LizR wrote:
So are these basises (bases?) something real, or just a sort of convention like lines of latitude? If they're a convention why would physics care about them?
You have an operator in a Hilbert space. This is an entirely abstract concept until you choose a basis in which to represent these things. It is just like choosing your axes in a geometrical problem, or like lines of latitude/longitude -- it is only a convention that we choose to take lines of latitude in planes orthogonal to the rotation axis, or the zero of longitude to be the Greenwich meridian.
Physicists should care about them because, since they are just a convention chosen by us, nothing in the physics should depend on them, just as the position of Auckland on the face of the earth does not depend on the Greenwich meridian. The problem, as I see it, is that physics does appear to be very concerned about bases -- we see definite values for experimental results only in one very particular basis and we do not see these results as represented in any of the other of the infinity of possible alternative bases.
Whether this is a problem best seen as the ambiguity of choosing a basis for the Hilbert space, or a problem of choosing how to represent the operator acting on that space, is not clear to me at the moment. These two are, of course, essentially the same thing, but there may be some significance to the priority question. Is it a matter of choosing eigenvectors, or is it a matter of the measurement operators we can actually construct in the laboratory?
If they're real, then could they normally be selected by our nature as beings embedded in space-time and hence strongly biased towards various types of measurement (positional, I assume) ?
I do not know how such a thing would work. It smells like anthropics gone mad....
How does collapse select a basis in which to operate that the MWI can't also select, when the MWI appear to be identical to collapse, just without the actual collapse?
Collapse does not select a basis. Collapse is actually not important in non-MWI approaches to QM. The traditional understanding would say that QM is firmly based in classical ideas, so comes complete with position and measurement operators carried over from classical mechanics -- just as commutators are carried over from the Poisson brackets of Hamiltonian mechanics. Measurements are constructed in a classical laboratory.... This is just an extension of Bohr Correspondence Principle, which I do not think can be completely abandoned. QM is not self-sustaining.
Bruce
PS please excuse my ignorance.
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