DrChinese said:
I understood that BM posited explicitly non-local mechanisms.
That's true -- but of course it really depends on what you mean by "non-local mechanisms." That's why we need some definite definition or definitions, so we don't get caught in the trap of defining "locality" one way when we look at one theory, and then defining it some other way when we look at another theory.
The Bohmian dynamics is explicitly non-local. What happens in one place can instantaneously affect what happens in another place. In particular, the velocity of a particle over there can be instantaneously affected (according to Bohm's theory) by some fiddling I do over here. Now, if your gut reaction to this is to say "Well that *obviously* violates relativity!", I am inclined to agree. But I will just point out that exactly the same thing is true in OQM: the state of a particle over there can be instantaneously affected (according now to OQM!) by some fiddling I do over here. So this also "obviously" violates relativity. And Bell Locality gives a precise meaning to this claim. Both theories violate Bell Locality. That is just a fact, and it is nice because it doesn't depend on anything subjective like what is "obvious", etc.
Now it is a further and separate question: can the "obviously relativity-violating" non-locality of either theory be used to send a signal FTL? The answer turns out to be No for both theories. They're both signal local. So if you think that all relativity really requires is signal locality, then there is no grounds for vetoing either of these theories.
The problem with this view, however, is clear. "Signalling" is a very human-centered concept. If relativity really prohibits superluminal signalling, that should only be because signalling is a particular kind of causal interaction (namely one that is harnessed in a certain way by humans for certain human purposes). So *really* everyone believes that relativity prohibits any kind of superluminal causation whatever. It requires "local causality."
But the problem is, if you agree with Bell and me that "Bell Locality" is a good formal definition of "local causality" (i.e., consistency with relativity), then it turns out that no empirically viable theory can be consistent with relativity! One is really *stuck* with just the kind of thing that bothers most people about Bohm's theory -- namely, that it "obviously" involves non-local mechanisms.
I presumed - possibly incorrectly - that it might mean that non-local effects might at some point might be distinguishable in some way.
You mean that if there is non-locality in the theory, that one should be able to use it to transmit information, i.e., to send signals? That just isn't necessarily true. OQM and Bohm are two examples of theories that violate Bell Locality but are nevertheless signal local. (OQM's non-locality can't be used to send signals because of the randomness involved in the collapse postulate -- although making a measurement here causes, according to OQM, a distant particle to acquire some new state, I can't *control* which state it acquires and hence can't control the causality well enough to send a signal using it. Bohm's non-locality can't be used to send signals because of uncertainty in the initial conditions: if only we knew both the initial wf *and* the initial particle positions, then we would be able to *notice* that a particle ended up in a different place than it *should* have... but alas our knowledge of those initial particle positions is given by the Born rule, so the non-local effects are washed out.)
And it seems to me that there must be some element of the theory that would require some adjustment to relativity, although I guess that the fundamentals are not changing.
Oh, I agree with you, Bohmian Mechanics *does* require some (major!) adjustment to relativity. For example, you better have some kind of preferred frame or ether or whatever in order to give *meaning* to a statement like: the velocity of a particle over there is affected *instantaneously* when such-and-such happens over here. (Or better: the formal equivalent of this which is Bohm's guidance formula for an N-particle state.) You really just can't "wed" Bohm's theory to relativity. You can keep the formalism of relativity and you can keep the Lorentz invariance *at the level of empirical predictions* -- but you can't keep *fundamental* Lorentz invariance. You have to build in some extra spacetime structure or whatever to make the theory's dynamical equations make sense.
That sounds bad, right? The problem is: you have to do the same thing in OQM, for exactly the same reasons. The dynamical equations of OQM (in particular, the collapse rule) requires some objective simultaneity slices through spacetime, and that just isn't a structure that relativity can provide.
