Damascene Philosophy

Thought ExperimentsXIV

Are you a Boltzmann brain?

Given enough time, random fluctuations could assemble a single brain with your memories out of chaos. In some cosmologies, such brains vastly outnumber real observers.

Reading time
4 min
Difficulty
Deep
Branch
Reality
First posed
Ludwig Boltzmann's fluctuation hypothesis, 1890s; named by Andreas Albrecht and Lorenzo Sorbo, 2004
In a universe of random fluctuations, a lone brain with false memories is far likelier than a whole ordered cosmos.

The setup

The second law of thermodynamics says that entropy, roughly the amount of disorder, tends to increase. A hot cup of coffee cools; ice melts; eggs break and never unbreak. But the law is statistical, not absolute. Disorder increases because there are vastly more disordered arrangements than ordered ones. Very rarely, by pure chance, a system can fluctuate into a more ordered state.

In the 1890s Ludwig Boltzmann, one of the founders of statistical mechanics, wondered whether our whole ordered universe might be such a fluctuation: a rare, temporary dip in entropy in an otherwise eternal, disordered cosmos. That would explain why we find ourselves in a low-entropy world.

But there is a problem, sharpened by later physicists. Small fluctuations are overwhelmingly more likely than large ones. A fluctuation that produces just a single brain, complete with false memories of a whole life and universe, floating briefly in the void, is far more probable than one that produces an entire universe of billions of galaxies. So if Boltzmann's picture were right, the typical observer would be a lone Boltzmann brain, not a person in a vast, ordered cosmos.

Why it matters

The paradox has become a real constraint on cosmology. Some models of the far future of our universe, in which it expands forever into a near-empty state with a small but nonzero temperature, seem to predict that Boltzmann brains would eventually vastly outnumber ordinary observers. Many physicists treat this as a sign that such a model is wrong.

It is also a dizzying version of skepticism. If the theory predicts that most observers with your experiences are momentary flukes, then by the theory's own lights you are probably one, and your memories of the evidence for the theory are fake.

Key terms

  • EntropyRoughly, a measure of disorder, or of how many microscopic arrangements are compatible with a system's large-scale state. In a closed system it tends to increase.
  • Second law of thermodynamicsThe law that the total entropy of an isolated system never decreases over time. It underlies the difference between past and future in everyday life.
  • Boltzmann brainA hypothetical self-aware brain that forms by a random fluctuation out of disorder, complete with false memories. Some cosmological models predict such brains should vastly outnumber ordinary observers.
  • Typicality assumptionThe assumption that you should reason as if you are a typical member of the class of observers in your situation.
  • Cognitive instabilityThe property of a theory that, if believed, undermines your reasons for believing it. A cosmology predicting that you are probably a Boltzmann brain is said to be cognitively unstable.

The positions

Position I

It rules out theories

A cosmological theory that predicts Boltzmann brains dominate is self-undermining, and should be rejected for that reason.

Position II

Typicality reasoning is flawed

The paradox depends on assuming we are typical observers. That assumption is unjustified.

Position III

The universe began in a special state

Our ordered universe is not a fluctuation. It began in an extremely low-entropy state, for reasons physics has yet to explain.

Arguments and objections

It rules out theories

Best argument
Sean Carroll argues that such theories are 'cognitively unstable': if you believed one, you would have to believe you are probably a Boltzmann brain, in which case your belief in the theory, based on evidence you think you remember, is unjustified. A theory that destroys the grounds for believing it cannot be rationally accepted. This gives cosmologists a real criterion for choosing models.
Strongest objection
It is unusual to reject a physical theory on the grounds that it would make us doubt our evidence. Nature need not care whether its laws allow us to trust ourselves.

Typicality reasoning is flawed

Best argument
We know a great deal about ourselves: we have coherent memories, an ordered environment, and evidence that keeps fitting together moment to moment. Boltzmann brains, which would mostly have incoherent experiences and dissolve within moments, are not in our reference class. Reasoning as if we were a random sample of all possible observers is a mistake.
Strongest objection
Some Boltzmann brains would, by chance, have exactly our experiences. The question is what fraction of observers with our experiences are Boltzmann brains, and in some cosmologies the answer is nearly all.

The universe began in a special state

Best argument
Most cosmologists hold that the low entropy of our universe is explained by its initial conditions at the Big Bang, which philosopher David Albert calls the 'past hypothesis'. This explains the arrow of time and why we remember the past. Boltzmann brains are only a problem for models in which the universe lasts long enough, in the right state, to produce them in vast numbers.
Strongest objection
The past hypothesis is not an explanation but a postulate. Why the universe began in such an improbable state remains one of the deepest open questions in physics.

Who argued what

  • It rules out theories Sean Carroll, Don Page
  • Typicality reasoning is flawed James Hartle, Mark Srednicki
  • The universe began in a special state David Albert, Roger Penrose

Variations

The single coin

Imagine an infinite sea of coins being randomly flipped. Somewhere, by chance, a thousand heads appear in a row. Elsewhere, a million. The thousand-head runs vastly outnumber the million-head runs. If you found yourself in a run of heads and knew only that, which is more likely: that you are in a short run or a long one? This is the logic behind the Boltzmann brain problem.

Go deeper

Why we remember the past, not the future

The laws of physics are almost perfectly symmetric in time. The arrow of time, the fact that we remember the past, that causes precede effects, and that entropy increases, seems to come from the low-entropy beginning of the universe. Memories are records, and records form when entropy increases. A Boltzmann brain would have 'memories' that are not records of anything; they would be random fluctuations that merely look like records.

Related ideas

Thought experiment

Are we living in a simulation?

If advanced civilisations can run vast numbers of simulated worlds, simulated minds would vastly outnumber real ones. So which are you more likely to be?

Thought experiment

Are you a brain in a vat?

A brain kept alive in a vat, wired to a computer that feeds it a perfect simulation of life. From the inside, it would seem exactly like your life.

Question

Is time real?

Time feels like a river carrying us from past to future. Physics describes it more like a map, with no moving 'now' anywhere on it.

Question

How do you know anything at all?

You believe you are reading a screen. Can you rule out every way that belief might be false? If not, do you really know it?

Question

Why is there something rather than nothing?

Nothing at all would have been simpler. No universe, no laws, no questions. Yet here everything is.

Question

Are there other versions of you?

On one serious reading of quantum mechanics, every possible outcome happens, each in its own branch of reality, with its own copy of you.

Further reading and sources

Open questions

  • What evidence could you have that you are not a momentary fluctuation?
  • Should physics reject a theory because it would make us doubt our own minds?
  • Why did the universe begin in such an ordered state?

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