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> Oh, and, furthermore, the article says that in a bounded region, we have reason to expect the dimension of the space to be finite dimensional? This surprises
by bjornsing 6y ago
> Oh, and, furthermore, the article says that in a bounded region, we have reason to expect the dimension of the space to be finite dimensional? This surprises me.
Does it? Iirc a classic basis for a countably infinite Hilbert space is a Fourier series. If you have a finite space to describe, and a maximum frequency you need to represent (which I would say is reasonable to assume), then you only need a finite dimensional space.
- drdeca 6y agoI guess the maximum frequency is the surprising thing to me? Idk, I guess I thought maybe the limited information was, not really limiting the dimension? Or, maybe I thought because of no clean objective separation between the observable universe, and the rest of it, that that would cause an issue? Not really sure what I was thinking. I guess it makes sense that it would be finite dimensional. Hm, actually, I am confused about what counts as the observable universe. Is it that which is in our past light cone, or, that which is in a future light cone of our past light cone, or? Also, there’s the issue of time in different reference frames. If the state of the observable universe, is supposed to be given by a vector in the same Hilbert space at each time t, uh, well, that appears to depend on the reference frame. Like, the points in space time that are “simultaneous” depends on the reference frame. So, a vector which describes the state of the universe in a given time slice in a given reference frame, I don’t see how it would also describe it for a different reference frame.