The Boltzmann Brain Problem

By Graham Everhart

You think, therefore you are, but are you who you think you are? You may be an intelligent arrangement of random particles called a Boltzmann Brain. The existence of Boltzmann Brains remains one of the strangest unsolved problems in cosmology today.

The following is my interpretation of the papers, presentations, and other works of Sean Carroll, a physics professor at Caltech who specializes in cosmology. I have simplified concepts, taken all the math out, and added context where appropriate.

Boltzmann Brains are named after Ludwig Boltzmann, a 19th-century Austrian physicist. His theory, published in 1895, used entropy to analyze the origin of the universe. Entropy is simply the amount of disorder in something. A clean room has low entropy because things are organized and take up little space. A messy room has high entropy because everything is all over the place. The fundamental law of entropy — so fundamental that it gets an ordinal number — is that it will always increase over time. Entropy can decrease in one area, but must increase in another area to compensate. That’s how rooms are kept clean: entropy is transferred out of the room and into trash cans, closets, other rooms, or elsewhere.

In Boltzmann’s time, the universe was assumed to be infinitely old. This presented a problem: if the universe is infinitely old, then shouldn’t entropy be at a maximum? And if entropy is at a maximum, how come we still live on a low-entropy planet orbiting a low-entropy star within a low-entropy galaxy? Shouldn’t the universe be nothing but high-entropy blobs of diffuse particles instead of low-entropy blobs like planets and stars and galaxies?

His solution: the universe is infinitely old, and therefore has had an infinite amount of time to generate spontaneous entropy decreases known as fluctuations. In fact, it’s had an infinite amount of time to generate an infinite number of fluctuations — including ones large enough to create low-entropy “mini-universes.” According to Boltzmann, we live in one such fluctuation. It just so happens to contain a planet called Earth, orbiting a star called the Sun, in a galaxy called the Milky Way. Problem solved, right?

“But Graham! You just said that entropy must always increase. How can it just decrease out of the blue?”

Let’s model the universe with a bull stampede on a soccer field. At the start, all the bulls are within the center circle. Because the bulls are concentrated and not spread out, they are in a low-entropy state.


As time progresses, the bulls will run all over the place, expanding to fill the whole field. They are now in a high-entropy state.


But given enough time, every bull will visit every spot on the field. In fact, every combination of every bull on every spot on the field will eventually come to pass.




Bulls4Bulls5.pngA select few of those combinations have significantly lower entropy than normal. They’re rare, mind you, and dissipate quickly. But during those brief moments, the bulls’ entropy would spontaneously decrease, and a fluctuation would occur. Boltzmann imagined these stampedes throughout the universe instead of on a soccer field, and with quantum particles doing the stampeding instead of bulls.

“But Graham, scientists have proved that the universe is 13.8 billion years old!”

It’s a theory, definitely! But that theory is based on the oldest objects that we can see with our telescopes. We know for certain that the universe is not younger than 13.8 billion years, but it could be much older than that.

“But Graham, fluctuations that create entire mini-universes must be incredibly rare!”

Ah! You’re absolutely right.

In 1931, Sir Arthur Eddington discovered the dark side of Boltzmann’s theory: large fluctuations are much rarer than smaller ones. A fluctuation that creates a teapot should be more common than a fluctuation that creates a Boeing 747. Therefore, a blob of particles that thinks it lives in a low-entropy mini-universe is monumentally more likely to fluctuate into existence than an actual low-entropy mini-universe. These disembodied consciousnesses are the Boltzmann Brains mentioned in the introduction. If Boltzmann’s theory is correct, then it’s all but certain that neither you nor anything around you exists — not your family, not your friends, not the Metamodern Perspective column you’re reading right now. “You” are an ordered collection of photons and neutrinos and gravitons, interacting with each other in an otherwise heat-dead universe to simulate every memory you’ll ever make and every sensation you’ll ever feel. Eventually, the fluctuation that created your Boltzmann brain will unravel and return to maximum entropy. Maybe you’ll get a glimpse of the void all around you before you die.

If reality isn’t real, then what is? How much of what you experience are just shadows on the walls of Plato’s maximum-entropy cave?

Don’t lose hope! Astrophysicists are scrambling to disprove Boltzmann Brains. The following possibilities are under consideration:

  • The universe really is just 13.8 billion years old.
    • At some point in time, the universe will reach maximum entropy and spawn universe-dreaming Boltzmann Brains of its own. We just aren’t there yet.
  • Boltzmann Brains are less likely to form than mini-universes.
    • No one knows how a Boltzmann Brain works. It could require a larger and/or more specific fluctuation than one that creates a mini-universe.
  • The laws of physics prevent the existence of Boltzmann Brains somehow.

Our boy Sean Carroll believes that Boltzmann Brains are a paradox. Here’s why:

  1. Given your “understanding” of the “universe,” you’re probably a randomly generated Boltzmann Brain.
  2. If Boltzmann Brains are randomly generated, then their understandings of their “universes” probably don’t match the real universe.
  3. If you’re a Boltzmann Brain, then your understanding of the universe is probably wrong.
  4. If your understanding of the universe is wrong, then Boltzmann Brains probably don’t exist.
  5. If Boltzmann Brains don’t exist, then you’re not a Boltzmann Brain.


What do you think? I’d love to hear your thoughts on Boltzmann Brains. You can email me at or talk to me in person.


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