Are You A Boltzmann Brain?

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If you’re a Boltzmann brain, then I’m likely a figment of your imagination as you float around in otherwise empty (or at least high-entropy) space, a minimum assemblage of whatever matter or energy is required to generate your thoughts and images. You emerged as a “quantum fluctuation” of particles out of the quantum fields that underlie space itself – your mother was the vacuum (no offense intended). Yes, you were an unlikely fluctuation, but given enough time – and an eternity is more than enough time – you were bound to happen at some point. In fact, at least absent assumptions far more speculative and untested than those of statistical mechanics and quantum physics, it was far more likely that you would emerge as an isolated brain – or whatever assemblage of particles you really are – in infinite space than that the Big Bang would have occurred with just the right properties to give rise to the universe as we observe it.

The idea that you could be mistaken about everything except the fact of your own bare existence as a conscious mind is nothing new. In his Meditations, Descartes developed such a scenario on his way convincing himself that his own mind certainly existed, and hence (along with several controversial assumptions) that a benevolent, omnipotent God must exist, and therefore that our everyday beliefs about the physical world are highly likely to be true (as long as we form them carefully). To make his skeptical scenario psychologically vivid and a worthy antagonist to defeat, Descartes imagined that a malevolent demon might be deceiving him in every possible way. Of course, Descartes recognized that his demon scenario was utterly improbable, but since in his view knowledge had to be built on an absolutely certain foundation, he thought that the mere possibility of such a demon could undermine his previously uncritical faith in his common sense beliefs, and that showing that such a demon could not cause him to reasonably doubt his own existence would go a long way towards establishing a firm foundation for math, physics, and the other sciences. Critics, of course, love to point out that a mere possibility is insufficient to justify a reasonable doubt. It is possible that a mountain of gold will soon emerge in my back yard, but that mere possibility gives me no reason to doubt that I shouldn’t quit my day job just yet. The possibility of a demon similarly can provide no reasonable ground for doubting my common sense beliefs. By contrast, the disturbing aspect of the Boltzmann brain scenario is that our best-tested physical theories actually suggest that being a Boltzmann brain is not only possible, it’s actually more likely – much more likely – than the situation in which we believe ourselves to be.

To explain why we observe a relatively orderly, amenable universe around us, even though a higher-entropy, less amenable sort of universe is far more likely to emerge from the cosmos on purely statistical grounds, we naturalists often appeal to an “anthropic principle”: in an infinite universe, some regions are likely to be more amenable to life than others, and life will quite predictably exist only in those regions where its evolution is possible. But the statistical reasoning that supports the probability of your being a Boltzmann brain also undercuts such appeals to anthropic principles. Sean Carroll puts this nicely in his book, “From Eternity To Here”-

… Maybe, we might reason [in accordance with an anthropic principle], in order for an advanced scientific civilization such as ours to arise, we require a “support system” in the form of an entire universe filled with stars and galaxies, originating in some sort of super-low-entropy early condition. Maybe that could explain why we find such a profligate universe around us.

No. Here is how the game should be played: You tell me the particular thing you insist must exist in the universe, for anthropic reasons. A solar system, a planet, a particular ecosystem, … whatever you like. And then we ask, “Given that requirement, what is the most likely state of the rest of the universe [given statistical mechanics and quantum theory], in addition to the particular thing we are asking for?”

And the answer is always the same: The most likely state of the rest of the universe is to be in equilibrium. If we ask, “What is the most likely way for an infinite box of gas in equilibrium to fluctuate into a state containing a pumpkin pie?,” the answer is “By fluctuating into a state that consists of a pumpkin pie floating by itself in an otherwise homogeneous box of gas.” Adding anything else to the picture, either in space or in time – an oven, a baker, a previously existing pumpkin patch – only makes the scenario less likely, because the entropy would have to dip lower to make that happen.

It’s important to emphasize that Carroll’s point here isn’t to argue that we should in fact believe that we are Boltzmann brains, but rather to provide a sort of reductio ad absurdum of the limited set of assumptions and theories that lead us to that conclusion. Still, upon finishing Carroll’s book, which avoids the Boltzmann brain conclusion only by indulging in some extremely tentative cosmological speculations, it’s hard to simply dismiss the possibility that we are, in fact, Boltzmann brains.