Sean Carroll

So all of which is to say,

If the universe as a whole were described by a finite dimensional Hilbert space, there would be a very, very, very long time between recurrences, but they would eventually happen.

And the reason why I've never been excited by that possibility is the Boltzmann brain problem.

If you imagine that, okay, I'm going to imagine a universe with a finite dimensional Hilbert space.

Its quantum state will just cycle through Hilbert space until it eventually comes back to where it left.

And I'm going to invent an interpretation

for that quantum state in terms of space time.

And I'm gonna say, okay, at some moment, there was kind of a big bounce, sort of a big bang slash crunch phase.

And from there, my quantum state does things which I interpret as the universe expands and cools and structure forms and all those things.

And then it is just sitting there in thermal equilibrium for a recurrence time, for a very, very, very long time.

But it's not in exact thermal equilibrium.

There are fluctuations, and those fluctuations can make Boltzmann brains or Boltzmann observers, Boltzmann fluctuations of whatever kind you like.

And the universe lasts for so long between the recurrences that most people like you and me are going to be random fluctuations out of thermal equilibrium, not people who really grow up in a thermodynamically sensible environment in the aftermath of the Big Bang.

So because of this Boltzmann brain problem, I never thought that finite dimensional Hilbert spaces gave you a good description of the universe as a whole, at least not in conventional quantum mechanics as we understand it.

Now, of course, maybe that doesn't bother you because you say, well, I hear all these questions and this has to do with Ben Lloyd's question.

Isn't the universe expanding?

Isn't it supposed to expand forever?

Shouldn't Hilbert space be infinite dimensional?

Maybe, you know, but we have to be careful.

And these are some of the things that we don't currently understand.