Travis,
I just meant that any observation in BM requires the description of the whole measuring apparatus in BM terms. As I was told recently (arXiv:1408.1651), it is morally wrong to think otherwise, even if position is meaasured. Of course, BM seems to have a special relationship to position and I have seen the agreement of the particle/system density with the QM configuration probability density cited as an argument for the “empirical equivalence” with QM. That may suggest a more direct link to some casual readers, but as I showed in the paper criticized in the above arXiv paper, you also get wrong results. Of course, on the other hand it is apparently not only morally right, but mandatory to consider the observation of a pointer’s position to be obviously given by Bohmian positions (In an earlier post you wouldn’t even grant a slight smearing, which I only put in to make the agreement a bit less demanding). I find this switch from “morally wrong in the small” to “obvious in the large” in need of better explanation.
(Don’t get me started on surreal. On the one hand, since you don’t see the trajectories anyway, I don’t care too much. On the other, one can discuss whether they can be connected to other things we know, and physical intuitions of various sorts, for example those based on locality of interactions, which also do make sense experimentally. Bob Griffith’s examples go in that direction. )
For your Einstein box example, I have to limit myself to a few comments. After all we are already two days overtime (relative to the workshop announcement). (1) It may surprise you, but the projection postulate is not part of operational quantum mechanics, for the simple reason that it is often not true. (2) A measurement of the right/left dichotomy can be described for many practical purposes by just assuming the rule for the probabilities. That this leads to a macroscopically fixed record is an assumption made before the theory even starts. Justifying that is not part of the theory. (3) If you do bring in the counter, making this an example of indirect measurement, then what you say about linearity and entanglement is undisputed. (4) If you think that what you call a pointer here leads to macroscopically fixed records, think again. You can easily reverse this “measurement” coherently (routine lab practice these days), which is certainly not prevented by assigning any “real” Y, which is every bit as elusive as the “real X”. So the Bohmian positions may be a justification for saying that things are always really somewhere, if that soothes you. But that is not the kind of certainty we demand of pointers. If your decoherence assumptions are sufficiently strong, i.e., if you establish that records remain fixed no matter how many people or machines look at them or interact with them in any of the typical ways macroscopic systems interact according to statistical mechanics (which is very special in comparison to full many-body quantum mechanics), then you would have a justification for calling your second thingy a pointer. Since the many body language is the only one you allow for the measurement device this is not an unreasonable request from me. For QM that kind of measurement theory is a nice-to-have, but quite unnecessary for either theory or applications. (5) The overlap of supports condition is an artifact of the position dogma, and quite often not satisfied. For me the fact that momentum eigenfunctions (or the projections for positive/negative momenta, to stay close to your example) is secondary. But I am too tired to sort that out for you. (6) Getting some notion of orthodoxy from the textbooks is an easy way to set up an effigy. I completely agree that there are many bad textbooks and confused texts by Bohr, and almost all are weak on foundational questions. But the theory is not just in textbooks, and it might be a more interesting target to get some best practice examples and test your theory on those (Or shoot at my textbook, when it comes out). What would it add? Do the trajectories actually give you an insight? Or is their only role, on honest inspection, to just be there and soothe your ontological pains? Would De-Bohmified furniture really look different to you?
So long, Reinhard
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