Sean Carroll

When you hear people say things like reality is a vector in Hilbert space, those people are more likely to be physicists like myself than real card-carrying philosophers.

Although, of course, I dabble back and forth.

And what that means is that reality, whatever it is, is exactly modeled, is exactly represented by a vector in Hilbert space evolving according to the Schrodinger equation.

Sometimes that sentence is shortened to just saying reality is a vector in Hilbert space.

And then I think there's some tedious discussion that happens about, well, are you saying that the mathematical structure is real or whatever?

Like, no.

That's not actually what is being said.

We're just trying to get through our day without having every single caveat attached to every single sentence that we say.

What we're trying to say is there's reality, physical world, and it is what it is.

It's not sort of expressible in terms of anything else.

It is reality.

It's sort of unique in that way.

But it is represented mathematically as a vector in Hilbert space.

So any question you could ask about reality can be turned into a question about that vector in Hilbert space and how it evolves with time.

Now that's an especially simple version of ontology.

More complicated versions of ontology are also entertained by plenty of people.

And the question about high-dimensional classical phase space is very well put.

People argue about that, okay?

If I say, if I didn't know about quantum mechanics and I was a Newtonian physicist and I thought that the world was made of these particles moving in three-dimensional space.

They're N particles, capital N particles.