A Paradox: Do LHV Theories Need the HUP?

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DrChinese

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ttn said:
In short: the people who applaud Bell for snuffing out the hidden variables program, yet retreat to Orthodox QM as an acceptable theory, are engaged in a deadly contradiction. You can't have it both ways. If Bell Locality really is what relativity requires, then both OQM and hidden variable theories are going to have to be rejected as inconsistent with relativity (or, we'll have to junk relativity). On the other hand, if it's OK for orthodox QM to violate Bell Locality, then it's OK for hidden variable theories to violate it as well. In which case Bell's Theorem wouldn't rule out local hidden variable theories at all, and would cease to be interesting. All I'm suggesting is that we not tolerate double standards. Anyone who rejects (say) Bohm's theory because it violates Bell Locality, ought also to reject OQM on those same grounds. And vice versa, of course.
No, there is no contradiction to us in this category. oQM, as we all agree, is not a theory which must satisfy Bell's Inequality. The reason is that oQM does not claim that Bell Reality holds. So there is no "retreat" here.

Any local realistic theory WILL meet the conditions that trigger the Bell Inequality requirement. That is because the local realist program requires it, and by this I mean in the spirit of EPR. So the question is: would Einstein (say) have agreed with the twin requirements of Bell Locality and Bell Reality. I think he would, as most local realists do. (In fact, I have never even heard a local realist deny these as applying - although I'm sure someone must have made that argument too).

I personally consider oQM to be a local non-realistic theory. That is because oQM respects the essential tenets of relativity . I know this drives you crazy, because Bell's Theorem defines locality such that oQM is non-local. But HELLO, that definition doesn't matter at all to oQM because oQM does not require Bell Reality anyway. So Bell's Inequality - and therefore Bell's Theorem - has no applicability for oQM.

I do reject Bohmian Mechanics on the grounds that it violates special relativity. I also reject it on the grounds it is an ad hoc theory. But it is a very mild rejection on both points. If, in the future, it is developed to a point that it can be experimentally segregated from the predictions of oQM, and its predictions are superior to oQM, then I will change my mind.
 

ttn

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DrChinese said:
I personally consider oQM to be a local non-realistic theory. That is because oQM respects the essential tenets of relativity . I know this drives you crazy, because Bell's Theorem defines locality such that oQM is non-local. But HELLO, that definition doesn't matter at all to oQM because oQM does not require Bell Reality anyway. So Bell's Inequality - and therefore Bell's Theorem - has no applicability for oQM.
I do reject Bohmian Mechanics on the grounds that it violates special relativity. I also reject it on the grounds it is an ad hoc theory. But it is a very mild rejection on both points. If, in the future, it is developed to a point that it can be experimentally segregated from the predictions of oQM, and its predictions are superior to oQM, then I will change my mind.
The only thing that drives me crazy is the inconsistency. If you decided you didn't like Bell Locality as a measure of what special relativity "really requires", I'd have no objection to your saying "I personally consider oQM to be a local... theory." But then, if you are consistent, you'd have to say that Bohmian Mechanics is a local theory too -- sure, it violates Bell Locality, but it's consistent with relativity (because it respects signal locality or whatever).

Don't you see that you are engaged in a contradiction here???

OQM and Bohm both violate Bell Locality. They both *respect* signal locality. So if you have some vested interest in making the conclusion come out a certain way (namely "Bohm is non-local, but OQM is local") you should at *least* have the courtesy to provide some kind of definition of locality according to which that statement is *true*. Otherwise you look like some kind of ignorant idealogue who just insists on OQM somehow "winning", all evidence to the contrary notwithstanding. The fact is, the two theories are on *precisely equal* footing, at least so far as Bell Locality and Signal Locality and Empirical Adequacy are concerned. Then, of course, Bohm wins hands down when it comes to clarity, precision, and not suffering from things like the measurement problem.

But if you want to just ignore all that and believe, for no reason, that "Bohm is non-local, but OQM is local"... I can't stop you.
 

DrChinese

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ttn said:
Don't you see that you are engaged in a contradiction here???
OQM and Bohm both violate Bell Locality. They both *respect* signal locality. So if you have some vested interest in making the conclusion come out a certain way (namely "Bohm is non-local, but OQM is local") you should at *least* have the courtesy to provide some kind of definition of locality according to which that statement is *true*. Otherwise you look like some kind of ignorant idealogue who just insists on OQM somehow "winning", all evidence to the contrary notwithstanding. The fact is, the two theories are on *precisely equal* footing, at least so far as Bell Locality and Signal Locality and Empirical Adequacy are concerned. Then, of course, Bohm wins hands down when it comes to clarity, precision, and not suffering from things like the measurement problem.

But if you want to just ignore all that and believe, for no reason, that "Bohm is non-local, but OQM is local"... I can't stop you.
Sorry, I do not mean to mis-characterize BM. And your comment about consistency is reasonable.

I understood that BM posited explicitly 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. 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.
 

ttn

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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.
 

DrChinese

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ttn said:
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.
It's not necessarily bad, and I don't mean to make it sound that way. But I am trying to identify the essential things that make me want to say "oQM could be a local theory" (I am not sure it is, mind you) and also say "BM is a non-local theory".

I don't really think I am so far off, as best as I can tell the issues I have are exactly those that are discussed in many papers - new and old. A lot depends on what you are looking at and where you are going with it.
 

ttn

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DrChinese said:
It's not necessarily bad, and I don't mean to make it sound that way. But I am trying to identify the essential things that make me want to say "oQM could be a local theory" (I am not sure it is, mind you) and also say "BM is a non-local theory".
Not to be rude, but it seems an awful lot like "the essential thing" that makes you want to say these two things is just that lots of other people have said them. This despite the fact that they are, in fact, inconsistent with each other, as has been clarified in recent posts here.

OQM and Bohm are on equal footing in terms of locality, and the latter is a better theory on other grounds. Anybody who denies either of those things is either just confused or operating on the mindless inertia of stale history. Forget about what is popular and look at the facts.
 

DrChinese

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ttn said:
Forget about what is popular and look at the facts.
The "facts", in this case, are far from clear. You of all people should know that. As to what is popular, that is a lot different from what is commonly accepted within science. It is popular opinion that the big bang is "just a theory" but science has come a lot further than that. You talk a big story but the "fact" is that you have no more new predictive medicine to prescribe than I do. Chill... there is plenty for us all to learn.

You must realize that I want to find a common ground and have worked hard to find that point. Either of us could find references to support any position about locality we care to push. I am interested in learning what makes the position of Bohmian Mechanics so interesting to you. Even if I don't change my fundamental position, I feel I have gained from the interchange. I hope you have too.

Now that I have all that feelgood stuff off my chest... would you care to give me a reference or two that will tell me a little more about BM? I have read some of Bohm's latter material, but he really didn't seem to talk about it too much. I have some of his "holographic paradigm" essays, and some other material on the relationship of causality and chance, but none of this went very far into this theory.
 

ttn

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DrChinese said:
Now that I have all that feelgood stuff off my chest... would you care to give me a reference or two that will tell me a little more about BM? I have read some of Bohm's latter material, but he really didn't seem to talk about it too much. I have some of his "holographic paradigm" essays, and some other material on the relationship of causality and chance, but none of this went very far into this theory.
Read Shelly Goldstein's article at

http://plato.stanford.edu/entries/qm-bohm

"The Undivided Universe" (by Bohm and Hiley) is pretty good. Peter Holland's book "The Quantum Theory of Motion" is also nice. And check out Jim Cushing's "Quantum Mechanics: Historical Contingency and the Quantum Hegemony" for a historical perspective. And Bohm's 1952 papers are quite readable and clear. And you can never go wrong by reading Bell's articles, many of which discuss Bohm's theory (of which he was a huge fan).


On the touchy feely side, I assure you I'm perfectly calm about all this. But you have an annoying tendency to briefly get something, and then suddenly retreat to your old standard positions, even after they have been shown clearly to involve contradictions. And this isn't about who can cite what paper, as you keep suggesting. It's about what's true. I'm operating under the assumption that you actually understand QM and how it works, so that you can actually grasp for yourself the fact that OQM violates Bell Locality (for example). If you're just accepting that on faith from some authority, then I can understand why you would later retreat to a more comfortable position. But it seemed like you knew what you were talking about well enough to see for yourself that it is actually a fact. But then, why would you turn around and start talking again about your desire to believe that OQM is local and Bohm is nonlocal? If that just isn't true (and it isn't) and if you saw that for yourself, how could you still desire this? It makes it look like, after all, you aren't interested in finding the truth. Well, I hope I'm wrong. Check out some of the Bohm references and see what you think.
 

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