Dream a little dream of me

One of the more terrifying concepts to arise out of physics is the idea of the Boltzmann brain.

The Boltzmann brain was first postulated by, and is named after, the Austrian physicist Ludwig Boltzmann, who also discovered the mathematical laws governing entropy.  He was one of several scientists who contributed to the idea of the "heat death of the universe" -- that because of the Second Law of Thermodynamics, eventually the universe will reach a state of zero free energy and maximum entropy.  After that -- quantum fluctuations and random motion aside (more on that in a moment) -- the universe will be a thin, more-or-less uniform, cold fog of particles, in which nothing else will happen.  Forever.

Boltzmann committed suicide at age 62.  I'm almost sure his research had nothing to do with it.

In any case, the Boltzmann brain idea came up when he was pondering the state of the universe following the heat death, which (by current models) isn't going to happen for another 10^100 years, so don't fret if you have unused vacation time.  The question that puzzled Boltzmann most was what got the universe into a low-entropy state to begin with; after all, if you see a ball rolling down a hill, its behavior isn't at all strange, but it leaves unanswered the question of how the ball got to the top of the hill in the first place.  He came to the conclusion that random movement of the particles in the fog could, given long enough, create low entropy regions just by chance.  In fact, given the infinitely long time he postulated the heat death stage would last, any possible configuration of particles would show up eventually.

Interestingly, in the hundred-plus years since Boltzmann came up with all this, scientists are still trying to work out all the implications of this.  A 2004 paper by Sean Carroll and Jennifer Chen looked at the question of how long it would take for a random, uniform, maximum-entropy universe to spontaneously generate a second Big Bang -- and thus a new, low-entropy universe -- through quantum fluctuations and quantum tunneling, and came up with a figure of 10^10^10^56 years.

Boltzmann, though, was more interested in smaller stuff.  He asked an unsettling question: was it possible, through random movement of particles, for them to come together in such a way as to form an exact copy of himself, with all of his thoughts and memories and so on?

His conclusion: once again, given enough time, it's not just possible, it's inevitable.  In fact, calculations have shown that we should expect such "Boltzmann brains" to outnumber all other sentient beings by a vast margin.

[Nota bene: keep in mind that Boltzmann died prior to the discovery of quantum physics; as Carroll and Chen discussed, adding in quantum effects actually increases the likelihood of these kinds of weird, accidental rearrangements.]

Now comes the kicker.  Suppose you yourself aren't an "ordinary" observer, but a "Boltzmann brain" -- a disembodied, and presumably temporary, sentient arrangement of particles, that happened to have the correct configuration to contain all the thoughts, perceptions, and memories you currently have.  Would there be any way for you to know?

The answer is almost certainly "no."  "I am confident that I am not a Boltzmann brain," physicist Brian Greene said.  "However, we want our theories to similarly concur that we are not Boltzmann brains, but so far it has proved surprisingly difficult for them to do so."

It bears mention that there could be some caveats here that might save us from this rather terrifying possibility.  Current studies of dark energy and the cosmological constant have a significant bearing on the ultimate fate of the universe.  If, as some recent research suggests, the strength of dark energy is decreasing over time, we might be in a universe destined not for heat death, but for a collapse that could reset the entropy content -- and, possibly, a subsequent rebirth.  But that is still very much uncertain, and the majority of physicists are still of the opinion that the expansion is going to continue indefinitely.

Boltzmann Brain World, here we come.

The topic comes up because scientists are still debating the implications of this -- and many of them trying to rule out the Boltzmann brain concept because it's so damned unsettling.  Just last week, there was a paper in the journal Entropy by David Wolpert, Carlo Rovelli, and Jordan Scharnhorst, called "Disentangling Boltzmann Brains, the Time-Asymmetry of Memory, and the Second Law," which considered the fact that just about all physical laws are time-reversible, yet our memories seem not to be.  This is, however, exactly what we would expect if we were Boltzmann brains, because if that were true, memory itself would just be an illusion, a present-moment effect caused by the random configuration of particles that give the ephemeral sense of a past.  Here's the passage from the paper that rocked me back on my heels:

Reasonable as the arguments just presented might be, in the abstract, how, concretely, can they hold?  How could we have all of our human memories concerning the past be fallacious?  How could entropy increase into our past rather than decrease, as required by the time-symmetric nature of all derivations of the Second Law that are consistent with the microscopic laws of physics?  How could it be that our memories are wrong? 

Such flaws in our memory would require some exquisite fine-tuning, that all the neurons in our brains happen to be in the state corresponding to particular memories, when in fact nothing of the sort is true.  Amazingly though, standard arguments of statistical physics tell us that it is almost infinitely more likely for this to be the case, rather than for entropy to continue to decrease into our past, as demanded by the Second Law.

I read this three times and I shuddered every time.

Thanks bunches, Boltzmann.  I'm sure I'll sleep just fine tonight.  If I actually exist, that is.  [Image is in the Public Domain]

So it can't be rigorously ruled out that we're disembodied brains in an entropic sea, dreaming a little dream of being people.  In this formulation, the Second Law of Thermodynamics is, in fact, time-reversible; entropy increases both into the past and into the future, even if our illusory memories make it seem like that isn't true.  We arose from random fluctuations, and flutter about for a while thinking we're real, then after a few moments subside back into the fog again.

And on that wonderful note, I'll leave you.  If you need me, I'll be hiding under my blankie, hugging my teddy bear.

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