Dr. Pullin and Dr. Gambini,
First, I really enjoyed your essay. I read a draft of your LQG book a couple of years ago and find your point of view enlightening. It is particularly nice to see an approach to QM with a view toward quantum gravity simultaneously shed light on the measurement problem. I do have a few questions, however.
1. Your principal point seems to be that to solve the measurement problem, "decoherence is not enough, but decoherence together with background independence is enough." However, I am not quite sure how you distinguish between background independence and covariance, and hence whether it is background independence itself, or more specifically the types of background-independent structures that arise in certain models of quantum gravity that supply the missing pieces. To be clear, I understand background independence in very general terms to be about the dynamical character of what we call spacetime, and I understand covariance to be about the absence of privileged observers. I explain this more adequately in my essay:
On the Foundational Assumptions of Modern Physics
It may be that you are defining things differently, but I would like to know for certain.
2. You characterize physical law as describing what does happen rather than prescribing what must happen, and so far I agree. However, there is the middle ground of what MAY happen, and here I think there is some subtlety. On the one hand, I have long believed that the way in which the metric is viewed as governing the scope of causality in relativity puts the cart before the horse; surely the future of an event ought to be considered the set of events it actually influences, rather than the set of events it "may" influence according to the geometry. On the other hand, it does seem reasonable (and even inevitable) to place limits on what is deemed possible; for instance, in Feynman's sum-over-histories method, one must decide which paths, geometries, spin networks, triangulations, causal sets, or whatever, to sum over, and this implicitly limits what "may" happen. Would you agree that physical laws may reasonably be accorded "veto power" in this sense?
3. A matter of terminology: I assume that your description of the Copenhagen interpretation as involving state reduction from superpositions to "statistical mixtures" rather than to particular eigenstates is just a way of talking about the density matrix?
4. As far as I can tell, your "Montevideo interpretation" of QM seems to be described in terms of Hilbert spaces and operators, rather than sums-over-histories. Is this merely a matter of convenience, or is there a problem with the sum-over-histories method in this context?
Take care,
Ben Dribus