Sean Carroll

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.

In particular, two well-known successful physicists, Tom Banks and Willie Fischler, have for a long time, for 20 years now, been pushing the idea that

that the fundamental dimensionality of Hilbert space, not just of our observable patch.

So there's one argument that is very, very believable that says the dimensionality of the part of Hilbert space describing our observable universe is finite dimensional.

But Tom and Willie want to say, no, the whole universe has a Hilbert space that is infinite dimensional.

Sorry, that is also finite dimensional and about the size.

And really the dramatic thing they're trying to say is there isn't –

independent universe beyond our horizon.

Basically, everything in the universe is just sort of the same thing as we see within our visible horizon, but maybe remixed from the point of view of some other observer somewhere else.

So nobody sees a boundary to spacetime or anything like that, but everyone has a horizon around them and can only observe a finite amount of universe.