Scholarpedia article on Bell's Theorem

[DrChinese]

I honestly have no clue what you have in mind with this word "simultaneous". I think you mean to be referring back to the actual EPR paper, where they talk about simultaneous values for non-commuting operators. ... What do you mean by "realism"? See, you really need to be more careful/precise/clear with what you mean by "realism".

I think I have been quite clear on this point. The standard definition for realism in this context is that there exist simultaneous elements of reality for non-commuting (and commuting) observables, exactly following EPR and their definition for "elements of reality". Not sure how hard that is to grasp, I say the same thing every time and quote from the paper repeatedly. EPR says that it is unreasonable to require elements of reality to be simultaneously predictable. That included, we have a working definition of realism.

So to be clearer: If I can predict a with certainty, and I can predict b and c etc with certainty, and I assume the definition of realism a la EPR, then I would define a, b and c are real. That is, of course, subject to challenge. I don't know of any major interpretations in which definite simultaneous counterfactual real values can be assigned to these if they do not commute. In other words, realism is soundly rejected by all. This is in direct contradiction to Einstein's view that an electron has well defined spin, position etc at all times.

 

[ttn]

I think I have been quite clear on this point. The standard definition for realism in this context is that there exist simultaneous elements of reality for non-commuting (and commuting) observables, exactly following EPR and their definition for "elements of reality". Not sure how hard that is to grasp, I say the same thing every time and quote from the paper repeatedly.

OK.

So to be clearer: If I can predict a with certainty, and I can predict b and c etc with certainty, and I assume the definition of realism a la EPR, then I would define a, b and c are real. That is, of course, subject to challenge. I don't know of any major interpretations in which definite simultaneous counterfactual real values can be assigned to these if they do not commute. In other words, realism is soundly rejected by all. This is in direct contradiction to Einstein's view that an electron has well defined spin, position etc at all times.

First off, Einstein never said any such thing. What's expressed in the EPR paper (and I assume this is what you meant) is that (e.g.) one of the two electrons in the pair has both a well defined position and momentum. Or if we translate to the spin version of the argument, each electrons has simultaneous pre-existing non-contextual definite values for spin-along-a, spin-along-b, spin-along-c, etc. So let's pretend that Einstein actually claimed that.

The question is, why did he claim that? Your view seems to be "he just did, he just assumed it." But that is wrong. He claimed that because he had just presented a perfectly valid logical argument showing that this conclusion *followed* from locality (plus certain predictions of ordinary QM, namely, the perfect correlations). Of course, Einstein, inventor of relativity theory, had no reason to doubt that locality was true. So he actually believed the conclusion of this argument. But that he turned out to be wrong about *that* in no way invalidates the *argument*. It's still true that "the only way to explain the perfect correlations in a local theory is with pre-existing values [i.e., what you insist on calling "realism"]". Einstein was not wrong about *that*!

And this matters, because if it's still true that

1: locality --> X

and (I don't think anybody doubts)

2: X --> contradiction with experiment

then it's still true that

locality --> contradiction with experiment

even if we no longer accept 1 as a reason to believe X, indeed, whether we believe X or not.

It just doesn't matter. You keep coming back to this idea that you can somehow elude Bell's conclusion (that nonlocality is true) by disagreeing with Einstein. But it's a matter of elementary logic. You cannot elude Bell's conclusion merely by saying "Einstein was wrong to believe X". If you want to elude Bell's conclusion you have to actually find something wrong with Einstein's argument from locality to X. Whether X is true, and whether locality is true, are not the same thing as whether locality --> X.

 

[DrChinese]

1. First off, for the millionth time, a, b, and c are angles. They are axes along which one might contemplate measuring the spin/polarization of a particle. They aren't properties. So it doesn't even make any sense to talk about whether "there are simultaneous definite values for a, b, and c" or not. Presumably what you mean is whether there are simultaneous definite values for spin-along-a, spin-along-b, and spin-along-c. OK. You're right that, for Bohmian mechanics, spin is contextual. That means, basically, that Bohmian mechanics does not claim that spin-along-a, spin-along-b, and spin-along-c all exist with simultaneous definite values.

2. OK, so let me drop the sarcasm and ask you straight: how precisely do you propose to redefine words? I *think* your point in the first paragraph was supposed to be that, actually, Bohmian mechanics is not realistic (because it is contextual). OK, fine, I'm cool with that. But that's not going to show *anything* about locality. Bohmian mechanics will still be nonlocal, no matter how you define "realistic". So... how do you propose to redefine "local" such that Bohmian mechanics becomes a local theory?

1. Is it really hard for you to see that when I say a, I actually mean the element of reality which corresponds to certain prediction I am making at angle a? Do I really need to say those words? You say "spin-along-a" here, what difference does the notation make to our conclusions? I really think people can understand that a b and c are angles, there are outcomes of measurements at those angles, and there might be elements of reality associated with those outcomes. You use the same shortcuts when it is convenient to you.

2. Seriously, I never said otherwise. By all definitions, I would call dBB type theories non-local.

What I said was that IF I wanted to, I might alter the definitions of Bell such that "realism is not tenable by any theory agreeing with the predictions of QM"*. Rather than the usual conclusion that "local realism is not tenable by any theory agreeing with the predictions of QM". And in contrast to your conclusion: "locality is not tenable by any theory agreeing with the predictions of QM".

My point being that there really are no candidate realistic theories, because it is almost universally accepted that - as a result of Bell - there cannot be simultaneous values for non-commuting elements of reality. Exactly in accordance with garden variety QM.

*Please note that I am not making/advancing this argument, just showing that definitions matter to wording of one's conclusion. We don't need to debate whether my argument is a good one or not; the fact that I am not ready to push it is a simple nod that it isn't good enough to do anything useful for anyone at this point. Most essentially already hold this opinion in one form or another as it is.

 

[DrChinese]

It's still true that "the only way to explain the perfect correlations in a local theory is with pre-existing values [i.e., what you insist on calling "realism"]". Einstein was not wrong about *that*!

That's not what EPR said, and Einstein never said that. At least not that I am aware of. Perhaps you have a quote similar to that? (Not one where you deduce this, please.) EPR was arguing that a more complete specification of the system was possible, specifically that there were definite values for non-commuting observables. Their focus was more on demonstrating that reality was not observer dependent, rather than locality requires the existence of hidden variables.

But I see where you would be tempted to go from your statement above to your argument about locality. And in some ways, I think it is good since I certainly can't imagine a local mechanism without hidden variables which delivers perfect correlations (using your definition of locality). That does not change the fact that Bell is dependent on realism as an assumption. You should address the strongest arguments against your position. There is no justification, other than by assumption, for the use of a, b and c in the Bell argument unless there is experimental support for it. Which there is not.

 

[ttn]

1. Is it really hard for you to see that when I say a, I actually mean the element of reality which corresponds to certain prediction I am making at angle a? Do I really need to say those words? You say "spin-along-a" here, what difference does the notation make to our conclusions? I really think people can understand that a b and c are angles, there are outcomes of measurements at those angles, and there might be elements of reality associated with those outcomes. You use the same shortcuts when it is convenient to you.

I'm not trying to be anal about it. I'm not saying "nobody but me gets to take notational shortcuts!". But, try as I might, I have trouble following what you are saying much of the time. So maybe your notation/terminology is not as clear as you take it to be. For example, you always make a big fuss about how Bell introduced a *third* angle, c, in the a/b/c triplet. Whereas before people had only talked about 2. Or something like that. None of that makes any sense to me. You can only measure polarization along *one* angle (without radically altering the state), and according to QM a state can only possesses a definite value along one such angle at a time. Talking about there being definite values for *two* such angles thus already means one is endorsing some kind of "hidden variable" or "realism" or whatever. Yet you always say, no, 2 is fine, it's 3 that introduces some big new suspicious issue. So I am constantly feeling: either what he's saying is complete nonsense, or he's using terminology in a way I don't understand. I try whenever possible to give the benefit of the doubt and assume the latter. Hence my complaining about what seems like dubious/confusing terminology.

2. Seriously, I never said otherwise. By all definitions, I would call dBB type theories non-local.

What I said was that IF I wanted to, I might alter the definitions of Bell such that "realism is not tenable by any theory agreeing with the predictions of QM"*. Rather than the usual conclusion that "local realism is not tenable by any theory agreeing with the predictions of QM". And in contrast to your conclusion: "locality is not tenable by any theory agreeing with the predictions of QM".

I don't think you understood my complaint. I don't understand *at all* what you think you can do here. It's really simple. Either you redefine "realism" to mean "locality" -- which is obviously just a stupid pointless trick. Or you think you can redefine "locality" in a way that still preserves some semblance of the usual meaning of that concept, but which now allows local theories to be compatible with the predictions of QM. Well, I want to see it. Talk is cheap. Tell me your proposed formulation of "locality".

My point being that there really are no candidate realistic theories, because it is almost universally accepted that - as a result of Bell - there cannot be simultaneous values for non-commuting elements of reality. Exactly in accordance with garden variety QM.

But don't you see that this is totally irrelevant to bell's proof that locality is untenable? Suppose instead of "realism" we focus on the class of theories according to which all the particles are coated in a tasty layer of pink frosting. Call these the pinkistic theories. Now, it can be shown that

locality + pinkism --> contradiction with QM predictions and with experiment

It is also true, as I look around at various extant candidate theories, that none of them are pinkistic.

Does this mean that, instead of accepting Bell's conclusion that locality is untenable, I can *instead* deny pinkism? No, it does not mean this. Because it can *also* be shown that

locality --> contradiction with QM predictions and with experiment

That is, you don't *need* to assume pinkism to get the contradiction. You *only* need to assume locality. Pinkism was actually a *superfluous premise* in the first argument! So (until/unless you can show what's wrong with the proof that locality --> contradiction...) you have to accept that locality is untenable *whether or not you believe pinkism*. Pinkism, it turns out, is just a red herring. It has nothing whatsoever to do with Bell's theorem.

Of course, maybe there are *other* reasons -- perhaps even really strong reasons -- to deny pinkism. Maybe we can even all agree that pinkism is false. What of it? It has no implications for Bell's theorem.

Everything I've just said remains true if one substitutes "realism" for "pinkism". Note in particular that we can all agree that "realism" (as Dr C has defined it here) is false. This is known from the various no-hidden-variables theorems (Kochen-Specker, etc.) which show that there is no consistent way to assign pre-existing values to non-commuting observables and reproduce the quantum statistics. So *that* is why there are no extant "realist" theories. We know they can't exist (and make the right predictions)! But ... again ... what in the world does that have to do with Bell's proof of the untenability of locality?

Nothing!

*Please note that I am not making/advancing this argument, just showing that definitions matter to wording of one's conclusion. We don't need to debate whether my argument is a good one or not; the fact that I am not ready to push it is a simple nod that it isn't good enough to do anything useful for anyone at this point. Most essentially already hold this opinion in one form or another as it is.

Well, I guess I think we *do* need to debate whether your argument is good or not. You keep making it. You keep suggesting that there is some loophole here, some way of saying a bunch of words about realism or whatever that somehow amounts to there being, actually, a *choice* about whether we deny locality or instead deny something else. But there is no valid substance to any of what you're saying. You fail to grasp Bell's actual argument, bring up a bunch of distracting red herrings, and then say a bunch of vague words about how it all comes down to definitions/semantics. None of that constitutes a valid argument against what Bell has claimed to show.

 

[ttn]

EPR was arguing that a more complete specification of the system was possible, specifically that there were definite values for non-commuting observables.

Correct.

Their focus was more on demonstrating that reality was not observer dependent, rather than locality requires the existence of hidden variables.

Also correct, but misleading. Recall that Podolsky wrote the paper and Einstein said the main point was buried. The main point Einstein had in mind was: locality. So yes, it's true that "their focus was [not so much on] locality". But it *should* have been, according to Einstein at least.

See, e.g., my article "Einstein's boxes" (from AJP several years ago, or online here

http://arxiv.org/abs/quant-ph/0404016

) for the sorts of Einstein quotes you seek.

As to the EPR paper itself, the use of locality is hidden in the assumption that the "reality criterion" can be *applied* to the case at hand. That is, they say that an element of reality exists if we can predict in advance what the value will be for some property *without in any way disturbing the system*. Well, what grounds do we have for thinking that measuring some property on this particle over here, won't affect the physical state of that other particle over there? Locality.

It is indeed unfortunate that this wasn't spelled out more clearly in the paper. Einstein thought so too. Podolsky's text makes way too big a fuss over the "reality criterion", and way too *little* a fuss over the reason we expect it to *apply* to the case at hand.

But I see where you would be tempted to go from your statement above to your argument about locality. And in some ways, I think it is good since I certainly can't imagine a local mechanism without hidden variables which delivers perfect correlations (using your definition of locality).

OK, that's a good start. Actually it can be made more precise and rigorous -- that is, it is possible (indeed, surprisingly trivial) to show rigorously that the appropriate sort of "hidden variables" are *required* by locality + perfect correlations. So it's stronger than just "I can't think of a way to do it".

That does not change the fact that Bell is dependent on realism as an assumption.

How many millions of times have I explained, in detail, that this is not true? That realism is *not* an assumption of Bell, but instead something that gets *inferred* from locality?

You should address the strongest arguments against your position.

I'm trying. Let me know when you find one.

There is no justification, other than by assumption, for the use of a, b and c in the Bell argument unless there is experimental support for it. Which there is not.

So, your whole thing comes down to: if we can't measure it, it doesn't exist? I don't agree with that, on philosophical grounds. But that is irrelevant here. Because actually what you say is just plain false. There *is* a "justification ... for the use of a, b and c in the Bell argument". That justification is: the EPR argument, which *proves* -- savor that word -- that locality requires a, b, and c.

Really, given what you've said, here's how you should think about all this.

Step 1: (the EPR argument) locality --> a, b, and c

Step 2: (the Dr C argument) a, b, and c can't exist because we can't measure them all simultaneously

Conclusion: locality is false (because it implies something that we know is wrong).

My point is that you should be *quicker* than me or others to conclude that locality is wrong. You think you already know that one of the things it entails, is false! Of course, if you tried to present this as a proof for nonlocality, you'd have people like me disagreeing with step 2 of the argument! So I don't consider this 2-part argument as a valid proof of nonlocality! But my point is, if you accept "step 1" (as you seem to, at least sometimes) and you accept "step 2" (as you seem to), you should conclude that locality is false. Instead, you think that step 2 somehow "undoes" step 1. That is, you think denying "a, b and c" somehow constitutes a refutation of the EPR argument. Of course it does not. You don't refute an argument by simply denying the conclusion.

Or maybe you're using a special Dr C version of quantum logic or something.

 

[DrChinese]

For example, you always make a big fuss about how Bell introduced a *third* angle, c, in the a/b/c triplet. Whereas before people had only talked about 2. Or something like that. None of that makes any sense to me. You can only measure polarization along *one* angle (without radically altering the state), and according to QM a state can only possesses a definite value along one such angle at a time. Talking about there being definite values for *two* such angles thus already means one is endorsing some kind of "hidden variable" or "realism" or whatever. Yet you always say, no, 2 is fine, it's 3 that introduces some big new suspicious issue.

Before EPR: 1 (ONE: a) value is what QM says you can know with certainty of any non-commuting set (along with mixed variations A, B, C...). I hope this is obvious. Let's call that result_of_A_observation (or just a).

EPR says: I can know 2 (TWO: a, b) values: result_of_A_observation AND result_of_B_observation (which tells me something if I could otherwise predict with certainty). This requires a bit of an assumption though about reasonable definitions of reality (let's call that realism).

BELL says: If I extend the EPR assumption of realism to a simultaneous unmeasured/counterfactual 3rd value result_of_C_observation (THREE: a, b, c), then a contradiction arises.

I hope this is clear and I got my a, b, c's right.

 

[Gordon Watson]

1. Is it really hard for you to see that when I say a, I actually mean the element of reality which corresponds to certain prediction I am making at angle a? Do I really need to say those words? You say "spin-along-a" here, what difference does the notation make to our conclusions? I really think people can understand that a b and c are angles, there are outcomes of measurements at those angles, and there might be elements of reality associated with those outcomes. You use the same shortcuts when it is convenient to you.

2. Seriously, I never said otherwise. By all definitions, I would call dBB type theories non-local.

What I said was that IF I wanted to, I might alter the definitions of Bell such that "realism is not tenable by any theory agreeing with the predictions of QM"*. Rather than the usual conclusion that "local realism is not tenable by any theory agreeing with the predictions of QM". And in contrast to your conclusion: "locality is not tenable by any theory agreeing with the predictions of QM".

My point being that there really are no candidate realistic theories, because it is almost universally accepted that - as a result of Bell - there cannot be simultaneous values for non-commuting elements of reality. Exactly in accordance with garden variety QM.

*Please note that I am not making/advancing this argument, just showing that definitions matter to wording of one's conclusion. We don't need to debate whether my argument is a good one or not; the fact that I am not ready to push it is a simple nod that it isn't good enough to do anything useful for anyone at this point. Most essentially already hold this opinion in one form or another as it is.

With apologies: I'm away from my office and not yet able to efficiently join this debate.

BUT, to add my support to alternative views of Bell's theorem, to reinforce some thoughts in the quote above, and to encourage questioning of the "realism" assumed in Bell's Theorem:

I find no reason anywhere to abandon Einstein-locality!

 

[DrChinese]

Step 2: (the Dr C argument) a, b, and c can't exist because we can't measure them all simultaneously

Just want to be clear: this is not MY assertion at all. We must either follow the EPR program and consider this as a reasonable assumption, or not. Once we define Realism to include this assumption, we can proceed.

If a person objects, as EPR says: "Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted."

So obviously we must agree that this is an assumption or the EPR result falls, since that is exactly what they said. Ditto, the Bell result falls as well if this is not agreed to (notice they say two or more). And apparently, this is quite a source of debate so I say it is a rather important assumption, yes. EPR explicitly acknowledge it!

 

[ttn]

Before EPR: 1 (ONE: a) value is what QM says you can know with certainty of any non-commuting set (along with mixed variations A, B, C...). I hope this is obvious. Let's call that result_of_A_observation (or just a).

EPR says: I can know 2 (TWO: a, b) values: result_of_A_observation AND result_of_B_observation (which tells me something if I could otherwise predict with certainty). This requires a bit of an assumption though about reasonable definitions of reality (let's call that realism).

BELL says: If I extend the EPR assumption of realism to a simultaneous unmeasured/counterfactual 3rd value result_of_C_observation (THREE: a, b, c), then a contradiction arises.

I hope this is clear and I got my a, b, c's right.

That indeed clarifies what you're thinking, but basically I think you're barking up the wrong tree. The same exact reasoning that gives EPR's *second value*, gives as many values as you want. The only reason the EPR paper stresses the *two* values is that they (really, he, Podolsky) want(s) to show that more values exist than QM (in particular the so called eigenstate-eigenvalue link) can accommodate. To establish that, two values will suffice. Though it remains true that actually their argument establishes 3, 4, ... infinity.

As a further historical digression, note that even focusing on *two* values in this way is a kind of unfortunate and unnecessary. If the point is just to show that QM is incomplete, it'd be perfectly sufficient to show that even just a single *one* of these properties possesses a definite value. Remember we're talking about an entangled state here, so according to the usual QM eigen-eigen link, "particle 2" over there doesn't possesses a definite value for spin along *any* direction. (It's not an eigenstate of the particle 2 spin operator for *any* direction.) So really all EPR needed was to say, look: by measuring some arbitrary spin component on particle 1, we can discover "without in any way disturbing particle 2" the value of the corresponding spin component of particle 2. So that (one single) spin component of particle 2 must exist, even though ordinary QM says it doesn't have a definite value. So QM is incomplete.

See how all this one vs. two vs. three business is a red herring? What's important is just that locality + perfect correlations require that *all* the spin components of particle 2 must exist, that is, particle 2 must possesses a pre-determined value for spin along *any direction you like*. That is the right way to understand what the EPR argument actually shows. Then, if you want to merely argue that locality --> the incompleteness of ordinary QM, that's easy, you just need to mention a single direction. If you want to derive a Bell inequality you need to mention several. But whatever. There's no more or worse "realism" in 2 or 3 than in 1, and it's the same one argument that gets you 1, 2, 3, and as many more as you might happen to want.

 

[ttn]

Just want to be clear: this is not MY assertion at all. We must either follow the EPR program and consider this as a reasonable assumption, or not. Once we define Realism to include this assumption, we can proceed.

If a person objects, as EPR says: "Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted."

So obviously we must agree that this is an assumption or the EPR result falls, since that is exactly what they said. Ditto, the Bell result falls as well if this is not agreed to (notice they say two or more). And apparently, this is quite a source of debate so I say it is a rather important assumption, yes. EPR explicitly acknowledge it!

I don't think you (correctly) understand what is going on in this passage you quote from the EPR paper. Now, in your defense, it is admittedly cryptic. Einstein thought and said so too, and we should take that seriously. In other words, we should not take the text of the EPR paper too seriously. When Einstein says it flubs and obscures the argument, we should listen to him, and hence rely on *other texts* to try to understand *his* views.

That said, here is what I think is the correct way to understand the passage you quoted. Actually, the just-following part (which you have also recently quoted) is highly relevant, so let me include the whole passage uninterrupted:

...We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality *only when they can be simultaneously measured or predicted*. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definitely of reality could be expected to permit this.

Now look carefully at the sentences after the one you had quoted. What are they about? They are about ... LOCALITY. He doesn't exactly say that, and it could surely have been made a bit clearer, but look at what he actually wrote. It amounts to this: "to say that whether P or Q of the distant particle exists depends on which of those quantities I *actually* measure over here, would mean that what's real over there depends on what I freely choose to do here." In other words: that would violate locality!

Thus, I think one should understand the infamous last sentence -- "No reasonable definition of reality could be expected to permit this" -- as a statement about locality. He is trying to express that *non-locality* should be considered unreasonable! But it would have been much clearer, and certainly better for the historical development on these issues, if he had just written: "locality requires this" instead of injecting simultaneously an assessment of how reasonable or unreasonable it is to consider rejecting locality. In any case, setting aside the question of whether or not one should believe locality (clearly E, P and R would all have believed it, but the point here is that that doesn't really matter) the idea being expressed is just what I keep saying: you'd have to deny locality (or the QM-predicted perfect correlations) to deny that (here) Q and P have pre-existing definite values.

 

[DrChinese]

That indeed clarifies what you're thinking, but basically I think you're barking up the wrong tree. The same exact reasoning that gives EPR's *second value*, gives as many values as you want. The only reason the EPR paper stresses the *two* values is that they (really, he, Podolsky) want(s) to show that more values exist than QM (in particular the so called eigenstate-eigenvalue link) can accommodate. To establish that, two values will suffice. Though it remains true that actually their argument establishes 3, 4, ... infinity.

Of course I agree. As you say (and I thought I said), 2 values are sufficient for EPR, and more are implied. But 2 was not sufficient for Bell though. He had to have at least 3, one of which is counterfactual. Hopefully, you don't question that.

Look, there is no need for you to spend time with me on this. I am not really arguing with you so much as laying out some of the counter-reasoning* to readers who are following this thread.

*Which is the standard view of most physicists.

 

[billschnieder]

I think there is some very unfortunate choice of words being used here is adding to the confusion. EPR never suggested that outcomes of measurements *exist* prior to measurement. Such a statement commits a modal fallacy and can be rejected outright. They said elements of reality corresponding to *definite* predictions *exist*, not that the outcomes themselves *exist* prior to the measurement. Therefore to say

perfect correlations require that *all* the spin components of particle 2 must exist

is unfortunate. Maybe what was meant here is that the spin components have *definite* values (cf. EPR's "predict with certainty"). Which does not mean the same thing as they *exist*.

This is particularly important when you start comparing experimental outcomes, which ALL *exist*, with inequalities involving predictions which although all simultaneously valid, can not simultaneously *exist*. Failure to understand this distinction is at the root of many unnecessary paradoxes.

 

[ttn]

Of course I agree. As you say (and I thought I said), 2 values are sufficient for EPR, and more are implied. But 2 was not sufficient for Bell though. He had to have at least 3, one of which is counterfactual. Hopefully, you don't question that.

Well, at least one of the 2 was already counterfactual. So I still fail to see why you think anything important was added by going from 2 to 3. (It's also relevant that there are Bell type inequalities with only 2 settings on each side. Again: 2, 3, whatever. There is no issue here. Barking up the wrong tree.)

Look, there is no need for you to spend time with me on this. I am not really arguing with you so much as laying out some of the counter-reasoning* to readers who are following this thread.

*Which is the standard view of most physicists.

But that is exactly why I consider it worth my time to spend time with you on this. You do such a perfect job of expressing "the standard view of most physicists", and I think a lot of good might come from the audience seeing Bell's unorthodox views (or at least my best attempt to channel them) pitted up against these standard views in open discussion.

 

[camboy]

Hi ttn,

Sorry to butt in. I'm thoroughly enjoying this debate, and I've digested your article and enjoyed it. For me you win on points (and possibly even a technical knockout - sorry Dr. C.).

But that is exactly why I consider it worth my time to spend time with you on this. You do such a perfect job of expressing "the standard view of most physicists", and I think a lot of good might come from the audience seeing Bell's unorthodox views (or at least my best attempt to channel them) pitted up against these standard views in open discussion.

I agree - this debate is well worth having.

Now if you go further along this path the ultimate pit of hell into which you can descend is to argue with the very wonderful Lubos Motl. His views on nonlocality are here, and - not unexpectedly - they're pretty scathing and in direct contradiction to the conclusions of your article. Now, of course it's not worth arguing with him on his blog site, since he mostly just deletes comments that disagree with him. Nevertheless, is there anything substantive in his arguments that you can see?

 

[ttn]

Hi ttn,

Sorry to butt in. I'm thoroughly enjoying this debate, and I've digested your article and enjoyed it.

Thanks, and thanks for saying so. It's nice to know that there are people watching and getting something out of this!

Now if you go further along this path the ultimate pit of hell into which you can descend is to argue with the very wonderful Lubos Motl. His views on nonlocality are here, and - not unexpectedly - they're pretty scathing and in direct contradiction to the conclusions of your article. Now, of course it's not worth arguing with him on his blog site, since he mostly just deletes comments that disagree with him. Nevertheless, is there anything substantive in his arguments that you can see?

I have read some of Motl's comments on (e.g.) Bohm's theory before. Hadn't seen this particular post though. I skimmed it, only reading carefully the part where he purports to explain "misconceptions about nonlocality in QM". Basically everything he says is standard stale white bread orthodoxy: a rather dilute mixture of vague anti-realism, positivism, the (erroneous) identification of causal influences with signaling, and vitriol exuded toward the whole issue. It's of course telling that he doesn't even mention Bell. I'm sure (despite the in-passing reference to Bertlmann's Socks) that he's never actually read that paper, or any of Bell's other papers. Otherwise, don't you think he'd try to actually say what's wrong with *Bell's argument* -- instead of just talking tediously about what he feels is the right way to understand orthodox QM?

Note also that the essence of his attempt to argue that (you know, contrary to what the crackpot morons like me think) orthodox QM is perfectly local, is actually just a proof that the marginal distribution of outcomes on one system is independent of what might (or might not) be measured on an entangled system. So if I were going to discuss the issue with him, perhaps I would start by asking whether he thinks that the de Broglie - Bohm pilot wave theory is also local since, of course, it is also true in that theory that the marginal on one side is independent of what's measured on the other side. Presumably he'd so "no, obviously it's not, you &*#@ing moron" and then we could start discussing how to define "locality" so it captures the idea of "causal influences only coming from the past light cone" rather than merely this constraint on the marginals (which is roughly equivalent to a prohibition on signaling) ... and then a miracle occurs ... and then he becomes convinced that, yes, actually, if you formulate a precise notion of "locality" in *that* sense, then yes, not only Bohmian mechanics but also ordinary QM is nonlocal and indeed it can be proved that *any* theory sharing QM's empirical predictions will have to be nonlocal.

Somewhat more seriously, though, if someone were going to try to engage him on this issue, I'd say just recommend that he read "Bertlmann's Socks" or "La Nouvelle Cuisine" and challenge him to explain what's wrong with Bell's argument.

 

[camboy]

Hi ttn,

Thanks for the response. I esssentially agree with you..

It's of course telling that he doesn't even mention Bell.

To be fair, I just searched for the word 'Bell' in the article, and it comes up with:

"Entanglement isn't any sign of a nonlocality. Bell's inequalities guaranteed that the experimentally observed correlations can't be explained by a local realist theory. But in a striking contrast with the popular scientific literature, the wrong assumption isn't locality; it's realism. Locality is just a property of relativistic and similar theories, whether they're quantum or classical. And indeed, it holds. The validity of locality was one of the key results of Einstein's special relativistic revolution of 1905, a revolution that can't be undone anymore."

"On the contrary, realism is an assumption behind all classical theories, whether they're relativistic or not. And it's been shown invalid in the 1920s because classical physics has been shown wrong. Only probabilities of actual measurements may be predicted by physics. This is what the quantum revolution of the mid 1920s is all about. The new picture of the world is "local, non-realist". Everyone who suggests that it's "nonlocal, realist" apparently misunderstands both major revolutions of the 20th century physics, quantum mechanics and relativity."

Hardly an in-depth discussion, but still..

Somewhat more seriously, though, if someone were going to try to engage him on this issue, I'd say just recommend that he read "Bertlmann's Socks" or "La Nouvelle Cuisine" and challenge him to explain what's wrong with Bell's argument.

I'm sure he will be utterly delighted if one of us were to suggest that, or to point out what is wrong with his arguments. Perhaps he might even buy you a present to show his gratitude? I love it when people buy me presents.

 

[ttn]

To be fair, I just searched for the word 'Bell' in the article, and it comes up with:

"Entanglement isn't any sign of a nonlocality. Bell's inequalities guaranteed that the experimentally observed correlations can't be explained by a local realist theory. But in a striking contrast with the popular scientific literature, the wrong assumption isn't locality; it's realism. Locality is just a property of relativistic and similar theories, whether they're quantum or classical. And indeed, it holds. The validity of locality was one of the key results of Einstein's special relativistic revolution of 1905, a revolution that can't be undone anymore."

"On the contrary, realism is an assumption behind all classical theories, whether they're relativistic or not. And it's been shown invalid in the 1920s because classical physics has been shown wrong. Only probabilities of actual measurements may be predicted by physics. This is what the quantum revolution of the mid 1920s is all about. The new picture of the world is "local, non-realist". Everyone who suggests that it's "nonlocal, realist" apparently misunderstands both major revolutions of the 20th century physics, quantum mechanics and relativity."

Hardly an in-depth discussion, but still..

Oh yeah, I stopped reading at the end of the "misconceptions..." section and didn't even notice that the next section was about QFT rather than one of the other weirdo thing he talks about.

So, Dr C will be pleased -- here's a real live regular physicist who thinks we get to choose whether to reject "locality" or "realism". But, IMHO, the opinion of this particular regular physicist is completely worthless since he has never actually looked into these issues but is instead just repeating what he read in textbooks written by others who had never actually looked into it...

I'm sure he will be utterly delighted if one of us were to suggest that, or to point out what is wrong with his arguments. Perhaps he might even buy you a present to show his gratitude? I love it when people buy me presents.

I seem to recall that several years ago another Bohm-fan (and PhysicsForums participant) posted some comments on one of Motl's blog posts, and his (Motl's) responses made me think it wasn't worth trying to discuss any of this stuff with him. I can deal with ignorance and I can deal with hostility, but the combination tends to be unfruitful and unpleasant to argue with.

 

[zonde]

As a further historical digression, note that even focusing on *two* values in this way is a kind of unfortunate and unnecessary. If the point is just to show that QM is incomplete, it'd be perfectly sufficient to show that even just a single *one* of these properties possesses a definite value. Remember we're talking about an entangled state here, so according to the usual QM eigen-eigen link, "particle 2" over there doesn't possesses a definite value for spin along *any* direction. (It's not an eigenstate of the particle 2 spin operator for *any* direction.) So really all EPR needed was to say, look: by measuring some arbitrary spin component on particle 1, we can discover "without in any way disturbing particle 2" the value of the corresponding spin component of particle 2. So that (one single) spin component of particle 2 must exist, even though ordinary QM says it doesn't have a definite value. So QM is incomplete.

Are you sure that EPR was arguing for particles possessing some definite properties?
It seems possible to me that EPR was attacking Heisenberg's "uncertainty as measurement disturbance" view. So in that case the goal of EPR argument would be to show incompatibility between QM formalism and hidden variables which it does.

If we would think that QM formalism is compatible with hidden variables then argument with one value would give nothing.

 

[harrylin]

Would you not say that the question of what pattern of drops it produces if we pushed on it is a measurable attribute of the orange, and that this question has a well-defined answer even if we do NOT push on it?

No I would not say that it is a measurable attribute of the orange: the exact way this measurement is done influences the outcome, and this may be not exactly reproducible so that it is a property of both the orange and the detection instrument.

 

[harrylin]

Well, at least one of the 2 was already counterfactual. So I still fail to see why you think anything important was added by going from 2 to 3. (It's also relevant that there are Bell type inequalities with only 2 settings on each side. Again: 2, 3, whatever. There is no issue here. Barking up the wrong tree.) [..]

I think that DrC is here simply acknowledging an objection that has been raised in the literature and which is rather incompatible with your reply: A single EPRB experimental data point corresponds to a measured property at the two locations, along the 2 directions a and b. Not 1, and certainly not 3. Your reply seems to deny that fact; and why do you call such a measurement fact "counterfactual"?

 

[ttn]

I think that DrC is here simply acknowledging an objection that has been raised in the literature and which is rather incompatible with your reply: A single EPRB experimental data point corresponds to a measured property at the two locations, along the 2 directions a and b. Not 1, and certainly not 3. Your reply seems to deny that fact; and why do you call such a measurement fact "counterfactual"?

You are confusing two very different things:

1. A Bell-experiment in which a pair of particles is sent out, and then the polarization along one direction is measured on each of the two particles. So, there's an "a" and a "b" involved, sure, but they refer to the polarization measurements on two separate particles.

2. The EPR argument, in which a hypothetical measurements along any axis on one particle, establishes (according to the EPR argument, i.e., assuming locality) that the corresponding property (i.e., the polarization along that same axis) is an "element of reality" for the distant particle. Here there's really only one angle in the mix: measure particle 1 along "a" and infer that particle 2 has a definite value along "a". But, the argument goes, you could measure along "b" instead, in which case you'd establish that particle 2 has a definite value along "b". Or if you prefer, "c". My main point before was that none of these measurements need be actually performed. It's really a thought experiment. So even if you only run the argument for "a" there is still a "counter-factual" element. Certainly if you run the argument for both "a" and "b" at least one is "counter-factual" in the sense that, if you make any actual measurements on particle 1 at all, you can only actually measure along "a" or "b" but not both.

But your comments suggest that you don't appreciate yet that the EPR argument is something distinct from just running the Bell experiment.

 

[DrChinese]

Hi ttn,

Sorry to butt in. I'm thoroughly enjoying this debate, and I've digested your article and enjoyed it. For me you win on points (and possibly even a technical knockout - sorry Dr. C.).

I agree - this debate is well worth having.

No offense taken. If ttn has converted you, then I too think the debate is worthwhile. He makes a lot of good points (wrong of course LOL) and deserves a voice. I always enjoy his forays here.

So, Dr C will be pleased -- here's a real live regular physicist who thinks we get to choose whether to reject "locality" or "realism". But, IMHO, the opinion of this particular regular physicist is completely worthless since he has never actually looked into these issues but is instead just repeating what he read in textbooks written by others who had never actually looked into it...

Now, you say this, but I don't think you really mean it. I can show you any number of quotes of Aspect, Zeilinger, et al (those that work in the field every day) that completely contradict everything you are saying. For example, from one of THE watershed experimental papers:

http://arxiv.org/abs/quant-ph/9810080
Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, Anton Zeilinger, 1998:

"After Bell’s discovery that EPR’s implication to explain the correlations using hidden parameters would contradict the predictions of quantum physics, a number of experimental tests have been performed [3–5]. All recent experiments confirm the predictions of quantum mechanics. Yet, from a strictly logical point of view, they don’t succeed in ruling out a local realistic explanation completely, because of two essential loopholes."

I could post these all day long, and you know it. Note the choice of words: "hidden parameters" (not local hidden parameters) and "local realistic" (not local). As I say, most folks in the field soundly reject realism as defined by EPR and Bell. None of these gents have changed their published views since (that I have seen - perhaps you will correct me on this point, because I suspect they all know your work).

My point to everyone again being: if you change definitions, as EPR says, you change your conclusions. If I adopted ttn's definitions, I too would arrive at his conclusion. There is a good reason why the scientific field rejects ttn's analysis: like me, they reject the premise. As a result, there is really nothing for me to defend here. Each is free to choose their starting point.

 

[harrylin]

You are confusing two very different things:

1. A Bell-experiment in which a pair of particles is sent out, and then the polarization along one direction is measured on each of the two particles. So, there's an "a" and a "b" involved, sure, but they refer to the polarization measurements on two separate particles.

2. The EPR argument, in which a hypothetical measurements along any axis on one particle, establishes (according to the EPR argument, i.e., assuming locality) that the corresponding property (i.e., the polarization along that same axis) is an "element of reality" for the distant particle. Here there's really only one angle in the mix: measure particle 1 along "a" and infer that particle 2 has a definite value along "a".

Oops - indeed, I mixed up the angles a and b and angle settings a, b and c! Giving the same symbols to different things should be avoided.
I highly appreciate that clarification. However, my comment still stands for both detectors measuring along the same angle.

[..] even if you only run the argument for "a" there is still a "counter-factual" element. Certainly if you run the argument for both "a" and "b" at least one is "counter-factual" in the sense that, if you make any actual measurements on particle 1 at all, you can only actually measure along "a" or "b" but not both.

So, when you measure both along the same direction, then surely your measurement outcomes for these two measurements are factual; not one of these results is counterfactual. However, for Bell's argument, an additional assumption must be made about a third measurement result. Thus I suspect that you and DrC mean the same thing but use different ways to say it! As a reminder, I commented on his sentence:
"As you say (and I thought I said), 2 values are sufficient for EPR, and more are implied. But 2 was not sufficient for Bell though. He had to have at least 3, one of which is counterfactual. Hopefully, you don't question that."

But your comments suggest that you don't appreciate yet that the EPR argument is something distinct from just running the Bell experiment.

You may be very right about that: I consider the Bell experiment as an attempt to test a variant of the EPR argument...

 

[ttn]

I can show you any number of quotes of Aspect, Zeilinger, et al (those that work in the field every day) that completely contradict everything you are saying.

I know what you mean, but there's no contradiction. I never said "everybody who works in/on foundations agrees with me". Rather I said that the opinions of those who *don't* work in/on (and indeed who despise) foundations don't really matter that much because they are just repeating what they were taught in kindergarten.

You are of course absolutely right that there are big famous serious people who have thought seriously about Bell and who hold orthodox views that conflict with my/Bell's views. Zeilinger is indeed a prominent example. Mermin another. But none of that proves I'm wrong. I just think these guys have missed the EPR argument (and Bell's post-1964 papers!) so they don't understand the implications of Bell's theorem correctly at all.

You for example quote from on of Z's papers:

"After Bell’s discovery that EPR’s implication to explain the correlations using hidden parameters would contradict the predictions of quantum physics..."

Well, that's just not a correct statement of what Bell discovered -- at least if you ask Bell.

My point to everyone again being: if you change definitions, as EPR says, you change your conclusions. If I adopted ttn's definitions, I too would arrive at his conclusion. There is a good reason why the scientific field rejects ttn's analysis: like me, they reject the premise. As a result, there is really nothing for me to defend here. Each is free to choose their starting point.

That I do not agree with at all. It is *not* an issue of definitions. It's an issue of whether you ignore the EPR argument or not.

 

[ttn]

So, when you measure both along the same direction, then surely your measurement outcomes for these two measurements are factual; not one of these results is counterfactual.

Yes, obviously nobody thinks that the outcome of a real, actually-performed measurement is somehow not factual. (Well, maybe MWI people think that...)

However, for Bell's argument, an additional assumption must be made about a third measurement result.

No, that is not true. Bell's derivation talks about what some candidate local theory will predict for various experiments. It is not literally, directly about actually-performed measurements (such that there's some assumption about the reality of some mysterious third counterfactual doodad). It's about what a local theory will predict. All of this business about counterfactuals is a total red herring.

I consider the Bell experiment as an attempt to test a variant of the EPR argument...

It is completely wrong to think of the Bell experiments as an attempt to test the EPR argument. The EPR argument is ... AN ARGUMENT. It's not a theory, or a prediction, or any other kind of thing that it makes sense to "test". One doesn't test arguments, one *makes* them. One judges whether they are good arguments or bad arguments. I think the EPR argument is a good (I mean valid) argument. So did Bell. So did Einstein. But no experiment is ever going to be able to show one way or the other that the argument is or isn't valid. The most it can do is show that one of the premises or the conclusion is true or false.

 

[DrChinese]

It is completely wrong to think of the Bell experiments as an attempt to test the EPR argument. The EPR argument is ... AN ARGUMENT. It's not a theory, or a prediction, or any other kind of thing that it makes sense to "test". One doesn't test arguments, one *makes* them. One judges whether they are good arguments or bad arguments. I think the EPR argument is a good (I mean valid) argument. So did Bell. So did Einstein. But no experiment is ever going to be able to show one way or the other that the argument is or isn't valid. The most it can do is show that one of the premises or the conclusion is true or false.

We sort of agree here, although your interpretation of the conclusion is wrong. The conclusion is not: The ability to predict with certainty implies non-locality. This is not stated anywhere.

The correct conclusions of EPR are: QM is incomplete if realism (elements of reality independent of simultaneous observation) is assumed. If realism is not assumed, then reality here is dependent on the choice of an observer there. To other readers: It is a bit difficult to parse, but it is in these words of the final paragraphs of EPR - you can draw your own conclusions if you think I am misinterpreting (bold added):

"Starting then with the assumption that the
wave function does give a complete description
of the physical reality, we arrived at the con-
clusion that two physical quantities, with non-
commuting operators, can have simultaneous
reality. Thus the negation of (1) leads to the
negation of the only other alternative (2). We
are thus forced to conclude that the quantum-
mechanical description of the physical reality
given by wave functions is not complete.

"One could object to this conclusion on the
grounds that our criterion of reality is not suf-
ficiently restrictive. Indeed, one would not ar-
rive at our conclusion if one insisted that two
or more physical quantities can be regarded
as simultaneous elements of reality only when
they can be simultaneously measured or pre-
dicted. On this point of view, since either one
or the other, but not both simultaneously, of
the quantities P and Q can be predicted, they
are not simultaneously real. This makes the
reality of P and Q depend upon the process
of measurement carried out on the first system
in any way. No reasonable definition of reality
could be expected to permit this."

Historically, there has never been much question about the correctness of this argument - certainly not from the Copenhagen side of the fence. Their view was that the realism is an invalid assumption, and we live in an observer dependent world - so no problem-o! Both of these are consistent with EPR, as I presented above. The question to the local realistic side has always been whether there is a deeper level of reality. So far, it has not been found to exist in a local setting despite the explicit EPR belief that it would be found.

 

[ttn]

We sort of agree here, although your interpretation of the conclusion is wrong. The conclusion is not: The ability to predict with certainty implies non-locality. This is not stated anywhere.

The correct conclusions of EPR are: QM is incomplete if realism (elements of reality independent of simultaneous observation) is assumed. If realism is not assumed, then reality here is dependent on the choice of an observer there.

I've already made my interpretation of EPR clear in previous posts, so I also don't want to get into a big debate about this. But I think it should be clear that what you say here is at least missing a pretty big part of the story -- though I repeat again that the text of EPR was not written by Einstein and Einstein thought (correctly in my opinion) that the main point was somehow buried/obscure.

But Dr C, you say above that one of the *conclusions* of EPR is that "QM is incomplete if realism (elements of reality...) is assumed." It can't be right that that's any kind of *conclusion*. It's rather a completely trivial and completely obvious statement. QM says that a system only possesses a definite value for some property when it is in an eigenstate of the corresponding operator; non-commuting operators don't have simultaneous eigenstates; so QM says non-commuting properties cannot have definite values. Now you are using "realism" here to mean basically the statement that non-commuting properties *do* have definite values. So it is just a perfectly straightforward and mundane and obvious application of terminology to say that "realism" contradicts "completeness" and vice versa. This isn't something you need any kind of *argument* for. It isn't something you *conclude*. It's just a way of putting new terminology ("realism" or whatever) to the same issue that was already put in terms of "completeness".

So, I submit, to whatever extent you think of this as EPR's *conclusion*, it just shows that you have missed whatever the real argument/point/conclusion was supposed to be.

This real argument/point/conclusion is of course closer to the second thing you mentioned: "If realism is not assumed, then reality here is dependent on the choice of an observer there." But that's still a confusing/obscure way to put it. It's not at all about whether "realism" is *assumed*. And "reality here being dependent on the choice of an observer there" is of course our old friend, nonlocality. So it would be much clearer to put it this way: denying realism implies nonlocality. Or equivalently: locality implies realism.

Historically, there has never been much question about the correctness of this argument - certainly not from the Copenhagen side of the fence. Their view was that the realism is an invalid assumption, and we live in an observer dependent world - so no problem-o! Both of these are consistent with EPR, as I presented above. The question to the local realistic side has always been whether there is a deeper level of reality. So far, it has not been found to exist in a local setting despite the explicit EPR belief that it would be found.

You really try my patience. First off, it's completely ridiculous to say there has never been much question about the correctness of this argument -- unless what you mean is that virtually everybody thought the argument was unquestionably *wrong*.

But more importantly (and frustratingly to me since we've been around this SOOOOO many times), you can't say "realism is an invalid assumption" when realism is not an assumption at all. It's rather the conclusion of the simplest statement of the argument, namely: locality implies realism. And surely this is what EPR were trying to show. They had to *work hard* to show that locality --> realism. That's the essence of the argument. Then, once they establish that, it's a trivial semantic issue to say "and therefore QM isn't complete since realism means there are more elements of reality than are sanctioned by QM". You mistake the trivial part at the end for the real argument -- partly because Podolsky himself put WAAAYYY too much emphasis on that part. In doing so you miss the whole essence of the argument, just as so many copenhagenish/orthodoxish people have done before you.

Note by the way how completely bizarre it is to respond to "locality --> realism" by saying "yeah, but we reject realism so we don't have to worry about nonlocality". The whole freaking point of EPR was that if you reject realism you ipso facto have to endorse nonlocality! So to say such a thing is to confess that you've missed the argument.

 

[DrChinese]

But Dr C, you say above that one of the *conclusions* of EPR is that "QM is incomplete if realism (elements of reality...) is assumed." It can't be right that that's any kind of *conclusion*. It's rather a completely trivial and completely obvious statement.

"Starting then with the assumption that the
wave function does give a complete description
of the physical reality, we arrived at the con-
clusion that two physical quantities, with non-
commuting operators, can have simultaneous
reality. Thus the negation of (1) leads to the
negation of the only other alternative (2). We
are thus forced to conclude that the quantum-
mechanical description of the physical reality
given by wave functions is not complete."

So apparently, you are saying EPR provides a trvial conclusion to the question: "Can A Quantum-Mechanical Description of Physical Reality Be Considered Complete? Somehow, I think the authors might disagree with your assessment.

Look, you can draw whatever deductions you like from their paper, but this is in fact their conclusion.

 

[harrylin]

[..] Bell's derivation talks about what some candidate local theory will predict for various experiments. It is not literally, directly about actually-performed measurements (such that there's some assumption about the reality of some mysterious third counterfactual doodad). It's about what a local theory will predict. All of this business about counterfactuals is a total red herring.

I understood this business about counterfactuals to be about what a local theory will predict - which is why I:
1. so far never really disagreed with that stuff
and
2. never went along with it either; it seems to me to just add noise and fog to the discussions.

It is completely wrong to think of the Bell experiments as an attempt to test the EPR argument. The EPR argument is ... AN ARGUMENT. It's not a theory, or a prediction, or any other kind of thing that it makes sense to "test". One doesn't test arguments, one *makes* them. One judges whether they are good arguments or bad arguments. I think the EPR argument is a good (I mean valid) argument. So did Bell. So did Einstein. But no experiment is ever going to be able to show one way or the other that the argument is or isn't valid. The most it can do is show that one of the premises or the conclusion is true or false.

Sorry for my sloppy reply there - I was time pressed. Sure, I understand Bell's theorem to be a development based on EPR's argument. I mentioned that in my reply to DrC in post #309.