bhobba
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Fredrik said:The Schlosshauer quote talks about "the preferred states of a system" and how they are determined by the system's interactions with its environment. So it only says that given a decomposition, there's a preferred basis. It doesn't suggest that there's a preferred decomposition.
It becomes clearer as you read more of the reference I quoted from. But basically it singles out the basis of observables that commute with the interaction Hamiltonian between the system and the environment that is causing the decoherence - obviously they are the ones that don't vary with time. Mostly, from what I have read, that is something like a coulomb interaction and evidently the observable that tends to commute with is position.
I guess the assumption is given any interaction Hamiltonian a unique observable and hence basis exists that it commutes with. That at least one exists is the problem of any outcomes at all - but there is another one - there may be more than one - although I am unaware of any such cases.
Regarding the other stuff such as a unique set of worlds I think we run into semantic issues with MWI. Basically there is really only one universe but when decoherence occurs the basis it produces as the mixture that continues to evolve is thought of as separate worlds. This however is just a way to describe the situation - its not really a separate world - there is really only one world or universe. This doesn't mean I hold to the MWI - its far too 'extravagant' as one guy I seem to recall said about it with all these new 'worlds' being created exponentially and with a different version of me in every one of them.
Thanks
Bill
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