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On 6/12/2018 8:25 PM, Bruce Kellett wrote:

From: *Brent Meeker* <meeke...@verizon.net>An isolated system has energy eigenvalues. But any realisticmacroscopic system is only going to conserve energy approximately. Ithink energy eigenvalues are found in atoms and maybe molecules. Butlarger systems (C60 Bucky balls?) tend to emit and absorb photonsthat localize them in a position basis.I am glad you said "a position basis" and not "the position basis" --a mistake that is frequently made. Position is an operator in a highdimensional Hilbert space, and there are an infinite number ofpossible bases for this space, each corresponding to a differentoperator in the space. Which one of these operators (and bases) is"the" position basis? The answer from decoherence theory is that it isthe basis that is stable against environmental decoherence. But, as Ipointed out in a post on the 'Entanglement' thread, this is defined bythe operator that commutes with the interaction Hamiltonian. However,the interaction Hamiltonian is usually defined in terms of pointparticle interactions, so commutes with the position operator becauseit contains that operator itself. So that particular definition of thestable basis is circular -- any chosen operator in the positionHilbert space would fit the bill provided it was used for both theposition measurement and the interaction Hamiltonian.

`But is it a vicious circle? Aren't all the position bases going to be`

`physically equivalent?`

Brent

We have to look elsewhere for the final explanation of "the preferredbasis". It might be that quantum gravity will give an explanation interms of the nature of quantum space-time. But it is possible thatBohr was right all along, and the only final explanation is that the"classical position" is the only stable basis, making the classicalprior to the quantum (which might not be an entirely satisfactoryoutcome!)Bruce --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it, sendan email to everything-list+unsubscr...@googlegroups.com<mailto:everything-list+unsubscr...@googlegroups.com>.To post to this group, send email to everything-list@googlegroups.com<mailto:everything-list@googlegroups.com>.Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.

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