meekerdb wrote:
One reason may be that the primary interactions important for life are more position than momentum dependent. A tiger can only eat you if you and the tiger are near each other. If there were beings that lived in orbit then perhaps they would have evolved to directly perceive orbital parameters instead of position.
I have never been comfortable with the idea that evolution plays a fundamental role in the resolution of the basis problem. That would mean that somehow basis selection is something that gets encoded in our DNA and I find that implausible.
Once again, the basis problem is not a choice between position, momentum or energy pointers. The basis is the eigenvector set for possible measurement result eigenvalues once you have chosen to measure one of these quantities. I find the failure to clearly distinguish this is one of the weaknesses of Schlosshauer's otherwise excellent discussion of decoherence and einselection. Once you have chosen to measure position, say, you still have to specify the actual 'position' operator that will be used. It is that choice of operator with its specific eigenvectors that gives the eigenvalues that are the possible results of your measurement.
That aside however, I think that Schlosshauer's treatment (following Zurek) in terms of operators that commute with the interaction Hamiltonian relevant to the decoherence interactions between the system and the environment is basically correct. If you choose a different operator as your position operator, it will not in general commute with the conventional 'classical' position operator with eigenvalues evenly distributed along the real line. Focusing on the interaction Hamiltonian focuses on the dynamics and not on the properties of any particular observer. It is also relevant that in many cases the interaction with the environment is in terms of forces that are dependent on distance, hence position is the relevant determinate property of such systems.
The eigenvectors in position space are further determined by the precise details of the interaction. In particular, the interactions we know are direct interactions between point particles (Coulomb, gravitational, weak, strong, etc) so the operators in the interaction Hamiltonian refer to local interactions of point particles. Any alternative position operator would correspond to superpositions of these states, so would appear to us as giving intrinsically non-local interactions.
But Schlosshauer does make the point that physical laws that go to make up the interaction Hamiltonian are discovered and formulated by us, so they can contain only the determinate quantities of our experience. Thus the derivation of determinacy from these laws might seem circular. Schlosshauer seems content to accept this circularity and demand only that his analysis be consistent with observation.
I would go a little further and claim that since we discover the laws of nature and do not invent them, the nature of the interaction Hamiltonian is also something discovered. Thus, the particular basis that gives physically robust and determinate quantities is also something inherent in nature -- it is discovered, not invented. Another way of saying this is that the classical world is a given, as much as is the quantum world. One is not subsumed by the other, but they are dual aspects of the reality we inhabit.
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