On 6/12/2018 8:25 PM, Bruce Kellett wrote:
From: *Brent Meeker* <meeke...@verizon.net>

An isolated system has energy eigenvalues.  But any realistic macroscopic system is only going to conserve energy approximately.  I think energy eigenvalues are found in atoms and maybe molecules.  But larger systems (C60 Bucky balls?) tend to emit and absorb photons that 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 high dimensional Hilbert space, and there are an infinite number of possible bases for this space, each corresponding to a different operator in the space. Which one of these operators (and bases) is "the" position basis? The answer from decoherence theory is that it is the basis that is stable against environmental decoherence. But, as I pointed out in a post on the 'Entanglement' thread, this is defined by the operator that commutes with the interaction Hamiltonian. However, the interaction Hamiltonian is usually defined in terms of point particle interactions, so commutes with the position operator because it contains that operator itself. So that particular definition of the stable basis is circular -- any chosen operator in the position Hilbert space would fit the bill provided it was used for both the position 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 preferred basis". It might be that quantum gravity will give an explanation in terms of the nature of quantum space-time. But it is possible that Bohr was right all along, and the only final explanation is that the "classical position" is the only stable basis, making the classical prior to the quantum (which might not be an entirely satisfactory outcome!)

Bruce

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