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Dear Robert (if I may),
I would very much like to understand better the relationship between BM and the consistent history approach. I think Shelly once made the point that they are actually somewhat similar in spirit, as they aim for a consistent transition from the micro to the macro level. I will certainly take a look at your paper . I’m not sure if I’ll be able to add anything meaningful, but I might try.
However, I believe the Bohmian position regarding “surrealistic trajectories” has been discussed many times. The Bohmian predictions are not wrong – they are just counter-intuitive. Of course, our classical intuition is based on locality and interactions in Bohmian mechanics are strikingly nonlocal (as they have to be). Once you’re willing to take BM seriously, “surrealistic” trajectories are not really a problem, you just have to accept them as a prediction of the theory that does conform with experiment. However, if you had an alternative theory that was just as clear and successfull as BM but which made more intuitive predictions concerning such which-way experiments, that would be a legitimate argument in favor of that theory.
Concerning your other worry about BM: In BM, the objective, physical state of a subsystem is given by (Q,psi), where Q are the positions of the particles and psi the (effective) wave-function of the system. This state determines the outcome of any measurement of a macroscopic “observable”. In this sense, the experimentalist is right that his pointer position reveals an objective fact about the measured system, although not an intrinsic property that the particles posses outside the context of measurement. Moreover, if you analyze the interactions of different particles/systems, you will find that what we call “energy” or “spin” or “momentum” etc. has pretty much the familiar functional role – although, on an ontological level, everything can be further reduced to the motion of particles.
(On a side note: the position representation is distinguished in BM, because BM is a theory about stuff in physical space. But of course, on the level of the wave-function, you are free to do all the familiar operations.)
The Bohmian usually feels that this modest anti-realism regarding quantum observables is exactly what the appearent paradoxes of SQM and the familiar no-go theorems à la Kochen-Specker suggests. However, I understand why someone would like even more realism regarding these quantitites. I the consistent histories approach can achieve this, without twisting the notion of probability too much, it would be a remarkable feat.