Sean Carroll

The important point is that we have, by hypothesis, we're imagining a situation where there are randomly fluctuating things happening.

And in that set of randomly fluctuating things, they fluctuate forever.

So the fluctuations don't damp out and quiet down, right?

They will just keep going fluctuations forever and ever and ever.

And the fluctuations are random and more or less ergodic is the word that we use.

So in other words, any configuration that you can imagine that is compatible with conservation of energy and things like that will eventually come to pass in these random fluctuations.

and then you can do statistical mechanics on this and you can show that usually the system will be in very very high entropy states basically thermal equilibrium there will be fluctuations and you can tell me the relative likelihood of those fluctuations namely if the fluctuation decreases the entropy of its surroundings by a factor delta s

change in entropy, s is for entropy, then the probability, the relative probabilities of such a fluctuation goes e to the minus delta s, which is to say you will get non-zero probabilities for every single fluctuation you can imagine, but the larger the fluctuation you care about, the less frequently it will happen, the less likely it will be.

So the reason why it doesn't matter what counts for a Boltzmann brain is that if you tell me what you think should count, OK, so maybe what you think should count is just a brain out there in empty space with nothing else going on.

Maybe you think, no, no, no, it wouldn't count unless there was a period of time over which

the brain gathered information maybe has a body with some sensory organisms organs rather maybe you just insist that there be like a whole planet with an atmosphere and a star or whatever you want okay you tell me what you want fine

With overwhelming probability in this scenario, that thing that you want will exist much, much more often as a random fluctuation from the surrounding thermal equilibrium than it will as something that developed in a thermodynamically sensible way from a very low entropy Big Bang boundary condition.

So people have put work into thinking about like how much of a fluctuation do you need for Boltzmann brains and things like that.

But it really basically doesn't matter quantitatively.

As long as you have an eternal universe with random fluctuations in it, most observers are going to be minimal observers.

such fluctuations.

Even if you literally said, I insist that the fluctuation include me and my environment and literally everything I can see inside my past light cone for the last 14 billion years.

I think that would be entirely unjustified for you to say that, but even if you did, the fluctuation would be just that big and nothing else.

And tomorrow, when you look outside and look at the microwave background, it will be gone.

Because you didn't need that, right?