would call the "multiverse") is in thermal equilibrium, about which he knew a lot more than Lucretius. But he also understood that the Second Law was only statistical, not absolute. Eventually there would be statistical fluctuations that took the thermal gas and turned them into something that looks like our universe (which, as far as Boltzmann knew, was just the galaxy). We are now smart enough to know that this kind of scenario doesn't work, at least in its unmodified form. The problem is that fluctuations are rare, and large fluctuations are much more rare; a universe-size fluctuation would be rare indeed. Who needs 100 billion galaxies when one will do? Or even just one observer? This objection was forcefully put forward by none other than Sir Arthur Eddington in 1931:

A universe containing mathematical physicists [which is obviously the correct anthropic criterion -- ed.] will at any assigned date be in the state of maximum disorganization which is not inconsistent with the existence of such creatures.

These days, we throw away the rest of the mathematical physicist and focus exclusively on the cognitive capacities thereof, and call the resulting thermodynamic monstrosity a Boltzmann Brain. The conclusion of this argument is: the universe we see around us is not eternal in time and bounded in phase space. Because if it is, over the long term we really would just see statistical fluctuations, and we would most likely be lonely brains. So either the universe is not eternal -- so that it doesn't have time to fluctuate ergodically throughout phase space -- or its set of states is not bounded -- so that it evolves forever, but doesn't sample every possible configuration. Sorry about that, Lucretius. You'll be happy to know that we're still struggling with these same issues. Except that you're dead and famously railed against the irrationality of belief in life after death. So probably you don't care.

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