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ttn
#26
Aug16-05, 08:30 PM
P: 733
Quote Quote by vanesch
For instance, the quantum fields (as long as they evolve unitarily) ARE such geometrical objects (although very complicated! I think they must be a cross section of a fibre bundle over Minkowski space, and the fiber is the set of Hermitean operators over Hilbert space) - as far as I understand this.
I don't understand this very well either, but I'd like to. I think it's key for understanding MWI's claim to be local.

Simple question for whoever: in what sense precisely does something like an N-particle-wave-function or a quantum field in QFT "live" in space-time? Certainly not in any obvious way at all, right?


This is indeed what I intended to, thanks for making this clear :-)
And, we both agree that OQM with the projection postulate is just as ugly - it is a small mistery why so many people working in highbrow QFT and string theory simply don't know this !
Amen brother.



I think that MWI allows this, in contrast with Bohm and OQM ; as long as you accept that the unitary evolution is "local in principle" (geometrical) - at least if the Lagrangian is a Lorentz-scalar, then the object describing "reality" is the wavefunction which is, and remains, a geometrical object, and is never projected.
I'd like to know what kind of geometrical object it is, exactly. I mean, some arbitrary state in QFT definitely does *not* attribute some particular field value to each point on spacetime. A state is not a field *configuration* in the classical sense. It is, rather, an arbitrary superposition of such configurations. So suppose we have such a thing and it evolves deterministically according to a Sch equation forever. Is this "local"?



The second thing you need are world lines of consciousnesses. I never worked this out in complete detail, but I'd think that the world line defines a local reference frame for each conscious observer and as such this reference frame has a geometrical meaning (the vierbein associated with the world line). In this reference frame, it hops from branch to branch in the wavefunction, according to its own local Born rule. As you point out correctly, MWI people have a great difficulty DERIVING this Born rule, so I just postulate it, that's easier. I don't think it violates this geometrical definition of locality, because choices are only to be made when the local body associated with the consiousness entangles, which is determined purely by local interactions.
So a "quantum experience" is the universal wavefunction (a geometrical object) and a world line of a consciousness (I think it can be made a geometrical object too). It observes an aspect of the universal wave function.
Egad. As soon as you go solipsist on me, I stop believing that this can possibly be consistent, in any serious way, with relativity. All this talk of consciousness interacting with... If you take this seriously, isn't the whole idea of a 3+1 universe just one of those delusions in our minds??? etc....