Local realism ruled out? (was: Photon entanglement and )

[JesseM]

I don't know. Generally speaking, the projection postulate immediately introduces nonlocality.

Is there something wrong with "introducing nonlocality" in this context? All I'm claiming is that the rule of assuming unitary evolution, and then applying the Born rule/projection postulate at the very end to determine probabilities of different recorded outcomes, is a well-defined pragmatic procedure for generating theoretical predictions about experiments which can be compared with the actual results you find when the experiment is done in real life and the measurement results all written down somewhere. As always, it's just a pragmatic rule for generating predictions about the kinds of results we can write down, it's not meant to be a coherent description of what actually goes on physically at all moments.

Do you disagree that this is a well-defined procedure for generating predictions about the actual results seen in quantum experiments?

Right now I don't quite know how the procedure you describe is supposed to be used to prove the violations in quantum mechanics. Before I see the proof, I cannot tell you if there is any difference or not.

Again, I don't feel like spending a lot of time looking for a paper that specifically uses the von Neumann approach to derive theoretical predictions about EPR type experiments. But do you disagree that the procedure I'm using is the same one von Neumann was proposing? If you don't disagree, don't you think it's fairly implausible that this procedure would fail to predict Bell inequality violations, but no one would have noticed this before despite the procedure being known for decades?

Also, now that you hopefully understand that I'm not talking about applying to projection postulate to each measurement but only once at the very end to all the records, you might reconsider the comment I made about one of the papers I linked to:

Also, note the paper http://www.lps.uci.edu/barrett/publications/SuggestiveProperties.pdf I linked to above, which shows that in the limit as the number of measurements (without collapse) in an EPR type experiment goes to infinity the state vector will approach "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". This does at least imply that in the limit as the number of measurements goes to infinity, if we "collapse" the records at the very end, the probability that the records will show measurement results that were "randomly distributed and statistically correlated in just the way the standard theory predicts" should approach 1 in this limit. Do you disagree?

To put it another way, applying only unitary evolution to a series of N measurements and looking at the state S at the end means that, in the limit as N approaches infinity, S approaches "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". So, this implies that if we apply unitary evolution to a series of N measurements and then apply the projection postulate/Born rule at the very end, then in the limit as N approaches infinity, the probability that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" must approach 1. This isn't quite what I wanted to prove (that even for a small number of measurements, the von Neumann rule gives probabilities which violate Bell inequalities) but it's close.

Anyway, strictly speaking, the projection postulate is not compatible with unitary evolution, whether you use the postulate at the end, at the beginning, or in the middle.

Who cares if it's incompatible when it's just a pragmatic rule for making predictions, not intended to be a coherent theoretical description of what's really going on at all times? The pragmatic rule says that you model the system as evolving in a unitary way until all the measurements are done, then at the end you apply the projection postulate/Born rule to get predictions about the statistics of measurement records. If you see this final application of the projection postulate/Born rule as a violation of unitary evolution, fine, the pragmatic rule says you apply unitary evolution up to the final time T, then at time T you discard unitary evolution and apply the projection postulate. That's a coherent pragmatic rule (nothing wrong with requiring different rules at different times, as long as you know which to use when) even if it makes little sense as a theoretical picture.

 

[akhmeteli]

Is there something wrong with "introducing nonlocality" in this context?

JesseM, everything is wrong with it. Let us remember what we are talking about, in the first place. The question in the title of this thread is "Local realism ruled out?" I offered two arguments (sorry that I have to repeat them one more time):

1. There has been no experimental evidence of violations of the genuine Bell inequalities.
2. The violation of the inequalities in quantum theory is theoretically proven using mutually contradictory assumptions.

And then the conclusion: both experimental and theoretical arguments in favor of nonlocality are controversial, to say the least.

Now, what are trying to prove?

That it is possible to theoretically prove the violations in quantum theory, if you preliminarily introduce nonlocality in the measurement procedure? I could not agree more! But how does this proves nonlocality? This is circular reasoning, for crying out loud!

I fully agree that you can theoretically prove violations if you use the projection postulate! But I reject the projection postulate as anything but an approximation, because it contradicts unitary evolution! Take a standard proof of the Bell theorem, and it proves violations in quantum theory using the projection postulate! No need to spend hours looking for the proof!

All I'm claiming is that the rule of assuming unitary evolution, and then applying the Born rule/projection postulate at the very end to determine probabilities of different recorded outcomes, is a well-defined pragmatic procedure for generating theoretical predictions about experiments which can be compared with the actual results you find when the experiment is done in real life and the measurement results all written down somewhere. As always, it's just a pragmatic rule for generating predictions about the kinds of results we can write down, it's not meant to be a coherent description of what actually goes on physically at all moments.

Do you disagree that this is a well-defined procedure for generating predictions about the actual results seen in quantum experiments?

I do agree that this is is a well-defined procedure for generating... But what does this prove? Let me give you an example of a well-defined procedure: at the end of any experiment aimed at measuring some value you don't bother to read any records and just declare that this value is equal to 5 (in your favorite system of units). Do you agree that this is a well-defined procedure? I bet you do! It cannot even be disproven by experiments! What's wrong then with this procedure? Everything! I don't even know where to start to criticize it! Your procedure is not so absurd, as the projection postulate is at least an approximation, but strictly speaking it's still absurd, as the projection postulate contradicts unitary evolution.

Another thing. I suspect that you can prove nonlocality of classical electromagnetism if you introduce nonlocality in the measurement procedure. But is this what you really want?

Again, I don't feel like spending a lot of time looking for a paper that specifically uses the von Neumann approach to derive theoretical predictions about EPR type experiments. But do you disagree that the procedure I'm using is the same one von Neumann was proposing? If you don't disagree, don't you think it's fairly implausible that this procedure would fail to predict Bell inequality violations, but no one would have noticed this before despite the procedure being known for decades?

I agree that you can prove violations if you use the projection postulate. And no need to look for such a proof - a standard proof of the Bell inequality will do. But how does this undermine my arguments?

Also, now that you hopefully understand that I'm not talking about applying to projection postulate to each measurement but only once at the very end to all the records, you might reconsider the comment I made about one of the papers I linked to:

To put it another way, applying only unitary evolution to a series of N measurements and looking at the state S at the end means that, in the limit as N approaches infinity, S approaches "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". So, this implies that if we apply unitary evolution to a series of N measurements and then apply the projection postulate/Born rule at the very end, then in the limit as N approaches infinity, the probability that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" must approach 1. This isn't quite what I wanted to prove (that even for a small number of measurements, the von Neumann rule gives probabilities which violate Bell inequalities) but it's close.

I commented on this article in post 709.

Who cares if it's incompatible when it's just a pragmatic rule for making predictions, not intended to be a coherent theoretical description of what's really going on at all times? The pragmatic rule says that you model the system as evolving in a unitary way until all the measurements are done, then at the end you apply the projection postulate/Born rule to get predictions about the statistics of measurement records. If you see this final application of the projection postulate/Born rule as a violation of unitary evolution, fine, the pragmatic rule says you apply unitary evolution up to the final time T, then at time T you discard unitary evolution and apply the projection postulate. That's a coherent pragmatic rule (nothing wrong with requiring different rules at different times, as long as you know which to use when) even if it makes little sense as a theoretical picture.

You can say the same about my "5-procedure". And that's not very good for your procedure.

I'd say your procedure's viability hinges on how good an approximation the projection postulate is. But when you start to use this procedure in the area where the projection postulate is not a good approximation, your procedure will probably no better than my "5-procedure". And, as I said, I doubt that you can use approximations, such as the projection postulate, to prove nonlocality, as "approximate nonlocality" does not make much sense.

 

[JesseM]

JesseM, everything is wrong with it. Let us remember what we are talking about, in the first place. The question in the title of this thread is "Local realism ruled out?" I offered two arguments (sorry that I have to repeat them one more time):

1. There has been no experimental evidence of violations of the genuine Bell inequalities.
2. The violation of the inequalities in quantum theory is theoretically proven using mutually contradictory assumptions.

And then the conclusion: both experimental and theoretical arguments in favor of nonlocality are controversial, to say the least.

Now, what are trying to prove?

That it is possible to theoretically prove the violations in quantum theory, if you preliminarily introduce nonlocality in the measurement procedure? I could not agree more! But how does this proves nonlocality? This is circular reasoning, for crying out loud!

How could a proof possibly prove an empirical result? The proof is just intended to show that the statistical predictions of a local realist theory would differ from the statistical predictions of QM. If everyone agrees the pragmatic procedure I described is one way to define the "predictions of QM", then if that procedure predicts Bell inequality violations, that's all you need for the proof. No one would claim that the proof alone shows that QM's predictions will turn out to be empirically true, that of course is a matter for experiment.

I fully agree that you can theoretically prove violations if you use the projection postulate! But I reject the projection postulate as anything but an approximation, because it contradicts unitary evolution! Take a standard proof of the Bell theorem, and it proves violations in quantum theory using the projection postulate! No need to spend hours looking for the proof!

Sure, if you apply the projection postulate multiple times. I was just making the point that I think you can just apply it (or the Born rule, whichever) once at the very end, once all the measurements have been completed. The advantage of this is twofold:

1. You don't have to worry about the definition of which interactions constitute "measurements" and which don't, so there isn't the same ambiguity about how to apply the pragmatic rule

2. If you take a quantum system and model it as evolving in a unitary rule throughout some time interval, then apply the Born rule once at the very end to find the probability it'll be in different states, my understanding is that the probabilities you derive should be identical to those predicted by Bohmian mechanics (where there is no need for the Born rule since the measuring-device pointers have well-defined positions at all times, and the wavefunction is just understood as a classical ensemble of possible arrangements of positions with different probabilities). I believe it's only if you model each measurement as causing a separate "collapse" according to the projection postulate that your predictions would only be "approximately" equal to those given by the Bohmian analysis of the same situation.

I do agree that this is is a well-defined procedure for generating... But what does this prove? Let me give you an example of a well-defined procedure: at the end of any experiment aimed at measuring some value you don't bother to read any records and just declare that this value is equal to 5 (in your favorite system of units). Do you agree that this is a well-defined procedure? I bet you do!

No, it's not solely a procedure "for generating predictions about the actual results seen in quantum experiments", because you've also added a rule about what we must do when conducting the actual experiments (not look at the results). My procedure didn't tell you anything about how the experiments should be conducted, it was just a procedure to generate theoretical predictions about any quantum experiment (or at least any where you have measured the initial state of the system so you can evolve it forward) which could be compared with the empirical results of that experiment.

Another thing. I suspect that you can prove nonlocality of classical electromagnetism if you introduce nonlocality in the measurement procedure. But is this what you really want?

In classical electromagnetism all the local variables have well-defined values at all times (just like Bohmian mechanics), and their values evolve in a local way, so even if we assume we can magically become aware of all the values throughout space at a single instant, there will be no Bell inequality violations in the statistics. Of course if you imagined a "measurement procedure" that instantly changed all the local values at the moment of measurement, just like the projection postulate instantly changes the system's quantum state, then you might get Bell inequality violations depending on the nature of this change, but this theory would no longer resemble what we mean by "classical electromagnetism". In contrast, the procedure I describe above where you use the Born rule to get predictions about measurement-records is one that everyone would agree matches what physicists mean when they talk about the predictions of "QM". And again, Bell was just trying to prove that local realism is inconsistent with what everyone understands to be the predictions of "QM." You seem to be making some theoretical point that you don't find this surprising since the predictions of "QM" involve a nonlocal rule, but who cares? The proof is not intended to show that this result is surprising.

Also, now that you hopefully understand that I'm not talking about applying to projection postulate to each measurement but only once at the very end to all the records, you might reconsider the comment I made about one of the papers I linked to:

To put it another way, applying only unitary evolution to a series of N measurements and looking at the state S at the end means that, in the limit as N approaches infinity, S approaches "an eigenstate of reporting that their measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts". So, this implies that if we apply unitary evolution to a series of N measurements and then apply the projection postulate/Born rule at the very end, then in the limit as N approaches infinity, the probability that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" must approach 1. This isn't quite what I wanted to prove (that even for a small number of measurements, the von Neumann rule gives probabilities which violate Bell inequalities) but it's close.

I commented on this article in post 709.

Yes, but your comment was made when you still seemed confused about the procedure I was suggesting, that's why I re-introduced it with the comment in bold. Your comments in post #709 were:

JesseM, with all due respect, a couple of lines later the author writes: "Note, however, that since the linear dynamics can be written in a perfectly local form, there are in fact no nonlocal causal connections in the bare theory. ...Just as reports of determinate results, relative frequencies, and randomness would generally be explained by the bare theory as illusions the apparent nonlocality here would be just that, apparent." :-)

Of course, the "bare theory" is local, but it also doesn't make any well-defined statistical predictions about empirical results. My point was that if you combined their conclusion about the "bare theory" with the procedure I (and von Neumann) suggest where you do introduce a single application of the Born rule/projection postulate at the very end of a series of measurements, then you can show that in the limit as the number of measurements approaches infinity, the von Neumann procedure will predict with probability 1 that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts".

Now, it may be that you have no objection to the idea that this procedure will predict Bell inequality violations, as suggested by your comment "I fully agree that you can theoretically prove violations if you use the projection postulate!" I thought, though, that previously when you were asking me to "prove it", you were asking for a proof that the procedure I described (unitary evolution with a single application of the Born rule at the very end) would predict Bell inequality violations. That's why I brought up this paper, since it helps justify the conclusion that this is almost certainly true, even if I can't provide a detailed proof.

Who cares if it's incompatible when it's just a pragmatic rule for making predictions, not intended to be a coherent theoretical description of what's really going on at all times? The pragmatic rule says that you model the system as evolving in a unitary way until all the measurements are done, then at the end you apply the projection postulate/Born rule to get predictions about the statistics of measurement records. If you see this final application of the projection postulate/Born rule as a violation of unitary evolution, fine, the pragmatic rule says you apply unitary evolution up to the final time T, then at time T you discard unitary evolution and apply the projection postulate. That's a coherent pragmatic rule (nothing wrong with requiring different rules at different times, as long as you know which to use when) even if it makes little sense as a theoretical picture.

You can say the same about my "5-procedure". And that's not very good for your procedure.

Except that your procedure is useless for making predictions about the sort of experiments physicists actually do in quantum physics (since your procedure requires that physicists discard measurement results without looking at them), while mine works just fine for this pragmatic purpose.

I'd say your procedure's viability hinges on how good an approximation the projection postulate is.

As I said, I think my (and von Neumann's) procedure would exactly agree with the predictions of Bohmian mechanics for a given system at the end of a given time period, and Bohmian mechanics does not require the projection postulate. I think you'll probably disagree with that statement about Bohmian mechanics, though, so I need to go back and address your most recent posts on that subject.

 

[akhmeteli]

How could a proof possibly prove an empirical result? The proof is just intended to show that the statistical predictions of a local realist theory would differ from the statistical predictions of QM.

I fully agree. But QM is a well established (experimentally as well) theory, so such a proof of difference, generally speaking, could be an argument against all local realistic theories.

If everyone agrees the pragmatic procedure I described is one way to define the "predictions of QM", then if that procedure predicts Bell inequality violations, that's all you need for the proof. No one would claim that the proof alone shows that QM's predictions will turn out to be empirically true, that of course is a matter for experiment.

I agree (subject to your “ifs”).

Sure, if you apply the projection postulate multiple times. I was just making the point that I think you can just apply it (or the Born rule, whichever) once at the very end, once all the measurements have been completed. The advantage of this is twofold:

1. You don't have to worry about the definition of which interactions constitute "measurements" and which don't, so there isn't the same ambiguity about how to apply the pragmatic rule

2. If you take a quantum system and model it as evolving in a unitary rule throughout some time interval, then apply the Born rule once at the very end to find the probability it'll be in different states, my understanding is that the probabilities you derive should be identical to those predicted by Bohmian mechanics (where there is no need for the Born rule since the measuring-device pointers have well-defined positions at all times, and the wavefunction is just understood as a classical ensemble of possible arrangements of positions with different probabilities). I believe it's only if you model each measurement as causing a separate "collapse" according to the projection postulate that your predictions would only be "approximately" equal to those given by the Bohmian analysis of the same situation.

JesseM, my response still crucially depends on what exactly you use –the projection postulate or the Born rule.
If you use the projection postulate, no matter one time or a billion times, you manually introduce nonlocality. In this case I immediately concede that you can prove violations in QM (it does not matter if I am right or wrong about it), but I refuse to accept this proof as an argument against local realism, as this proof a) contains mutually contradictory assumptions, and 2) uses nonlocality as one of its assumptions.
If you use the Born rule… Well, the objections I offered above would not look equally strong (although it is not quite clear to me how compatible with dynamics the Born rule is). But then another issue arises: can you get a proof of violations in QM? I am not ready to concede this point. Again, I fully understand that you have better things to do than to look for such a proof, but that does not mean I must concede this point. I think the burden of proof of nonlocality is on those who want nonlocality. The Bell theorem, on the face of it, looks like such a proof, but, as I said repeatedly, it contains mutually contradictory assumptions. If you want to convince me that it is possible to cure this defect, or to prove violations in Bohmian mechanics without using the projection postulate or something similar, I need more than your word, sorry.

No, it's not solely a procedure "for generating predictions about the actual results seen in quantum experiments", because you've also added a rule about what we must do when conducting the actual experiments (not look at the results). My procedure didn't tell you anything about how the experiments should be conducted, it was just a procedure to generate theoretical predictions about any quantum experiment (or at least any where you have measured the initial state of the system so you can evolve it forward) which could be compared with the empirical results of that experiment.

I disagree. This “rule” is not essential and can be removed (so, if you wish, you can look at the results and still say that the value equals 5 :-) ). My idiotic procedure still has something in common with your much more decently looking procedure: it is not compatible with dynamics.

In classical electromagnetism all the local variables have well-defined values at all times (just like Bohmian mechanics), and their values evolve in a local way, so even if we assume we can magically become aware of all the values throughout space at a single instant, there will be no Bell inequality violations in the statistics. Of course if you imagined a "measurement procedure" that instantly changed all the local values at the moment of measurement, just like the projection postulate instantly changes the system's quantum state, then you might get Bell inequality violations depending on the nature of this change, but this theory would no longer resemble what we mean by "classical electromagnetism".

I am certainly not trying to prove that classical electrodynamics is nonlocal, I am just trying to say that you can prove nonlocality where there is no trace of it, if you use a nonlocal measurement procedure.

In contrast, the procedure I describe above where you use the Born rule to get predictions about measurement-records is one that everyone would agree matches what physicists mean when they talk about the predictions of "QM".

Again, if it’s the Born rule, I could tentatively agree (but then you don’t have a proof of violations in QM), but if it’s the projection postulate, I stand by my objections.

And again, Bell was just trying to prove that local realism is inconsistent with what everyone understands to be the predictions of "QM." You seem to be making some theoretical point that you don't find this surprising since the predictions of "QM" involve a nonlocal rule, but who cares? The proof is not intended to show that this result is surprising.

It does not matter much if this inconsistency is surprising or not. It does matter though if Nature is local realistic or not (at least it matters for me; that does not mean that I won’t be able to accept nonlocality if and when it is thoroughly confirmed experimentally). So I am trying to make point that the proof of inconsistency is dubious, as it uses mutually contradictory assumptions. I am also trying to make a point that it is not possible to reasonably embrace those contradictory assumptions anyway, and I put my bet on unitary evolution and against the projection postulate. You see, irrespective of the results of future experiments, we’ll have to modify either unitary evolution or the projection postulate anyway, local realism or no local realism. A logical contradiction is just not acceptable.

Yes, but your comment was made when you still seemed confused about the procedure I was suggesting, that's why I re-introduced it with the comment in bold. Your comments in post #709 were:

Of course, the "bare theory" is local, but it also doesn't make any well-defined statistical predictions about empirical results. My point was that if you combined their conclusion about the "bare theory" with the procedure I (and von Neumann) suggest where you do introduce a single application of the Born rule/projection postulate at the very end of a series of measurements, then you can show that in the limit as the number of measurements approaches infinity, the von Neumann procedure will predict with probability 1 that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts".

Now, it may be that you have no objection to the idea that this procedure will predict Bell inequality violations, as suggested by your comment "I fully agree that you can theoretically prove violations if you use the projection postulate!" I thought, though, that previously when you were asking me to "prove it", you were asking for a proof that the procedure I described (unitary evolution with a single application of the Born rule at the very end) would predict Bell inequality violations. That's why I brought up this paper, since it helps justify the conclusion that this is almost certainly true, even if I can't provide a detailed proof.

Again, I don’t care about any proof if you use the projection postulate (as in this case the proof of nonlocality contains circular reasoning anyway), but I need a proof if you use the Born rule. As confirmed by my quotes from the article, the latter does not contain anything like such proof.

Except that your procedure is useless for making predictions about the sort of experiments physicists actually do in quantum physics (since your procedure requires that physicists discard measurement results without looking at them), while mine works just fine for this pragmatic purpose.

Yes, but just because it uses a better approximation than my procedure. Where this approximation fails (and it cannot but fail somewhere, as, strictly speaking, it is incompatible with unitary evolution), your procedure will fail.

As I said, I think my (and von Neumann's) procedure would exactly agree with the predictions of Bohmian mechanics for a given system at the end of a given time period, and Bohmian mechanics does not require the projection postulate. I think you'll probably disagree with that statement about Bohmian mechanics, though, so I need to go back and address your most recent posts on that subject.

Again, if you use the Born rule in your procedure, I could tentatively agree, if it’s the projection postulate, then I disagree, as there is no collapse in Bohmian mechanics

 

[JesseM]

I fully agree. But QM is a well established (experimentally as well) theory, so such a proof of difference, generally speaking, could be an argument against all local realistic theories.

Well, yes--exactly! If you take "QM" to just mean the pragmatic procedure for making predictions that I describe, then this procedure has a great track record of agreement with experiment. So, even if this pragmatic procedure makes little sense as an ontological picture of what's "really going on", it should be inherently interesting to physicists to know whether the predictions of the pragmatic procedure are compatible with local realism. Of course showing that they're incompatible doesn't prove local realism is false in the real world, since it's possible you could have some local realist model whose predictions matched those of the pragmatic procedure in all the experiments that have been done to date, but which would differ from the pragmatic procedure in an ideal Bell test. Still most physicists would consider this unlikely, owing to the fact that most would agree such a model would almost certainly be very contrived and inelegant.

JesseM, my response still crucially depends on what exactly you use –the projection postulate or the Born rule.

But I already explained in post #716 that I didn't see a difference between the two if it was only done once at the end, they are both just ways of getting the same probabilities for the end results. I concluded by asking "So if you're not interested in what happens to the quantum state later, but just in the probabilities of seeing different combinations of measurement records at some time T after all the measurements are complete, I don't see the distinction between applying the "What difference are you seeing?" and your response in post #719 was "I don't know." So I would still say that there's no meaningful difference between them--if you want to say that the Born rule itself introduces nonlocality since it gives probabilities for a combination of simultaneous physical facts at different spatial locations, that's fine with me!

But then another issue arises: can you get a proof of violations in QM? I am not ready to concede this point.

I think so, if by "QM" you mean the pragmatic rule for generating predictions that I described (and which is the same as von Neumann's rule), which requires a single application of the Born rule to the quantum state of the system at some time after all measurements are completed and recorded. Are you actually suggesting that von Neumann's procedure might not actually predict Bell inequality violations, and that this has just gone unnoticed by physicists for decades? Or are you using "QM" to mean unitary evolution only, with no invoking the projection postulate or the Born rule? (unless the Born rule can somehow be derived from unitary evolution, which is what many-worlds advocates often try to do)

Again, I fully understand that you have better things to do than to look for such a proof

See above, I'm not even clear on what you're asking me to prove here.

The Bell theorem, on the face of it, looks like such a proof, but, as I said repeatedly, it contains mutually contradictory assumptions.

Bell's theorem has two parts: 1) in the type of experiment he specifies, local realism predicts that some Bell inequality will be obeyed, and 2) in the type of experiment he specifies, the predictions of "QM" as understood by physicists are that the Bell inequality will be violated. Your objection about "mutually contradictory assumptions" only seems to be an objection to 2), correct? But isn't it basically just a semantic disagreement, since you seem to define "QM" to mean "unitary evolution only" (which cannot be used to make predictions about any real-world experiment, since unitary evolution only gives complex amplitudes and empirically we never measure complex amplitudes), whereas most physicists would understand "QM" to mean the sort of pragmatic rule for making predictions that I describe.

If you want to convince me that it is possible to cure this defect, or to prove violations in Bohmian mechanics without using the projection postulate or something similar, I need more than your word, sorry.

Even if I could show that Bohmian mechanics can produce predictions of Bell inequality violations without invoking the projection postulate (and I think the links I gave already do this, despite your objections), what difference would it make to your argument? After all the guiding equation of Bohmian mechanics is explicitly nonlocal, so if you objected to the use of the projection postulate because it's nonlocal wouldn't you have the same objection to Bohmian mechanics?

I disagree. This “rule” is not essential and can be removed (so, if you wish, you can look at the results and still say that the value equals 5 :-) ).

But then you aren't comparing theoretical predictions with measurement results, you're comparing them with what you "say" about measurement results, where what you say is in most cases a lie.

I am certainly not trying to prove that classical electrodynamics is nonlocal, I am just trying to say that you can prove nonlocality where there is no trace of it, if you use a nonlocal measurement procedure.

Again, if by "nonlocal measurement procedure" you just mean instantly learn the values of the electromagnetic field at different locations without actually changing them in the process, then no, this won't lead to any Bell inequality violations in the results you learn.

Again, if it’s the Born rule, I could tentatively agree (but then you don’t have a proof of violations in QM), but if it’s the projection postulate, I stand by my objections.

But you never gave a coherent reason for disagreeing that there is no reason for distinguishing the two if we just make one "observation" of the records at the end of all measurements. Do you agree that if at the time we make an observation the quantum state of the records (obtained by unitary evolution) is \alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle then if we "observe" these records, regardless of whether we apply the Born rule or the projection postulate we will predict that the probability of a given result like 010 will just be the amplitude for that eigenstate times its complex conjugate, i.e. \alpha_3 \alpha_3*? Please tell me clearly whether you agree or disagree that the probability of 010 is going to be \alpha_3 \alpha_3* either way. If you don't disagree, then obviously the Born rule and the projection postulate are both making the exact same predictions about the statistics seen in the records at this time, so the probability of statistics that violate the Bell inequalities is the same either way.

So I am trying to make point that the proof of inconsistency is dubious, as it uses mutually contradictory assumptions. I am also trying to make a point that it is not possible to reasonably embrace those contradictory assumptions anyway, and I put my bet on unitary evolution and against the projection postulate. You see, irrespective of the results of future experiments, we’ll have to modify either unitary evolution or the projection postulate anyway, local realism or no local realism. A logical contradiction is just not acceptable.

But you never really addressed my point in post #721 that the "contradiction" only arises if you take the procedure as an ontological description of reality, that purely as a pragmatic procedure it's not contradictory since it's just telling you to use different rules at different times. Your response was just to compare this with your silly "pretend the answer is always 5" procedure, but of course that procedure doesn't have a long track record of accurately predicting experimental results like the QM procedure.

Again, I don’t care about any proof if you use the projection postulate (as in this case the proof of nonlocality contains circular reasoning anyway), but I need a proof if you use the Born rule.

Do you disagree that if a system's state is in an eigenstate of some operator, the Born rule says that on "observation" you are guaranteed to find the value associated with that eigenstate with probability 1? So, that means their conclusion (if we do N measurements, pure unitary evolution predicts that in the limit as N approaches infinity, the measurement records approach an eigenstate where "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts") implies the conclusion (if we do N measurements modeled by unitary evolution and then at the end apply the Born rule to the measurement records, in the limit as N approaches infinity the probability of finding that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" approaches 1)

As I said, I think my (and von Neumann's) procedure would exactly agree with the predictions of Bohmian mechanics for a given system at the end of a given time period, and Bohmian mechanics does not require the projection postulate. I think you'll probably disagree with that statement about Bohmian mechanics, though, so I need to go back and address your most recent posts on that subject.

Again, if you use the Born rule in your procedure, I could tentatively agree, if it’s the projection postulate, then I disagree, as there is no collapse in Bohmian mechanics

And again, if you assume unitary evolution until some time T, then regardless of whether you invoke "the Born rule" or "the projection postulate" at time T, the probabilities of finding different possible combinations of measurement results at time T will be exactly the same. And my argument is that Bohmian mechanics will also yield exactly the same predictions for probabilities of different possible combinations of measurement results at time T.

 

[akhmeteli]

Well, yes--exactly! If you take "QM" to just mean the pragmatic procedure for making predictions that I describe, then this procedure has a great track record of agreement with experiment. So, even if this pragmatic procedure makes little sense as an ontological picture of what's "really going on", it should be inherently interesting to physicists to know whether the predictions of the pragmatic procedure are compatible with local realism. Of course showing that they're incompatible doesn't prove local realism is false in the real world, since it's possible you could have some local realist model whose predictions matched those of the pragmatic procedure in all the experiments that have been done to date, but which would differ from the pragmatic procedure in an ideal Bell test. Still most physicists would consider this unlikely, owing to the fact that most would agree such a model would almost certainly be very contrived and inelegant.

So it’s a matter of opinion. Note that this pragmatic procedure is doomed to fail somewhere anyway, as it contradicts the unitary evolution.

But I already explained in post #716 that I didn't see a difference between the two if it was only done once at the end, they are both just ways of getting the same probabilities for the end results. I concluded by asking "So if you're not interested in what happens to the quantum state later, but just in the probabilities of seeing different combinations of measurement records at some time T after all the measurements are complete, I don't see the distinction between applying the "What difference are you seeing?" and your response in post #719 was "I don't know." So I would still say that there's no meaningful difference between them

If you believe there is no difference, why don’t you choose just one of those two that you like more, even if just to give some focus to the discussion? But I explained to you how my reasoning will depend on your choice: if you choose the projection postulate, I’ll say that your proof of nonlocality in QM contains circular reasoning; if you choose the Born rule, then I’ll say that you don’t have a proof of nonlocality. So the difference is in how the discussion will develop depending on your choice. You may call this difference meaningful or not meaningful, but it is at least important for the course of further discussion.

--if you want to say that the Born rule itself introduces nonlocality since it gives probabilities for a combination of simultaneous physical facts at different spatial locations, that's fine with me!

On the face of it, this may be a possibility, but I think I won’t try to formulate my opinion on this issue at this point, because right now it does not look critical for the discussion.

I think so, if by "QM" you mean the pragmatic rule for generating predictions that I described (and which is the same as von Neumann's rule), which requires a single application of the Born rule to the quantum state of the system at some time after all measurements are completed and recorded.

Again, if you use the Born rule, rather than the projection postulate in your procedure, it’s not at all obvious that you’ll be able to prove violations in QM.

Are you actually suggesting that von Neumann's procedure might not actually predict Bell inequality violations, and that this has just gone unnoticed by physicists for decades?

Yes, I am actually suggesting that (again, provided you use the Born rule, not the projection postulate). As for “gone unnoticed”… I don’t know. For many people, the difference between the Born rule and the projection postulate may be just a meaningless subtlety :-)

Or are you using "QM" to mean unitary evolution only, with no invoking the projection postulate or the Born rule? (unless the Born rule can somehow be derived from unitary evolution, which is what many-worlds advocates often try to do)

This is an interesting question. I cannot exclude a possibility that my criticism of the projection postulate is actually valid for the Born rule as well (or maybe just for some forms of the Born rule), but I am not sure. There is no doubt that the projection postulate is incompatible with unitary evolution as it destroys superpositions and creates irreversibility. Is the Born rule compatible with unitary evolution? I don’t know. Let me just mention that an acquaintance of mine, who coauthored a series of articles describing the quantum measurement procedure by a rigorous model (http://arxiv.org/abs/quant-ph/0702135), told me that, according to the results for their model, the Born rule is also just an approximation. But it does not look like the Born rule in its simplest form (i.e. as it is used in Bohmian mechanics, for example) introduces nonlocality.

See above, I'm not even clear on what you're asking me to prove here.

I am just saying that I do not accept without proof that it is possible to prove violations in QM using just unitary evolution and the Born rule.

Bell's theorem has two parts: 1) in the type of experiment he specifies, local realism predicts that some Bell inequality will be obeyed, and 2) in the type of experiment he specifies, the predictions of "QM" as understood by physicists are that the Bell inequality will be violated. Your objection about "mutually contradictory assumptions" only seems to be an objection to 2), correct?

Correct.

But isn't it basically just a semantic disagreement, since you seem to define "QM" to mean "unitary evolution only" (which cannot be used to make predictions about any real-world experiment, since unitary evolution only gives complex amplitudes and empirically we never measure complex amplitudes), whereas most physicists would understand "QM" to mean the sort of pragmatic rule for making predictions that I describe.

As I said, to make predictions, you may use some form of the Born rule as a purely operational principle.

Even if I could show that Bohmian mechanics can produce predictions of Bell inequality violations without invoking the projection postulate (and I think the links I gave already do this, despite your objections), what difference would it make to your argument?

I do not agree that your links do that, and I offered specific arguments.
As for what difference it would make to my argument… I’d say significant difference. Right now my argument is quite simple: violations in quantum mechanics are proven using 1) unitary evolution and 2) the projection postulate, and 1) and 2) are mutually contradictory. If you prove violations in Bohmian mechanics without using the projection postulate or something similar, this proof could be translated into a proof for standard QM, so my argument in its current form will not hold, and I’ll have to analyze the Born rule trying to find out if it is compatible with unitary evolution.

After all the guiding equation of Bohmian mechanics is explicitly nonlocal, so if you objected to the use of the projection postulate because it's nonlocal wouldn't you have the same objection to Bohmian mechanics?

It is explicitely nonlocal, but it is not obvious that it cannot have a local form. For example, there is no faster-than-light signaling in Bohmian mechanics, if we assume the standard equivariant distribution. Furthermore, the evolution there is the same unitary evolution as in standard quantum mechanics, which has a solid experimental basis. I reject the projection postulate not just because it is nonlocal, but because it contradicts unitary evolution. Let me also mention that “my” model, while local, can have a seemingly nonlocal form (that of a quantum field theory).

But then you aren't comparing theoretical predictions with measurement results, you're comparing them with what you "say" about measurement results, where what you say is in most cases a lie.

But still, using your wording, it “is a well-defined pragmatic procedure for generating theoretical predictions about experiments which can be compared with the actual results you find when the experiment is done in real life and the measurement results all written down somewhere.” I just wanted to show you that this is not enough. The procedure must make sense.

Again, if by "nonlocal measurement procedure" you just mean instantly learn the values of the electromagnetic field at different locations without actually changing them in the process, then no, this won't lead to any Bell inequality violations in the results you learn.

But the projection postulate changes the values in the process.

But you never gave a coherent reason for disagreeing that there is no reason for distinguishing the two if we just make one "observation" of the records at the end of all measurements. Do you agree that if at the time we make an observation the quantum state of the records (obtained by unitary evolution) is \alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle then if we "observe" these records, regardless of whether we apply the Born rule or the projection postulate we will predict that the probability of a given result like 010 will just be the amplitude for that eigenstate times its complex conjugate, i.e. \alpha_3 \alpha_3*? If you don't disagree, then obviously the Born rule and the projection postulate are both making the exact same predictions about the statistics seen in the records at this time, so the probability of statistics that violate the Bell inequalities is the same either way.

Please see the answer above in this post starting with words “If you believe there is no difference,”

But you never really addressed my point in post #721 that the "contradiction" only arises if you take the procedure as an ontological description of reality, that purely as a pragmatic procedure it's not contradictory since it's just telling you to use different rules at different times. Your response was just to compare this with your silly "pretend the answer is always 5" procedure, but of course that procedure doesn't have a long track record of accurately predicting experimental results like the QM procedure.

No, it does not, and it is extremely silly indeed, but its mere existence suggests that if you use some nonsense as a measurement procedure, there is always a risk of getting some nonsense as a result. I just cannot embrace logical contradictions, sorry. There is a theorem in logic that if you assume that some false statement is true, that implies that any false statement is true.

Do you disagree that if a system's state is in an eigenstate of some operator, the Born rule says that on "observation" you are guaranteed to find the value associated with that eigenstate with probability 1? So, that means their conclusion (if we do N measurements, pure unitary evolution predicts that in the limit as N approaches infinity, the measurement records approach an eigenstate where "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts") implies the conclusion (if we do N measurements modeled by unitary evolution and then at the end apply the Born rule to the measurement records, in the limit as N approaches infinity the probability of finding that "the measurement results were randomly distributed and statistically correlated in just the way the standard theory predicts" approaches 1)

I gave the quote from his article suggesting that those records may be an illusion. Rather damning:-) If you think such an illusion may be OK, then what exactly is wrong with my 5-procedure?:-)

And again, if you assume unitary evolution until some time T, then regardless of whether you invoke "the Born rule" or "the projection postulate" at time T, the probabilities of finding different possible combinations of measurement results at time T will be exactly the same. And my argument is that Bohmian mechanics will also yield exactly the same predictions for probabilities of different possible combinations of measurement results at time T.

Please see the answer above in this post starting with words “If you believe there is no difference,”

 

[JesseM]

So it’s a matter of opinion. Note that this pragmatic procedure is doomed to fail somewhere anyway, as it contradicts the unitary evolution.

Why is it doomed to fail? You think nature must obey unitary evolution? Isn't it possible nature follows some other nonlocal rule like the guiding equation of Bohmian mechanics, and that the predictions of this nonlocal rule about measurement records would happen to agree mathematically with the pragmatic procedure of calculating a "wavefunction" for the system, evolving it in a unitary way according to the Schroedinger equation, and then applying the Born rule/projection postulate to the records once all measurements in the experiment are finished?

If you believe there is no difference, why don’t you choose just one of those two that you like more, even if just to give some focus to the discussion? But I explained to you how my reasoning will depend on your choice: if you choose the projection postulate, I’ll say that your proof of nonlocality in QM contains circular reasoning; if you choose the Born rule, then I’ll say that you don’t have a proof of nonlocality.

That still doesn't make sense to me. If we find that unitary evolution predicts a system's wavefunction is in state S at time T, then if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T. Thus, if applying the "projection postulate" predicts statistics which violate Bell inequalities, applying the "Born rule" is guaranteed to do so as well. Do you have the slightest doubt that this is true? If so that would suggest to me that you just aren't very well-versed in the mathematical formalism of QM, that your understanding is more conceptual. There's no shame in that, I said before that this was true of my understanding of Bohmian mechanics (and my knowledge of QM math doesn't go beyond the undergrad level), but if that's the case it would help me understand your doubts about my argument if you would say so. On the other hand, if you do claim to understand the mathematical meaning of things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule, then please tell me if you have any mathematical doubts about this argument from post #716, and if so what they are:

For example, if there were three measurements which could each yield result 1 or 0, then at the end right before "observation" the records will be a single quantum state which can be expressed as a sum of eigenstates:

\alpha_1 \mid 000 \rangle + \alpha_2 \mid 001 \rangle + \alpha_3 \mid 010 \rangle + \alpha_4 \mid 011 \rangle +\alpha_5 \mid 100 \rangle + \alpha_6 \mid 101 \rangle + \alpha_7 \mid 110 \rangle + \alpha_8 \mid 111 \rangle

where the \alpha_i are complex amplitudes. Then if you apply the "projection postulate", you're saying the quantum state will randomly become one of those eigenstates, with the probability of it going to a given eigenstate like \mid 010 \rangle being \alpha_3 \alpha_3* (i.e. the amplitude times its complex conjugate). And the "Born rule" just tells you that the probability of getting a given result like 010 is \alpha_3 \alpha_3*.

Would you disagree with the idea that if the measurement records constitute an "observable" we can express the quantum state as a sum of eigenstates of that observable? Would you disagree that both the Born rule and the projection postulate would say the probability of getting a given value for an observable is found by taking the amplitude associated with the corresponding eigenstate (when you express the quantum state as a sum of eigenstates for that observable) and multiplying it by its complex conjugate?

 

[akhmeteli]

Sorry, I have not replied for some time – was a bit busy.

Why is it doomed to fail? You think nature must obey unitary evolution? Isn't it possible nature follows some other nonlocal rule like the guiding equation of Bohmian mechanics, and that the predictions of this nonlocal rule about measurement records would happen to agree mathematically with the pragmatic procedure of calculating a "wavefunction" for the system, evolving it in a unitary way according to the Schroedinger equation, and then applying the Born rule/projection postulate to the records once all measurements in the experiment are finished?

Well, generally speaking, a lot of things are possible, but I am pretty conservative and try to preserve as much of what we have as possible. Unitary evolution has been thoroughly tested, and I don’t see any reason to discard it. It may happen that the projection postulate is correct, and unitary evolution is wrong, but my bet is on unitary evolution.

That still doesn't make sense to me. If we find that unitary evolution predicts a system's wavefunction is in state S at time T, then if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T. Thus, if applying the "projection postulate" predicts statistics which violate Bell inequalities, applying the "Born rule" is guaranteed to do so as well. Do you have the slightest doubt that this is true? If so that would suggest to me that you just aren't very well-versed in the mathematical formalism of QM, that your understanding is more conceptual. There's no shame in that, I said before that this was true of my understanding of Bohmian mechanics (and my knowledge of QM math doesn't go beyond the undergrad level), but if that's the case it would help me understand your doubts about my argument if you would say so. On the other hand, if you do claim to understand the mathematical meaning of things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule, then please tell me if you have any mathematical doubts about this argument from post #716, and if so what they are:

OK, so you refuse to choose just one of those: either the Born rule or the projection postulate. Then I have to retract (or caveat, if you wish:-) ) my concession that it is possible to prove nonlocality using the projection postulate. Indeed, I am inclined to agree that “if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T.” However, I don’t think you can prove the violations using just probabilities from the projection postulate, but not the collapse, so we have not moved any further.

Would you disagree with the idea that if the measurement records constitute an "observable"

I am not sure about this “if”, as records are not permanent.

we can express the quantum state as a sum of eigenstates of that observable? Would you disagree that both the Born rule and the projection postulate would say the probability of getting a given value for an observable is found by taking the amplitude associated with the corresponding eigenstate (when you express the quantum state as a sum of eigenstates for that observable) and multiplying it by its complex conjugate?

I would agree with that, but, as I explained above, this does not seem to lead to any progress in our discussion. If you remove collapse from the projection postulate, I don’t think you’ll be able to prove the violations.

 

[JesseM]

OK, so you refuse to choose just one of those: either the Born rule or the projection postulate. Then I have to retract (or caveat, if you wish:-) ) my concession that it is possible to prove nonlocality using the projection postulate. Indeed, I am inclined to agree that “if we apply "the Born rule" at time T to find probabilities for different possible combinations of measurement results at T, we are guaranteed mathematically to get exactly the same probabilities as if we applied the "projection postulate" to S at time T.” However, I don’t think you can prove the violations using just probabilities from the projection postulate, but not the collapse, so we have not moved any further.

That doesn't make sense to me either. The "probabilities from the projection postulate" are precisely the probabilities that the state will "collapse" onto each possible eigenstate, which is supposed to be the eigenstate corresponding to what's actually observed. So if at time T the amplitude for \mid 010 \rangle is \alpha_3 (obtained via unitary evolution), that means that if you observe the records at time T there is a probability of \alpha_3 \alpha_3* that the state will collapse to the eigenstate \mid 010 \rangle and that you will observe results 010.

And remember, the Bell inequalities deal with probabilities too! For example, one inequality says that if two experimenters are measuring spins of entangled particles, and each experimenter has a choice of three possible angles to measure spin along, then if there is a probability 1 that they see opposite results when they measure spin along the same axis, that means there must be a probability of at least 1/3 that they see opposite results when they measure along different axes, according to local realism. Meanwhile for a certain choice of detector angles the QM prediction is that the probability of seeing opposite results for different angles is only 1/4, so QM is understood to be incompatible with local realism. If we pick a time T shortly after both particles' spins have been measured and recorded, and "observe" the measurement records at T, then if the "projection postulate" predicts a probability 1 of opposite results for detectors set to the same angle but a probability 0.25 of opposite results for detectors set to different angles, that prediction is incompatible with local realism.

Meanwhile, it would help me if you would tell me whether you do have a good working understanding of the QM math or if your understanding is more conceptual...like I asked before, do you understand the mathematical meaning of "things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule"?

 

[Eye_in_the_Sky]

I rather see QM as non-separable, causally local ...

Exactly what we believe ...

It sounds to me like the two of you are agree upon (... among other things) the following:

The entanglement phenomenon exhibited in the Alice-and-Bob scenario can be construed as:

(i) "nonseparable" ,

and

(ii) obeying the principle of "local causality" .

... Am I correct in this assessment?

 

[RUTA]

It sounds to me like the two of you are agree upon (... among other things) the following:

The entanglement phenomenon exhibited in the Alice-and-Bob scenario can be construed as:

(i) "nonseparable" ,

and

(ii) obeying the principle of "local causality" .

... Am I correct in this assessment?

I can't speak for jambaugh, but this is correct for Relational Blockworld.

 

[akhmeteli]

Sorry, it has taken me a long time to reply – was a bit busy.

That doesn't make sense to me either. The "probabilities from the projection postulate" are precisely the probabilities that the state will "collapse" onto each possible eigenstate, which is supposed to be the eigenstate corresponding to what's actually observed. So if at time T the amplitude for \mid 010 \rangle is \alpha_3 (obtained via unitary evolution), that means that if you observe the records at time T there is a probability of \alpha_3 \alpha_3* that the state will collapse to the eigenstate \mid 010 \rangle and that you will observe results 010.

I agree, if you use the projection postulate, you can prove the violation of the Bell inequalities in QM. The question is can you prove that using the Born rule? It is my understanding that the Born rule gives the probability that the system is in a certain state, And I conceded that these probabilities may be the same that you get from the projection postulate. However, to prove the violation of the Bell inequalities you need the correlations. To get the correlations, you need the values of the observables. If, according to measurement results, the system is in the eigenstate \mid 010 \rangle, that does not mean automatically that you will observe results 010. This may sound outrageous, but what can I do? This is a direct consequence of unitary evolution: measurement cannot turn a superposition into a mixture. You need the projection postulate to get the values of the observables, and what projection postulate states directly contradicts unitary evolution.

Meanwhile, it would help me if you would tell me whether you do have a good working understanding of the QM math or if your understanding is more conceptual...like I asked before, do you understand the mathematical meaning of "things like wavefunction evolution, expressing the wavefunction as a sum of eigenstates of a particular measurement operator, and of the projection postulate and the Born rule"?

I am not enthusiastic about broadcasting details of my background, so I’ll try to PM you.

 

[JesseM]

I agree, if you use the projection postulate, you can prove the violation of the Bell inequalities in QM. The question is can you prove that using the Born rule? It is my understanding that the Born rule gives the probability that the system is in a certain state,

Depends what you mean by that--the Born rule gives probabilities of measurement results, not of quantum states.

And I conceded that these probabilities may be the same that you get from the projection postulate. However, to prove the violation of the Bell inequalities you need the correlations. To get the correlations, you need the values of the observables. If, according to measurement results, the system is in the eigenstate \mid 010 \rangle, that does not mean automatically that you will observe results 010.

But the measurement results are the "results 010". We never measure the quantum state directly, we measure observables like position (including the position of pointers), it's only if we use the projection postulate that we can infer a measurement of result 010 implies the system is in an eigenstate \mid 010 \rangle (in an everett interpretation where there is no 'collapse', this inference would be unjustified since there might be some other versions of ourselves who got different measurement results, so the system can still be in a superposition of different eigenstates).

This may sound outrageous, but what can I do? This is a direct consequence of unitary evolution: measurement cannot turn a superposition into a mixture. You need the projection postulate to get the values of the observables

...or the Born rule.

and what projection postulate states directly contradicts unitary evolution.

While the Born rule does not as explicitly contradict unitary evolution, it also seems that no one has a very convincing way of deriving it from unitary evolution alone (and those that attempt to do so usually assume a many-worlds type framework where parallel versions of the experimenter experience different outcomes). So you're free to say that the Born rule doesn't really make sense given the hypothesis of unitary evolution alone, but I don't think there's any good basis for denying that modeling Aspect-type experiments using unitary evolution until time T, then applying the Born rule to find the probabilities of different combinations of observable measurement records, yields probabilistic predictions that violate Bell inequalities.

I am not enthusiastic about broadcasting details of my background, so I’ll try to PM you.

Thanks. But to be clear, I wasn't asking for personal information about universities attended and so forth, just a general statement about your level of technical knowledge in this subject (and your PM suggests that you do have an in-depth knowledge of the math).

 

[akhmeteli]

Depends what you mean by that--the Born rule gives probabilities of measurement results, not of quantum states.

Sometimes the Born rule is defined in terms of probabilities of states – see, e.g. http://plato.stanford.edu/entries/qm/.

But the measurement results are the "results 010". We never measure the quantum state directly, we measure observables like position (including the position of pointers), it's only if we use the projection postulate that we can infer a measurement of result 010 implies the system is in an eigenstate \mid 010 \rangle (in an everett interpretation where there is no 'collapse', this inference would be unjustified since there might be some other versions of ourselves who got different measurement results, so the system can still be in a superposition of different eigenstates).

OK, so you define the Born rule in terms of probabilities of outcomes of measurements and, in particular, use it for measurement of more than one observable.

...or the Born rule.

Perhaps I could agree that if you formally apply this definition of the Born rule, you can get violations in quantum mechanics, but this has little to do with the actual measurements in Bell experiments (see below), so the Born rule for several measurements is little if at all better than the projection postulate.

While the Born rule does not as explicitly contradict unitary evolution, it also seems that no one has a very convincing way of deriving it from unitary evolution alone (and those that attempt to do so usually assume a many-worlds type framework where parallel versions of the experimenter experience different outcomes). So you're free to say that the Born rule doesn't really make sense given the hypothesis of unitary evolution alone, but I don't think there's any good basis for denying that modeling Aspect-type experiments using unitary evolution until time T, then applying the Born rule to find the probabilities of different combinations of observable measurement records, yields probabilistic predictions that violate Bell inequalities.

I think there is such a basis. Indeed, there is nothing either in unitary evolution or in the Born rule about “observable measurement records”. As I said, those “records” are not even permanent. The Born rule only tells us about some abstract results of some abstract measurements. So you should modify your statement. In Bell experiments, the spin projections of the two particles of the singlet are measured independently. I cannot imagine how the spin projections of two spatially separated particles can be measured in one measurement. If, however, you apply the Born rule to the actual measurements, you get something that contradicts unitary evolution. Indeed, after the measurement on the first particle, whatever “record” you get, the system is still in a superposition, so you can get both results for the other particle.
So I’d say the replacement of the projection postulate by the Born rule for several variables does not change the reasoning: the Born rule still contradicts unitary evolution, at least for the actual Bell experiments. And it is difficult to agree with your approach. As far as I understand, you are saying that yes, there is a contradiction, but it’s OK for some reason. I see this differently. While for some purposes this may be "OK", it's not "OK" when we are trying to decide, for example, the issue in the title of this thread: Has local realism been ruled out? What happens is people first adopt assumptions that contradict both unitary evolution and local realism, such as the projection postulate or the Born rule for several variables, and then “rule out” local realism.

 

[JesseM]

Sometimes the Born rule is defined in terms of probabilities of states – see, e.g. http://plato.stanford.edu/entries/qm/.

No, I don't think so. If you look at the actual equation they give for the Born rule in section 3.4, the equation is giving a probability of getting a given eigenvalue, not a given eigenstate/eigenvector. The verbal discussion in the paragraph preceding that equation is a bit confusing because they assume the Born rule is always coupled with the collapse postulate, so that the probability of getting a given eigenvalue would be the same as the probability of collapsing to the corresponding eigenstate, but the two assumptions are logically separable, and the article follows every other source I've seen in defining the Born rule in terms of the probability of getting a particular eigenvalue (which is understood as a possible measurement result).

OK, so you define the Born rule in terms of probabilities of outcomes of measurements and, in particular, use it for measurement of more than one observable.

Applying the Born rule to pointer states at the end of the experiment is just the von Neumann procedure, as I pointed out before.

I think there is such a basis. Indeed, there is nothing either in unitary evolution or in the Born rule about “observable measurement records”.

I don't understand what you mean by "nothing in" them "about" measurement records. Unitary evolution and the Born rule apply the same way to all quantum systems, they don't give specific rules for pointer states so I guess in that sense you could say there is "nothing in" them about pointer states, but nor do they give specific rules for electrons going through a double-slit or for any other particular quantum system, would you say "there is nothing in unitary evolution or in the Born rule about electrons"? The point is that unitary evolution and the Born rule can be applied in exactly the same way to any quantum system you like, so why not apply them to the macroscopic measuring devices and their records/pointer states in just the way you'd apply them to microscopic systems?

As I said, those “records” are not even permanent.

Who said they had to be permanent? The point is just to pick some time T shortly after all the experiments have been done, and apply the Born rule at T to find the probabilities of observing different measurement records at T. Maybe in the distant future all records of this experiment will be lost and no one will remember what the actual results were, but so what? This is just a procedure for making predictions about empirical results in the here-and-now.

The Born rule only tells us about some abstract results of some abstract measurements.

Don't know what you mean by that. Any time you use a theoretical model to make predictions about a real-world experiment, the model is always simplified, you couldn't possibly model the precise behavior of every single particle involved in the experiment, so in that sense all models are "abstract", but they are nevertheless highly useful in making predictions about real-world experiments, otherwise we'd just be doing pure math and not physics!

So you should modify your statement. In Bell experiments, the spin projections of the two particles of the singlet are measured independently. I cannot imagine how the spin projections of two spatially separated particles can be measured in one measurement.

I think you need to review the links I gave you earlier about von Neumann's procedure for calculating probabilities (see post #706 in particular). Again, there is no problem with measurements being made prior to the moment we apply the Born rule, it's just that each measurement is modeled as causing the measuring-device to become entangled with the system being measured exactly as you'd expect from unitary evolution, with no attempt to talk about probabilities at that point. Then at some time T after all measurements have already been performed, the Born ruler is applied to the pointer states of all the measuring devices. Obviously in the a real Bell experiment, at some point all the data will be collected in one place so scientists can review it, what's wrong with waiting until then to apply the Born rule to find the probability that a scientist will see different combinations of results on their computer screen?

If, however, you apply the Born rule to the actual measurements,

Any time someone looks at data you could call it a type of "measurement", including looking at a computer screen where the results of some prior measurements at different locations have been collected. The point of von Neumann's procedure is not to apply the Born rule to those prior measurements, to just model them according to standard unitary evolution, and just apply the Born rule at the very end to the collected measurement records.

you get something that contradicts unitary evolution.

How so?

Indeed, after the measurement on the first particle, whatever “record” you get, the system is still in a superposition, so you can get both results for the other particle.

But von Neumann's approach doesn't involve multiple successive applications of the Born rule, just a single one after all the experiments have been completed.

So I’d say the replacement of the projection postulate by the Born rule for several variables does not change the reasoning: the Born rule still contradicts unitary evolution, at least for the actual Bell experiments.

You haven't really explained why you think it contradicts unitary evolution. Many advocates of the many-worlds interpretation have tried to argue that the Born rule would still work for a "typical" observer in that interpretation, despite the fact that in the MWI unitary evolution goes on forever and thus each experiment just results in a superposition of different versions of the same experimenter seeing different results. Also, have a look at the paper at http://www.math.ru.nl/~landsman/Born.pdf which I found linked in wikipedia's article on the Born rule, the concluding paragraph says "The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle."

Besides, you talk as though "unitary evolution" were a sacred inviolate principle, but in fact all the empirical evidence in favor of QM depends on the fact that we can connect the abstract formalism of wavefunction evolution to actual empirical observations via either the Born rule or the collapse postulate--without them you can't point to a single scrap of empirical evidence in favor of unitary evolution! Of course if unitary evolution + collapse/Born rule produces a lot of successful predictions, then on the grounds of elegance there seems to be a good basis for hoping that the same unitary evolution that governs interactions between particles between measurements also governs interactions between particles and measuring devices (since measuring devices are just very large and complex collections of particles)...that's why my hope is that a totally convincing derivation of the Born rule from the MWI will eventually be found. But to just say "the Born rule and the collapse postulate violate the sacred principle of unitary evolution, therefore they must be abandoned", and to not even attempt to show how "unitary evolution" alone can yield a single solitary prediction about any empirical experiment ever performed, seems to be turning unitary evolution into a religious creed rather than a scientific theory.

I see this differently. While for some purposes this may be "OK", it's not "OK" when we are trying to decide, for example, the issue in the title of this thread: Has local realism been ruled out?

If the predictions of "quantum mechanics" are understood in von Neumann's way, then we can say that local realism is incompatible with the predictions of "quantum mechanics", and that "quantum mechanics" has a perfect track record so far in all experimental tests that have been done (including Aspect-type experiments, although none so far have done a perfect job of closing all loopholes). If on the other hand you choose to define "quantum mechanics" as unitary evolution alone, then unless you have some argument for why the Born rule should still work as MWI advocates do, your version of "quantum mechanics" is a purely abstract mathematical notion that makes no predictions about any real-world empirical experiments whatsoever.

 

[akhmeteli]

No, I don't think so. If you look at the actual equation they give for the Born rule in section 3.4, the equation is giving a probability of getting a given eigenvalue, not a given eigenstate/eigenvector. The verbal discussion in the paragraph preceding that equation is a bit confusing because they assume the Born rule is always coupled with the collapse postulate, so that the probability of getting a given eigenvalue would be the same as the probability of collapsing to the corresponding eigenstate, but the two assumptions are logically separable, and the article follows every other source I've seen in defining the Born rule in terms of the probability of getting a particular eigenvalue (which is understood as a possible measurement result).

It is not obvious that b_i is an eigenvalue, not an eigenstate. While b_i was defined earlier in the text, it was defined as an expansion coefficient, not as an eigenvalue. And the narrative suggests that the author is talking about the probability of the eigenstate. But anyway, let’s use your definition.

I don't understand what you mean by "nothing in" them "about" measurement records. Unitary evolution and the Born rule apply the same way to all quantum systems, they don't give specific rules for pointer states so I guess in that sense you could say there is "nothing in" them about pointer states, but nor do they give specific rules for electrons going through a double-slit or for any other particular quantum system, would you say "there is nothing in unitary evolution or in the Born rule about electrons"? The point is that unitary evolution and the Born rule can be applied in exactly the same way to any quantum system you like, so why not apply them to the macroscopic measuring devices and their records/pointer states in just the way you'd apply them to microscopic systems?

I mean the Born rule is not about “records”, either observable or not, it is about the final results of observation (please advise if you disagree). These are two different things, as, for example, "records” are never final.

Who said they had to be permanent? The point is just to pick some time T shortly after all the experiments have been done, and apply the Born rule at T to find the probabilities of observing different measurement records at T. Maybe in the distant future all records of this experiment will be lost and no one will remember what the actual results were, but so what? This is just a procedure for making predictions about empirical results in the here-and-now.

As I said, this procedure can be satisfactory for one purpose and unsatisfactory for another one. We are talking about the Born rule as applied to Bell experiments. In this case your procedure should be as follows: you have to take the records of measurements for two spatially separated particles and observe them simultaneously to obtain the input to the correlation. If you observe the records simultaneously (and that means in the same place), you cannot do that fast enough to eliminate the possibility of subluminal signaling (i.e. to close the locality loophole). On the other hand, you cannot be sure the records were the same at the time of the measurement, as the records are not permanent.

Don't know what you mean by that. Any time you use a theoretical model to make predictions about a real-world experiment, the model is always simplified, you couldn't possibly model the precise behavior of every single particle involved in the experiment, so in that sense all models are "abstract", but they are nevertheless highly useful in making predictions about real-world experiments, otherwise we'd just be doing pure math and not physics!

I mean the following. You cannot apply the Born rule in a specific form to an arbitrary measurement. For example, you cannot apply the Born rule defining the probability of the system having certain coordinates to a momentum measurement. In the same way, if you apply the Born rule for spin projections of two spatially separated particles, strictly speaking, the measurement should be designed to measure the two spin projections simultaneously, so perhaps you need some nonlocal measurement arrangement (nightlight said something to this effect). That’s not what happens in Bell experiments, where you measure the spin projections separately, and then combine the results. As I said above, this is something different.

I think you need to review the links I gave you earlier about von Neumann's procedure for calculating probabilities (see post #706 in particular). Again, there is no problem with measurements being made prior to the moment we apply the Born rule, it's just that each measurement is modeled as causing the measuring-device to become entangled with the system being measured exactly as you'd expect from unitary evolution, with no attempt to talk about probabilities at that point. Then at some time T after all measurements have already been performed, the Born ruler is applied to the pointer states of all the measuring devices. Obviously in the a real Bell experiment, at some point all the data will be collected in one place so scientists can review it, what's wrong with waiting until then to apply the Born rule to find the probability that a scientist will see different combinations of results on their computer screen?

I disagree that “there is no problem” – “at some time T after all measurements have already been performed” you cannot close the locality loophole, as “all the data will be collected in one place”, and you cannot state with certainty that the records have not changed. And that is “what's wrong with waiting until then”.

How so?

On the one hand, the probability of nonzero sum of spin projections is zero, according to the Born rule. On the other hand, according to unitary evolution, the spin projection measurement cannot turn the superposition into a mixture, so the spin projection measurement on the second particle can yield any value, so, according to the Born rule, the probability of nonzero sum of spin projections is not zero.

But von Neumann's approach doesn't involve multiple successive applications of the Born rule, just a single one after all the experiments have been completed.

But Bell experiments involve independent measurements on the two spatially separated particles.

You haven't really explained why you think it contradicts unitary evolution. Many advocates of the many-worlds interpretation have tried to argue that the Born rule would still work for a "typical" observer in that interpretation, despite the fact that in the MWI unitary evolution goes on forever and thus each experiment just results in a superposition of different versions of the same experimenter seeing different results.

See above

Also, have a look at the paper at http://www.math.ru.nl/~landsman/Born.pdf which I found linked in wikipedia's article on the Born rule, the concluding paragraph says "The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle."

I am not trying to say that the Born rule per se contradicts unitary evolution (I am not sure about that), it’s the Born rule as applied for Bell experiments that contradicts unitary evolution (see above).

Besides, you talk as though "unitary evolution" were a sacred inviolate principle, but in fact all the empirical evidence in favor of QM depends on the fact that we can connect the abstract formalism of wavefunction evolution to actual empirical observations via either the Born rule or the collapse postulate--without them you can't point to a single scrap of empirical evidence in favor of unitary evolution!

My reasoning is as follows: yes, a local realistic theory cannot produce all the predictions of standard quantum mechanics, however, the postulates of standard quantum mechanics are mutually contradictory, so you cannot blame local realistic theories for failing to reproduce all predictions of standard quantum theory. So if you question unitary evolution, you also question standard quantum mechanics, therefore you cannot reasonably blame local realistic theories for failing to reproduce all predictions of standard quantum theory. And I can use unitary evolution with the Born rule for just one observable as an operational rule to get empirical evidence in favor of unitary evolution.

Of course if unitary evolution + collapse/Born rule produces a lot of successful predictions, then on the grounds of elegance there seems to be a good basis for hoping that the same unitary evolution that governs interactions between particles between measurements also governs interactions between particles and measuring devices (since measuring devices are just very large and complex collections of particles)...that's why my hope is that a totally convincing derivation of the Born rule from the MWI will eventually be found. But to just say "the Born rule and the collapse postulate violate the sacred principle of unitary evolution, therefore they must be abandoned", and to not even attempt to show how "unitary evolution" alone can yield a single solitary prediction about any empirical experiment ever performed, seems to be turning unitary evolution into a religious creed rather than a scientific theory.

See above

If the predictions of "quantum mechanics" are understood in von Neumann's way, then we can say that local realism is incompatible with the predictions of "quantum mechanics", and that "quantum mechanics" has a perfect track record so far in all experimental tests that have been done (including Aspect-type experiments, although none so far have done a perfect job of closing all loopholes).

You see, thermodynamics also “has a perfect track record so far in all experimental tests that have been done”, however, irreversibility is at odds with dynamics, be it classical or quantum dynamics

If on the other hand you choose to define "quantum mechanics" as unitary evolution alone, then unless you have some argument for why the Born rule should still work as MWI advocates do, your version of "quantum mechanics" is a purely abstract mathematical notion that makes no predictions about any real-world empirical experiments whatsoever.

Again, you can use unitary evolution with the Born rule for just one observable, as an operational rule.

 

[yoda jedi]

100% detection efficiency?
(If you already did it on some post above, you can only write the post number.)

not yet.

There have been experiments that closed the detector efficiency loophole

wrong.



----------------

..."detection-loophole-freeBell experiment seems possible in the near future"...

 

[akhmeteli]

Let me add (belatedly) that the article mentioned in post 574 of this thread has just been published (you may wish to look at the postprint of the article and the exact reference to it at http://www.akhmeteli.org/akh-prepr-ws-ijqi2.pdf ).

It should be noted that some results of the article have already been significantly improved. For example, the elimination of the matter field from scalar electrodynamics has been done somewhat cleaner. Furthermore, while the extension to spinor electrodynamics in the article is much less general, some surprising new results suggest that the results for scalar electrodynamics can be fully valid for spinor electrodynamics.

 

[JesseM]

here have been experiments that closed the detector efficiency loophole

wrong.



----------------

..."detection-loophole-freeBell experiment seems possible in the near future"...

Didn't notice this post before. For some examples of experiments with ions that have already closed the detection loophole (without simultaneously closing the locality loophole, as I noted), see here (pdf file) and here.

 

[yoda jedi]

Photonic.

Phys. Rev. A 83, 032123 (2011)
Detection loophole in Bell experiments: How postselection modifies the requirements to observe nonlocality
http://arxiv.org/pdf/1010.1178
http://pra.aps.org/abstract/PRA/v83/i3/e032123

A common problem in Bell-type experiments is the well-known detection loophole: if the detection efficiencies are not perfect and if one simply postselects the conclusive events, one might observe a violation of a Bell inequality, even though a local model could have explained the experimental results. In this paper, we analyze the set of all postselected correlations that can be explained by a local model, and show that it forms a polytope, larger than the Bell local polytope. We characterize the facets of this postselected local polytope in the Clauser-Horne-Shimony-Holt scenario, where two parties have binary inputs and outcomes. Our approach gives interesting insights on the detection loophole problem.


.

 

[akhmeteli]

Let me make a quick update, as the thread drew a lot of interest.

In post 574 in this thread, I announced some results for scalar electrodynamics published by now in the International Journal of Quantum Information (http://www.akhmeteli.org/akh-prepr-ws-ijqi2.pdf) and relevant to this thread. However, the results of that article for spinor electrodynamics (which is more realistic) were much less general and less satisfactory. Since then I obtained some surprising results for spinor electrodynamics and the Dirac equation: http://arxiv.org/abs/1008.4828 (accepted for publication in the Journal of Mathematical Physics), which opened a way for extension of the results of my previous article to spinor electrodynamics in its entirety.

 

[akhmeteli]

I obtained some surprising results for spinor electrodynamics and the Dirac equation: http://arxiv.org/abs/1008.4828 (accepted for publication in the Journal of Mathematical Physics), which opened a way for extension of the results of my previous article to spinor electrodynamics in its entirety.

So here's the link to the published version of the article - http://akhmeteli.org/wp-content/uploads/2011/08/JMAPAQ528082303_1.pdf , and the abstract:

"Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of the fourth order for the remaining complex component. This equation is generally equivalent to the Dirac equation. Furthermore, following Schrödinger [Nature (London), 169, 538 (1952)], the remaining component can be made real by a gauge transform, thus extending to the Dirac field the Schrödinger conclusion that charged fields do not necessarily require complex representation. One of the two resulting real equations for the real function describes current conservation and can be obtained from the Maxwell equations in spinor electrodynamics (the Dirac-Maxwell electrodynamics). As the Dirac equation is one of the most fundamental equations, these results both belong in textbooks and can be used for development of new efficient methods and algorithms of quantum chemistry."

 

[akhmeteli]

Another quick update: the extension to spinor electrodynamics (which is more realistic than scalar electrodynamics) has been described in a short article in Journal of Physics: Conference Series ( http://dx.doi.org/10.1088/1742-6596/361/1/012037 - free access):

"2. After introduction of a complex 4-potential (producing the same electromagnetic field as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of the electromagnetic field.

3. The resulting theories for the electromagnetic field can be embedded into quantum field
theories."

The details can be found in the references of the article.

 

[Gordon Watson]

Another quick update: the extension to spinor electrodynamics (which is more realistic than scalar electrodynamics) has been described in a short article in Journal of Physics: Conference Series ( http://dx.doi.org/10.1088/1742-6596/361/1/012037 - free access):

"2. After introduction of a complex 4-potential (producing the same electromagnetic field as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of the electromagnetic field.

3. The resulting theories for the electromagnetic field can be embedded into quantum field
theories."

The details can be found in the references of the article.

NB: To avoid side-tracking this thread, I've reproduced this post at https://www.physicsforums.com/showpost.php?p=3909153&postcount=289 :- I suggest any discussion-arising should be done there. GW

Hi Andrey, and congratulations on the publication of another advance in your work. However, with respect to the passage copied below AND your concern about breaching Bell inequalities, I suggest that you need to carefully distinguish this dichotomy, imho:

The (1) "violation of a Bell inequality" is NOT the same as (2) "falsifying local realism".

I am certain that valid experiments (and good theory) will continue to deliver (1): a violation of Bell inequalities. I am confident that no experiments will ever falsify (2): local realism (properly defined).

To these ends, and to this latter end in particular, I'd welcome your comments on the breaching of Bell inequalities AND the explicit local realism (and any other matter) in https://www.physicsforums.com/showpost.php?p=3905795&postcount=287

PS: As previously discussed, I believe that the BOLD-ed sentence below greatly weakens your work. Me believing it to be a FALSE hope (as opposed to Bell's positive one, as discussed and delivered in the above link).

With best regards,

Gordon
....

From http://iopscience.iop.org/1742-6596/361/1/012037/pdf/1742-6596_361_1_012037.pdf -- "Of course, the Bell inequalities cannot be violated in such a theory. But there are some reasons to believe these inequalities cannot be violated either in experiments or in quantum theory. Indeed, there seems to be a consensus among experts that “a conclusive experiment falsifying in an absolutely uncontroversial way local realism is still missing” [4]. On the other hand, to prove theoretically that the inequalities can be violated in quantum theory, one needs to use the projection postulate (loosely speaking, the postulate states that if some value of an observable is measured, the resulting state is an eigenstate of the relevant operator with the relevant eigenvalue). However, such postulate, strictly speaking, is in contradiction with the standard unitary evolution of the larger quantum system that includes the measured system and the measurement device, as such postulate introduces irreversibility and turns a superposition of states into their mixture. Therefore, mutually contradictory assumptions are required to prove the Bell theorem, so it is on shaky grounds both theoretically and experimentally and can be circumvented if, for instance, the projection postulate is rejected. [Emphasis added by GW: other issues arising not addressed here.]​

NB: To avoid side-tracking this thread, I've reproduced this post at https://www.physicsforums.com/showpost.php?p=3909153&postcount=289 :- I suggest any discussion-arising should be done there. GW

 

[akhmeteli]

NB: To avoid side-tracking this thread, I've reproduced this post at https://www.physicsforums.com/showpost.php?p=3909153&postcount=289 :- I suggest any discussion-arising should be done there. GW

Dear Gordon Watson,

Thank you for your comment. I think it is relevant to this thread as well.

Hi Andrey, and congratulations on the publication of another advance in your work.

Thank you

However, with respect to the passage copied below AND your concern about breaching Bell inequalities, I suggest that you need to carefully distinguish this dichotomy, imho:

The (1) "violation of a Bell inequality" is NOT the same as (2) "falsifying local realism".

I guess this statement is technically correct, as, for example, violations of the Bell inequalities cannot exclude superdeterministic theories.

I am certain that valid experiments (and good theory) will continue to deliver (1): a violation of Bell inequalities.

With all due respect, this is just your opinion, not a fact. For example, there is no loophole-free experimental evidence of violations. I am not ready to concede this point, sorry.

I am confident that no experiments will ever falsify (2): local realism (properly defined).

I would also be surprised to hear about such experiments falsifying local realism, but who knows...

To these ends, and to this latter end in particular, I'd welcome your comments on the breaching of Bell inequalities AND the explicit local realism (and any other matter) in https://www.physicsforums.com/showpost.php?p=3905795&postcount=287

I will look at that thread, but I am not sure I will be able to comment - these are difficult and sometimes controversial issues.

PS: As previously discussed, I believe that the BOLD-ed sentence below greatly weakens your work. Me believing it to be a FALSE hope (as opposed to Bell's positive one, as discussed and delivered in the above link).

From http://iopscience.iop.org/1742-6596/361/1/012037/pdf/1742-6596_361_1_012037.pdf -- "Of course, the Bell inequalities cannot be violated in such a theory. But there are some reasons to believe these inequalities cannot be violated either in experiments or in quantum theory. Indeed, there seems to be a consensus among experts that “a conclusive experiment falsifying in an absolutely uncontroversial way local realism is still missing” [4]. On the other hand, to prove theoretically that the inequalities can be violated in quantum theory, one needs to use the projection postulate (loosely speaking, the postulate states that if some value of an observable is measured, the resulting state is an eigenstate of the relevant operator with the relevant eigenvalue). However, such postulate, strictly speaking, is in contradiction with the standard unitary evolution of the larger quantum system that includes the measured system and the measurement device, as such postulate introduces irreversibility and turns a superposition of states into their mixture. Therefore, mutually contradictory assumptions are required to prove the Bell theorem, so it is on shaky grounds both theoretically and experimentally and can be circumvented if, for instance, the projection postulate is rejected. [Emphasis added by GW: other issues arising not addressed here.]​

[/B]

Again, with all due respect, you offer your opinion, not your reasons.

 

[Gordon Watson]

Dear Gordon Watson,

Thank you for your comment. I think it is relevant to this thread as well.

Thank you

Thanks Andrey, I'm happy to discuss it here, and in detail. [That suggestion came from the concern that a focus on classical probability theory and Malus' Method (i.e., on what is essentially high-school maths and logic; with little more required) would distract from the maths that you're working with in your papers.]

Now, wrt this statement: The (1) "violation of a Bell inequality" is NOT the same as (2) "falsifying local realism", you say:

I guess this statement is technically correct, as, for example, violations of the Bell inequalities cannot exclude superdeterministic theories.

However, understanding the point at issue, you would NOT be able to offer this response; imho!

[EDIT: this emphasised above to clearly identify that the response's reference to "I guess ... technically correct ... cannot exclude super deterministic theories" is inadequate in the face of what can be clearly shown: that a DEFINITE local realistic formulation demolishes your escape clause. That is "I guess ... " to a TRUISM is not acceptable. Agree; or refute the truism, please. /EDIT]

For it can be clearly shown, with neither mystery nor complication, that a DEFINITE local realistic formulation demolishes your escape clause. MOREOVER, the formulation is right in line with Bell's hope: It begins with the acceptance of Einstein-locality (EL). It continues with Bell's hope:

"... the explicit representation of quantum nonlocality [in 'the de Broglie-Bohm theory'] ... started a new wave of investigation in this area. Let us hope that these analyses also may one day be illuminated, perhaps harshly, by some simple constructive model. However that may be, long may Louis de Broglie continue to inspire those who suspect that what is proved by impossibility proofs is lack of imagination," (Bell 2004: 167). "To those for whom nonlocality is anathema, Bell's Theorem finally spells the death of the hidden variables program.³¹ But not for Bell. None of the no-hidden-variables theorems persuaded him that hidden variables were impossible," (Mermin 1993: 814). [All emphasis and [.] added by GW; see https://www.physicsforums.com/showpos...&postcount=287]

Bell (2004): Speakable and Unspeakable in Quantum Mechanics; 2nd edition. CUP, Cambridge.

Mermin (1993): Rev. Mod. Phys. 65, 3, 803-815. Footnote #31: "Many people contend that Bell's Theorem demonstrates nonlocality independent of a hidden-variables program, but there is no general agreement about this."
​

So, this suggests that you are up against a proven fact (and not just an opinion ); this TRUISM:

"The (1) "violation of a Bell inequality" is NOT the same as (2) "falsifying local realism."

... reinforcing a conclusion held by many, for many years.

Next, in response to: "I am certain that valid experiments (and good theory [including current QM]) will continue to deliver (1): a violation of Bell inequalities," you say:

With all due respect, this is just your opinion, not a fact. For example, there is no loophole-free experimental evidence of violations. I am not ready to concede this point, sorry.

The point is this (if you seek to down-play the good theories): VALID EXPERIMENTS already violate Bell's Theorem (with loopholes for the desperate)! Moreover, such loopholes are being reduced almost daily! Why then would better experiments reverse that trend AND suddenly NOT-violate Bell's Theorem? AGAINST the whole history of VALID QM experimentation? Especially WHEN the idealised maths (that you're to examine) show that ideal experiments WILL continue the violation!

To put the position clearly: You will one day concede this point; imho. So why not see what needs be adjusted in your work NOW to avoid this later capitulation with its consequent complications?

I would also be surprised to hear about such experiments falsifying local realism, but who knows...

Good! Do we agree then, that Einstein-locality remains at the core of our personal world-views?

I will look at that thread, but I am not sure I will be able to comment - these are difficult and sometimes controversial issues.

Thanks; that's all that is asked! In an attempt to be helpful wrt to your work; with any and all critiques of my work most welcome.

You write: "But there are some reasons to believe these inequalities cannot be violated either in experiments or in quantum theory." AGAINST which, in effect, the message is: "Please, abandon this false hope!" You respond:

Again, with all due respect, you offer your opinion, not your reasons.

Please: Reasons are clearly given, at the level of high-school maths and logic, here: https://www.physicsforums.com/showpos...&postcount=287

With best regards, Gordon

 

[lugita15]

Gordon, do you agree or disagree with akhmeteli's point that the only way you can have viable local hidden-variable model in the face of a Bell inequality violation (with no experimental loopholes) is if your hidden-variable model is superdeterministic, i.e. violates the no-conspiracy condition?

 

[lugita15]

Hi lugita, DISAGREE: on the understanding that by "super-determinism" you mean "NO free-will on the part of Alice and Bob."

As to "violating the no-conspiracy condition" -- best you spell that out for me, please.

The no-conspiracy condition, which is one of the assumptions used in Bell's proof, states that the result Alice observes by measuring her photon is independent of the angle setting at which Bob measures his photon. This assumption rules out several possibilities at once:
1. The Universe conspires to make Alice and Bob make the exact measurement decisions needed to make Bell's inequality appear violated when it would really not be if Alice and Bob's measurement decisions were totally random.
2. The universe tells the photons what Alice and Bob are going to do, so that the photons can plan their strategy to anticipate the measurement decisions

Etc. Someone who believes in local hidden variables but denies no-conspiracy is called a superdeterminist. Given this, are you one?

Concerning your "classical challenge", I think your time may be better spent trying to understand the core of Bell's reasoning, which is only a few steps of simple logic, rather than focusing on the gory details of his original proof, which discusses things like factorization of conditional probability and integrating over lambda. Why don't you take a look at Herbert's version of Bell's proof, which is simpler by leaps and bounds than Bell's original paper and can thus allow us to identify the locus of your disagreement with Bell.

EDIT: Sorry, I forgot the link:

http://quantumtantra.com/bell2.html

 

[akhmeteli]

Gordon, do you agree or disagree with akhmeteli's point that the only way you can have viable local hidden-variable model in the face of a Bell inequality violation (with no experimental loopholes) is if your hidden-variable model is superdeterministic, i.e. violates the no-conspiracy condition?

Dear lugita15,

I am afraid I have to disagree with your interpretation of my words in the answer to Gordon Watson. I only agreed with GW that

"violation of a Bell inequality" is NOT the same as (2) "falsifying local realism"

, and I mentioned superdeterminism just as an example to explain why I had to agree with GW's statement. I did not say that superdeterminism is "the only way you can have viable local hidden-variable model in the face of a Bell inequality violation (with no experimental loopholes)". I may have conceded this point elsewhere for the sake of argument, but I don't want to take sides on this issue - I just don't know enough about it.

 

[lugita15]

Dear lugita15,

I am afraid I have to disagree with your interpretation of my words in the answer to Gordon Watson. I only agreed with GW that

, and I mentioned superdeterminism just as an example to explain why I had to agree with GW's statement. I did not say that superdeterminism is "the only way you can have viable local hidden-variable model in the face of a Bell inequality violation (with no experimental loopholes)". I may have conceded this point elsewhere for the sake of argument, but I don't want to take sides on this issue - I just don't know enough about it.

Sorry for putting words in your mouth, akhmeteli! Let me state that as my point, then.