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Leaving aside the debatable point about whether bell's violation rules out all local theories or just local realism, is there general agreement that if the assumptions are valid, violation of Leggett's inequalities rules out any non-local model that treats properties other than position as real as argued here:
http://link.springer.com/article/10.1007/s10701-013-9723-7
If this is the case, why is position so privileged toward realism in BM, unlike all other properties? Does it having anything to do with distinguishing the difference between 'measurement' of the position operator versus measurement of the Bohmian particle positions. So in that case, position is, in some sense, not privileged or am I misunderstanding?
The Foundational Significance of Leggett’s Non-local Hidden-Variable TheoriesA frequently heard complaint about Bohmian mechanics is that it is non-local. The correct response to this is to refer to the experimental violations of Bell’s inequalities, which show that non-locality is not a peculiarity of Bohmian mechanics, but an experimental fact. In a parallel fashion, experimental violations of Leggett’s inequalities furnish a reply to another complaint that is sometimes made against Bohmian mechanics, namely its non-realism with respect to all properties except position. Experimental tests of Leggett-type models support the Bohmian approach by demonstrating that a realism about polarization, even in the modest sense of (2), is in conflict with empirical data. The Bohmian should therefore not join Laudisa in denouncing Leggett’s research program as irrelevant, but should rather welcome it as significantly supporting his own position, by showing that non-realism about the polarization of individual photons is not just a theoretical postulate, but an experimental fact.
http://link.springer.com/article/10.1007/s10701-013-9723-7
If this is the case, why is position so privileged toward realism in BM, unlike all other properties? Does it having anything to do with distinguishing the difference between 'measurement' of the position operator versus measurement of the Bohmian particle positions. So in that case, position is, in some sense, not privileged or am I misunderstanding?