Sean Carroll

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.

And that's all of the universe.

And so it's a finite dimensional Hilbert space.

Now, Tom and Willie have a complicated version of why that does not give you a Boltzmann brain problem.

Basically, they're not Everettians.

They're more Copenhagen-esque, and they have strict rules for what counts as an observer and things like that, and none of it really makes a lot of sense to me, even though I have tried, because I'm just so Everettian deep down that I have trouble wrapping my brain around what they're saying.

But as an Everettian...

It's very straightforward.

There's a quantum state.

It's evolving.

That's all you have to work with.

And so if most of the time people like me, if I conditionalized on the existence of an observer like myself, then I found that, oh, it's just a random fluctuation in empty space.