Imagine a disembodied brain floating in outer space, simulating reality as we know it. Its memories of its entire life and loved ones originating from sheer randomness, by a coincidental arrangement of particles. Sounds crazy? Let me try and convince you why this might be the story of your life (statistically speaking).

But before that, let’s talk about Boltzmann. Ludwig Boltzmann revolutionised physics with many groundbreaking ideas, his most excellent gift to science being the Kinetic Theory of Gases. Boltzmann showed that thinking of gasses as amalgamations of particles in constant random motion could explain the three laws of Thermodynamics. Boltzmann figured out why the entropy of a closed system (like the universe!) must always increase. Entropy can be thought of as the number of configurations of possible states that the constituents of a system that arrange themselves in. It’s just a measure of the “specialness” of the different attributes of a system’s particles. The more special the attributes, the lower the entropy. Khanacdemy has some brilliant videos to build a strong intuition on the intricacies of entropy.

Ludwig Boltzmann

For example, take our the air molecules in the lower part of Earth’s atmosphere. Air molecules are moving randomly and after an infinite amount of time, they pass through all possible arrangements that they could have. If I were to plonk you in this atmosphere and ask you to distinguish between the different arrangements of the air molecules, you’d have a pretty hard time. This is an example of a high entropy situation, and it characterises almost all of the arrangements that you’ll see in the atmosphere. BUT since the air molecules are in random motion, it’s totally possible (but stupidly improbable) that they will all simultaneously do something weird, like moving in the same straight line or forming neat big concentric circles.

Boltzmann said that entropy of a closed system increases because the system is more probable to take on arrangements of particles that are unordered simply due to the fact they are more abundant. It’s all statistical. Please note that this only applies to our macroscopic world, microscopic dips in entropy happen all the time, but it’s the bigger picture that we’re concerned with.

Now, on to Boltzmann Brains.

Imagine an infinitely large universe, forever in thermal equilibrium. Given infinite time, all sorts of dips in entropy will happen. Particles would form stars, galaxies, black holes or maybe something especially weird like amino acids, all of these situations extremely improbable. But can you think of something that’s more improbable? How about this: all the particles in the infinitely large universe end up in exactly the same location. Sound familiar? Well it should, I’ve just described the big bang!

According to Boltzmann, systems are always most probable to progress towards a state of higher entropy, and whenever a dip in entropy occurs, the smaller the dip the more probable it is. So what sounds more probable, collapsing a whole universe’s worth of particles to a single position, or just collapsing a galaxy’s worth of particles to a single position? Collapsing a galaxy’s worth of particles to a single position or just collapsing a planet’s worth of particles? Collapsing a planet’s worth of particles, or have a swath of particles converse directly into a single human brain in the right right arrangement to have an illusion of memory and sensation that mimics our current experience? That would be a Boltzmann brains. In a universe dominated by structure that results from entropy fluctuations, a vast majority of conscious being (like you, and I guess me too) would Boltzmann brains.

It’s the logical conclusion if we suppose that the Big Bang resulted from an Entropy Fluctuation. AH HA, but there’s the catch. IF the universe resulted from an entropy fluctuation. There is no evidence to back this up (to be fair, none against it either), further more, the conclusion is unfplseiable, and therefore sits comfortably in the realm of philosophy, not science. There have been many arguments against us being Boltzmann Brains, but this I’m afraid is for you to explore. Think about the many reasons why this hypothesis may be wrong and try and convince yourself. Proving what we know to be false, as you know, is the best way get closer to the truth.

Originally published at on January 28, 2021.