A Clarification regarding argument in EPR paper

[RespectableCheese]

TL;DR Summary

The argument presented in the EPR paper seems flawed/confusing, curious about the reasoning.

Greetings all. I read through the original EPR paper recently and ran into some confusion regarding the central argument. As I understand it, the authors assert the following two definitions:

Assumption 1: A physical theory is called complete if every element in physical reality has a corresponding element in the physical theory.

Assumption 2: If a physical quantity can be predicted with certainty, then its corresponding element exists in physical reality.

They then go on to make the following assertion:

Proposition 1: It cannot be the case that both (1) The quantum theory is a complete physical theory and (2) The eigenvalues corresponding to two non-commuting observables have simultaneous physical reality.

They then go on to show how in principle an entangled system could in theory be constructed such that by measuring either one of two non-commuting observables on one of the entangled system's subsystems, a definite value for that observable's eigenvalue could be yielded at the un-measured system. To preserve the property of locality for that system, it would have to be the case that the observables' eigenvalues at the un-measured subsystem, while initially assumed to be indefinite, were actually well-defined and predictable all along. Therefore in this case the eigenvalues of non-commuting values do in fact have simultaneous reality, and so, by the law of disjunction elimination and the truth of proposition 1, it follows that the quantum theory is in-complete.

This conclusion clearly follows if proposition 1 is assumed true, however I am having some difficulty in figuring out how that proposition is justified from just the assumptions given. Their justification is given verbatim as follows:

"For if both of them had simultaneous reality - and thus definite values - these values would enter into the complete description, according to the description of completeness. If the wave function provided such as complete description of reality, it would contain these values; these would then be predictable. This not being the case, we are left with the alternatives stated."

I don't see how this argument follows, given the known empirical reality that the eigenvalues of non-commuting observables can not be predicted simultaneously with absolute certainty. For the predictability of a physical quantity is, from assumption 2, only a sufficient but not necessary condition for those elements existing in physical reality, and so the fact alone that they are not predictable proves nothing. An additional implicit assumption would have to be that if a quantity exists in a physical theory, then it is predictable.

It seems like it would be more elegant to say that, in the constructed example with the entangled system, it is possible according to the quantum theory to predict with certainty and simultaneity eigenvalues for non-commuting observables, and that since this is empirically impossible, the theory itself must be flawed in some manner.

As I understand it Einstein later distanced himself from this paper and clarified that his main issue was with the non-locality that was implied by entangled quantum states. So perhaps it's not fruitful to pick this paper apart, but I thought it might be worth bringing up.

The paper is also attached below for convenience. Thanks.

 

[mad mathematician]

What does constitue as "physical reality"?

Do we assume materialism in the background?

 

[PeroK]

"For if both of them had simultaneous reality - and thus definite values - these values would enter into the complete description, according to the description of completeness. If the wave function provided such as complete description of reality, it would contain these values; these would then be predictable. This not being the case, we are left with the alternatives stated."

I don't see how this argument follows, given the known empirical reality that the eigenvalues of non-commuting observables can not be predicted simultaneously with absolute certainty. For the predictability of a physical quantity is, from assumption 2, only a sufficient but not necessary condition for those elements existing in physical reality, and so the fact alone that they are not predictable proves nothing. An additional implicit assumption would have to be that if a quantity exists in a physical theory, then it is predictable.

It seems like it would be more elegant to say that, in the constructed example with the entangled system, it is possible according to the quantum theory to predict with certainty and simultaneity eigenvalues for non-commuting observables, and that since this is empirically impossible, the theory itself must be flawed in some manner.

As I understand it Einstein later distanced himself from this paper and clarified that his main issue was with the non-locality that was implied by entangled quantum states. So perhaps it's not fruitful to pick this paper apart, but I thought it might be worth bringing up.

The paper is also attached below for convenience. Thanks.

I would tend to agree with your analysis.

 

[Morbert]

They then go on to show how in principle an entangled system could in theory be constructed such that by measuring either one of two non-commuting observables on one of the entangled system's subsystems, a definite value for that observable's eigenvalue could be yielded at the un-measured system. To preserve the property of locality for that system, it would have to be the case that the observables' eigenvalues at the un-measured subsystem, while initially assumed to be indefinite, were actually well-defined and predictable all along. Therefore in this case the eigenvalues of non-commuting values do in fact have simultaneous reality, and so, by the law of disjunction elimination and the truth of proposition 1, it follows that the quantum theory is in-complete.

[...]

I don't see how this argument follows, given the known empirical reality that the eigenvalues of non-commuting observables can not be predicted simultaneously with absolute certainty. For the predictability of a physical quantity is, from assumption 2, only a sufficient but not necessary condition for those elements existing in physical reality, and so the fact alone that they are not predictable proves nothing. An additional implicit assumption would have to be that if a quantity exists in a physical theory, then it is predictable.

They can't be predicted simultaneously, but the observer can choose to measure either of the two non-commuting quantities, and hence learn the corresponding quantity of the distant, undisturbed system. How is the observer free to learn about either quantity of the undisturbed system?

 

[martinbn]

I don't understand your confusion. The EPR argument goes like this: you can predict with 100% certainty the value of an observable without disturbing the system, therefore (according to EPR) this value should be already there. But the theory doesn't have that, so it (the theory) must be incomplete (in the EPR sense).

 

[PeroK]

I don't understand your confusion. The EPR argument goes like this: you can predict with 100% certainty the value of an observable without disturbing the system, therefore (according to EPR) this value should be already there. But the theory doesn't have that, so it (the theory) must be incomplete (in the EPR sense).

I thought that part of the problem was that there are many ways in which you can try to get round the HUP, but it's only when you specify the details of your experiment that the HUP asserts itself, sometimes in quite subtle ways.

For example, you could try to set up an experiment where you know the spin of an electron about two coordinate axes at the same time. See section 6.4.3 here.

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

But by suitable fiddling with the beam, the magnetic field strengths and so on it should
be possible in principle, at least from the point of view of classical physics, to minimize this effect,
or at least determine exactly how much precession occurs, and take account of it. But in practice,
it turns out that all these attempts fail.

The same might be true of measurements of position and momentum for a pair of particles If you take a too-classical approach, then you can imagine an experiment where one particle's position and one particle's momentum are measured simultaneously to a jointly higher precision than allowed by the HUP, throwing each particle into an impossible state. Again, however, it's in the practical details of the experiment where the HUP asserts itself. Or, to put it in more modern terms: the attempted preparation of an impossible state cannot be made to work.

 

[martinbn]

I thought that part of the problem was that there are many ways in which you can try to get round the HUP, but it's only when you specify the details of your experiment that the HUP asserts itself, sometimes in quite subtle ways.

For example, you could try to set up an experiment where you know the spin of an electron about two coordinate axes at the same time. See section 6.4.3 here.

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

But by suitable fiddling with the beam, the magnetic field strengths and so on it should
be possible in principle, at least from the point of view of classical physics, to minimize this effect,
or at least determine exactly how much precession occurs, and take account of it. But in practice,
it turns out that all these attempts fail.

The same might be true of measurements of position and momentum for a pair of particles If you take a too-classical approach, then you can imagine an experiment where one particle's position and one particle's momentum are measured simultaneously to a jointly higher precision than allowed by the HUP, throwing each particle into an impossible state. Again, however, it's in the practical details of the experiment where the HUP asserts itself. Or, to put it in more modern terms: the attempted preparation of an impossible state cannot be made to work.

But they are not talking about measurement of two conjugate variables, just predicting the values. And their calculation is not problematic. It is the interpretations of their argument that disagree with each other.

 

[PeroK]

But they are not talking about measurement of two conjugate variable

Of course they are. The paper says "Suppose now the quanitity A is measured and is is found that it has the value $a_k$."

 

[martinbn]

Of course they are. The paper says "Suppose now the quanitity A is measured and is is found that it has the value $a_k$."

There they are just explaining the reduction of the state postulate.

 

[PeroK]

There they are just explaining the reduction of the state postulate.

The only way to be certain of a measureable is to measure it and send the state to an eigenstate/function. That's what EPR are doing. See the paragraph after equation (18):

Thus, by measuring either A or B we are in a position to predict with certainty ...

The whole argument is based on complementary measurments on an entangled system.

 

[martinbn]

The only way to be certain of a measureable is to measure it and send the state to an eigenstate/function. That's what EPR are doing. See the paragraph after equation (18):

Thus, by measuring either A or B we are in a position to predict with certainty ...

The whole argument is based on complementary measurments on an entangled system.

I don't disagree with that, may be I didn't phrase it well. But their concern is the predicted values, not the measured ones.

 

[PeroK]

I don't disagree with that, may be I didn't phrase it well. But their concern is the predicted values, not the measured ones.

That's interesting. They terminate their argument at a point where there appears to be no contradiction with QM. I must confess that I thought the argument was more sophisticated than that.

 

[Demystifier]

It seems like it would be more elegant to say that, in the constructed example with the entangled system, it is possible according to the quantum theory to predict with certainty and simultaneity eigenvalues for non-commuting observables, and that since this is empirically impossible, the theory itself must be flawed in some manner.

The paper was written in 1935, at that time it was not so clear that such thing is empirically impossible. Even today, just because nobody knows how to do it in the laboratory doesn't imply that it's absolutely impossible. They wanted to prove a theorem, so they didn't want an argument that depends on successes of experimental physics. They wanted an argument that depends only on theoretical assumptions.

 

[martinbn]

That's interesting. They terminate their argument at a point where there appears to be no contradiction with QM. I must confess that I thought the argument was more sophisticated than that.

I think (might be wrong), that they don't claim that there is a contradiction, but that there are values that should be there but are not in the theory, hence it is incomplete.

 

[RespectableCheese]

I don't understand your confusion. The EPR argument goes like this: you can predict with 100% certainty the value of an observable without disturbing the system, therefore (according to EPR) this value should be already there. But the theory doesn't have that, so it (the theory) must be incomplete (in the EPR sense).

I'm not sure that's exactly how their reasoning goes; they seem to be trying to say that, under the assumption of locality, the eigenvalues of two non-commuting observables can have simultaneous reality at a system, but that this cannot be the case given our apparent inability to empirically measure such values simultaneously. The strict logic of their argument doesn't seem to hold together though if you follow it rigorously. Technically the fact that you can make those predictions with absolute certainty actually does follow directly from the established theory (as demonstrated by their constructed example), but it doesn't seem to line up with empirical reality.

 

[PeroK]

I think (might be wrong), that they don't claim that there is a contradiction, but that there are values that should be there but are not in the theory, hence it is incomplete.

That's what I meant to say. It's interesting how much water has flowed under the bridge since 1935 and yet this paper remains one of the most famous. It's quite underwhelming and reinforces my view that the arguments against QM were always much weaker than they were given credit for.

 

[RespectableCheese]

The paper was written in 1935, at that time it was not so clear that such thing is empirically impossible. Even today, just because nobody knows how to do it in the laboratory doesn't imply that it's absolutely impossible. They wanted to prove a theorem, so they didn't want an argument that depends on successes of experimental physics. They wanted an argument that depends only on theoretical assumptions.

This is the relevant paragraph from the paper:

"More generally, it is shown in quantum mechanics that, if the operators corresponding to two physical quantities, say A and B, do not commute, that is, if AB ≠ BA, then the precise knowledge of one of them precludes such a knowledge of the other. Furthermore, any attempt to determine the latter experimentally will alter the state of the system in such a way as to destroy the knowledge of the first."

The empirical impossibility of measuring non-commuting observables simultaneously follows from the theory, true. I suppose a better way of phrasing it is that it is possible to contrive a scenario in the theory (the authors' constructed example with the entangled state) that makes contradictory predictions compared to other aspects of the theory (the impossibility of having simultaneous perfect knowledge of non-commuting eigenvalues).

 

[martinbn]

I'm not sure that's exactly how their reasoning goes; they seem to be trying to say that, under the assumption of locality, the eigenvalues of two non-commuting observables can have simultaneous reality at a system, but that this cannot be the case given our apparent inability to empirically measure such values simultaneously.

I don't think that they say that. They say that the theory as it is doesn't have simultaneous values of noncommuting observables. I don't think it has to do with what we can measure and what not.

The strict logic of their argument doesn't seem to hold together though if you follow it rigorously.

Where does it break?

Technically the fact that you can make those predictions with absolute certainty actually does follow directly from the established theory (as demonstrated by their constructed example), but it doesn't seem to line up with empirical reality.

 

[martinbn]

That's what I meant to say. It's interesting how much water has flowed under the bridge since 1935 and yet this paper remains one of the most famous. It's quite underwhelming and reinforces my view that the arguments against QM were always much weaker than they were given credit for.

I think this is because today entanglement is understood (at least mathematically). Then it was one of the first time they've seen it.

 

[PeroK]

The empirical impossibility of measuring non-commuting observables simultaneously follows from the theory, true.

Actually, it's much subtler than that. You would be better to read Cresser's section on spin measurements than the EPR paper. It's great that you are looking at original papers, but that was an anti-QM paper and I can't see how the argument even stacks up.

PS There's been so much progress since this paper that almost anything it says may be out of date and have been superseded by theoretical developments in the past 90 years.

 

[RespectableCheese]

I don't think that they say that. They say that the theory as it is doesn't have simultaneous values of noncommuting observables. I don't think it has to do with what we can measure and what not.

Where does it break?

I'm making that inference from these two statements:

"If, without in any way disturbing a system, we can predict with certainty, (i.e. with probability equal to unity) the value of a physical quantity..."

"For if both of them had simultaneous reality - and thus definite values - these values would enter into the complete description, according to the description of completeness. If the wave function provided such as complete description of reality, it would contain these values; these would then be predictable."

If a quantity is "predictable" with certainty, that seems to imply that you can first claim that you will observe some particular value, given your knowledge of the state of the physical system at a point in time, and then be certain to actually observe just that value after measuring the state.

The logic seems to break down in the second quoted paragraph - there's no reason to infer that if a complete physical theory contains definite values, they are therefore predictable (by the authors' definition of a complete theory). If the values exist in a theory, and the theory is complete, then they exist in physical reality, but this doesn't imply that they be predictable with certainty, because absolute predictability is a sufficient but not necessary criterion for physical existence, as the authors state explicitly.

This paper frustrates me because they seem to have the right idea but they fumbled the details in a really baffling way.

 

[PeroK]

This paper frustrates me because they seem to have the right idea but they fumbled the details in a really baffling way.

If they had had the right idea then the the experiments to test Bell's theorem would have proved QM wrong. That's where these ideas were eventually tested experimentally.

 

[martinbn]

The logic seems to break down in the second quoted paragraph - there's no reason to infer that if a complete physical theory contains definite values, they are therefore predictable (by the authors' definition of a complete theory). If the values exist in a theory, and the theory is complete, then they exist in physical reality, but this doesn't imply that they be predictable with certainty, because absolute predictability is a sufficient but not necessary criterion for physical existence, as the authors state explicitly.

No, you have it backwards. They don't say that values that exist should be predictable. They say that values which are predictable with certainty should exist.

 

[RespectableCheese]

Actually, it's much subtler than that. You would be better to read Cresser's section on spin measurements than the EPR paper. It's great that you are looking at original papers, but that was an anti-QM paper and I can't see how the argument even stacks up.

Oh yes, I'm aware that this is basically just a historical artifact, clearly we've progressed since then. The statement about non-commuting observables is a consequence of the uncertainty principle, which was established at that time.

Do you mean you think the EPR argument is flawed as well? I guess Einstein was already fairly old at this point; kind of amusing to see how even brilliant scientists aren't immune to getting out of touch. It did get people talking about entanglement though.

 

[RespectableCheese]

If they had had the right idea then the the experiments to test Bell's theorem would have proved QM wrong. That's where these ideas were eventually tested experimentally.

Yes, that is correct. I mean they had the right idea in noting the tension between QM and locality; they assume locality and derive contradictory results.

 

[RespectableCheese]

No, you have it backwards. They don't say that values that exist should be predictable. They say that values which are predictable with certainty should exist.

That's exactly what I mean, that's the issue with their argument. It would have to be the other way around for their logic to hold together.

 

[Demystifier]

I think this is because today entanglement is understood (at least mathematically). Then it was one of the first time they've seen it.

In one paper I argue that Einstein used a version of EPR argument already in 1930.
https://arxiv.org/abs/1203.1139

 

[martinbn]

That's exactly what I mean, that's the issue with their argument. It would have to be the other way around for their logic to hold together.

No! Why?

 

[RespectableCheese]

No! Why?

"For if both of them had simultaneous reality - and thus definite values - these values would enter into the complete description, according to the description of completeness. If the wave function provided such as complete description of reality, it would contain these values; these would then be predictable. This not being the case, we are left with the alternatives stated."

This logic can only follow in two cases:

1) Physical reality of a quantity implies predictability (not the case, based on their definition)
2) A value's existence in a complete theory implies predictability (not stated)

 

[martinbn]

"For if both of them had simultaneous reality - and thus definite values - these values would enter into the complete description, according to the description of completeness. If the wave function provided such as complete description of reality, it would contain these values; these would then be predictable. This not being the case, we are left with the alternatives stated."

This logic can only follow in two cases:

1) Physical reality of a quantity implies predictability (not the case, based on their definition)
2) A value's existence in a complete theory implies predictability (not stated)

This is not their argument! Their argument is
1) every value that can be predicted with certainty should be in the theory, if the theory is complete
2) here is an example of something that can be predicted with certainty but is not in the theory
Therefore the theory is not complete.

 

[RespectableCheese]

This is not their argument! Their argument is
1) every value that can be predicted with certainty should be in the theory, if the theory is complete
2) here is an example of something that can be predicted with certainty but is not in the theory
Therefore the theory is not complete.

No, you second point is backwards.

"... [the theory] would contain these values; these would then be predictable. This not being the case, we are left with the alternatives stated."

This chain of reasoning is immediately preceded by:

"More generally, it is shown in quantum mechanics that, if the operators corresponding to two physical quantities, say A and B, do not commute, that is, if AB ≠ BA, then the precise knowledge of one of them precludes such a knowledge of the other. Furthermore, any attempt to determine the latter experimentally will alter the state of the system in such a way as to destroy the knowledge of the first."

(The values they are referring to in the first quoted segment are the eigenvalues of non-commuting observables).

 

[PeroK]

2) here is an example of something that can be predicted with certainty but is not in the theory
Therefore the theory is not complete.

The argument seems quite weak in another way. It's like making a big deal out of a probability of 1 (or 0) and saying it's not really a probability any more. That it's only really a probability when it's strictly between 0 and 1.

 

[martinbn]

The argument seems quite weak in another way. It's like making a big deal out of a probability of 1 (or 0) and saying it's not really a probability any more. That it's only really a probability when it's strictly between 0 and 1.

Yes, for them if the probability for measuring and finding a value is 1, then the value must have been so before the measurement.

 

[RespectableCheese]

This is not their argument! Their argument is
1) every value that can be predicted with certainty should be in the theory, if the theory is complete
2) here is an example of something that can be predicted with certainty but is not in the theory
Therefore the theory is not complete.

I'm not sure I understand this - what is the "something" that actually can be predicted with certainty but is not "in the theory"?

 

[Morbert]

That's exactly what I mean, that's the issue with their argument. It would have to be the other way around for their logic to hold together.

Their argument doesn't rest on the two quantities A and B of a remote system being simultaneously predictable. Their argument instead rests on the freedom to to learn, with certainty, either the value of A or the value of B of a remote system without ever disturbing it.

 

[martinbn]

I'm not sure I understand this - what is the "something" that actually can be predicted with certainty but is not "in the theory"?

Simultaneous values for momentum and position of particle B are not in the theory. Using particle A they can measure and then predict the corresponding value for B. But B is far away, so it has not been disturbed. Which means that both values must be real.

 

[RespectableCheese]

Simultaneous values for momentum and position of particle B are not in the theory. Using particle A they can measure and then predict the corresponding value for B. But B is far away, so it has not been disturbed. Which means that both values must be real.

Oh, I see what you're saying - that's referring to the latter part of their argument. Given that both values are physically real, this line of reasoning:

"From this follows that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. For if both of them had simultaneous reality—and thus definite values—these values would enter into the complete description, according to the condition of completeness. If then the wave function provided such a complete description of reality, it would contain these values; these would then be predictable. This not being the case, we are left with the alternatives stated."

Is used to conclude that the theory is not complete. (Because then (2) is false, so (1) must be true by disjunctive elimination). But it's this argument where I see the flaw, as I described earlier.

 

[DrChinese]

"For if both of them had simultaneous reality - and thus definite values - these values would enter into the complete description, according to the description of completeness. If the wave function provided such as complete description of reality, it would contain these values; these would then be predictable. This not being the case, we are left with the alternatives stated."

I don't see how this argument follows, given the known empirical reality that the eigenvalues of non-commuting observables can not be predicted simultaneously with absolute certainty. For the predictability of a physical quantity is, from assumption 2, only a sufficient but not necessary condition for those elements existing in physical reality, and so the fact alone that they are not predictable proves nothing. An additional implicit assumption would have to be that if a quantity exists in a physical theory, then it is predictable.

You are quite correct, there is something missing here. They actually make an additional assumption at the end of the paper:

"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 no both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depends upon the process of measurement carried out on the first system, which does not disturb the second system in any way."

And they explicitly assume:

"No reasonable definition of reality could be expected to permit this".

 

[DrChinese]

The paper is also attached below for convenience.

Your link did not work for me. If anyone needs it:

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete ?

 

[RespectableCheese]

You are quite correct, there is something missing here. They actually make an additional assumption at the end of the paper:

"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 no both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depends upon the process of measurement carried out on the first system, which does not disturb the second system in any way."

And they explicitly assume:

"No reasonable definition of reality could be expected to permit this".

I don't think that really addresses the concern - in that excerpt the authors refute a potential objection to the criterion of reality they had assumed (that is, that an element of a system is physically real if it can be predicted with absolute certainty without disturbing the system). The latter half of their argument relies on the hypothetical case of the entangled system, in which either eigenvalue for the two non-commuting observables can be predicted with absolute certainty and without disturbing the second, distant system. The potential objection they address here posits that for two values to be considered simultaneously real by the given criterion, they must be simultaneously predictable. Because in the contrived example, the observer can only make one measurement of the two observables, they are not simultaneously predictable. This would imply that the reality of one or the other eigenvalue is then determined at the time of measurement, the measured eigenvalue gaining the status of phsyical reality at the expense of the unmeasured. The authors then dismissed this as being in principle unsatisfactory as a general criterion of physical reality. There is no additional assumption made; they describe a potential objection and reject it.

 

[DrChinese]

I don't think that really addresses the concern - in that excerpt the authors refute a potential objection to the criterion of reality they had assumed (that is, that an element of a system is physically real if it can be predicted with absolute certainty without disturbing the system). The latter half of their argument relies on the hypothetical case of the entangled system, in which either eigenvalue for the two non-commuting observables can be predicted with absolute certainty and without disturbing the second, distant system. The potential objection they address here posits that for two values to be considered simultaneously real by the given criterion, they must be simultaneously predictable. Because in the contrived example, the observer can only make one measurement of the two observables, they are not simultaneously predictable. This would imply that the reality of one or the other eigenvalue is then determined at the time of measurement, the measured eigenvalue gaining the status of phsyical reality at the expense of the unmeasured. The authors then dismissed this as being in principle unsatisfactory as a general criterion of physical reality. There is no additional assumption made; they describe a potential objection and reject it.

True enough. But that exact objection (I call it an assumption) is precisely what Bell exploited!

Bell said: let’s assume both can’t be predicted, but merely have values. And in fact all (but at least 3) potential measurement settings have definite preexisting values. That leads to Bell Inequalities, and we know where those lead.

In other words: if they (at least 3) have values, what are they? There aren’t such values, independent of the experimenter’s choice of measurement basis. So pick out of this what you choose to be the critical assumption, and you’re home.

 

[PeterDonis]

The authors then dismissed this as being in principle unsatisfactory as a general criterion of physical reality.

And the problem is, as Bell first deduced theoretically, and as has now been confirmed experimentally, that there is no model that would be satisfactory to EPR in terms of capturing their notion of physical reality, that also agrees with experiments.

In other words, we now know, experimentally, that however "reality" works is not reasonable according to EPR.

 

[RespectableCheese]

True enough. But that exact objection (I call it an assumption) is precisely what Bell exploited!

Bell said: let’s assume both can’t be predicted, but merely have values. And in fact all (but at least 3) potential measurement settings have definite preexisting values. That leads to Bell Inequalities, and we know where those lead.

In other words: if they (at least 3) have values, what are they? There aren’t such values, independent of the experimenter’s choice of measurement basis. So pick out of this what you choose to be the critical assumption, and you’re home.

I mean that's a true enough statement about Bell's theorem but I don't see what it has to do with this paper.

 

[RespectableCheese]

And the problem is, as Bell first deduced theoretically, and as has now been confirmed experimentally, that there is no model that would be satisfactory to EPR in terms of capturing their notion of physical reality, that also agrees with experiments.

In other words, we now know, experimentally, that however "reality" works is not reasonable according to EPR.

I think their initial criterion of reality (that a quantity's being predictable with absolute certainty without disturbing the system of the corresponding element entails that element's physical reality) could still hold even given Bell's results, which imply that local hidden variable theories are not tenable; in their example of the entangled state, it's possible for the distant system to obtain a definite real value when the measurement is made by abandoning the condition of local realism.

 

[PeterDonis]

in their example of the entangled state, it's possible for the distant system to obtain a definite real value when the measurement is made by abandoning the condition of local realism.

Only for the case where both measurements are made in the same direction (about the same spin axis). But that case isn't the one that violates the Bell inequalities. The cases that violate those inequalities are cases where the two spin measurements on the two entangled particles are not made about the same axis. A "definite real value" for the spin doesn't just commit the particle to a particular result for a spin measurement about one axis; it commits the particle to particular results for any spin measurement. EPR didn't even address that issue, but it's crucial: a "definite real value" actually means a lot more than EPR appear to have realized.

 

[RespectableCheese]

Only for the case where both measurements are made in the same direction (about the same spin axis). But that case isn't the one that violates the Bell inequalities. The cases that violate those inequalities are cases where the two spin measurements on the two entangled particles are not made about the same axis. A "definite real value" for the spin doesn't just commit the particle to a particular result for a spin measurement about one axis; it commits the particle to particular results for any spin measurement. EPR didn't even address that issue, but it's crucial: a "definite real value" actually means a lot more than EPR appear to have realized.

I think this already pretty tangential, but I'm not sure what you're getting at; their criterion of reality is that a value being predictable with certainty is sufficient for the corresponding element to exist in physical reality. So I don't think that situation violates their criterion, i.e. by demonstrating a case where a value that can be predicted with absolute certainty does not have real phsyical existence.

 

[PeterDonis]

a value being predictable with certainty is sufficient for the corresponding element to exist in physical reality

Yes, but what does "exist in physical reality" mean?

In the case of spin, if a particle's spin about a certain axis "exists in physical reality" (because it's entangled with another particle whose spin has just been measured about that axis), that has implications for its spin about other axes as well. EPR didn't consider those implications. But Bell did.

 

[RespectableCheese]

Yes, but what does "exist in physical reality" mean?

In the case of spin, if a particle's spin about a certain axis "exists in physical reality" (because it's entangled with another particle whose spin has just been measured about that axis), that has implications for its spin about other axes as well. EPR didn't consider those implications. But Bell did.

I think they just mean that it has the ontological status of existing in the objective physical world? Maybe that sounds like a circular definition. They were reasoning metaphysically, that is, prior to any particular scientific theory or empirical observation, with their definition of completeness and criterion for physical reality.

What exactly is it about the Bell states that makes their criterion inconsistent/untenable? From a purely logical standpoint you'd have to provide an example of a case where you can predict with absolute certainty a particular quantity for some element that does not exist in physical reality, in the most general meaning of that term. This just seems impossible a priori. Otherwise what are you predicting? You would have some well-defined physical quantity, say mass, for which a specific value can be predicted with certainty for a physical system, but for which no actual physical element exists in that system to which that quantity is attached. As far as reasoning from first principles goes this seems pretty unbreakable as a sufficient criterion for something existing in the objective physical world.

 

[PeterDonis]

From a purely logical standpoint you'd have to provide an example of a case where you can predict with absolute certainty a particular quantity for some element that does not exist in physical reality

No, that's not the issue. The issue is with an element that, according to their criterion, does "exist in physical reality", because we can predict it with certainty, and what that implies. Again, in the case under discussion, we have two particles whose spins are entangled, so if we measure particle A's spin about, say, the $z$ axis, we can now predict with certainly particle B's spin about the $z$ axis, so the latter must "exist in physical reality".

But if particle B's spin about the $z$ axis "exists in physical reality", what about particle B's spin about, say, an axis tilted by 60 degrees from $z$? EPR don't discuss that at all. They don't even appear to have considered it.

But Bell showed that, once you say that particle B's spin about the $z$ axis "exists in physical reality", that has implications for particle B's spin about other axes--and those implications require that the Bell inequalities are obeyed. But we know, experimetally, that the Bell inequalities are violated.

The only way to avoid the implications of Bell inequality violations is to make "exists in physical reality" basically mean nothing over and above its definition: yes, if we measure particle A's $z$ spin, we can predict with certainty particle B's $z$ spin. But that's all it can mean.

And that's not the position EPR were arguing for. They were arguing for the position that "exists in physical reality" means more than just being able to predict something with certainty--being able to predict something with certainty was just an indicator to them. They were arguing that QM must be incomplete because it doesn't include these extra things that "exist in physical reality". But any such "more complete" model of reality would have to obey the Bell inequalities--and reality itself doesn't.

 

[PeroK]

This just seems impossible a priori.

QM does, in fact, predict the impossible! Bell's inequality was a limit on what was possible. The mathematics of QM predicted that QM could do better. And, experiments showed that nature can, in fact, do the impossible. Precisely as QM predicted.