Is QM Inherently Non-local in EPR and Bell Discussions?

[DrChinese]

This thread is following up on some comments being made in another thread by ttn and others, including myself. The basic questions are:

i) Is QM inherently non-local?
ii) If yes, when did this result become clear?

These questions are offshoots of discussions of EPR and Bell. For most readers, posts to this thread will probably end up seeming to be a debate over fine points that may not matter. Or maybe they do matter...

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ttn has argued that QM is inherently non-local, and feels that result was known shortly after EPR. ttn is also, to some degree at least, a member of the Bohmian mechanics (BM) school although I do not purport to convey ttn's position.

On the other hand, I have a more orthodox position on QM that is frequently associated with the Copenhagen interpretation (QM-CI). As such, I do not tend to go much further than the formalism. Of couse, I like to speculate as much as anyone.

Regarding i) above:

I do not believe QM is non-local, assuming certain definitions of locality. As has been pointed out previously:

"According to quantum theory, action at a space-like separated
region does not change the probability of an outcome of a local
measurement." (The fact that anything "non-local" has occurred is never evident until such time as the space-like separated measurement results are brought together.)

I would not characterize the above defintion of locality as universally accepted, although it is certainly popular enough. In fact, the very conclusions you arrive at are usually dependent on your definition of locality.

On the other hand: if you want to explain the "perfect" correlations when you perform Bell tests at 0 degrees between the Alice and Bob polarizers, non-local effects seem to be a pretty good explanation too.

Regarding ii) above:

ttn has argued that the non-locality of QM was evident after EPR, in fact was a conclusion of EPR. I argue that it absolutely was not a conclusion of EPR. It is *possible* that some might deduce that from some readings of EPR. But it was never stated as such in the paper itself.

ttn has also offered up a quote from Einstein's later writing in support of this position. However, I would like to point out the following. Einstein assumed locality was a fact. Since he assumed the predictions of QM were otherwise correct, he felt QM was incomplete and local reality would win in the end. Such a viewpoint would REQUIRE Einstein to believe that an test of the EPR paradox would show that the predictions of QM were wrong. I.e. there would certainly be no perfect correlations!

But guess what! That would mean that if the Aspect tests were performed without ever knowing about the Bell inequality, and instead simply as a resolution of the EPR paradox... that local reality would have been refuted. If that is true: WHAT DO YOU NEED BELL FOR?

The fact is, Einstein would have been shocked at such results. But others would still have argued that local reality was not excluded. It took Bell to rule out ALL local realistic theories. But the caveat to that is that Bell still does not prove that QM is non-local. You must look elsewhere to draw this conclusion.

 

[ttn]

"According to quantum theory, action at a space-like separated
region does not change the probability of an outcome of a local
measurement."

Too vague. The probability of an outcome of a nearby measurement can be different, depending on whether we conditionalize on space-like separated information (e.g., the setting or outcome of a distant measurement). That already implies a kind of non-locality if the probabilities in question are all conditionalized on a complete specification of the particle states (in the past light cone(s) of the measurement events in question). According to QM, knowing the complete state of the world in the past light cone of a given measurement isn't enough to predict the probability of a given outcome -- conditionalizing also on space-like separated information changes the probabilities. In other words, the probabilites really *depend* on things that are going on at spacelike separation.

The only way to deny that this is a real nonlocal action at a distance is to deny the completeness doctrine. If we had conditionalized on only partial information about the states, then the fact that the probabilities change when we also conditionalize on space like separated information, wouldn't be a big deal.

On the other hand: if you want to explain the "perfect" correlations when you perform Bell tests at 0 degrees between the Alice and Bob polarizers, non-local effects seem to be a pretty good explanation too.

Don't mistake that for the argument, though! Nobody thinks that non-locality is proved, just because non-locality is *a* way of accounting for the observed correlations. The whole point is: it's the *only* way. But you have to really understand Bell to see that.

ttn has argued that the non-locality of QM was evident after EPR, in fact was a conclusion of EPR. I argue that it absolutely was not a conclusion of EPR. It is *possible* that some might deduce that from some readings of EPR. But it was never stated as such in the paper itself.

I never said non-locality was a conclusion of EPR. The assumed that locality was true, and proved that, for QM, locality entails in-completeness... and hence concluded that the theory wasn't complete. But this is logically equivalent to the proposition that, if you assume completeness, the theory is non-local.

But even that is an overly cumbersome way to say it. It's better to just define what you mean by locality and then look at the theory and see how it works. And it's trivial to see that if you are talking about Bell Locality, orthodox QM violates it.

ttn has also offered up a quote from Einstein's later writing in support of this position. However, I would like to point out the following. Einstein assumed locality was a fact. Since he assumed the predictions of QM were otherwise correct, he felt QM was incomplete and local reality would win in the end. Such a viewpoint would REQUIRE Einstein to believe that an test of the EPR paradox would show that the predictions of QM were wrong. I.e. there would certainly be no perfect correlations!

Huh? It's a trivial matter to explain the perfect correlations in a local way, if you just add the assumption that there are hv's which determine the outcome. You just say: half the pairs come out with the left particle "up" and the right particle "down", with the other half vice versa. Then you always get perfect anti-correlation, and there's nothing non-local going on. There's no need to disagree with this particular prediction of QM. The perfect anti-correlation can be explained easily with a local hvt.

But guess what! That would mean that if the Aspect tests were performed without ever knowing about the Bell inequality, and instead simply as a resolution of the EPR paradox... that local reality would have been refuted. If that is true: WHAT DO YOU NEED BELL FOR?

I don't follow you.

The fact is, Einstein would have been shocked at such results. But others would still have argued that local reality was not excluded. It took Bell to rule out ALL local realistic theories. But the caveat to that is that Bell still does not prove that QM is non-local. You must look elsewhere to draw this conclusion.

I certainly agree that Einstein would have been shocked to discover that no local theory can agree with experiment -- i.e., that locality is false.

Re: Bell, terminology is getting the best of you. Bell's Theorem doesn't prove that orthodox QM is non-local. It isn't even about orthodox QM -- it's about hidden variable theories. So you're right that "bell still does not prove that QM is non-local." But nobody said it did. What proves that orthodox QM is nonlocal is just, well, orthodox QM. You just look at how the theory works and ask: does it respect Bell Locality? The answer is no. That is trivial. You don't need a theorem. What you *do* need a theorem for is to decide whether some *other* theory (with hv's) might reproduce the QM predictions while respecting Bell Locality. Bell's theorem proves no such theory exists. And experiment proves that the QM predictions are correct. Conclusion: no local theory can match experiment. Nature violates Bell Locality.

 

[RandallB]

i) Is QM inherently non-local?
ii) If yes, when did this result become clear?

Always a lot of angles to argue local/non-local when you look at EPR-Bell or entanglement. But I believe you can see it in the double slit paradox as well.
This “paradox” is only resolved by the uncertainty of HUP/QM. For those not fully up on the double slit paradox; with only single Photons (or electrons) fired at a double slit a pattern is still accumulated that extends both to the left and right of the slits. For the pattern built out on the sides and the photons coming though the closest slit, there must be some form of signaling or help coming via the far away slit. What ever that help is covers a longer distance & therefore travels faster (i.e. FTL). Without some explanation this remains a paradox – BUT QM explains it Non-Locally with, superposition, guide-wave, even MWI & Strings can explain it, all HUP/QM. It’s the need for a faster than light resolution here that requires one of the “non-local” explanations of QM above. It’s the requirement for “uncertainty” within them that defines QM as a “Non-Local” theory.

I’d credit Niels Bohr as first to see “QM inherently non-local” as part of its definition maybe better than Einstein. He defended QM against EPR hard because he new the QM Theory was dead if LR could be show true. I think Einstein would have been happy to modify it to make more “complete”. But by the Bohr definition (pretty well accepted by most) QM has come to mean “Uncertainty”, without that it would mean something new would be required.

Recognizing Non-Local reality as part of the definition of QM is one thing.
But as to when did that “result become clear” I think we’d have to say that it has been accepted as correct by most but doubted by at least some.

Von Newman had the accepted “proof” that EPR was wrong, but Einstein didn’t give.
But in the 60’s Bell should Von Newman’s math as “absurd” and gave the Bell-Theorem hoping that LR could show as real! He readily admitted disappointment experiments showing otherwise.
But were Einstein here I have little doubt that he would say that; Since Bell was able to show Von Newman as wrong, how sure can we be that someone someday might not show the Bell- Proof to be wrong – can we not have some uncertainty about that?

So as to: “when did this result become clear?” Maybe it isn’t clear yet.

Note: Ref a good book by J.S. Bell, “Speakable Unspeakable QM”, recently reprinted
RB

 

[DrChinese]

So as to: “when did this result become clear?” Maybe it isn’t clear yet.

The funny thing is, that there are plenty of people who think the debate is resolved. The only problem is that they all see the outcome differently.

 

[DrChinese]

1. Too vague. The probability of an outcome of a nearby measurement can be different, depending on whether we conditionalize on space-like separated information (e.g., the setting or outcome of a distant measurement). That already implies a kind of non-locality if the probabilities in question are all conditionalized on a complete specification of the particle states (in the past light cone(s) of the measurement events in question).

2. I never said non-locality was a conclusion of EPR.

3. Huh? It's a trivial matter to explain the perfect correlations in a local way, if you just add the assumption that there are hv's which determine the outcome.

1. Vague is a strange comment. I think it is clear that this is not only a true statement, but meaningful for plenty of people. This particular quote is from Vaidman. I completely disagree that the probability of a detection changes due to an event outside the past light cone of the measurement - I cannot imagine you arguing otherwise.

And I don't also don't agree that an incomplete specification has been demonstrated. The question is: was there a more complete specification at the time the entangled pair was created? No, there is no such specification. After you learn some more, then naturally you have a conditionalized view of things. What is non-local about that? You can learn this same information from either of the entangled particles, not exactly a shocking development.

2. I am trying to make sure I do not mis-characterize your views. I think it is more accurate to say that you believe that EPR proved QM was non-local if it is complete. Is that correct?

If so, I will repeat that EPR's conclusion was that if QM is complete, then there is not simultaneous reality to non-commuting observables. Realistically, I think this particular conclusion was understood prior to EPR (at least to a few) although EPR nicely draws a line in the sand on the matter.

Please don't get me wrong: I am a great supporter of EPR (but it does have some flaws).

3. There is not a local realistic way to explain the perfect correlations, if you consider the behavior of PDC entangled pairs. You don't need Bell's Theorem to realize that something is terribly wrong with naive LR explanations (the ones you call trivial). Recall the original post in the thread "A Paradox: Do LHV Theories Need the HUP?" to see that this is probably not possible any more to argue. Use 2 orthogonal BBO crystals and you get the "perfect" correlations. Use 1 and you get nothing but randomness, even though the naive LR explanation should still apply.

 

[DrChinese]

Re: Bell, terminology is getting the best of you.

I don't think terminology is getting the better of me in the least. From my perspective, your terminology is far off! But it really should be no surprise to either of us.

I think it is necessary to have common meaning for these terms and ideas to discuss them intelligently. Any survey of the literature will show exactly how difficult this is with EPR/Bell subject matter. Most authors struggle to nail down terms like "locality" (your Norsen reference needs 6 pages to make a dent in the subject, for example). And even after such definition, there is simply not full agreement anyway. But if we can come to common meaning, then more productive discussion can follow.

I don't mind shifting to terminology you prefer (when there are differences in expression) if that makes the discussion easier. But please, it is a bit condescending to suppose that you are somehow in possession of the only "correct" key to decoding the language - or even the most common usage thereof. That is why I often quote EPR and Bell directly RATHER than use lingo which may create disagreement. So I would encourage you to be lenient in this regard, and simply home in on areas in which our usage obviously diverges.

I am very interested in your ideas, and understanding better some of the concepts that drive your views. In many areas I suspect we are far more in agreement than in disagreement. And I absolutely agree with you that Bell is about classes of Hidden Variable theories, and is not a test of QM itself.

 

[ttn]

1. Vague is a strange comment. I think it is clear that this is not only a true statement, but meaningful for plenty of people. This particular quote is from Vaidman. I completely disagree that the probability of a detection changes due to an event outside the past light cone of the measurement - I cannot imagine you arguing otherwise.

According to the mathematical condition called "Bell Locality", we must have
$P(A|\hat{a},\hat{b},B,\lambda) = P(A|\hat{a},\lambda)$
where A is some outcome of Alice's experiment, a-hat is some controllable parameter of Alice's experiment (like the orientation of her SG device), lambda is a complete specification of the state of the system in the past light cone of Alice's measurement, and b-hat and B are variables outside that past light cone. (Obviously in the case at hand we are particularly interested in the setting and outcome of Bob's experiment, both of which are assumed to be spacelike separated from alice's experiment.)

Now suppose this condition is violated. What does that mean? It means that the probability for event A changes depending on whether you do or don't conditionalize on some information that isn't in the past light cone of the event in question. This wouldn't necessarily imply non-locality -- it only does so when we conditionalize on a complete description, lambda. But we're doing that, by assumption. So any violation of Bell Locality means that, in some sense (made precise by the equation above!), the outcome at A (or the probabilities for the various possible outcomes at A) depends on something going on in a spacelike separated region.

Now we simply ask: does orthodox QM respect this mathematical condition? Answer: no, it doesn't. Orthodox QM *violates* Bell Locality.

So, yes, I absolutely do think that the probability of an event changes (according to orthodox QM) due to an event outside the past light cone. That's just what a violation of Bell Locality *means*. Of course, you have to be careful about what you mean by "the probability". If you take out the conditionalization on the complete specification lambda, or if you talk about marginal probabilites, etc., then you can state truthfully that the probability of an event doesn't depend on what's going on outside the past light cone (according to oQM). But if the probabilities we're talking about are the ones appearing in the equation above, then there is no ambiguity and no question about the facts: oQM violates this condition.

BTW, who cares about this condition? Why should we accept this particular definition of locality? Because it's the very one Bell uses in deriving his theorem. So if you want to say his theorem proves that hvt's have to be nonlocal, you must apply the same condition to oQM when you ask: is it local?

And I don't also don't agree that an incomplete specification has been demonstrated. The question is: was there a more complete specification at the time the entangled pair was created? No, there is no such specification. After you learn some more, then naturally you have a conditionalized view of things. What is non-local about that? You can learn this same information from either of the entangled particles, not exactly a shocking development.

Completeness isn't merely a claim about what someone does or can know. In Bohm's theory, for example, you can prepare a particle by putting its wf in a certain state, and it turns out that you can't *independently* control the particle's position. You have to accept a Born-rule P(x) distribution. So you can know the wf but you can't know the particle position (initially). But that doesn't mean the wf alone provides a complete description. Bohm's theory says the position exists, whether we know it or not, so, according to Bohm's theory, a complete specification of the state has to include both the wf and the position.

2. I am trying to make sure I do not mis-characterize your views. I think it is more accurate to say that you believe that EPR proved QM was non-local if it is complete. Is that correct?

Yes.

If so, I will repeat that EPR's conclusion was that if QM is complete, then there is not simultaneous reality to non-commuting observables. Realistically, I think this particular conclusion was understood prior to EPR (at least to a few) although EPR nicely draws a line in the sand on the matter.
Please don't get me wrong: I am a great supporter of EPR (but it does have some flaws).

Then I'll have to repeat that you haven't understood their argument (and that maybe it's podolsky's fault for writing a crappy paper). Read Einstein's later comments on this, e.g., in his essays in the Schilpp volume, in the Born-Einstein letters, read Arthur Fine's book, read "Einstein's Boxes", etc.

3. There is not a local realistic way to explain the perfect correlations, if you consider the behavior of PDC entangled pairs. You don't need Bell's Theorem to realize that something is terribly wrong with naive LR explanations (the ones you call trivial). Recall the original post in the thread "A Paradox: Do LHV Theories Need the HUP?" to see that this is probably not possible any more to argue. Use 2 orthogonal BBO crystals and you get the "perfect" correlations. Use 1 and you get nothing but randomness, even though the naive LR explanation should still apply.

Maybe I'm taking you too literally, but there is a trivial way to explain the *perfect correlations*. Remember, there are perfect correlations (anti-correlations actually) for the case where Alice and Bob measure along the same axis. Whenever Alice gets "up", Bob gets "down" and vice versa. Here's the trivial model which explains those perfect anti-correlations: each particle in each pair carry an "instruction set" that tells them how to react (up or down) to a measurement along any axis at all, and the two particles' instruction sets are anti-correlated... so if the first particle's instruction set includes "be up if you are measured along the x-direction", the second particle's will include "be down if you are measured along the x-direction"... and so forth for *all* the other directions. Obviously such a model will correctly predict the perfect correlations that are observed when Alice and Bob measure along the same axis.

Can it also predict the empirically observed (and QM-predicted) correlation rates when Alice and Bob *don't* measure along the same axis? No, there are no instruction sets that will allow that. That's bell's theorem.

 

[DrChinese]

Maybe I'm taking you too literally, but there is a trivial way to explain the *perfect correlations*. Remember, there are perfect correlations (anti-correlations actually) for the case where Alice and Bob measure along the same axis. Whenever Alice gets "up", Bob gets "down" and vice versa. Here's the trivial model which explains those perfect anti-correlations: each particle in each pair carry an "instruction set" that tells them how to react (up or down) to a measurement along any axis at all, and the two particles' instruction sets are anti-correlated... so if the first particle's instruction set includes "be up if you are measured along the x-direction", the second particle's will include "be down if you are measured along the x-direction"... and so forth for *all* the other directions. Obviously such a model will correctly predict the perfect correlations that are observed when Alice and Bob measure along the same axis.

Can it also predict the empirically observed (and QM-predicted) correlation rates when Alice and Bob *don't* measure along the same axis? No, there are no instruction sets that will allow that. That's bell's theorem.

But the fact is that this explanation fails with a PDC setup. You get perfect correlations when the input pump passes through 2 orthogonal BBO crystals. The explanation works fine, because the instruction set works for the case where Alice and Bob have the same settings. So why does that explanation fall apart when you remove one of the BBO crystals? You still have a pair of entangled photons, the only difference is that they are not in a superposition! The trivial theory says these should also be perfectly correlated, but they aren't. (The superposition only appears with the 2 crystals, not the 1.) Thus our trivial explanation - which is supposed to be local realistic - now needs to incorporate the HUP and collapse postulate. That means it cannot be realistic because these are QM elements.

This was a point I was making in the other thread - that there are lots of problems with LR theories over and above Bell's Inequality. Of course, that is a lot easier to see post-Bell.

 

[ttn]

But the fact is that this explanation fails with a PDC setup. You get perfect correlations when the input pump passes through 2 orthogonal BBO crystals. The explanation works fine, because the instruction set works for the case where Alice and Bob have the same settings. So why does that explanation fall apart when you remove one of the BBO crystals? You still have a pair of entangled photons, the only difference is that they are not in a superposition! The trivial theory says these should also be perfectly correlated, but they aren't. (The superposition only appears with the 2 crystals, not the 1.) Thus our trivial explanation - which is supposed to be local realistic - now needs to incorporate the HUP and collapse postulate. That means it cannot be realistic because these are QM elements.
This was a point I was making in the other thread - that there are lots of problems with LR theories over and above Bell's Inequality. Of course, that is a lot easier to see post-Bell.

When you remove one of the crystals, the state of the photon pair is different, right? Certainly the state-according-to-QM (i.e., the wf) is different. And QM's predictions for outcomes/correlations are hence also different. So why shouldn't somebody's pet LHV theory also be able to attribute a different joint state to the two particles?

Don't get me wrong. There's nothing to be gained by trying to cook up a LHV explanation for all possible experimental permutations. I mean, who cares, since we already know that *no LHV theory can agree with the results of the Bell experiment*? That means LHV theories aren't viable, and whether or not they can explain some other random isolated experiment is, well, irrelevant and uninteresting.

That said, I'd be willing to bet a nickel that a LHV explanation could be found for whatever the correlations are when Alice and Bob measure along the same axis (no matter *what* the initial preparation of the pair is like). But I'm just speculating here.

One other point. If I read you right, you said that any theory which includes HUP and/or wf collapse wouldn't be "realistic" because these (HUP and collapse) are elements of QM. Again, you need to be more careful. Bohm's theory incorporates the HUP (interpreted epistemologically rather than ontologically, of course) and can actually deduce the collapse rule (rather than postulate it as a separate measurement axiom, as in the orthodox theory). But isn't Bohm's theory "realistic"? Maybe I'm just not sure what you mean by "realistic".

 

[DrChinese]

According to the mathematical condition called "Bell Locality", we must have

$P(A|\hat{a},\hat{b},B,\lambda) = P(A|\hat{a},\lambda)$

where A is some outcome of Alice's experiment, a-hat is some controllable parameter of Alice's experiment (like the orientation of her SG device), lambda is a complete specification of the state of the system in the past light cone of Alice's measurement, and b-hat and B are variables outside that past light cone. (Obviously in the case at hand we are particularly interested in the setting and outcome of Bob's experiment, both of which are assumed to be spacelike separated from alice's experiment.)

Now suppose this condition is violated. What does that mean? It means that the probability for event A changes depending on whether you do or don't conditionalize on some information that isn't in the past light cone of the event in question. This wouldn't necessarily imply non-locality -- it only does so when we conditionalize on a complete description, lambda. But we're doing that, by assumption. So any violation of Bell Locality means that, in some sense (made precise by the equation above!), the outcome at A (or the probabilities for the various possible outcomes at A) depends on something going on in a spacelike separated region.

Now we simply ask: does orthodox QM respect this mathematical condition? Answer: no, it doesn't. Orthodox QM *violates* Bell Locality.

So, yes, I absolutely do think that the probability of an event changes (according to orthodox QM) due to an event outside the past light cone. That's just what a violation of Bell Locality *means*. Of course, you have to be careful about what you mean by "the probability". If you take out the conditionalization on the complete specification lambda, or if you talk about marginal probabilites, etc., then you can state truthfully that the probability of an event doesn't depend on what's going on outside the past light cone (according to oQM). But if the probabilities we're talking about are the ones appearing in the equation above, then there is no ambiguity and no question about the facts: oQM violates this condition.

BTW, who cares about this condition? Why should we accept this particular definition of locality? Because it's the very one Bell uses in deriving his theorem. So if you want to say his theorem proves that hvt's have to be nonlocal, you must apply the same condition to oQM when you ask: is it local?

This is a pretty good definition of Bell Locality, but certainly you must be aware it is one of many. In fact, it is not the one used in Bell because outcome independence was not part of it as I hav e always read it (see Bell (1) and (2) and text between which makes this pretty clear).

But I thought these always evaluated to .5 anyway. So the likelihood of Alice seeing + or - doesn't change as b is varied (parameter independence).

So, yeah, I guess I am concluding that I don't see how this condition is violated by QM. And yes, I realize some authors have written it and have seen it repeated before as fact. But nothing changes about Alice's results when something is done at space-like separated region around Bob.

You see, the "non-local" element to QM is really entailed in the collapse of the wave function. I don't understand that mechanism (does anyone?) either, and I am not sure if it is actually non-local at all. Once the collapse occurs, nothing mysterious (or spooky ) really goes on. And collapse is something that occurs on single particles everywhere all the time. So I say the mystery is in the collapse, not in the correlations or the factorization.

You make a measurement on an entangled particle and the superposition collapses. Everything thereafter is fully local and within everyone's light cone! But there is no reality to the unmeasured particle observables. This is consistent between entangled multi-particle scenarios and single particle scenarios in oQM scenarios.

 

[DrChinese]

One other point. If I read you right, you said that any theory which includes HUP and/or wf collapse wouldn't be "realistic" because these (HUP and collapse) are elements of QM. Again, you need to be more careful. Bohm's theory incorporates the HUP (interpreted epistemologically rather than ontologically, of course) and can actually deduce the collapse rule (rather than postulate it as a separate measurement axiom, as in the orthodox theory). But isn't Bohm's theory "realistic"? Maybe I'm just not sure what you mean by "realistic".

Certainly there are ways to incorporate results that mimic the HUP in some LR theories. But Local Realistic theories have problems keeping the application of HUP going fully because because it usually violates either the locality or realistic requirement. Keep in mind that EPR assumed that you could beat the HUP, and essentially so do all LR theories. WF collapse also causes problems in LR theories for similar reasons. I don't consider this to be a problem with BM because it is designed to be more flexible. In other words, it can be realistic (see definition below) because it gets to use its non-local elements to keep the application of the HUP going much further than LR theories can.

Realistic means that particle attributes (observables) have simultaneous definite (real) values independent of their observation - I am trying to be consistent with Einstein's definition of this. So essentially realism means that the HUP is something that arises from our inability to see into the subatomic world, rather than a literal depiction of it. Non-realism, in constrast, drops this requirement just as non-local theories drop the requirement of locality. So the idea of a non-realistic theory does not entail some weird kind of universe, it is simply a universe in which particle attributes are not required to be constrained to definite values when not being observed.

In a world of virtual particles and path integrals, this doesn't seem so weird to me personally. (In fact, I don't think guide waves seem too weird either.) Keep in mind that I think a scientific proof that oQM should evolve to a non-local realistic theory would be great. (Although I wouldn't want Vanesch to feel he isn't loved either.) I just happen to sit on a line in which I am not ready to commit either to non-locality or non-reality. Of course, I have to suffer with the collapse postulate and the baggage it brings so I am not sure if I am in any better position net.

 

[Hurkyl]

"According to quantum theory, action at a space-like separated
region does not change the probability of an outcome of a local
measurement."

May I attempt a restatement?

Suppose we have a state p defined on a space-time region R.

Suppose we have another space-time region S that is causally determined by R. (In the purely geometric sense)

QM is local in the sense that the time-evolution of QM uniquely determines, from p, a state defined on S. (I will call this causal-local, unless someone has a better name for it!)

Furthermore, QM is complete in the sense that any probability only involving observables that are causally determined by R is uniquely determined by p. (I will call this causal-complete)

 

[DrChinese]

When you remove one of the crystals, the state of the photon pair is different, right? Certainly the state-according-to-QM (i.e., the wf) is different. And QM's predictions for outcomes/correlations are hence also different. So why shouldn't somebody's pet LHV theory also be able to attribute a different joint state to the two particles?

Because the explanation they cooked up still applies.

Of course, I agree with your basic assumption that they could continuously modify their theory as new facts present themselves until their theory makes no sense at all. In fact it CAN'T make sense. "CAN'T" in the sense that it is a totally useless ad hoc theory. That is because all LHV theories (post Bell especially!) are useless ad hoc theories. They purport to do nothing but give the same results as QM anyway. That is their entire purpose, to yield the predictions of QM without adding anything at all. Theories such as SED are an example of something I consider to be totally ad hoc. We already have QM! We don't need another equivalent QM.

I realize that with work in Everett's MWI, Bohm's BM, and Cramer's TI, folks are looking for improvements on QM. But one of the things that slows work in all of these areas is the fact that there is no obvious differences in the physical predictions of these theories. They must first yield oQM as a starting point to be taken seriously, yet this is precisely what makes them weak. Something of a "chicken and egg" problem. You got to admit that hurts resource allocation in research devoted to them.

I hope I am not stepping on any toes in saying the above... I am sure I am guilty of coming up with ad hoc explanations of my own.

 

[ttn]

Keep in mind that EPR assumed that you could beat the HUP, and essentially so do all LR theories.

EPR didn't *assume* this -- they *proved* it, based on the assumption of locality. They showed that if you make the locality assumption, the correlations predicted by QM (and long since confirmed by experiment) mean that definite pre-measurement values exist for observables that are governed by a HUP. This is not just some kind of arbitrary assumption. It's actually required by locality.

Realistic means that particle attributes (observables) have simultaneous definite (real) values independent of their observation - I am trying to be consistent with Einstein's definition of this. So essentially realism means that the HUP is something that arises from our inability to see into the subatomic world, rather than a literal depiction of it. Non-realism, in constrast, drops this requirement just as non-local theories drop the requirement of locality. So the idea of a non-realistic theory does not entail some weird kind of universe, it is simply a universe in which particle attributes are not required to be constrained to definite values when not being observed.

I don't strongly disagree with anything here, but there are a few dangerous points. In the first sentence you equate attributes with observables. But some of the properties that are observables according to QM are treated very differently according to other theories like Bohmian Mechanics. Another way to say this is that what *attributes* a particle even *possesses* is a very theory-dependent kind of thing. OQM and Bohmian Mechanics (just to use the typical cleanest examples) disagree about what properties these are. So I think it's ultimately not really defensible to describe one of these theories as "realistic" and the other as "non-realistic". Both are realistic, if that means that they both say that particles possesses exactly those properties that, according to the theory in question, they actually possess. (Yes, I'm aware that sentence didn't actually say anything. That's my point.) That's really the whole point of the completeness doctrine: there's some real state of the system and it is *completely* characterized by the wave function. That means (in the general case) that the particle doesn't have a particular value for most properties like position, momentum, spin-z component, etc. That's not "non-realistic" or "realistic" -- it's just a particular *theory* about what is real. And in that regard it is no different from Bohm's theory, this being just a *different* theory about what is real, i.e., what properties particles have.
This is why I really don't think the realistic/non-realistic terminology has any place in this debate. "Hidden variables" is a terrible term (for reasons I explained earlier) but at least we can give it an unambiguous meaning: anything that a given theory posits in addition to the wave function is a "hidden variable." So Bohm's theory is a hvt, and oQM isn't. And theories which purport to explain the correlations in EPR/Bell experiments by attributing definite spin components to each particle separately are hvt's. etc.

I just happen to sit on a line in which I am not ready to commit either to non-locality or non-reality. Of course, I have to suffer with the collapse postulate and the baggage it brings so I am not sure if I am in any better position net.

You make it sound like there is a choice between non-locality or non-reality. But this is not so. You do have a choice between reality or non-reality (whatever that means)... Let's be more careful: you can choose whether or not to accept the completeness doctrine. OQM and Bohm are both able to account for the NRQM results -- the former using the wf alone (but lots of weird extra measurement axioms) and the latter using the wf and definite particle positions (with no extra measurement axioms).
But there is no choice between locality and non-locality. OQM is nonlocal, Bohm is nonlocal, and there is a proof that no local theory can agree with experiment. So there simply is no choice here. You're stuck with nonlocality if you want to agree with experiment. So your only choice is between a nonlocal ugly theory full of "unprofessional vagueness and ambiguity", and a nonlocal "physicist's theory" that makes intuitive sense and treats all of reality from micro- to macro- on an even footing.

 

[DrChinese]

May I attempt a restatement?

Suppose we have a state p defined on a space-time region R.

Suppose we have another space-time region S that is causally determined by R. (In the purely geometric sense)

QM is local in the sense that the time-evolution of QM uniquely determines, from p, a state defined on S. (I will call this causal-local, unless someone has a better name for it!)

Furthermore, QM is complete in the sense that any probability only involving observables that are causally determined by R is uniquely determined by p. (I will call this causal-complete)

Hurkyl, in your opinion, wouldn't you say that most oQMers follow this program?

 

[Hurkyl]

Hurkyl, in your opinion, wouldn't you say that most oQMers follow this program?

I can't claim to have a qualified opinion, but I certainly think so.

 

[ttn]

May I attempt a restatement?
Suppose we have a state p defined on a space-time region R.
Suppose we have another space-time region S that is causally determined by R. (In the purely geometric sense)
QM is local in the sense that the time-evolution of QM uniquely determines, from p, a state defined on S. (I will call this causal-local, unless someone has a better name for it!)

The non-locality of orthodox qm is associated with the collapse postulate, not Sch's equation. So if your restatement here is meant to apply only to the unitary evolution part, it is true but misses the point. And if your restatement is supposed to be general (applying to either/both kinds of evolution that orthodox QM says happen) then it is just false.

 

[DrChinese]

...at least we can give it an unambiguous meaning: anything that a given theory posits in addition to the wave function is a "hidden variable." So Bohm's theory is a hvt, and oQM isn't.

I agree with this.

EPR held out the hope of a more complete specification of the system than the QM wavefunction allows. A more complete specification implies oQM is incomplete. How this is incompleteness is filled in leads to the terms "reality" or "realistic" (corresponding to EPR's "element of reality") or "hidden variables" (implying a deeper underlying mechanism).

But... you could assert the same thing about ANY physical theory, not just QM. I.E. General relativity is incomplete. Nope, it's not incomplete until the better thing actually comes along. THEN it's incomplete.

 

[ttn]

Of course, I agree with your basic assumption that they could continuously modify their theory as new facts present themselves until their theory makes no sense at all. In fact it CAN'T make sense.

I agree with the stuff about LHV theories being useless and ad hoc. But you're being irrationally hard on them if you ridicule them merely for adjusting their initial-state-assignment based on a new experimental setup! I mean, come on, you do this in regular QM, too. The initial quantum state depends on the preparation. And if instead of QM you believe in pumpkin dynamics, then the initial pumpkin state is going to need to depend on the preparation. *That* isn't proof that the pumpkin theory is useless and ad hoc.

"CAN'T" in the sense that it is a totally useless ad hoc theory. That is because all LHV theories (post Bell especially!) are useless ad hoc theories. They purport to do nothing but give the same results as QM anyway. That is their entire purpose, to yield the predictions of QM without adding anything at all. Theories such as SED are an example of something I consider to be totally ad hoc. We already have QM! We don't need another equivalent QM.

This is a dangerous attitude. If you have 7 theories that all give the same empirical predictions, you can't point to one of them and say: the other 6 are useless because we already have this one. The whole problem is: which one do you point to? If they're all equivalent, it's a mistake to pick one based on some random historical or sociological process (like Bohr effectively brainwashed lots of people) and say that that one is special just because it "got in first" or whatever. Judge the theories based on which one is the best theory, not based on which one got in first, which one has the most adherents, which one the textbooks tend to use, etc. That stuff is all non-scientific, sociological.
What we need is a good, consistent, logical theory to explain the experiments. Do you really think orthodox QM does that better than any of the other alternatives? If so, OK. But don't tell me Bohm's theory is out merely because it makes the same predictions as something else. If that's damning for Bohm, it should, by symmetry, be equally damning to the something else, too.

 

[Hurkyl]

The non-locality of orthodox qm is associated with the collapse postulate, not Sch's equation. So if your restatement here is meant to apply only to the unitary evolution part, it is true but misses the point.

Yes, it neglects any comment on wavefunction collapse, but it was meant to. The point of the statement of "causal-locality" is to emphasize the manner in which QM is local. QM does not throw locality to the wind -- the behavior which some call nonlocality only arises when you ask a special kind of question (which itself could be called a nonlocal question).

But in any case, I was just trying to state more rigorously that quote by DrChinese, which you called vague.

 

[DrChinese]

This is a dangerous attitude.

I don't think so. The proof is in the pudding in the final analysis. oQM has earned its stripes, can't really be any argument about that. Other theories have simply been playing catch up; so far they really haven't. Let's face it, a handful of scientists developed much of QM in a few short years in the 1920's. BM and MW have been around for decades and has had the attention of some people, if not a lot.

I am certainly a fan of pure research, so don't get me wrong. Sometimes, a strikeout is as good as a hit in the field of physics. But where does it end if all that is produced are equivalent predictions? If there are limited resources, then there is competition for funding. So there will always be some level of accountability for time spent researching new ideas. Scientists with established credentials have the advantage. I don't purport to have the answers but it is silly to ignore the obvious hard questions.

 

[ttn]

I don't think so. The proof is in the pudding in the final analysis. oQM has earned its stripes, can't really be any argument about that. Other theories have simply been playing catch up; so far they really haven't. Let's face it, a handful of scientists developed much of QM in a few short years in the 1920's. BM and MW have been around for decades and has had the attention of some people, if not a lot.
I am certainly a fan of pure research, so don't get me wrong. Sometimes, a strikeout is as good as a hit in the field of physics. But where does it end if all that is produced are equivalent predictions? If there are limited resources, then there is competition for funding. So there will always be some level of accountability for time spent researching new ideas. Scientists with established credentials have the advantage. I don't purport to have the answers but it is silly to ignore the obvious hard questions.

Don't equate the formalism and predictions of a theory with the theory. If you assign the Copenhagen interpretation "ownership" over the formalism of QM, then, yes, it looks like these other little guys like Bohm are just coming along and trying to tell a different story without making any new predictions. And then, yes, it's hard to understand why one should drop the thing that gave rise to all the predictions, in favor of something that's just coat-tailing on them.

But this is all completely wrong. As I noted in another post, this is wrong in terms of the historical facts. de Broglie's pilot wave theory was actually around *first* -- Schroedinger then posited "wave mechanics" by taking de Broglie's ideas and deliberately *dropping* reference to definite particle positions, and this idea (that the wf is a complete description) later became central to the orthodox view. I note this only to correct the misconception that the orthodox view existed first, and then de Broglie and/or Bohm came along and tried to *add* something to it ("hidden variables").

But the more important way in which the above attitude is wrong is this: the Copenhagen interpretation did not in any way "give rise to" the formalism and predictions of QM. It is an *interpretation* of the formalism -- one which *goes beyond* the formalism to tell a story about a possible real world in which that formalism is true. So we have things like the completeness doctrine, the postulated measurement axioms, HUP interpreted as ontological, i.e., as a description of objective indefiniteness of properties, etc. Let me ask you: how many new discoveries have all of these extra-formal principles led to? I mean, really, what has the completeness doctrine ever actually accomplished?

It's true, you can ask similar questions about the story postulated by, say, Bohm: what does it buy us to think of particles as having definite trajectories at all times, if there is uncertainty in initial conditions that prevents us from really saying anything other than that the probability distribution at the end of the experiment will be given by Born's rule? It's a fair question -- but it's only fair if you ask it of all the contenders in the race. You can't just give Copenhagen's postulates a pass (on the premise that it has none or that they are so obviously right that there is no need to raise questions about what supports them) and then dismiss something like Bohm on the grounds that it makes some postulates or tries to tell a story.

BTW, I notice that your comments have shifted from the issue of locality/nonlocality to some other focus. Does that mean you now concede that orthodox QM is as non-local as Bohm's theory? If so, I can see why you are now trying to change the subject. Because once that is made clear, support for Copenhagen starts to look increasingly indefensible.

 

[ttn]

Yes, it neglects any comment on wavefunction collapse, but it was meant to. The point of the statement of "causal-locality" is to emphasize the manner in which QM is local. QM does not throw locality to the wind -- the behavior which some call nonlocality only arises when you ask a special kind of question (which itself could be called a nonlocal question).
But in any case, I was just trying to state more rigorously that quote by DrChinese, which you called vague.

Well, whatever. But if you're going to just leave the measurement axioms aside, then there's not even any point discussing whether QM is nonlocal or not. It's just blatantly refuted by everyday mundane things such as cats never being observed in superpositions of alive and dead.

The fact is, the collapse postulate is a *necessary* part of orthodox QM. You can't just sweep it (and its implications, like non-locality) under the rug and pretend it isn't there. You can make up a new theory (like MWI) that doesn't have the collapse postulate, sure. But then you are in the difficult position of having to defend that quite crazy theory. Or you can talk about the orthodox theory, collapse postulate and all, in which case you can't logically avoid seeing that the theory is nonlocal. But you can't resolve anything by sitting on the fence and refusing to talk about certain parts of the theory.

 

[DrChinese]

BTW, I notice that your comments have shifted from the issue of locality/nonlocality to some other focus. Does that mean you now concede that orthodox QM is as non-local as Bohm's theory? If so, I can see why you are now trying to change the subject. Because once that is made clear, support for Copenhagen starts to look increasingly indefensible.

Good try. I like to have an open mind. But I don't see that either of us has moved very far in the main discussion. Still, I gained because I learned about other perspectives different from my own. And it forces me to fill in a few things I was unclear about in the process. And that's a good thing!

 

[Sherlock]

The probability of an outcome of a nearby measurement can be different, depending on whether we conditionalize on space-like separated information (e.g., the setting or outcome of a distant measurement). That already implies a kind of non-locality if the probabilities in question are all conditionalized on a complete specification of the particle states (in the past light cone(s) of the measurement events in question). According to QM, knowing the complete state of the world in the past light cone of a given measurement isn't enough to predict the probability of a given outcome -- conditionalizing also on space-like separated information changes the probabilities. In other words, the probabilites really *depend* on things that are going on at spacelike separation.

The only way to deny that this is a real nonlocal action at a distance is to deny the completeness doctrine. If we had conditionalized on only partial information about the states, then the fact that the probabilities change when we also conditionalize on space like separated information, wouldn't be a big deal.

I'm thinking of the probability of detection as being equivalent to the average number of detections per unit of time. Is this ok?

QM calculates the average rate of detection for a certain number (> 1) of measurements wrt a particular preparation, doesn't it?
We can ask if changing the value of b-hat alters the average rate of detection at A. It doesn't. And we can ask if changes in the average rate of detection at B are invariably accompanied by changes in the average rate of detection at A. They aren't. In fact, the average rates of detection at A and B are the same and remain more or less constant for any and all runs in Bell tests. So, I don't understand in what sense it can be said that the probability of detection at A is dependent on what happens at B, or vice versa.

Also, it seems clear to me that the wave function is not a complete description of the physical reality of the incident disturbances. Violations of Bell inequalities can be taken as telling us that the wave function including lambda is also not a complete description of the physical reality of the incident disturbances.

So, from this, what can I conclude about the intrinsic nonlocality, or locality, of either qm or nature? As far as I can tell, this just leaves the assumption of locality, which is what we started with.

 

[DrChinese]

You go with what is commonly accepted, and I'll go with what's true.

(The above quote came from another thread, but I moved it here because of the nature of my reply.)

True? Well, that is something we could discuss too. From http://arxiv.org/PS_cache/quant-ph/pdf/0409/0409054.pdf :

"This experiment poses a strong constraint on the validity of de Broglie-Bohm theory, which is the most successful example of a non-local hidden variable theory, representing a very relevant progress on the line of a final clarification of foundations of quantum mechanics." oQM supported, BM ruled out by 7+ standard deviations.

I await the requisite hand-waving.

 

[Sherlock]

According to the mathematical condition called "Bell Locality", we must have
$P(A|\hat{a},\hat{b},B,\lambda) = P(A|\hat{a},\lambda)$
where A is some outcome of Alice's experiment, a-hat is some controllable parameter of Alice's experiment (like the orientation of her SG device), lambda is a complete specification of the state of the system in the past light cone of Alice's measurement, and b-hat and B are variables outside that past light cone. (Obviously in the case at hand we are particularly interested in the setting and outcome of Bob's experiment, both of which are assumed to be spacelike separated from alice's experiment.)
Now suppose this condition is violated. What does that mean? It means that the probability for event A changes depending on whether you do or don't conditionalize on some information that isn't in the past light cone of the event in question. This wouldn't necessarily imply non-locality -- it only does so when we conditionalize on a complete description, lambda. But we're doing that, by assumption. So any violation of Bell Locality means that, in some sense (made precise by the equation above!), the outcome at A (or the probabilities for the various possible outcomes at A) depends on something going on in a spacelike separated region.
Now we simply ask: does orthodox QM respect this mathematical condition? Answer: no, it doesn't. Orthodox QM *violates* Bell Locality.

Ok. If you "conditionalize", post-hoc, an individual result at A based on what happened at B wrt a given pair, then it might seem that the A result depends on the B result and setting. Hence nonlocality.

But, is this the way that I should be justifying, interpreting the basis for the qm superposition of states and the calculation of entangled results via the expansion? The way I'm thinking about it now, the justification is that the incident disturbances that A and B are associated with are treated as a nonseparable wave function, as entangled, because of the assumption that the entangled property or properties were created by a common emission event or process.

 

[ttn]

(The above quote came from another thread, but I moved it here because of the nature of my reply.)
True? Well, that is something we could discuss too. From http://arxiv.org/PS_cache/quant-ph/pdf/0409/0409054.pdf :
"This experiment poses a strong constraint on the validity of de Broglie-Bohm theory, which is the most successful example of a non-local hidden variable theory, representing a very relevant progress on the line of a final clarification of foundations of quantum mechanics." oQM supported, BM ruled out by 7+ standard deviations.
I await the requisite hand-waving.

I haven't read Genovese's paper yet, though this makes me think it's not worth reading. There is a long history of fallacious claims (by Ghose and others) to have found an experiment in which Bohm and OQM make different predictions. In all such cases, the problem is simply that the authors don't understand how Bohm's theory works. It is, after all, a *theorem* in Bohmian Mechanics that one can reproduce the Born rule probabilities for all experiments.

So no hand-waving is needed: the statement in this paper you mention is simply *wrong*.

 

[ttn]

Ok. If you "conditionalize", post-hoc, an individual result at A based on what happened at B wrt a given pair, then it might seem that the A result depends on the B result and setting. Hence nonlocality.
But, is this the way that I should be justifying, interpreting the basis for the qm superposition of states and the calculation of entangled results via the expansion? The way I'm thinking about it now, the justification is that the incident disturbances that A and B are associated with are treated as a nonseparable wave function, as entangled, because of the assumption that the entangled property or properties were created by a common emission event or process.

It is crucial that lambda be a complete description. It's only under that condition that the changing probabilities (when we conditionalize on something outside the past light cone) implies a real superluminal action at a distance.

So the question is: how could you ever know if a given lambda is a complete description of reality? Sounds like an impossible assignment, right? Well, that's the wrong way to think about it. We use Bell Locality to test whether a given *theory* (which makes some claim about what a complete description might look like) is local or not. Orthodox QM claims that the wf alone provides a complete description, so we just use that and ask if Bell Locality is respected. It isn't, for orthodox QM. Or pick some other theory, say Bohm's theory: we can just ask, if Bohm's theory provides a complete description, does it respect Bell Locality? Answer: no.

This is a key point. You don't need Bell's Theorem to test whether or not a specific candidate theory (i.e., specific candidate for what Bell's "lambda" might consist of) is local. You just ask if the theory respects Bell Locality.

What good then is the theorem? The theorem shows that a whole broad *class* of theories has to make predictions satisfying the inequality (which is known empirically to be violated). So the theorem wipes out a whole class of theories -- which means you don't even have to wait for someone to propose a particular theory to know that it isn't going to work.

But the important thing is this: make sure you don't think that the full proof that *nature* is non-local amounts merely to pointing out that orthodox QM violates Bell Locality. It does, but that doesn't prove anything about nature. Well, I guess it proves that *either* nature is nonlocal *or* that OQM is not operating with a complete description. This is of course just the EPR argument. If you accept that OQM is complete, you're left with a nonlocal theory. Or you can jettison completeness in order to try to save locality (which is what Einstein favored... but of course now we know that won't work).

 

[DrChinese]

I haven't read Genovese's paper yet... So no hand-waving is needed: the statement in this paper you mention is simply *wrong*.

I get this a lot from the local realist crowd too... denial. But as a courtesy, I will gladly withhold judgment until you can read the paper (and then hand wave).

 

[ttn]

I get this a lot from the local realist crowd too... denial. But as a courtesy, I will gladly withhold judgment until you can read the paper (and then hand wave).

What is the experiment which (allegedly) OQM and Bohm make different predictions? Who/what is cited in this paper, and what kind of experiment is it supposed to be? The ones I remember were double slit experiments involving two particles at once, proposed by Ghose et al. There was a whole flurry of papers on arxiv.org some years ago about this, and it emerged quite clearly that Ghose had made some assumptions which are actually false according to BM in his derivation of the "BM prediction". So if that's what's cited, forget about it. I'm not going to waste my time reading it. But if it's something new/different, I'll take a look.

 

[DrChinese]

The ones I remember were double slit experiments involving two particles at once, proposed by Ghose et al. There was a whole flurry of papers on arxiv.org some years ago about this, and it emerged quite clearly that Ghose had made some assumptions which are actually false according to BM in his derivation of the "BM prediction". So if that's what's cited, forget about it. I'm not going to waste my time reading it.

It is in the Ghose/double-slit groove. Of course, Genovese et al see it as relevant.

I sure have to believe that if BM is to have merit, there must be something it can offer over and above philosophical distinction. Is it different in ANY predictions from oQM?

 

[ttn]

It is in the Ghose/double-slit groove. Of course, Genovese et al see it as relevant.

Cool. Now I know not to waste my time reading Genovese's article.

I sure have to believe that if BM is to have merit, there must be something it can offer over and above philosophical distinction. Is it different in ANY predictions from oQM?

Sigh. Maybe you weren't paying attention yesterday when I addressed this issue. Let me re-frame it: I sure have to believe that if oQM is to have merit, there must be something it can offer over and above philosophical distinction. Is it different in ANY predictions from Bohmian Mechanics?

 

[Sherlock]

It is crucial that lambda be a complete description. It's only under that condition that the changing probabilities (when we conditionalize on something outside the past light cone) implies a real superluminal action at a distance.
So the question is: how could you ever know if a given lambda is a complete description of reality? Sounds like an impossible assignment, right? Well, that's the wrong way to think about it. We use Bell Locality to test whether a given *theory* (which makes some claim about what a complete description might look like) is local or not.

I thought we were testing whether a hidden variable formulation is viable or not (not whether it is local or not). In a local universe, the general form would have to be local, ie., containing P(A|a-hat, lamda) and P(B|b-hat, lambda) as separate factors. This general hidden variable formulation is incompatible with qm and it also doesn't agree with experiment, which qm does. So, in a local universe, hidden variable theories are ruled out, because, in a local universe, hidden variable theories have to have the general (separable) form that Bell specified. Does this necessarily tell us that qm or nature is nonlocal? I don't think so.

Orthodox QM claims that the wf alone provides a complete description, so we just use that and ask if Bell Locality is respected. It isn't, for orthodox QM. Or pick some other theory, say Bohm's theory: we can just ask, if Bohm's theory provides a complete description, does it respect Bell Locality? Answer: no.
This is a key point. You don't need Bell's Theorem to test whether or not a specific candidate theory (i.e., specific candidate for what Bell's "lambda" might consist of) is local. You just ask if the theory respects Bell Locality.
What good then is the theorem? The theorem shows that a whole broad *class* of theories has to make predictions satisfying the inequality (which is known empirically to be violated). So the theorem wipes out a whole class of theories -- which means you don't even have to wait for someone to propose a particular theory to know that it isn't going to work.
But the important thing is this: make sure you don't think that the full proof that *nature* is non-local amounts merely to pointing out that orthodox QM violates Bell Locality. It does, but that doesn't prove anything about nature. Well, I guess it proves that *either* nature is nonlocal *or* that OQM is not operating with a complete description. This is of course just the EPR argument. If you accept that OQM is complete, you're left with a nonlocal theory. Or you can jettison completeness in order to try to save locality (which is what Einstein favored... but of course now we know that won't work).

It was known before Bell that hidden variable theories were incompatible with qm, wasn't it? Of course, it was due to Bell and during his time that quantitative tests became possible and were carried out.


Anyway, I understand what you're saying. I've jettisoned completeness wrt both the qm wave function and any lambda that might be used to supplement it.


This allows (preserves) the assumption that nature is local, and in a local universe in which the principles of quantum theory provide for correct predictions regarding quantum correlations, then, via Bell and Bell tests, hidden variable theories are disallowed.


The qm principles and procedures themselves tell me nothing about the locality or nonlocality of nature. It isn't *necessary* to interpret the qm method of calculating probabilities as evidence for nonlocality. There is no physical, qualitative justification for such an interpretation (at the level of quantum processes) provided by the theory, afaik.


Note: I might have to change some of my statements, depending on what I learn. Just getting into what determines the phase factors, and exactly how the phase difference between different parts of the wave function control the magnitude of the interference terms. Looks pretty 'local' so far. :-)

Here's some statements by Bohm:

"Every Hermitean operator representing some observable quantity in the quantum theory will be tentatively assumed to have the property that an arbitrary acceptable wave function can be expanded as a series of its eigenfunctions."

"It is a fact that all operators of this kind that are now known have this property. This property is, as we shall see, so closely bound up with the interpretation of quantum theory that if it were ever found not to be satisfied, fundamental changes in the theory would probably be needed. Thus, it seems reasonable to postulate it here."

And, after discussing some calculational, representational, and interpretational stuff he says:

"The role of the expansion postulate in making possible our present interpretation of |C_a|^2 is clearly a key one. If it were not possible to expand an arbitrary psi as a series of psi_a, an integral part of our method of interpreting the wave function would then become untenable. The general requirements of consistency and unity of the theory would therefore suggest that in the absence of contradictions with experiment, we can safely regard the expansion postulate as a definition, or as a criterion which must be satisfied by an operator before we accept it as a suitable observable for use in the quantum theory. The fact that all observables now known satisfy this criterion is then experimental proof of the validity of this postulate."

I don't yet know all the details pertaining to why the theory was developed the way it was in the first place, but I'm pretty sure that the people who were developing it were assuming that nature is local. In any case, interpreting qm as a nonlocal theory seems to be unfounded.

 

[ttn]

I thought we were testing whether a hidden variable formulation is viable or not (not whether it is local or not).

Well, it depends on what we're talking about. If you're just staring at Bell's Locality Condition, you can't really use that to test whether or not some particular theory is viable. That's a question for the theory and for experiment, obviously.

"Bell Locality" is a particular definition of what it means for a theory to be local. So the obvious way to use it is to see if a theory satisfies it -- i.e., to see if a given theory is local. And if you're really clever you can also figure out a way to use it to put a constraint on all local theories. That's what Bell's theorem does.

In a local universe, the general form would have to be local, ie., containing P(A|a-hat, lamda) and P(B|b-hat, lambda) as separate factors.

It confuses the issue to talk about a local universe. We don't start by knowing what the universe is like. We start by having some theory/theories that purport to describe the universe. Then we can ask question of those various theories, such as: does it agree with experiment? is it local? etc. So I would restate what you said this way: a local theory will explain the outcomes A and B using expressions like the one you wrote (where there is no dependence on spacelike separated info).

This general hidden variable formulation

What does this have to do with hidden variables? It's a statement of *locality*. A local hv theory will work this way, yes. As will a local non-hv theory. It's a test of locality, period. A theory that works this way is local, whether it has hv's or not.

So, in a local universe, hidden variable theories are ruled out, because, in a local universe, hidden variable theories have to have the general (separable) form that Bell specified.

in a local universe, *any* theory has to have the general (separable) form that Bell specified. That is, if what you mean by locality is Bell Locality, then a local theory has to respect Bell Locality. But that's not a statement about hidden variable theories exclusively.

Does this necessarily tell us that qm or nature is nonlocal? I don't think so.

Look, it's really simple. Forget for the moment about hidden variables and everything else. Suppose you accept "Bell Locality" as a definition of what it means for a theory to be local. Just look at orthodox QM and ask: is it Bell Local? Answer: no. Now you think: is there some way I could fiddle with QM (e.g., by adding hidden variables) in order to construct a Bell Local theory (making sure of course to stay true to the QM predictions since those are verified by experiment)? Answer: no. (Bell's theorem.) So no Bell Local theory can agree with experiment, whether it has hidden variables or not. There's no empirically viable theory that is Bell Local. So nature violates Bell Locality. QED.

It was known before Bell that hidden variable theories were incompatible with qm, wasn't it?

Um, seeing as the statement is completely false, no, it wasn't known before Bell (nor after).

This allows (preserves) the assumption that nature is local, and in a local universe in which the principles of quantum theory provide for correct predictions regarding quantum correlations, then, via Bell and Bell tests, hidden variable theories are disallowed.

But so are NON-hidden-variable theories! Don't believe me? I'll give you a million dollars if you can construct a theory of any kind that respects Bell Locality but which agrees with the QM predictions for these experiments.

The qm principles and procedures themselves tell me nothing about the locality or nonlocality of nature.

That's right -- they tell you *only* that *if* QM is complete, then nature is nonlocal. That's EPR: the price of accepting completeness is rejecting locality (or equivalently: the price of holding onto locality is rejecting completeness).

The sensible response to this in the 30's should have been: well then to hell with the completeness doctrine! Let's look for a hidden variables theory that will allow us to respect relativity/locality! But only approximately one person had that much sense: Einstein. And he never succeeded in finding a local hvt that would agree with the qm predictions (which I think he accepted were probably right). Now we know why: the project was doomed to failure. You can't produce the QM predictions with a local theory.