How do you know you’re a person who has lived your life, rather than a just-formed brain full of artificial memories, momentarily hallucinating a reality that doesn't actually exist? That may sound absurd, but it’s kept several generations of top cosmologists up at night. They call it the Boltzmann brain paradox.
Its namesake, Ludwig Boltzmann, was a 19th century physicist operating in a period when scientists were passionately debating whether the universe had existed for an infinite or finite time. Boltzmann’s main claim to fame was revolutionizing thermodynamics, the branch of physics that studies energy. He put forward a new interpretation of entropy, which is a measure of the disorder of a system.
A glass is an ordered system, whereas a shattered glass is disordered. The second law of thermodynamics states that closed systems tend towards disorder: you won’t see a shattered glass return to its pristine state. Boltzmann’s insight was applying statistical reasoning to this behavior.
He found that a system evolves to a more disordered state because it’s more likely. However, the opposite direction isn’t impossible, just so unlikely that we’ll never witness things like scrambled eggs turning raw. But if the universe exists over an infinitely long time, extremely unlikely events will happen, including complex things forming out of random combinations of particles.
So what does that look like in a hypothetical infinitely old universe? In this unremarkable stretch of near-nothingness, about eight octillion atoms randomly come together to form a replica of the Thinker made of pasta. It instantly dissolves.
Over here, these particles suddenly form something like a brain. It’s filled with false memories of a lifetime up to the present moment, when it perceives a video saying these very words, before decaying. And finally, by random fluctuations, all the particles in the cosmos concentrate in a single point, and an entire new universe spontaneously bursts into existence.
Of those last two, which is more likely? The brain, by far— despite all its complexity, it’s a blip compared to an entire universe. Every one universe produced by random fluctuations has equivalent odds to heaps upon heaps of insta-brains.
So by this reasoning, it seems extremely more likely that everything you believe to exist is actually a brief illusion, soon to be extinguished. Boltzmann didn’t get quite that far in his thinking; the brains themselves were introduced by later cosmologists building on his work. But they, like just about everyone else, were pretty sure that they themselves weren't just ephemeral brains.
So the paradox was: how could they be correct and the universe be eternal? The resolution is something most take for granted today: that our universe has not existed forever, but rather time and space started with a Big Bang. So that’s the paradox over and done with, right?
Well, maybe not. In the last century, scientists have found evidence supporting the theory of the Big Bang everywhere we look. Yet while we know that the Big Bang happened, no one knows what, if anything, preceded and caused it.
Why did the universe begin in such an extremely ordered, and unlikely, state? Is our universe in an unending cycle of creation and collapse? Or might we be in one of many universes expanding within a multiverse?
In this context, Boltzmann’s paradox has found renewed interest by contemporary cosmologists. Some argue that leading models for where the universe came from still imply that Boltzmann brains are more likely than human brains, suggesting something’s amiss. Others counter that slight modifications of the cosmological models would avoid the problem, or that Boltzmann’s brains can’t actually physically form.
Some researchers even attempted to calculate the probability of a brain popping out of random quantum fluctuations long enough to think a single thought. They got this incredible number whose denominator is 10 to a number about a septillion times larger than the number of stars in the universe. The Boltzmann brain paradox, despite its absurdity, is useful because it creates a bar that models have to rise to.
If, compared to numbers like this one, the current state of the universe is exceedingly unlikely, something in the model is almost certainly wrong. Unless you’re the one who is wrong. .
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