QM objects do not have properties until measured?

[rubi]

I don't understand the criticism either. Can you explain it?
Can you point out the flaw in this argument of Maudlin:
"if a theory predicts perfect correlations for the outcomes of distant experiments, then either the theory must treat these outcomes as deterministically produced from the prior states of the individual systems or the theory must violate EPR-locality. The argument is extremely simple and straightforward. The perfect correlations mean that one can come to make predictions with certainty about how system S1 will behave on the basis of observing how the other, distant, system S2 behaves. Either those observations of S2 disturbed the physical state of S1 or they did not. If they did, then that violates EPR-locality. If they did not, then S1 must have been physically determined in how it would behave all along. That’s the argument, from beginning to end. (That’s also the point of Bell’s discussion of Bertlmann’s socks.) So preserving EPR-locality in these circumstances requires adopting a deterministic theory. Where, in this argument, does any presupposition about the geometry of the state space play any role? Nowhere."

There is no flaw in this argument. The fact that Maudlin thinks that this part of the argument is what Werner considers to be faulty clearly shows that he didn't understand the criticism at all. Non-simplicial state spaces can also account for some degree of determinism. However, one cannot prove Bell's inequality from non-simplicial state spaces, so the simplex structure is a crucial extra assumption. Thus, a violation of Bell's inequality says nothing about theories modeled by non-simplicial state spaces.

 

[atyy]

Well, there is one single notion of locality that applies to all theories that can be formulated on Lorentzian spacetimes (see my post #22 and wikipedia for additional information) and all other notions of locality must be derived from it. Bell's (and Maudlin's) criterion follows from the standard notion plus the assumption of classicality. It's a special case of the general principle.

Sure, but if Maudlin's locality is what you are calling classical local causality in your language, and a state is operationally defined as in operational quantum mechanics, then Maudlin's argument would be that one form of Bell's theorem is:

Operational quantum mechanics cannot be embedded into a classical locally causal theory.

The statement is of the form "X cannot be embedded into Y". There is of course a requirement for classicality in defining Y but not in defining X. So if Maudlin is referring to what one can put for X, then it is correct that there is no requirement for the state space to be a simplex.

 

[rubi]

Sure, but if Maudlin's locality is what you are calling classical local causality in your language, and a state is operationally defined as in operational quantum mechanics, then Maudlin's argument would be:

Operational quantum mechanics cannot be embedded into a classically locally causal theory.

If that was the case, I'd be happy, since then we're back at "no local realistic theory can reproduce all predictions of quantum mechanics", which is the standard reading of Bell's theorem, which pretty much all physicist agree with. However, I doubt that this is what Maudlin believes. The abstract of his paper is:

"On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier arguments of Einstein, Podolsky and Rosen. I retrace the history and logical structure of these arguments in order to clarify the proper conclusion, namely that any world that displays violations of Bell's inequality for experiments done far from one another must be non-local. Since the world we happen to live in displays such violations, actual physics is non-local."

Apparently, Maudlin believes that the violations of Bell's inequality imply that the world is non-local. In the paper, he makes it pretty clear in my opinion that he thinks that realism is not required as an additional assumption in Bell's theorem. Furthermore, in his reply to Werner, he leaves no doubt that he doesn't understand where the assumption of a simplicial state space is used. If Maudlin had just explained the standard reading of Bell's theorem, then the editors certainly wouldn't have asked Werner for a reply.

 

[atyy]

If that was the case, I'd be happy, since then we're back at "no local realistic theory can reproduce all predictions of quantum mechanics", which is the standard reading of Bell's theorem, which pretty much all physicist agree with. However, I doubt that this is what Maudlin believes. The abstract of his paper is:

"On the 50th anniversary of Bell's monumental 1964 paper, there is still widespread misunderstanding about exactly what Bell proved. This misunderstanding derives in turn from a failure to appreciate the earlier arguments of Einstein, Podolsky and Rosen. I retrace the history and logical structure of these arguments in order to clarify the proper conclusion, namely that any world that displays violations of Bell's inequality for experiments done far from one another must be non-local. Since the world we happen to live in displays such violations, actual physics is non-local."

Apparently, Maudlin believes that the violations of Bell's inequality imply that the world is non-local. In the paper, he makes it pretty clear in my opinion that he thinks that realism is not required as an additional assumption in Bell's theorem. Furthermore, in his reply to Werner, he leaves no doubt that he doesn't understand where the assumption of a simplicial state space is used. If Maudlin had just explained the standard reading of Bell's theorem, then the editors certainly wouldn't have asked Werner for a reply.

OK, but if we agree that Bell's theorem applies to operational QM, and operational QM has a state space that is not a simplex, then it is true that there is no requirement for classicality in the theories that Bell's theorem applies to.

 

[rubi]

OK, but if we agree that Bell's theorem applies to operational QM, and operational QM has a state space that is not a simplex, then it is true that there is no requirement for classicality in the theories that Bell's theorem applies to.

Bell's theorem still applies only to classical theories. It tells us what inequality a classical local theory must necessarily satisfy. It doesn't tell us anything about an inequality that a quantum theory (or any other theory with a non-simplicial state space) must satisfy, no matter whether it is local or not. The violation of the inequality thus only proves that those theories that predict its satisfaction must be excluded (i.e. all classical local theories).

 

[N88]

I don't understand the criticism either. Can you explain it?
Can you point out the flaw in this argument of Maudlin:
"if a theory predicts perfect correlations for the outcomes of distant experiments, then either the theory must treat these outcomes as deterministically produced from the prior states of the individual systems or the theory must violate EPR-locality. The argument is extremely simple and straightforward. The perfect correlations mean that one can come to make predictions with certainty about how system S1 will behave on the basis of observing how the other, distant, system S2 behaves. Either those observations of S2 disturbed the physical state of S1 or they did not. If they did, then that violates EPR-locality. If they did not, then S1 must have been physically determined in how it would behave all along. That’s the argument, from beginning to end. (That’s also the point of Bell’s discussion of Bertlmann’s socks.) So preserving EPR-locality in these circumstances requires adopting a deterministic theory. Where, in this argument, does any presupposition about the geometry of the state space play any role? Nowhere." (Emphasis added.)

I'm reluctant to intervene in helpful discussions on Bell's Theorem between Science Advisors and a Gold Member when another Science Advisor says:

Bell inequality violations have nothing at all to do with the measurement problem, hence should be off-topic in this thread. They address a completely different problem - that of local hidden variable theories.

But I see connections with my OP and zonde's question.

Isn't this the flaw in Maudlin's argument: "If they did not, then S1 must have been physically determined in how it would behave all along."

In the context of the OP question QM objects do not have properties until measured? I say that they do have SOME properties (spin s = 1/2, for example) before measurement. So, questioning Maudlin: S1 has properties that are correlated with those of its twin and these properties physically determine how it behaves all along; so, similar to human twins, there should be no mystery in the independent behaviour of widely-separated twins being correlated in Bell-tests?

 

[atyy]

Bell's theorem still applies only to classical theories. It tells us what inequality a classical local theory must necessarily satisfy. It doesn't tell us anything about an inequality that a quantum theory (or any other theory with a non-simplicial state space) must satisfy, no matter whether it is local or not. The violation of the inequality thus only proves that those theories that predict its satisfaction must be excluded (i.e. all classical local theories).

But isn't it the case that:

"Bell's theorem says that operational QM cannot be embedded into a classical locally causal theory" means that "Bell's theorem applies to operational QM"

?

 

[rubi]

But isn't it the case that:

"Bell's theorem says that operational QM cannot be embedded into a classical locally causal theory" means that "Bell's theorem applies to operational QM".

I'm not sure what you mean by "apply", but the direction of the argument is as follows:
1. Bell's theorem: Every classical local theory must satisfy Bell's inequality.
2. Quantum theory violates Bell's inequality.
3. Therefore, quantum theory can't be embedded into a classical local theory.
You want to run the argument backwards, but that doesn't work. Bell's theorem is only a theorem about classical local theories. But maybe I just don't understand what conclusion you want to draw.

 

[N88]

Bell's theorem still applies only to classical theories. It tells us what inequality a classical local theory must necessarily satisfy. It doesn't tell us anything about an inequality that a quantum theory (or any other theory with a non-simplicial state space) must satisfy, no matter whether it is local or not. The violation of the inequality thus only proves that those theories that predict its satisfaction must be excluded (i.e. all classical local theories).

But don't we have good reason to say that it is the classicality condition that provides the problem, not the locality condition?

In d'Espagnat's article http://www.scientificamerican.com/media/pdf/197911_0158.pdf at page 166 (and endorsed by Bell at page 147 in his 2004 book) we find: "These conclusions require a subtle but important extension of the meaning assigned to the notation A⁺ … … … ."

To me, that subtle but important extension seems to be exactly the classicality condition that Bell (1964) assigns to his λ? So, in the context of the OP, this Bell-endorsed "subtle but important extension" appears to be the false "classical" view that QM objects (which may have some properties in common, like spin s = 1/2) DO NOT have the properties measured in d'Espagnat's article and in typical Bell-tests prior to measurement? So reject the classicality of QM objects and retain locality?

 

[atyy]

I'm not sure what you mean by "apply", but the direction of the argument is as follows:
1. Bell's theorem: Every classical local theory must satisfy Bell's inequality.
2. Quantum theory violates Bell's inequality.
3. Therefore, quantum theory can't be embedded into a classical local theory.
You want to run the argument backwards, but that doesn't work. Bell's theorem is only a theorem about classical local theories. But maybe I just don't understand what conclusion you want to draw.

I agree with all three statements. Statement #3 is about quantum theory, so in that sense I would say that Bell's theorem does apply to quantum theory.

 

[N88]

I agree with all three statements. Statement #3 is about quantum theory, so in that sense I would say that Bell's theorem does apply to quantum theory.

It seems to me that Bell's theorem IS RELEVANT to quantum theory. So is this correct? Bell's theorem is relevant to the OP and QM because it shows that, prior to measurement and unlike typical classical objects, quantum objects do NOT have the properties measured in Bell-tests until they are measured.

 

[rubi]

But don't we have good reason to say that it is the classicality condition that provides the problem, not the locality condition?

In d'Espagnat's article http://www.scientificamerican.com/media/pdf/197911_0158.pdf at page 166 (and endorsed by Bell at page 147 in his 2004 book) we find: "These conclusions require a subtle but important extension of the meaning assigned to the notation A⁺ … … … ."

To me, that subtle but important extension seems to be exactly the classicality condition that Bell (1964) assigns to his λ? So, in the context of the OP, this Bell-endorsed "subtle but important extension" appears to be the false "classical" view that QM objects (which may have some properties in common, like spin s = 1/2) DO NOT have the properties measured in d'Espagnat's article and in typical Bell-tests prior to measurement? So reject the classicality of QM objects and retain locality?

The problem is either the classicality condition or the locality condition. I (and most physicists) would blame the classicality condition, since locality is probably the most successful heuristic we have in physics and dropping it would generate more problems than it solves, while dropping classicality seems to generate no intrinsic problems apart from being unintuitive. But of course everyone is free to choose their own conclusion, as long as they acknowledge that such a choice exists.

I agree with all three statements. Statement #3 is about quantum theory, so in that sense I would say that Bell's theorem does apply to quantum theory.

Well ok, you can put it that way, although I would prefer to say that Bell's theorem has consequences for QM rather than that it applies to QM, but that's just semantics. Those consequences are that QM cannot be both classical and local.

 

[atyy]

Well ok, you can put it that way, although I would prefer to say that Bell's theorem has consequences for QM rather than that it applies to QM, but that's just semantics. Those consequences are that QM cannot be both classical and local.

Yes, I believe it is just semantics between Werner and Maudlin. If in some sense one can say that Bell's theorem applies to QM, then it is true in some sense that Bell's theorem applies to theories whose state space is not a simplex (since the state space of QM is not a simplex).

 

[rubi]

Yes, I believe it is just semantics between Werner and Maudlin. If in some sense one can say that Bell's theorem applies to QM, then it is true in some sense that Bell's theorem applies to theories whose state space is not a simplex (since the state space of QM is not a simplex).

The problem with Maudlin isn't whether Bell's theorem applies to QM or not, but rather what the assumptions of Bell's theorem are. Maudlin claims that there is no assumption of classicality. The criticism is directed only towards this claim and this is more than just semantics. If there were no classicality assumption, then the violation of Bell's inequality would prove that QM is non-local. However, the classicality assumption is crucial and this is what Werner points out. Maudlin is objectively wrong when he claims that classicality is not an assumption.

 

[N88]

The problem is either the classicality condition or the locality condition. I (and most physicists) would blame the classicality condition, since locality is probably the most successful heuristic we have in physics and dropping it would generate more problems than it solves, while dropping classicality seems to generate no intrinsic problems apart from being unintuitive. But of course everyone is free to choose their own conclusion, as long as they acknowledge that such a choice exists. … …. Well ok, you can put it that way, although I would prefer to say that Bell's theorem has consequences for QM rather than that it applies to QM, but that's just semantics. Those consequences are that QM cannot be both classical and local.

Thanks, BUT: I see nothing counter-intuitive in expecting that sensitive objects (quantum objects) would be modified by measurements. So why would ANY physicist hold to the classical here? Why not, without question, reject the classical and retain the successful heuristic of locality? For, at the order of the quantum level, even classical objects are modified by measurements. Like the (now slightly dented) wall I just measured so that my partner could hang a picture "dead-center". (The external corner of the wall now dented by the measurement alone; even though, so far, only I have spotted it.)

 

[atyy]

The problem with Maudlin isn't whether Bell's theorem applies to QM or not, but rather what the assumptions of Bell's theorem are. Maudlin claims that there is no assumption of classicality. The criticism is directed only towards this claim and this is more than just semantics. If there were no classicality assumption, then the violation of Bell's inequality would prove that QM is non-local. However, the classicality assumption is crucial and this is what Werner points out. Maudlin is objectively wrong when he claims that classicality is not an assumption.

But it depends on what one is talking about when discussing whether the classicality assumption. The classicality assumption is needed in the definition of locality uses, but it is not needed in what Bell's theorem applies to (eg. QM), so if it is the latter that Maudlin is talking about, then he is correct.

 

[rubi]

Thanks, BUT: I see nothing counter-intuitive in expecting that sensitive objects (quantum objects) would be modified by measurements. So why would ANY physicist hold to the classical here? Why not, without question, reject the classical and retain the successful heuristic of locality? For, at the order of the quantum level, even classical objects are modified by measurements. Like the (now slightly dented) wall I just measured so that my partner could hang a picture "dead-center". (The external corner of the wall now dented by the measurement alone; even though, so far, only I have spotted it.)

Well, I and most people do reject classicality and keep locality. However, dropping classicality is worse than just saying "measurements modify the state", since that is also possible in a classical theory. Of course, having to drop even one of them is unfortunate, since both appear intuitive.

But it depends on what one is talking about when discussing whether the classicality assumption. The classicality assumption is needed in the definition of locality uses, but it is not needed in what Bell's theorem applies to (eg. QM), so if it is the latter that Maudlin is talking about, then he is correct.

Maudlin believes that Bell proved the following: "Every local theory, be it classical or not, satisfies Bell's inequality." This is definitely wrong and it spoils the rest of his argument. He wants to argue:
1. Every local theory, be it classical or not, satisfies Bell's inequality.
2. Quantum theory violates Bell's inequality.
3. Therefore quantum theory is not a local theory.
However, his statement of (1) is false and consequently, (3) is false as well, since it is based on a false premise. So the paper contains a severe mistake and Werner is right to criticize it.

 

[N88]

Well, I and most people do reject classicality and keep locality. However, dropping classicality is worse than just saying "measurements modify the state", since that is also possible in a classical theory. Of course, having to drop even one of them is unfortunate, since both appear intuitive.

I do not see why "classicality" of the type invoked by d'Espagnat and Bell appears intuitive. Locality, yes. Such classicality, no (for me). So could you expand on why you consider the dropping of such classicality is "unfortunate" and worse than just saying "measurements modify the state".

 

[atyy]

Maudlin believes that Bell proved the following: "Every local theory, be it classical or not, satisfies Bell's inequality." This is definitely wrong and it spoils the rest of his argument. He wants to argue:
1. Every local theory, be it classical or not, satisfies Bell's inequality.
2. Quantum theory violates Bell's inequality.
3. Therefore quantum theory is not a local theory.
However, his statement of (1) is false and consequently, (3) is false as well, since it is based on a false premise. So the paper contains a severe mistake and Werner is right to criticize it.

But Maudlin quite clearly qualifies his locality as "EPR-local", which is one of the usual synonyms for classical local causality.

 

[rubi]

I do not see why "classicality" of the type invoked by d'Espagnat and Bell appears intuitive. Locality, yes. Such classicality, no (for me). So could you expand on why you consider the dropping of such classicality is "unfortunate" and worse than just saying "measurements modify the state".

Well, for instance non-classicality implies that a particle can't have both a position and a momentum. How do you interpret this? Mathematically, it is not a problem, but I don't think it is intuitive.

But Maudlin quite clearly qualifies his locality as "EPR-local", which is one of the usual synonyms for classical local causality.

Maudlin believes that EPR-locality implies the conditions that are needed to prove Bell's theorem. However, EPR-locality does not imply classicality. It only implies a weak form of determinism, which can also be satisfied by theories that are formulated on non-simplicial state spaces. In order to prove Bell's theorem, you must make the additional assumption that the state space is a simplex. EPR-locality isn't enough.

Edit: If you claim that EPR-locality implies that the state space is a simplex, then I demand a proof for that.

 

[atyy]

Maudlin believes that EPR-locality implies the conditions that are needed to prove Bell's theorem. However, EPR-locality does not imply classicality. It only implies a weak form of determinism, which can also be satisfied by theories that are formulated on non-simplicial state spaces. In order to prove Bell's theorem, you must make the additional assumption that the state space is a simplex. EPR-locality isn't enough.

Edit: If you claim that EPR-locality implies that the state space is a simplex, then I demand a proof for that.

Hmmm, EPR locality is so vague that usually one just defines it to be classical local causality. At the heuristic level, there are two notions of locality (1) no superluminal transmission of information (2) classical local causality. Since EPR were not talking about (1), it is usually assumed that they were talking about (2). Operational QM is local in sense (1), but not (2). Is operational QM local in a sense that is neither (1) nor (2)?

 

[rubi]

Hmmm, EPR locality is so vague that usually one just defines it to be classical local causality.

Well Maudlin's argument is based on the idea that the assumptions of Bell's theorem are implied by the things he says earlier. He can't just define his earlier comments to prove the assumptions. Either they do, or they don't and if they don't, his argument is incomplete and he must admit that he needs an extra assumption.

At the heuristic level, there are two notions of locality (1) no superluminal transmission of information (2) classical local causality. Since EPR were not talking about (1), it is usually assumed that they were talking about (2).

(1) and (2) are not mutually exclusive, so you can't argue that EPR-locality must be either (1) or (2). I agree that it is a vague concept, but that doesn't free us from the obligation to make it formal if we want to use it in a mathematical argument like Bell's theorem.

Operational QM is local in sense (1), but not (2). Is operational QM local in a sense that is neither (1) nor (2)?

Every locality condition must imply (1), so QM is certainly local in the sense of (1). However, it can still satisfy a stronger locality condition in the sense of my post #22. The fact that Maudlins argument fails to imply a simplicial state space means that we still have the choice between rejecting classicality and rejecting locality. It is perfectly possible that there is no spooky action at a distance in QM.

 

[atyy]

Well Maudlin's argument is based on the idea that the assumptions of Bell's theorem are implied by the things he says earlier. He can't just define his earlier comments to prove the assumptions. Either they do, or they don't and if they don't, his argument is incomplete and he must admit that he needs an extra assumption.

Well, I won't defend Maudlin that far. I'm not a big fan of arguing from EPR. I prefer to just define classical local causality. I will say Maudlin is not a crackpot, and overall his message is not very far from what everyone agrees with: QM is local by no signalling, and not local by classical local causality.

Every locality condition must imply (1), so QM is certainly local in the sense of (1). However, it can still satisfy a stronger locality condition in the sense of my post #22. The fact that Maudlins argument fails to imply a simplicial state space means that we still have the choice between rejecting classicality and rejecting locality. It is perfectly possible that there is no spooky action at a distance in QM.

But is there really something between (1) and (2) that operational QM satisfies? There is a notion, but as far as I know, the notion is empty in operational QM. Looking at the other article by Zukowski and Brukner you linked to in post #20, they basically say locality should be defined as no superluminal signalling. Maudlin explicitly says QM is local if one defines it as no superluminal signalling.

Also, it seems (according to Maudlin) that Werner says that QM is local if we take the epistemic state to be the physical state. Isn't that problematic? How is that different from saying that the wave function is real, which as you agreed does make QM nonlocal?

 

[zonde]

Non-simplicial state spaces can also account for some degree of determinism.

I am trying to understand what Werner means by "assumption of simplex state space".
I found this:
"According to Maudlin, Bell makes no assumption of “realism” or (as I called it in my reply) of “classicality” (in short “C”), or a hidden-variable description."
And this:
"The first issue is the explanation of classicality “C”. I gave a technical definition, the simplex property, ... "

So as I understand "simplex state space" is basically the same as "hidden-variable description", right?

 

[zonde]

Isn't this the flaw in Maudlin's argument: "If they did not, then S1 must have been physically determined in how it would behave all along."

In the context of the OP question QM objects do not have properties until measured? I say that they do have SOME properties (spin s = 1/2, for example) before measurement. So, questioning Maudlin: S1 has properties that are correlated with those of its twin and these properties physically determine how it behaves all along; so, similar to human twins, there should be no mystery in the independent behaviour of widely-separated twins being correlated in Bell-tests?

Maudlin explains EPR dilemma in simple words:
you either say that entangled particles are like identical twins and therefore give perfectly correlated measurement outcomes under matching conditions
or
they secretly communicate instantaneously over unlimited distances.

And to be on the safe side we can state it more correctly by speaking about physical configuration in local neighborhood of detection events rather than particle properties alone.

 

[zonde]

The problem is either the classicality condition or the locality condition. I (and most physicists) would blame the classicality condition, since locality is probably the most successful heuristic we have in physics and dropping it would generate more problems than it solves, while dropping classicality seems to generate no intrinsic problems apart from being unintuitive. But of course everyone is free to choose their own conclusion, as long as they acknowledge that such a choice exists.

Nobody (I hope) is considering dropping locality as there is no philosophical framework for such a way of thinking. "Non-locality" of QM just means that QM approximates some physical mechanism that violates speed of light limit.

 

[rubi]

Well, I won't defend Maudlin that far. I'm not a big fan of arguing from EPR. I prefer to just define classical local causality. I will say Maudlin is not a crackpot, and overall his message is not very far from what everyone agrees with: QM is local by no signalling, and not local by classical local causality.

Well, I think Maudlin wants us to believe that his argument is watertight and he doesn't need an extra assumption like a simplicial state space. Otherwise he would just have admitted that he uses that assumption, after Werner pointed it out to him. See this quote from Werner: "Whether or not assuming classicality is a good choice is not the issue here. Therefore, at the end of the introduction of my comment I said: “Of course, I now have to say what this C is. I can only hope to do it
well enough that Maudlin will say: ’Yes, we assume that, of course’.” His reply shows beyond doubt that I failed." A honest scientist wouldn't try to hide his assumptions, so I can't take Maudlin seriously.

But is there really something between (1) and (2) that operational QM satisfies?

You need to draw a two-dimensional picture here with the axes "classicality" and "locality". (1) assumes no classicality but is a bit local. (2) is fully classical and fully local. However, quantum theory can be fully local but not classical at all, so it's not "between (1) and (2)".

There is a notion, but as far as I know, the notion is empty in operational QM. Looking at the other article by Zukowski and Brukner you linked to in post #20, they basically say locality should be defined as no superluminal signalling. Maudlin explicitly says QM is local if one defines it as no superluminal signalling.

I don't think the notion is empty. At least in the Bell situation, one can consistently supplement QM with a non-empty causality relation. I don't know about the general case. This is simply very unexplored terrain. Zukowski and Brukner are also not sure about their conclusion. The point is that until someone proves the incompatibility of a non-empty causality relation with QM, one can't claim that (1) is the only option.

Also, it seems (according to Maudlin) that Werner says that QM is local if we take the epistemic state to be the physical state. Isn't that problematic? How is that different from saying that the wave function is real, which as you agreed does make QM nonlocal?

I don't get this conclusion from Werner's articles. I think Maudlin misunderstands him. As long as the state is not a physical object, everything is fine.

I am trying to understand what Werner means by "assumption of simplex state space".
I found this:
"According to Maudlin, Bell makes no assumption of “realism” or (as I called it in my reply) of “classicality” (in short “C”), or a hidden-variable description."
And this:
"The first issue is the explanation of classicality “C”. I gave a technical definition, the simplex property, ... "

So as I understand "simplex state space" is basically the same as "hidden-variable description", right?

No, hidden-variable theories can also be modeled on non-simplicial state spaces. The assumption that the state space is a simplex just means that all observables are modeled as random variables on one single probability space.

Nobody (I hope) is considering dropping locality as there is no philosophical framework for such a way of thinking. "Non-locality" of QM just means that QM approximates some physical mechanism that violates speed of light limit.

A violation of the speed of light limit is a violation of locality. Locality is a well-defined concept in relativity theory. It is dropped for example in Bohmian mechanics.

 

[zonde]

No, hidden-variable theories can also be modeled on non-simplicial state spaces. The assumption that the state space is a simplex just means that all observables are modeled as random variables on one single probability space.

So you are saying that Werner gave two different definitions for the same thing?

 

[rubi]

So you are saying that Werner gave two different definitions for the same thing?

I don't know how you come to this conclusion? I certainly didn't say this. Werner states his definition precisely in his paper: "In a classical theory this convex set is a simplex, meaning that any state has a unique decomposition into extreme points, so can be understood as statistical mixture of dispersion free states: equivalently, any two measurements (POVMs, or decompositions of one into positive affine functionals) are the marginals of a joint measurement. We take these properties as a definition of classicality and it is this property I referred to as C in the introduction."

 

[Quandry]

Well, for instance non-classicality implies that a particle can't have both a position and a momentum. How do you interpret this? Mathematically, it is not a problem, but I don't think it is intuitive.

I hope I do not misunderstand this, but I regard it as quite intuitive. Momentum is directly proportional to the velocity, which is a measurement of change of position. A particle at any instant in time has a position, but no velocity.

 

[N88]

Well, I won't defend Maudlin that far. I'm not a big fan of arguing from EPR. …

Just like Einstein one year later, shouldn't we all be arguing against EPR (written by Podolsky in 1935)? Favouring the statistical interpretation, Einstein writes (J. Franklin Institute, 1936, V.221, p.376): "Such an interpretation eliminates also the paradox recently demonstrated by myself and two collaborators [ie, EPR], …."

As I see things developing here, it seems to me that EPR went for partial naive realism ["if we can predict with certainty"] and Bell (relatedly) worked on full naive realism (see post #44 above): and both variants of naive realism are rendered inapplicable by QM and Bell-tests.

That seems to put me firmly in the camp of those who reject the classicality in EPR-Bell in favour of locality.

See also next post from me re Maudlin and Zeilinger.

 

[N88]

… See also next post from me re Maudlin and Zeilinger.

As a matter of interest. In Musser's book (2015) - "Spooky Action at a Distance" - p.116: "When Maudlin ended [his talk, circa 2011, Dresden], Zeilinger raised his hand. … … and merely reasserted his conclusion: 'This inference of nonlocality seems to be based on a rather realistic interpretation of information. If you don't assume this, you don't need nonlocality.'"

 

[stevendaryl]

As I see things developing here, it seems to me that EPR went for partial naive realism ["if we can predict with certainty"] and Bell (relatedly) worked on full naive realism (see post #44 above): and both variants of naive realism are rendered inapplicable by QM and Bell-tests.

But my difficulty is that I have no idea what it means to reject realism. I can certainly understand what it means for a specific theory not to be realistic--it means that whatever notion of state is the subject of that theory is not to be taken to be a description of the physical world, but of our information about the physical world. For example, classical probability theory interprets probabilities as reflecting our ignorance about the world, and are not to be understood as facts about the world itself. If I split up a pair of shoes, and put each into a separate box, and send one shoe to Alice, and the other shoe to Bob, then Alice would describe the situation before she opens the box as: "P(Alice has a left shoe) = 50%, P(Bob has a left-shoe) = 50%". After opening the box, this situation would instantaneously change to either "P(Alice has a left shoe) = 0%, P(Bob has a left shoe) = 100%" or vice-versa. You don't have to worry about how Alice's action made Bob's probability change instantaneously, and whether that violates special relativity, because probabilities aren't physical quantities. They don't exist in the world, they exist inside Alice's head, and that's where the change takes place. So these probabilities are non-realistic--they don't reflect objective physical facts about the world.

But this notion of "realistic" is not about the world, it's about a theory. The theory is either realistic or not. It doesn't make any sense to me to say that the world is not realistic. Sort of by definition, "realistic" means to me "having to do with reality--that is, having to do with the real world". I can understand what it means to interpret the wave function realistically or not, but I really don't understand what it means to reject realism. Maybe it means that the best possible theory about the world is non-realistic?

On another topic:

People have been using the words "simplicial" and "non-simplicial" in this thread without defining them. rubi says that Bell's assumption about the existence of a parameter $\lambda$ is equivalent to the assumption that the underlying theory is simplicial. I take that to mean that for every situation, there is a "best", most-informative description of the situation? Or what does it mean? (I know what a simplex is, but how simplices relate to Bell's argument is unclear).

 

[atyy]

You need to draw a two-dimensional picture here with the axes "classicality" and "locality". (1) assumes no classicality but is a bit local. (2) is fully classical and fully local. However, quantum theory can be fully local but not classical at all, so it's not "between (1) and (2)".

I don't think the notion is empty. At least in the Bell situation, one can consistently supplement QM with a non-empty causality relation. I don't know about the general case. This is simply very unexplored terrain. Zukowski and Brukner are also not sure about their conclusion. The point is that until someone proves the incompatibility of a non-empty causality relation with QM, one can't claim that (1) is the only option.

Yes, there are notions between (1) and (2) but at least at present, they are not used in the derivation of a Bell inequality. At present there are 2 important routes to a bell inequality, and they use (1) and (2). In using (1) we have to supplement it with another assumption, eg. no randomness, while in using (2) there is no need for any additional assumption. So when people say they are giving up something to preserve locality, at present, they mean locality in the sense of (1). Maudlin doesn't dispute this.

There are things like consistent histories, but it is unclear whether this is an example of preserving "locality" by giving up "something", since consistent histories claims to preserve something like Einstein locality, whereas the locality that can be preserved by giving up something is merely no superluminal signalling.

I don't get this conclusion from Werner's articles. I think Maudlin misunderstands him. As long as the state is not a physical object, everything is fine.

Apparently Werner writes "Naturally, I have taken “physical state" here in the sense of the operational approach, as the quantity which allows us to determine the probabilities for all subsequent operations and measurements (“epistemic" rather than “ontic")."

If the epistemic state is taken to be the physical state, isn't that the same as taking the wave function to be physical?

 

[atyy]

As a matter of interest. In Musser's book (2015) - "Spooky Action at a Distance" - p.116: "When Maudlin ended [his talk, circa 2011, Dresden], Zeilinger raised his hand. … … and merely reasserted his conclusion: 'This inference of nonlocality seems to be based on a rather realistic interpretation of information. If you don't assume this, you don't need nonlocality.'"

At the end of the day, the important point that Maudlin is trying to make is that there is a measurement problem. One can certainly assert that it doesn't need to be solved. On the other hand, most physicists including Dirac and Weinberg, and all who suspect that MWI or consistent histories could be correct, have believed that there is a measurement problem.