bohm2 said:
Why should probability not ontologically exist? What kind of prejudice is that? I think quantum mechanics is telling us that it does exist, despite our intuition or instinct to the contrary. Our brains evolved and led us from success to success by hard-wiring in us a belief that nothing happens without a cause... this belief worked just fine, till we ran up against quantum mechanics.
I think that there is a conflict, or at least a tension, between objective probabilities and relativity, even before you throw in quantum mechanics. Subjective probability of course is not affected by quantum mechanics or relativity, and the sort of "collapse" that happens when an observer gets new information is a process that goes on inside someone's head, not in the world. But a purely subjective notion of probability seems incomplete when talking about quantum mechanics, for two reasons: First, there's absolutely no reason to think that subjective probability should evolve via Schrodinger's equation, and second, having one person detecting a particle should have no effect on somebody
else's subjective probability (until he finds out about it, anyway).
On the other hand, objective probability is hard to reconcile with relativity, unless it is of a very particular type. By "objective probability", I mean stochastic processes, in which the evolution of the state of the system is governed by a probabilistic transition matrix. However, when you consider relativity, there is no universal "time" to use for state evolution, there is only a local notion of time applicable within a small region. You could have a stochastic process based on local time, for instance, a particle's state could evolve nondeterministically as a function of the particle's proper time. However, that kind of stochastic evolution can't describe things like the probability of a particle being here or there, for the following reason:
Suppose that a particle has a 50/50 chance of being in one of two boxes, box A and box B, lightyears apart. Someone detects the particle in box A. A second later, (according to one reference frame), someone checks box B for the particle.
According to one reference frame, the particle has already been found, and so the second observer has zero chance of finding the particle. According to a second reference frame, the checking of the particle in B happens before the discovery of the particle in A. So in this frame, the particle has a nonzero chance of being found at B.
This frame-dependence of probability causes no problems for subjective probability, but doesn't really make sense for objective probability.
This is a long-winded way of saying that in my opinion, the weirdness of the way probability works in quantum mechanics is sort of to be expected, because there is no good way for objective probability to work consistently with relativity.
On the other hand, if there secretly were a universal time, then you could have an ordinary stochastic evolution based on that universal time. I'm not sure how the Bohm theory generalizes to relativistic quantum mechanics. Does it use a preferred rest frame for the nonlocal quantum interactions?