Mathematical expression of Bell's local realism

[NateTG]

So the question becomes: do you allow non-commuting measurements in a test of the simultaneous reality of non-commuting observables if that is a test on entangled particles? Even though such test is rejected if performed in the form as my (3)?
This is my question, and I am asking for comments. I would guess that the consensus answer would be: yes, it is OK on entangled particles Alice and Bob; but not on Alice alone.

If you mean, "does measuring Alice.a and Bob.b commute even if Alice.a and Alice.b are not commutatively observable?" then the answer depends a bit on which interpretation you chose, and I suppose, on what you mean by commute.
The problem with the definition of commute is that the order of the two measurements can be observer-dependant. So, from that perspective, the order in which the measurements occur cannot matter. On the other hand, from an information point of view, it appears to be the case that when measurement occurs at one particle, information is 'lost' at the other.
My understanding is that some people view such a pair of entangled particles as a single waveform that collapses when measurement occurs at either spatial location - which seems to indicate that the measurements are not commutative. Conversely, AFAICT Bohmian mechanics has no special properties for measurement, so it would appear that from the Bohmian point of view, the measurements are commutative.

 

[DrChinese]

And just a couple of points for those who think I am drifting into never never land in my treatment of Bell's Theorem without Locality:

1. What else is the GHZ theorem about if it is not about the simultaneous reality of non-commuting observables? Locality is not present as an assumption in that proof either.

2. We were just discussing a few days ago in this thread a published paper which says virtually the same thing, although coming at it from a different perspective ("All quantum observables in a hidden-variables model must commute simultaneously" by James Malley). Note that the non-commuting issue is central to his paper, just as it is to EPR. (There is a connection between this and the definition of reality; I just can't formulate that exact connection yet beyond what I have in my earlier posts. )

3. And these are not the only examples of theorems that are no-go for ALL realistic theories. So even if it is still a minority opinion, there is support for this perspective.

So I really just looking at the same issue - the role of reality and locality - from an angle that we are more familiar with - that being Bell. And don't get me wrong, I still take a mainstream oQM view of the situation.

 

[DrChinese]

If you mean, "does measuring Alice.a and Bob.b commute even if Alice.a and Alice.b are not commutatively observable?" then the answer depends a bit on which interpretation you chose, and I suppose, on what you mean by commute.

The problem with the definition of commute is that the order of the two measurements can be observer-dependant. So, from that perspective, the order in which the measurements occur cannot matter. On the other hand, from an information point of view, it appears to be the case that when measurement occurs at one particle, information is 'lost' at the other.

My understanding is that some people view such a pair of entangled particles as a single waveform that collapses when measurement occurs at either spatial location - which seems to indicate that the measurements are not commutative. Conversely, AFAICT Bohmian mechanics has no special properties for measurement, so it would appear that from the Bohmian point of view, the measurements are commutative.

In my mind, entangled Alice.a and Bob.b don't commute any more than Alice.a and Alice.b do. If you measure Bob.a after measuring Bob.b you have no guarantee you will get Bob.a=Alice.a.

Does anyone disagree with this interpretation?

 

[NateTG]

In my mind, entangled Alice.a and Bob.b don't commute any more than Alice.a and Alice.b do. If you measure Bob.a after measuring Bob.b you have no guarantee you will get Bob.a=Alice.a.
Does anyone disagree with this interpretation?

If we operate with the assumption that Bob.a and Bob.b don't commute, I don't see how that has anything to do with Bob.a and Alice.b commuting.

...
"Truely you have a dizzying intelect" - The Man in Black

 

[ttn]

My understanding is that some people view such a pair of entangled particles as a single waveform that collapses when measurement occurs at either spatial location - which seems to indicate that the measurements are not commutative. Conversely, AFAICT Bohmian mechanics has no special properties for measurement, so it would appear that from the Bohmian point of view, the measurements are commutative.

Ah, but Bohm's theory is explicitly non-local (and not, like OQM, in denial about it!). So, really, to even define Bohm's theory, we need to fix a preferred frame at the beginning -- this is the frame in which the "instantaneous action at a distance" occurs, i.e., involves the effect happening simultaneously with the distant cause. So then there is no longer any ambiguity about the order of the measurements. One just really did happen before the other. And whichever one happened first, caused the trajectory of the distant particle to veer off a bit from what it would otherwise have done, so the outcome of the second measurement is influenced by the performance of the first measurement.

But... of course... in a way that can't be used to send signals faster than light (even though there is definitely faster than light non-local dynamics at work!).

 

[ttn]

In my mind, entangled Alice.a and Bob.b don't commute any more than Alice.a and Alice.b do. If you measure Bob.a after measuring Bob.b you have no guarantee you will get Bob.a=Alice.a.
Does anyone disagree with this interpretation?

Um, yes, absolutely I disagree. Even in regular textbook QM, the spin operators for one particle commute with the spin operators for a different particle. I mean, of course they commute -- and this doesn't even have anything to do with whether you like OQM or Bohm's theory or whatever. If there's one thing people of all these different camps can agree about, it's that Alice.a commutes with Bob.b.

I also don't understand your second sentence. But it's probably irrelevant given my disagreement with the first.

 

[ttn]

If that were the argument of EPR, then Bell proved them wrong. But that wasn't their argument. Their conclusion was (almost verbatim): if QM is complete, then there is not simultaneous reality to non-commuting operators. Bell did not prove that conclusion to be wrong.

Well this is one of those things we've argued over in the past. I'll just remind everyone that Einstein's own summary of the EPR argument (or, at any rate, what the EPR argument was *supposed* to have been -- since, according to Einstein, Podolsky, who wrote the paper, kind of buried the main point in a bunch of distracting irrelevancies):

"By this way of looking at the matter it becomes evidence that the paradox [EPR] forces us to relinquish one of the following two assertions:
1. the description by means of the psi-function is complete [i.e., there are no hidden variables, or]
2. the real state of spatially separated objects are independent of each other [i.e., locality]
...it is possible to adhere to (2) if one regards the psi-function as the description of a (statistical) ensemble of systems (and therefore relinquishes (1)). However, this view blasts the framework of the 'orthodox quantum theory.'"

So here Einstein is clearly saying the point of EPR is that you have to either reject the completeness doctrine, or you have to accept non-locality. Or framing the same point slightly differently, the assumption of locality requires you to reject the completeness doctrine (and, in particular, accept the existence of a certain definite class of hidden variables -- just the kind, it turns out, that Bell later assumed in his theorem).

You are also repeating the *classic* misconception about how EPR relates to Bell. And it's really an elementary point of logic. EPR showed that locality --> hv's. (The assumption of locality requires the existence of certain hidden variables.) Bell showed that the existence of those hidden variables leads to a certain statement (the inequality) which has been shown to conflict with experiment. So it's correct in one sense to say that Bell proved EPR wrong -- namely, since EPR believed in locality, they accepted that they had shown the existence of the hidden variables (i.e., blasted the completeness doctrine). And Bell did indeed show that that *conclusion* is no longer viable. It's just *wrong* to believe in local hidden variables, because we now know that those variables entail Bell's inequality, which is empirically false.

But there's a different, and more relevant, sense in which Bell doesn't touch EPR: namely, Bell doesn't in any way show that the *reasoning* of EPR -- the proof that "locality entails hv's" -- is wrong. That reasoning is, was, and always will be completely valid. Locality really does require the existence of those hidden variables -- whether or not those hidden variables actually exist. So it is a really serious error (that is bound to lead to serious confusion) to say "we can just ignore the epr argument, since Bell showed they were wrong."

Let me make this as clear as possible by sketching out the logic involved:

EPR say:

Premise 1: Locality
Premise 2: Locality --> HV's
---
Conclusion: HV's

(where by "HV's" I mean the existence of the local hidden variables that determine the spin outcomes locally)

Bell says:

Premise 1: HV's
----
Conclusion: Inequality


Experiment says that "Inequality" is false. Well, that was a straight consequence of Bell's assumption "HV's", so it must be that "HV's" is false. But that was a logical consequence of EPR's two assumptions. One of those is controversial (namely "Locality --> HV's") but I think is entirely correct. (Basically, EPR's *reasoning* was valid; they did indeed prove that Locality requires hidden variables.) So the only thing to point to, as the flawed premise that led to the empirically false statement "Inequality", is EPR's premise 1: locality.

That, in a nutshell, is why I think the violation of Bell's inequality proves that nature is nonlocal. (Specifically: violates Bell Locality.) The reasoning of EPR plays (obviously) a crucial role here, and you can't just dismiss that by saying Bell proved they were wrong -- this just equivocates on what they were wrong about. Their conclusion turns out to be untenable, yes, but their *reasoning* for it was entirely valid... hence it is the locality premise that is left as the faulty assumption which led to the contradiction with experiment.

 

[DrChinese]

If we operate with the assumption that Bob.a and Bob.b don't commute, I don't see how that has anything to do with Bob.a and Alice.b commuting.

I am saying, for entangled Alice and Bob (which has Alice.b=Bob.b to begin with by definition):

Alice.a, Bob.b <> Alice.b, Bob.a

Just as:

Alice.a, Alice.b <> Alice.b, Alice.a

In other words, after testing Alice.b and Bob.b, I am certain to get Alice.b = Bob.b unless if I do Alice.a first. I mean, we are talking about a superposition of states. I don't know what else to call it except to say that the order of the measurements changes the outcome.

 

[DrChinese]

Um, yes, absolutely I disagree. Even in regular textbook QM, the spin operators for one particle commute with the spin operators for a different particle. I mean, of course they commute -- and this doesn't even have anything to do with whether you like OQM or Bohm's theory or whatever. If there's one thing people of all these different camps can agree about, it's that Alice.a commutes with Bob.b.

So you would say that applies to entangled particles too? For most people? Or would they make an exception when it comes to entangled particles? (I'm not trying to split hairs, I just want to make sure we are using lingo we agree upon. I won't use this terminology if you object.)

Keep in mind for your answer... there is absolutely nothing that requires Alice and Bob to be space-like separated. They can be in the same location in the same reference frame. We already know experimentally (Aspect, Weihs, etc.) that performing Bell tests with space-like separation does NOT affect the outcome. (Any reservations anyone has about test "loopholes" does not apply to this discussion.) So we CAN do our tests on Alice and Bob in specific sequences.

 

[ttn]

So you would say that applies to entangled particles too? For most people? Or would they make an exception when it comes to entangled particles? (I'm not trying to split hairs, I just want to make sure we are using lingo we agree upon. I won't use this terminology if you object.)

Keep in mind for your answer... there is absolutely nothing that requires Alice and Bob to be space-like separated. They can be in the same location in the same reference frame. We already know experimentally (Aspect, Weihs, etc.) that performing Bell tests with space-like separation does NOT affect the outcome. (Any reservations anyone has about test "loopholes" does not apply to this discussion.) So we CAN do our tests on Alice and Bob in specific sequences.

Yes, it's non-controversially true that the spin operators for different particles commute. This is not affected by the particles being entangled.

I'm not sure where you're going with this, though. That the operators do or don't commute just tells you something about how OQM works. It doesn't directly imply *anything* about what affects what, in reality.

 

[DrChinese]

Continuing with the argument...

Our previous result was:

To be explicit that we are talking about one photon, which we will call Alice:
(3) corr(Alice.a, Alice.b) + noncorr(Alice.a, Alice.c) – corr(Alice.b, Alice.c) ) / 2 >= 0


Internal Inconsistency of Realistic Theories
================================

It has been known for nearly 200 years that Alice.a and Alice.b have the correlated relationship cos2(a-b) per Malus’ Law – which has substantial experimental verification. This formula leads to an internal inconsistency for any realistic theory.

Where Alice has polarizer settings a=0 degrees, b=67.5 degrees, c=45 degrees:

corr(Alice.a, Alice.b) + noncorr(Alice.a, Alice.c) – corr(Alice.b, Alice.c) ) =
cos2(a-b) + cos2(a-c) – cos2(b-c) =
cos2(67.5 degrees) + cos2(45 degrees) – cos2(22.5 degrees) =
-.1036

This prediction is negative and clearly conflicts with the realistic prediction (3) above, which is non-negative. Recall that a single counterexample is sufficient to invalidate any theory. Thus:

(4) No realistic theory can be internally consistent if Malus’ Law is accepted.

Is this result valid and meaningful? Absolutely it is, and here is why: The inequality (3) above demonstrates a requirement of any realistic theory, a result which is uncontroversial. So why should (4) be controversial?

The objection raised is: the application of Malus’ Law is not valid to test (3) because measurements of Alice.a and Alice.b do not commute. The order of the measurements on Alice affects the outcomes; and measurements of Alice at various settings don’t give any additional information about Alice at any single point in time.

For instance: if we measure Alice.a and then Alice.b, and then measure Alice.a a second time – which we will call Alice.a’, our general result is:

1 > corr(Alice.a, Alice.a’) > .500

We would expect it to be very close to 1 if we had really learned new information about Alice when the Alice.b measurement was performed. As EPR noted: “…a measurement however disturbs the particle and thus alters its state.” [2]

Note: To rebut this objection: The reason that Alice.a and Alice.b don’t commute is precisely because our realistic assumptions do not hold. And that is exactly what we were trying to test! So we should not dismiss (4) a priori. We asked for a way to test the realistic assumptions and we got it in (3); and we demonstrated that this leads to an internal inconsistency. For the realistic assumptions to be valid, the internal relationship of Alice.a, Alice.b and Alice.c need to be something other than that described by Malus. In addition, rejecting (4) because Alice.a and Alice.b do not commute is unjustified because the is a consequence of QM; and so far we have not needed to assume QM to make our proof.

While it is asserted here that (4) is valid, we will continue on as if it were not. In the next section, we will circumvent the objection presented against result (4); namely that a direct test on Alice.a and Alice.b cannot be performed in such a way as to demonstrate that Alice.a and Alice.b are simultaneously valid.

 

[DrChinese]

Experimental Setup for Bell Test

Experimental Setup for Bell Test

Can we test (3) experimentally using a Bell test? EPR put forth an ingenious idea: if you had 2 particles that had a relationship of some known nature, perhaps you could factor that in and do a measurement on one particle to gain information about the other. They postulated that using this method, the limits of the Heisenberg Uncertainty Principle could be exceeded. At the time, there was no specific concept of entanglement. Later, Bohm discovered that a pair of particles could be theoretically created in the so-called singlet state – a form of entanglement. But no experimental setup was available at the time, and result (3) above was not yet known.

Bell saw that the singlet state could be used as a tool to extend his discovery of the requirement of realism to an experimental form. Although no direct test of (3) was possible, an indirect test was using this tool. For this, we require a test setup in which there is a pair of particles with identical states. This is obtainable, for example, using Type I Parametric Down Converted photons [3] – or analogously, using other types of entanglement in which the particles have orthogonal states. Such photons are in a superposition – a polarization entangled state.

Our program is that we cannot directly measure (Alice.a and Alice.b) simultaneously; nor (Alice.a and Alice.c); nor (Alice.b and Alice.c). But we can measure these indirectly using a second – “cloned” – particle. This particle is entangled with Alice, and we call it Bob. We need them to have this relationship:

(5) Alice.a = Bob.a, or generally: corr(Alice.a, Bob.a) = 1
Alice.b = Bob.b, or generally: corr(Alice.b, Bob.b) = 1
Alice.c = Bob.c, or generally: corr(Alice.c, Bob.c) = 1

This is NOT an assumption! This is an experimental requirement because we need there to be a demonstrable relationship if we are to perform such an indirect test. There must be entanglement and (5) must be demonstrated positively and unambiguously. If it could not, then there would be no purpose to continuing as we don’t have a way make an indirect observation of Alice using Bob.

Note: It may be still be objected that QM does not permit us to learn more about Alice using this indirect technique because it would violate the Heisenberg Uncertainty Principle. However, we have not so far used any element of QM in our proof and we will not do so now either. The technique of this proof follows standard concepts for Bell tests.

Assuming we could prove (5) experimentally, we would measure one desired observable property on Alice and another property on Bob. These results will allow us to test (3) indirectly using the following form, deduced from substitutions from (5):

(6) corr(Alice.a, Bob.b) + noncorr(Alice.a, Bob.c) – corr(Alice.b, Bob.c) ) / 2 >= 0

To rule out realistic theories by experiment, we need to prove (5) true and (6) false.

 

[ttn]

To rule out realistic theories by experiment, we need to prove (5) true and (6) false.

You're getting closer. But one can make the same objection to this "indirect" method of testing your inequality, as we made originally to the "direct" test: you can't assume that the result of the Alice.a measurement is the same as it would have been had you not first made the Bob.b measurement (or whatever). Right? *In principle*, just like measuring Alice.a might "screw up" a subsequent measurement of Alice.b (in the sense that that second measurement won't now give the same outcome as it would have given if you hadn't first made the first measurement), so Bob's measurement over there might "screw up" the value that is obtained from Alice's measurement over here. Right? In principle, this is possible.

Of course, some sort of *locality* assumption would eliminate this objection. But then it'd be clear that what's being tested by a "Bell test" is a conjunction of hidden variable and locality assumptions.

...and please also don't forget that the hidden variables *follow* from locality (EPR).

 

[DrChinese]

You're getting closer. But one can make the same objection to this "indirect" method of testing your inequality, as we made originally to the "direct" test: you can't assume that the result of the Alice.a measurement is the same as it would have been had you not first made the Bob.b measurement (or whatever). Right?

I was hoping you would appreciate that (5) must be true, before we continue to prove (6) false. So I think that point is clear - in fact you mentioned (5) in your own words in an earlier post today.

Now, here is the rub... (6) is fine unless you have some reason to suspect there is a problem in the experimental execution of it. After all, a confirmation of (5) also demonstrates there is no improper skewing. Unless of course, the improper skewing only shows up when we test at specific different angle settings in a very specific way, and disappears completely when the form is (5). But we will save that to the last part. It is clear that if we can prove (5) true then the last step is to prove (6) false. Agreeing that we are at this point is not the same as conceding anything at this point. Of course, we are bound to come to a point at which we will disagree, but this shouldn't be it. The test setup as I have it is fine if it can be executed to your satisfaction.

Please note how far we have come without any reference to locality. Considering, it's a pretty long way if that is all EPR & Bell is about. We really have Bell's Inequality at this point, even if we haven't tested it. And all I have assumed to get here is a very specific form of realism.

 

[ttn]

I was hoping you would appreciate that (5) must be true, before we continue to prove (6) false. So I think that point is clear - in fact you mentioned (5) in your own words in an earlier post today.

Yes, I agree that (5) is an empirically verified fact. When alice and bob measure along the same axis, the results are perfectly correlated.

Now, here is the rub... (6) is fine unless you have some reason to suspect there is a problem in the experimental execution of it. After all, a confirmation of (5) also demonstrates there is no improper skewing. Unless of course, the improper skewing only shows up when we test at specific different angle settings in a very specific way, and disappears completely when the form is (5). But we will save that to the last part. It is clear that if we can prove (5) true then the last step is to prove (6) false. Agreeing that we are at this point is not the same as conceding anything at this point. Of course, we are bound to come to a point at which we will disagree, but this shouldn't be it. The test setup as I have it is fine if it can be executed to your satisfaction.

How does (5) being empirically proved, in any way "demonstrate that there is no improper skewing?" The objection was that Bob's measurement might change Alice's outcome (from what it would have been to something else). I don't see that (5) has any bearing on that at all -- for all we know, the only reason (5) is *true* is that the earlier measurement "skews" the later one in such a way that we observe perfect correlation.

In short, you seem to be saying that what I would call the locality assumption (the outcome on one side is independent of what's done on the other) is somehow a consequence of (5) or something like it. I don't see that *at all*.

Please note how far we have come without any reference to locality. Considering, it's a pretty long way if that is all EPR & Bell is about. We really have Bell's Inequality at this point, even if we haven't tested it. And all I have assumed to get here is a very specific form of realism.

Well, you've written a lot of words. (So have I!) But I really don't think we've gotten anywhere here. You wrote an inequality that is untestable and called it a "Bell inequality". Then you said that you can get from your inequality to the Bell inequality if one makes the test "indirect" by measuring each of two entangled particles once (rather than measuring a single particle twice). But this only *works* as an indirect measurement of the thing your original inequality was about, if you assume that the one measurement doesn't affect the other. And the only way to *justify* such an assumption is to cite the locality principle. So what have we really got? As far as I can tell, we have nothing new: either it's just Bell's Theorem revisited (not that that's a bad thing) or it's some empty and pointless and untestable thing that nobody cares about.

 

[DrChinese]

Yes, I agree that (5) is an empirically verified fact. When alice and bob measure along the same axis, the results are perfectly correlated.

How does (5) being empirically proved, in any way "demonstrate that there is no improper skewing?" The objection was that Bob's measurement might change Alice's outcome (from what it would have been to something else). I don't see that (5) has any bearing on that at all -- for all we know, the only reason (5) is *true* is that the earlier measurement "skews" the later one in such a way that we observe perfect correlation.

In short, you seem to be saying that what I would call the locality assumption (the outcome on one side is independent of what's done on the other) is somehow a consequence of (5) or something like it. I don't see that *at all*.

Well, you've written a lot of words. (So have I!) But I really don't think we've gotten anywhere here. You wrote an inequality that is untestable and called it a "Bell inequality". Then you said that you can get from your inequality to the Bell inequality if one makes the test "indirect" by measuring each of two entangled particles once (rather than measuring a single particle twice). But this only *works* as an indirect measurement of the thing your original inequality was about, if you assume that the one measurement doesn't affect the other. And the only way to *justify* such an assumption is to cite the locality principle. So what have we really got? As far as I can tell, we have nothing new: either it's just Bell's Theorem revisited (not that that's a bad thing) or it's some empty and pointless and untestable thing that nobody cares about.

Well, now we're coming to the part where we can address the locality issue head on. I am not trying to sneak anything by. (5) is empirical, so there is no assumption involved. If you don't have (5), there is no reason to perform (6). And of course, (6) is the Inequality we want to test. Next I will show the assumption Bell made and how it is expressed mathematically. Then we can discuss the meat without worrying about anything else because we will have clearly separated the realism and locality issues so we know where and why they are needed.

 

[ttn]

If you don't have (5), there is no reason to perform (6).

This seems to sneak in the assumption I was pointing to last night. You make it sound like if we *do* have (5), there *is* some reason to perform (6). But I don't see any sense in which (5) is equivalent to (or can substitute for, or entails,...) the *locality* assumption which makes an empirical test of (6) *interesting*. So I look forward to your confronting that locality question head on.

 

[Tez]

I agree totally - the definition of locality must be clear, mathematically precise and lastly: something we can agree upon. If we don't see locality the same way, then naturally we will come to different conclusions. So before I answer about the PR boxes, I would like to ask this question back:
Is the purpose of this definition of locality to formulate a condition that is experimentally testable? Is it to use to differentiate a theory so we can call it local or non-local?
There are two different programs, as I see it:
a. Locality-oriented: Use a Bell test to determine if there exist non-local influences (either signal-type or not).
b. Reality-oriented: Use a Bell test to determine if there are simultaneous reality to non-commuting observables.
The standard view of the results of Bell tests is:
a. If you assume reality, then non-local effects are demonstrated by Bell tests for theories that are realistic. (Some people also extend the results to indicate that non-local effects are demonstrated independently of the assumption of reality. I believe ttn would qualify as a member of that camp.) However, note that the non-local effects are essentially limited to collapse of the wave function and nothing else because there is no violation of signal locality. So now our definition of locality is: wave function collapse cannot occur faster than c. Therefore: Non-local theories can be realistic. By this definition QM is both non-local and non-realistic.
b. If you assume locality, as I do, then realistic theories are not viable as a result of Bell tests. (I also believe - but I am a minority on this - that the underlying reality of particle observables is now excluded for ALL theories - local or not. I have not proven that - yet.) But locality does not need to be defined as above to reach this conclusion. It only needs to be defined as per the requirements of Bell's Theorem, which I believe will be shown to be much less restrictive than the above. And that definition should match Bell's verbatim: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet of particle 1, nor A on b." That is a very different definition of locality, as I am sure you would agree - and I didn't make it up, I am simply following it explicitly. Therefore: All theories that respect this particular type of locality must not be realistic too. They may, however, be non-local in other ways. By this definition, QM is "local" and non-realistic. So that is why Bell Locality must be defined differently than other possible definitions.
At least one of a. or b. is justified by the results of Bell tests. For most, a. or b. is just a personal preference. So it is easy to see that ttn sees a. as the answer, and I see b. as the answer.

Hmm - I'm not quite sure exactly what your question was in the end! To this: Is the purpose of this definition of locality to formulate a condition that is experimentally testable? I would say yes - what I'm trying to get at with the PR boxes "sidetrack" is a completely operational (i.e. experimental outcome oriented, classical data in the notebook - I'm sure you know what I mean) way of "defining" locality. Of course we could just call the definition something else, especially if you're using it in a contradictory fashion. I highly doubt there's an interesting argument to be made as to whether the definitions we use are "right" or not, but there is a sense in arguing whether they are useful.

To this: Is it to use to differentiate a theory so we can call it local or non-local? If one is careful, then yes it probably can. But I would do so only in the strictest operational sense to avoid the baggage that comes with theory dependent definitions. (For example it was only recently that an operational definition of contexuality was formed - the Kochen-Specker defintion is pretty much useless because it is theory dependent. This I think was an important step.)

So don't keep me in suspense, are PR boxes operationally local or non-local by your definition? If they are local then I suggest we coin a different term - slowcal perhaps to try and "split" the argument into a managable fashion.

I think it is pointless to look at non-commutativity of measurements on a single particle for telling us anything about these issues, as you seem to be advocating. It is not hard to extend Spekkens' "toy theory" [q-ph/0401052] (which is local, classical, and non-contextual, but in it repeated measurements on single systems certainly don't commute) to mimic the "one-particle" Bell experiment. Interestingly Spekkens' theory does not have a C* structure underlying it, despite its algebraic simplicity. So if you are someone (like Malley) who thinks every "physical" theory should have such a structure then you can deduce lots of theorems about restrictions on LHV's. But these restrictions are completely uninteresting IMO. Justify the C* structure physically to me first, then I'll worry about it...As an interesting aside on one way in which QM is indisputably local: a question which causes some of us sleepless nights is why QM should be formed in a complex Hilbert space and not a real or quaternionic one. One of the big differences between the three possibilities is that in complex-QM an arbitrary multiparticle state can be worked out (i.e. tomographically reconstructed) by local measurements on each particle. No joint measurements are required. This is not true in the other two cases...

 

[DrChinese]

Hmm - I'm not quite sure exactly what your question was in the end! To this: Is the purpose of this definition of locality to formulate a condition that is experimentally testable? I would say yes - what I'm trying to get at with the PR boxes "sidetrack" is a completely operational (i.e. experimental outcome oriented, classical data in the notebook - I'm sure you know what I mean) way of "defining" locality. Of course we could just call the definition something else, especially if you're using it in a contradictory fashion. I highly doubt there's an interesting argument to be made as to whether the definitions we use are "right" or not, but there is a sense in arguing whether they are useful.

To this: Is it to use to differentiate a theory so we can call it local or non-local? If one is careful, then yes it probably can. But I would do so only in the strictest operational sense to avoid the baggage that comes with theory dependent definitions. (For example it was only recently that an operational definition of contexuality was formed - the Kochen-Specker defintion is pretty much useless because it is theory dependent. This I think was an important step.)

So don't keep me in suspense, are PR boxes operationally local or non-local by your definition? If they are local then I suggest we coin a different term - slowcal perhaps to try and "split" the argument into a managable fashion.

I think it is pointless to look at non-commutativity of measurements on a single particle for telling us anything about these issues, as you seem to be advocating. It is not hard to extend Spekkens' "toy theory" [q-ph/0401052] (which is local, classical, and non-contextual, but in it repeated measurements on single systems certainly don't commute) to mimic the "one-particle" Bell experiment. Interestingly Spekkens' theory does not have a C* structure underlying it, despite its algebraic simplicity. So if you are someone (like Malley) who thinks every "physical" theory should have such a structure then you can deduce lots of theorems about restrictions on LHV's. But these restrictions are completely uninteresting IMO. Justify the C* structure physically to me first, then I'll worry about it...

As an interesting aside on one way in which QM is indisputably local: a question which causes some of us sleepless nights is why QM should be formed in a complex Hilbert space and not a real or quaternionic one. One of the big differences between the three possibilities is that in complex-QM an arbitrary multiparticle state can be worked out (i.e. tomographically reconstructed) by local measurements on each particle. No joint measurements are required. This is not true in the other two cases...

Tez,

Thanks for your comments. I may not be able to address them all in one post. I promise I will have a comment on the PR boxes soon. I am very interested in your thoughts.

I would say definitely that the exact definition of locality and reality in Bell's Theorem is meaningful. I am trying to formulate something that is in the spirit of EPR and Bell. I realize that there has been a lot of philosophizing about this subject; a lot of that tends to obscure some of the base issues. I don't care so much if you do or don't consider QM complete. But the idea that there are underlying deterministic elements that define every possible answer to every possible question about particle attributes seems unreasonable to me given experimental results of the past few decades.

So I guess if you cut through all that, I would say that I do not believe in realism or hidden variables in any form if these are supposed to exist in advance of measurements.

As to locality: I think that signal locality is here to stay; and that wave function collapse having non-local character is here to stay. So does that mean one believes in locality or non-locality? I don't know but I hope to find out.

I definitely think that Bell tests help to probe the non-local issue; I hope my comments haven't indicated otherwise. I do feel the basic purpose of Bell tests are to probe questions about realism first and foremost; but any conclusion you derive from them is useful. Can these tests tell us something more about wave function collapse? That seems pretty fundamental to me, and I keep thinking something is being left on the table about that.

 

[Rade]

So I guess if you cut through all that, I would say that I do not believe in realism or hidden variables in any form if these are supposed to exist in advance of measurements.

I have a question based on the above statement. Are you then saying that you then believe that the deuteron [NP] cluster of two strongly interacting nucleons did not exist in the universe before they were measured by humans ?

 

[DrChinese]

Defining Bell Locality

What about Bell Locality?
===================

Repeating some previous results; we want to test (5) and see it true; and if it is, then test (6) to determine if Bell's Inequality is violated or not:

(5) Alice.a = Bob.a, or generally: corr(Alice.a, Bob.a) = 1
Alice.b = Bob.b, or generally: corr(Alice.b, Bob.b) = 1
Alice.c = Bob.c, or generally: corr(Alice.c, Bob.c) = 1

(6) corr(Alice.a, Bob.b) + noncorr(Alice.a, Bob.c) – corr(Alice.b, Bob.c) ) / 2 >= 0

Note that (6) does not have any requirement as to location. Alice and Bob can be anywhere, as long as they are entangled. But there is a potential flaw which must be considered. The concern is that a measurement setting itself for Alice might somehow unreasonably distort the outcome for Bob. Were such the case, then our attempts to learn about Alice indirectly by measuring Bob would be in vain. Our results would be improperly skewed or contaminated. There are several possible ways to get around this:

a. One could assert – reasonably so – that it is the responsibility of the candidate realistic theory to explain how a controlled scientific test of (6) could skew the results downward below a value of zero; which would cause us to improperly reject the candidate theory (false negative). After all, this is not an issue in any other scientific experiment, and has the nature of an ad hoc argument. However, this route will not be acceptable to some on philosophical grounds.
b. Another way is to assume a special form of locality, i.e. that exactly necessary to achieve our proof. This is exactly what Bell did in his paper: “The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b.” [1] We define this special form of locality, Bell Locality, as:

(7) p(Bob.b+) = p(Bob.b+, Alice.a+) + p(Bob.b+, Alice.a-)
= p(Bob.b+, Alice.b+) + p(Bob.b+, Alice.b-)
= p(Bob.b+, Alice.c+) + p(Bob.b+, Alice.c-)
= .500
(…and similar for all permutations of the above.)

The above is an exact definition of Bell Locality. As we vary the measurement setting for Alice, there is no change in the outcomes for Bob – and vice versa. The important thing about this particular definition of locality is that it covers ALL possible scenarios in which there might be skewing due to the measurement apparatus itself influencing the outcome. If we assume (7), then there are no influences from one measurement apparatus to the other; and we are now free to test (6) and determine if Bell’s Inequality is violated.

But perhaps (7) is false. Can (7) be tested? Sure, (7) can easily be tested, and it is tested just as (5) was. In fact: if we test (7) and determine it is true, then we do not need to assume (7). That would be an advantage, because assuming (7) – rather than proving it – would weaken Bell’s Theorem. Of course, we already know that (7) must be true – for if it weren’t, then previous Bell tests would have picked this up. Otherwise, one would have a simple way to send a superluminal signal.

There are some who would insist on a stricter definition of Bell Locality; one in which both parameter independence and outcome independence are required. Bell himself later adopted this position. However, this goes beyond Bell’s original assumption. In fact, it is in conflict with observation! You cannot assume that which is demonstrably falseor the result will be false or circular. The problem clearly seen in this expression of Bell Locality as PI+OI:

(8) corr(Alice.a, Bob.a) =
corr(Alice.a, Bob.b) =
corr(Alice.a, Bob.c)
(…and similar for all permutations of the above.)

In (8), we consider both the setting and the outcome at Bob and compare this to the results at Alice as we vary Bob. (8) would need to be true to prove the conjunction of PI and OI. But this conflicts with (5) if a<>b<>c unless we always get the same answers regardless of what values of a, b and c we select. That would be a value of 1 per (5). Clearly, we are in a situation in which (8) will always be false. So the assertion is that (7) is right and (8) is wrong as a definition for Bell Locality; and that (7) is true and (8) is false.

It should be fair to consider the results of a correlation test if the results are based on the entanglement of Alice and Bob, since that is what we asked for and what we test for. It should be unfair to consider the results of a correlation test if the measurement device itself – and not the entanglement of Alice and Bob - is contaminating the results. These characteristics define (7) but not (8). We wanted a clone of Alice, and we will get it! We do not assert that the relationship between the results of Alice and Bob are random. We merely state that the selection of Alice’s measurement setting itself does not skew the results of the measurement on Bob.

We can also see that it is possible that non-local theories could be constructed that do not violate (7), as it is also possible that local theories could be constructed that do violate (7). In other words, we don’t really care if the theory is “local” by normal standards or not, since we are primarily concerned that (7) is true. We care if it is Bell Local.

Looked at another way: if (7) were not true, there is no Bell’s Theorem and even local realistic theories are viable! Bell’s Theorem – with or without the Locality assumption – still depends on (7). The only issue is whether it must be assumed, or whether it can be experimentally verified. If you accept the original Bell’s Theorem as valid with (7) assumed, you must accept the modified version presented here with (7) proved experimentally.

To summarize about the definitions of locality:

a. Signal locality: defined as the ability to transmit information faster than c. This has never been violated experimentally, and it would be reasonable to assume it IF it would solve problems with our proof of Bell’s Theorem. However, it is not useful to our proof as even when Alice and Bob are space-like separated, the Inequality is still violated (by experimental proof). In other words: QM is a signal local theory that has the non-local effects necessary to violate the inequality; therefore one could postulate other signal local realistic theories that do as well. So assuming signal locality gets us nothing. Signal locality is not useful for Bell’s Theorem.
b. Bell Locality, defined as the conjunction of Outcome Independence and Parameter Independence as represented here as (8): This is demonstrably false; and as such it cannot be assumed and has no place in Bell’s Theorem. You don’t need to perform an experimental test of (6) to see that (8) is false; and therefore there is no Bell’s Theorem in the first place. The entire point of Bell’s Theorem is to have the Inequality (6) to test; and we won’t have that with this definition because (5) and (8) are in conflict.
c. Bell Locality, defined by Bell and here verbatim as (7): this is experimentally verified and need no longer be assumed. As long as the measurement apparatus itself is not improperly skewing the results – which is considered by (7) – any result of the actual entanglement of Alice and Bob is admissible.

The above conclusions are likely to be a matter of disagreement to some.

 

[DrChinese]

I have a question based on the above statement. Are you then saying that you then believe that the deuteron [NP] cluster of two strongly interacting nucleons did not exist in the universe before they were measured by humans ?

I never said the particles themselves don't exist. I simply state that the particles did not have definite values for all possible observables. That is the definition of realism.

 

[DrChinese]

I'd rather not read through this whole argument - I just have a question for Dr. Chinese. Would you call the so-called "PR boxes" nonlocal? (See e.g. http://arxiv.org/abs/quant-ph/0506180 ) for an intro to them. They are basically a pair of hypothetical magic boxes (used in quantum information to help quantify nonlocal resources) which are "maximally nonlocal" but still do not allow for signalling. Normally they imagined as a pair of boxes into which Alice can feed into her box a 0 or a 1, Bob can feed into his box a 0 or a 1 and the outputs satisfy that when both parties input a 1 their outputs are different (i.e. 01 or 10, though which of these two cases is chosen randomly), but in the other three cases their outputs are the same (00, 11 - again each chosen with probability 1/2). (See Eq. 2 in the above paper). Its unclear to me whether you would call such boxes local or nonlocal, but they certainly don't allow signalling - since locally each party sees a 0 or 1 output with probability 1/2 regardless of what (they or) the other person does.

OK, I have looked over these a bit... I admit I need a little more time to properly digest it. It looks pretty good, not all that far off in some respects as to how I see it.

As I see their definition, they are essentially equating non-local with entangled. I realize that is an oversimplification and I don't mean to be literal in that statement. And I am not sure that what they are doing isn't absolutely correct.

Entangled particles exhibit non-local WF effects, in my opinion, because separability does not occur with space-like separation. I do not believe that the separability requirement should be included in Bell's Theorem however, for the reasons I have presented in (1)-(8) previously. I do not consider there to be any contradiction between accepting non-local WF collapse (by accepting entanglement as verifiable and verified) and the rejection of realism (by accepting Bell's Theorem as verifiable and verified).

 

[ttn]

a. One could assert – reasonably so – that it is the responsibility of the candidate realistic theory to explain how a controlled scientific test of (6) could skew the results downward below a value of zero; which would cause us to improperly reject the candidate theory (false negative). After all, this is not an issue in any other scientific experiment, and has the nature of an ad hoc argument. However, this route will not be acceptable to some on philosophical grounds.

I don't follow this. The worry, as you say, is that Alice's setting/measurement might affect the state of Bob's particle and hence his measurement outcome, so the "indirect" test (i.e., the test of (6)) wouldn't be a valid test of the original inequality. What exactly is this possible response to the worry? That somehow the burden of proof is on the "realist" to explain how such a disturbance could come about?

For one thing, I think it's ridiculous to just shove the burden that way. That measurement disturbs the state of the thing measured is a central principle in the orthodox quantum philosophy; it goes all the way back to Bohr's early writings and is encapsulated in the formal collapse postulate, which tells us the precise way in which quantum states are disturbed by measurements. So to imply that the idea of measurement disturbance is some crazy thing thought up by the "realist" is really outlandish. You don't have to be a realist to believe in measurement disturbance (*certainly* not in the very very strong sense in which you have been defining "realism" in this thread! -- but not in weaker senses, either).

Plus, the whole idea that Alice's setting could affect Bob's outcome is just an issue of *locality* (assuming Alice and Bob's measurements are spacelike separated). Yes, as you said, Alice and Bob could be in the same place -- in which case there's no plausible objection at all to the idea that one measurement could affect the other outcome. It's only by assuming that Alice and Bob are widely separated, that you remove the *plausbility* of the idea that Alice's measurement could affect Bob's outcome (specifically, by making any such disturbance conflict with relativity's prohibition on superluminal causation). Given all this, I really don't understand your first proposed answer to the "disturbance worry."

b. Another way is to assume a special form of locality, i.e. that exactly necessary to achieve our proof. This is exactly what Bell did in his paper: “The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b.” [1] We define this special form of locality, Bell Locality, as:
(7) p(Bob.b+) = p(Bob.b+, Alice.a+) + p(Bob.b+, Alice.a-)
= p(Bob.b+, Alice.b+) + p(Bob.b+, Alice.b-)
= p(Bob.b+, Alice.c+) + p(Bob.b+, Alice.c-)
= .500
(…and similar for all permutations of the above.)
The above is an exact definition of Bell Locality.

No, it isn't. This is merely the statement that the marginal probability for a certain outcome of a certain experiment of Bob's, equals the sum over the various joint probabilities involving various possible measurements/outcomes of Alice. If you want to find out what Bell Locality actually means, why don't you spend the $20 and get a copy of Bell's book (Speakable..., 2nd edition) where he discusses this in great detail (in particular in the article La Nouvelle Cuisine)?

As we vary the measurement setting for Alice, there is no change in the outcomes for Bob – and vice versa.

That is *not* what your equations above say, and it is *not* what Bell Locality says either. I've tried so many times to explain to you what Bell Locality is, but you never listen or get it -- so I won't bother trying again, but will simply urge you to read Bell's article to find out.

The important thing about this particular definition of locality is that it covers ALL possible scenarios in which there might be skewing due to the measurement apparatus itself influencing the outcome. If we assume (7), then there are no influences from one measurement apparatus to the other; and we are now free to test (6) and determine if Bell’s Inequality is violated.
But perhaps (7) is false. Can (7) be tested? Sure, (7) can easily be tested, and it is tested just as (5) was. In fact: if we test (7) and determine it is true, then we do not need to assume (7). That would be an advantage, because assuming (7) – rather than proving it – would weaken Bell’s Theorem. Of course, we already know that (7) must be true – for if it weren’t, then previous Bell tests would have picked this up. Otherwise, one would have a simple way to send a superluminal signal.

In other words, violation of Bell Locality (as you have defined it) entails a violation of signal locality. Oops! Bell Locality is a *stronger* condition than signal locality. There are theories (like OQM and BM) which *violate* Bell Locality but which are nonetheless signal local. So clearly by explicit counterexample your claim is false -- violation of Bell Locality does *not* entail violation of signal locality. Hopefully this fact will help you realize that you have not defined Bell Locality correctly.

There are some who would insist on a stricter definition of Bell Locality; one in which both parameter independence and outcome independence are required.

Well, whether it makes any sense to parse Bell Locality into PI and OI is a controversial question. What's not controversial is that Bell Locality *can* be so parsed -- because Bell Locality is a specific, clear mathematical condition which is in fact the conjunction of so-called OI and PI. But you make it sound like there's some debate over what Bell Locality means -- some people think it means what you wrote way above, while others argue for a stronger meaning that is equivalent to OI+PI. This is all nonsense. Bell Locality is what it is. There might be *confusion* about the meaning of it, but there's not wiggle room for controversy.

Bell himself later adopted this position.

Surely he's the authority who gets to decide! Or better: when I (and others) use the phrase "Bell Locality" what we *mean* is the specific mathematical locality condition that Bell adopted. There can be no controversy about this. There can, no doubt, be controversy about whether Bell Locality is a good test of consistency with relativity, etc.; but there is no space for controversy about the *meaning* of Bell Locality. You just have to go read Bell's article until you grasp what he said.

However, this goes beyond Bell’s original assumption.

No, it is the *basis* for his original assumption -- brought out more clearly in his later writings.

In fact, it is in conflict with observation!

Now that's just pure drivel. Bell Locality is not a criterion that can be empirically tested in a direct sense, because it crucially involves probabilities that conditionalize on a "complete description of the state of the system prior to measurement". And you *must* have a *theory* in hand to tell you what such a complete description might consist of. You can't just go into the lab and test Bell Locality. What you can do is take a theory (which provides some proposed account of what a complete state description consists of) and ask: is this theory Bell Local? To answer it, you look at the theory, not at experiment. What's nifty about Bell's Theorem is that he was able to prove that a whole *class* of theories must obey an inequality that can be empirically tested and in fact is empirically violated. That's how we now (indirectly) know that Bell Locality is not respected by Nature. It isn't because somebody did an experiment and found (in a direct sense) that Bell Locality is false.

That you would assert (not only) that it's possible to empirically test Bell Locality in this direct sense (but worse, that it has been tested and has been found false) is just further proof that what you are calling "Bell Locality" is in fact something *else* -- i.e., further proof that you are simply *confused*.

Another point: I have argued here many times that, based on the EPR argument and Bell's Theorem and the relevant experiments, we now know that no Bell Local theory can be empirically viable -- i.e., that Nature is not Bell Local. (Further, I believe this signals a deep conflict between quantum theory and relativity.) When I've tried to argue for this perspective here in the past, you've always been highly critical, claiming that Bell tests *don't* prove any kind of nonlocality (but instead speak to "realism" or whatever). Yet here you are now claiming practically in passing that Bell Locality is false -- that experiment tells us somehow directly that Bell Locality is wrong! Now don't get me wrong -- I think you have misconstrued what Bell Locality *is*, so I don't put much stock in this claim. But it makes me wonder why you were so argumentative before, if you actually (think you) agree with my conclusion (that Bell Locality is false).

You cannot assume that which is demonstrably falseor the result will be false or circular. The problem clearly seen in this expression of Bell Locality as PI+OI:
(8) corr(Alice.a, Bob.a) =
corr(Alice.a, Bob.b) =
corr(Alice.a, Bob.c)
(…and similar for all permutations of the above.)

Sorry, that too is *not* Bell Locality.

QM is a signal local theory that has the non-local effects necessary to violate the inequality; therefore one could postulate other signal local realistic theories that do as well. So assuming signal locality gets us nothing. Signal locality is not useful for Bell’s Theorem.

Yes, that's all correct. We need a stronger locality assumption than signal locality to get Bell's Inequality.

b. Bell Locality, defined as the conjunction of Outcome Independence and Parameter Independence as represented here as (8): This is demonstrably false; and as such it cannot be assumed and has no place in Bell’s Theorem. You don’t need to perform an experimental test of (6) to see that (8) is false; and therefore there is no Bell’s Theorem in the first place. The entire point of Bell’s Theorem is to have the Inequality (6) to test; and we won’t have that with this definition because (5) and (8) are in conflict.

Shouldn't this suggest that you are just confused about the derivation? If Bell assumed something that is demonstrably, empirically *false* in arriving at the inequality, nobody today would *care* (or even know!) about Bell's inequality.

c. Bell Locality, defined by Bell and here verbatim as (7): this is experimentally verified and need no longer be assumed.

Huh? I thought you said (what you call) Bell Locality is experimentally disproved, not verified.

The above conclusions are likely to be a matter of disagreement to some.

That statement, at least, I can agree with 100%!

 

[DrChinese]

I don't follow this. The worry, as you say, is that Alice's setting/measurement might affect the state of Bob's particle and hence his measurement outcome, so the "indirect" test (i.e., the test of (6)) wouldn't be a valid test of the original inequality. What exactly is this possible response to the worry? That somehow the burden of proof is on the "realist" to explain how such a disturbance could come about?

For one thing, I think it's ridiculous to just shove the burden that way. That measurement disturbs the state of the thing measured is a central principle in the orthodox quantum philosophy; it goes all the way back to Bohr's early writings and is encapsulated in the formal collapse postulate, which tells us the precise way in which quantum states are disturbed by measurements. So to imply that the idea of measurement disturbance is some crazy thing thought up by the "realist" is really outlandish. You don't have to be a realist to believe in measurement disturbance (*certainly* not in the very very strong sense in which you have been defining "realism" in this thread! -- but not in weaker senses, either).

Plus, the whole idea that Alice's setting could affect Bob's outcome is just an issue of *locality* (assuming Alice and Bob's measurements are spacelike separated). Yes, as you said, Alice and Bob could be in the same place -- in which case there's no plausible objection at all to the idea that one measurement could affect the other outcome. It's only by assuming that Alice and Bob are widely separated, that you remove the *plausbility* of the idea that Alice's measurement could affect Bob's outcome (specifically, by making any such disturbance conflict with relativity's prohibition on superluminal causation). Given all this, I really don't understand your first proposed answer to the "disturbance worry."

I will tackle a bit at a time...

When I do a test of the speed of light from point A to point B, no one criticizes the experiment by saying that the measurement apparatus at one end affects the measurement appparatus at the other end in just such a way as to make it falsely appear that the speed of light is c. What about a Bell test is different?

The answer is that entanglement is necessary for a Bell test. I demonstrated that in (5) above. You can reference (5) and see clearly that this entanglement condition has absolutely nothing to do with locality. It is a requirement to forming (6) which is the standard Bell Inequality.

Yet the very same entanglement we so require in (5) we try to deny in (6) by requiring PI+OI. How does that make sense? We need ONLY make sure that the measurement apparatus ITSELF (PI) is not the cause of any improper skewing. That is where (7) comes in.

It does not make sense to conclude: I have proven Bell's Inequality false because you require something (8) which is too strict to be true. You can't have entanglement in a test and expect your definition of Bell Locality (PI+OI) to be true; one precludes the other! And that is essentially by definition!

With oQM, there is a disturbance - WF collapse - which occurs at the time of the measurement. But it is not the apparatus itself which "causes" the outcome in the sense that there is a cause and effect relationship between the setting of the apparatus and the particular value of an outcome elsewhere. And that is the element we wish to rule out - that the apparatus setting is having some OTHER unknown influence on the value outcome separate from the measurement interaction itself. We accomplish that with (7).

The interaction between Alice and Bob is a legitimate test element, not something to be denied. oQM says that there is a connection - a shared reality - between the two, and realistic theories say there is not. (6) allows us to differentiate between these. If you advance a realistic theory, there is no shared reality - because now your definition of reality simply becomes too convoluted to be reasonable to anyone.

(WF collapse is non-local, and I believe this is demonstrated when (6) is demonstrated false and Alice and Bob are space-like separated. Yet as far as anyone knows, there is signal locality. So hopefully there is no disagreement about this.)

 

[DrChinese]

Huh? I thought you said (what you call) Bell Locality is experimentally disproved, not verified.

1. Would you say there is experimental evidence in favor of signal locality? Sure there is.

Would you say there is experimental evidence against the separability condition (PI+OI)? Sure there is.

Would you say there is experimental evidence in support of MY Bell Locality condition (7)? Sure there is.

So it depends which definition we are talking about.

2. Now let's agree about this much too...

(5 - entanglement) needs to be proven before we can do a valid test of (6 - Bell's Inequality). We agree on that much. And we also BOTH agree that there is in fact another condition which needs to be considered or confronted: that there might be improper skewing of the results if we perform (6). The disagreement is how strict the definition should be and at what level "skewing" is allowed.

a. In my program, I want a looser definition that is proven true (no improper skewing) - so that a test of (6) is meaningful - and then we will know if realism is viable. My definition matches Bell's verbatim words.

b. In your program, you want a stricter definition that can be proven false which supports your contention that WF collapse is non-local. You definition matches Bell's separability condition.

Assuming Bell's Inequality is violated: Your program excludes all fully* local theories. My program agrees with that, and also excludes all realistic theories.

*where "Fully" local = signal local plus local WF collapse.

 

[ttn]

Would you say there is experimental evidence against the separability condition (PI+OI)? Sure there is.

That's what I'm so surprised to hear you say. PI+OI is Bell Locality. So you are saying that there is experimental evidence against Bell Locality. Well, what is that evidence? You've always disagreed with my argument that EPR + Bell + experiment proves that Bell Locality is false... now you're "sure there is" experimental evidence disproving Bell Locality?

a. In my program, I want a looser definition that is proven true (no improper skewing) - so that a test of (6) is meaningful - and then we will know if realism is viable. My definition matches Bell's verbatim words.

Um, OK, suppose you make up some weaker condition: DC Locality. And suppose, combined with the assumption of "realism", you can derive some sort of inequality (or whatever) which turns out to be consistent with experiment. You think somehow from this you're going to conclude: aha, realism is false! That makes no sense.

b. In your program, you want a stricter definition that can be proven false which supports your contention that WF collapse is non-local. You definition matches Bell's separability condition.
Assuming Bell's Inequality is violated: Your program excludes all fully* local theories. My program agrees with that, and also excludes all realistic theories.
*where "Fully" local = signal local plus local WF collapse.

Given your definition of "realism", we already know it's false from (eg) Gleason's theorem. What more are you going for here?

If your program agrees with my claim that Bell Locality is false, why do you always disagree with me when I say that? Or maybe the problem is your footnote: what my program excludes is Bell Locality. There can be no Bell Local theory that agrees with experiment. But you are wrong that this kind of locality " = signal local plus local WF collapse." But I applaud your creativity in dreaming up so many new attempts to define "locality."

 

[Rade]

I never said the particles themselves don't exist. I simply state that the particles did not have definite values for all possible observables. That is the definition of realism.

Thank you for your answer--perhaps this is the basis of my confusion. When I say that some "thing" is "real", what I mean is that it "exists". But it is not clear to me that then this must mean that what exists must have, as you say, "definite values for all possible observables". Why must this be true to say that something is real ? I do not understand. Why cannot a thing have "probability values" and not "definite values" yet still be real -- for example, is that not what QM tells us, that what is out there is a probability type reality, not a definite reality. Any help with my confusion is appreciated.

 

[DrChinese]

That's what I'm so surprised to hear you say. PI+OI is Bell Locality. So you are saying that there is experimental evidence against Bell Locality. Well, what is that evidence? You've always disagreed with my argument that EPR + Bell + experiment proves that Bell Locality is false... now you're "sure there is" experimental evidence disproving Bell Locality?

If your program agrees with my claim that Bell Locality is false, why do you always disagree with me when I say that? Or maybe the problem is your footnote: what my program excludes is Bell Locality. There can be no Bell Local theory that agrees with experiment. But you are wrong that this kind of locality " = signal local plus local WF collapse." But I applaud your creativity in dreaming up so many new attempts to define "locality."

Well, first my priority is to learn. So no harm there.

Second, I think what I have been trying to say is that Bell's Theorem is not so much about locality as reality. And I am pretty comfortable with that at this point. But the great thing is, my journey has greatly aided me in understanding your position. Thank you very much for taking the time to critique my posts.

And I don't ever recall consciously trying to deny that WF collapse is non-local. I just don't happen to think that is the criteria that one should apply when calling a theory Bell Local - whether Bell did or did not himself. But that is mostly for theoretical reasons - and by that I mean strictly from the perspective of theory construction. A weaker theory of locality means a stronger Bell Theorem, no question about that. So in my mind, I believe I have the weakest definition of locality possible that leads to a meaningful version of Bell's Theorem. And I do not think the traditional definition is required for that one.

 

[DrChinese]

Thank you for your answer--perhaps this is the basis of my confusion. When I say that some "thing" is "real", what I mean is that it "exists". But it is not clear to me that then this must mean that what exists must have, as you say, "definite values for all possible observables". Why must this be true to say that something is real ? I do not understand. Why cannot a thing have "probability values" and not "definite values" yet still be real -- for example, is that not what QM tells us, that what is out there is a probability type reality, not a definite reality. Any help with my confusion is appreciated.

I do not believe that there are definite values for all possible observables of a particle. I believe that there is something fundamental about the act of measurement. So I am more in the "probability" camp than the "definite" camp. We know what we observe, and this shapes reality.

 

[DrChinese]

Summary of points about realism and locality

I will summarize a few of the points I have made during the course of my recent posts.

a. I defined realism by way of 2 assumptions:

Rule 1 Assumption:
1 >= p(a+, b+, c+) >= 0
(..and similar for all permutations of the above.)

Rule 2 Assumption:
p(a+) = p(a+, b+) + p(a+, b-)
= p(a+, b+, c+) + p(a+, b-, c+) + p(a+, b+, c-) + p(a+, b-, c-)
(…and similar for all permutations of the above.)

b. I used those alone, without any reference to locality, to develop a Bell-type Inequality for a single particle:

(3) corr(Alice.a, Alice.b) + noncorr(Alice.a, Alice.c) – corr(Alice.b, Alice.c) ) / 2 >= 0

And proved that:

(4) No realistic theory can be internally consistent if Malus’ Law is accepted.

c. We discussed why tests a la Malus would or would not be appropriate for (3). We looked at ways to develop a form of (3) that was an indirect test of correlations, using an entangled photon pair. This introduced a new experimental requirement (not an assumption):

(5) Alice.a = Bob.a, or generally: corr(Alice.a, Bob.a) = 1
Alice.b = Bob.b, or generally: corr(Alice.b, Bob.b) = 1
Alice.c = Bob.c, or generally: corr(Alice.c, Bob.c) = 1

We then used this to develop a true Bell Inequality that makes no reference to locality at all:

(6) corr(Alice.a, Bob.b) + noncorr(Alice.a, Bob.c) – corr(Alice.b, Bob.c) ) / 2 >= 0

d. We discussed the feasibility of using this for an experiment, and determined that there is a potential flaw that can be addressed if we could prove:

(7) p(Bob.b+) = p(Bob.b+, Alice.a+) + p(Bob.b+, Alice.a-)
= p(Bob.b+, Alice.b+) + p(Bob.b+, Alice.b-)
= p(Bob.b+, Alice.c+) + p(Bob.b+, Alice.c-)
= .500
(…and similar for all permutations of the above.)

(7) can be experimentally verified, and matches verbatim one of Bell’s definitions of locality. In fact, it already has been verified; it is sometimes called parameter independence (PI). Therefore it is possible to test the viability of all realistic theories via (6) - without the usual assumption of locality present.

e. However, we encountered criticism, valid, that (7) was not a faithful representation of Bell Locality as expressed mathematically by Bell; (7) is in fact the weakest definition we could have and still come to a meaningful version of Bell’s Theorem.

Additional criticism expresses doubts that (7) would be sufficient to lead to a convincing proof, primarily because outcome independence (OI) should also be included as an assumption. At this point, opinion diverges with the majority opinion probably being that (6) will not be convincing without assuming PI+OI - although I can always hope I shaped someone's opinion on this.

I stand by my assessment, but respect the opinions of my learned friends and fellow PF participants. Additional comments are welcome, and thanks to all who patiently followed.

-DrChinese

 

[DrChinese]

This is intended for Vanesch and other MWIers out there:

The definition of Bell locality (as PI only) I used to set up for a test of a Bell Inequality (6 above) is more restricted - weaker - than the definition often used as being PI+OI. My definition (7 below) does not factor in Alice's outcomes, only Alice's measurement settings. I believe this is correct, ttn and many others do not.

(7) p(Bob.b+) = p(Bob.b+, Alice.a+) + p(Bob.b+, Alice.a-)
= p(Bob.b+, Alice.b+) + p(Bob.b+, Alice.b-)
= p(Bob.b+, Alice.c+) + p(Bob.b+, Alice.c-)
= .500
(…and similar for all permutations of the above.)

Here is the advantage of this definition - if you can accept it, and also accept MWI as reasonable:

The definition of BL=PI+OI is demonstrably false. That requirement is that there is NO correlation between the outcomes at Alice and Bob other than the "perfect" correlation it takes to establish that entanglement is present (expressed as my 5 above). This is experimentally false. If you accept that definition, then MWI cannot be local because the WF collapse is non-local. But that was one of the advantages of MWI - the locality.

My definition (7) neatly solves this as follows: (7) is experimentally true. It also matches to what I think MWI would predict. So by this particular definition - which was designed to both be true and dovetail into Bell's Theorem - locality holds. (Just as it holds if your definition of locality is signal locality.)

So with (5) and (7) true by experiment, we are cleared to test (6) by experiment - which is a test of Bell's Inequality based ONLY on the assumption of realism and not based on locality in any way. The inequality is violated; therefore realism is not viable.

MWI is not a realistic theory, as I understand it, because each measurement causes a branching. All non-commuting observables do not have simultaneous real values. Is my understanding correct on how MWI would address the issue of realism? I don't want to speak wrongly...

 

[ttn]

And I don't ever recall consciously trying to deny that WF collapse is non-local. I just don't happen to think that is the criteria that one should apply when calling a theory Bell Local - whether Bell did or did not himself.

He didn't! And I never did either! Ugh, I don't know where you get all these weird new ideas every 30 seconds about who defines locality how. Bell Locality doesn't just mean something about wf collapse. It's true that in OQM the wave function collapse postulate violates Bell Locality. But Bell Locality is a perfectly clear test that doesn't in any way require wf collapse.

But that is mostly for theoretical reasons - and by that I mean strictly from the perspective of theory construction. A weaker theory of locality means a stronger Bell Theorem, no question about that. So in my mind, I believe I have the weakest definition of locality possible that leads to a meaningful version of Bell's Theorem. And I do not think the traditional definition is required for that one.

Well, I still think you are missing the main point, which is related to EPR. The reason "Bell Locality" is a useful and relevant criterion (in addition to its prima facie plausibility as a requirement of relativistic causality) is that *from it* follows the exact "local hidden variables" that permit the rest of Bell's Theorem to go through. You're probably right that if you just assume those hidden variables from the beginning, some weaker locality condition would permit you to derive an inequality. So then, assuming the inequality is empirically violated, you'd have to conclude that either the lhv's don't exist, or the weaker locality assumption is false. That is precisely the kind of reasoning that is the standard mis-understanding of what Bell proved (but with Bell Locality in place of the weaker locality condition). It is precisely why people erroneously think of Bell's theorem as a proof that hidden variables aren't viable, which we *know* is false because Bohm's theory *exists*. The correct approach starts with the EPR type argument which shows that the existence of the lhv's *follows* from (Bell) Locality, and only then passes to Bell's Theorem (which shows that the lhv's are in conflict with experiment).

If your point in this thread has been to argue that lhv's don't exist, you're barking up the wrong tree. Everybody agrees they don't exist. That's just what Bell's Theorem proves, and there's no controversy about that. The controversy is over why anybody wanted to believe in those lhv's in the first place. If it's only to save some philosophical bias for "realism", then you'd be right: so much the worse for realism. But if the reason for believing in the lhv's is because they're required by *locality*, then the conclusion is: so much the worse for locality. That latter is, in my opinion, the correct perspective.

 

[DrChinese]

He didn't! And I never did either! Ugh, I don't know where you get all these weird new ideas every 30 seconds about who defines locality how. Bell Locality doesn't just mean...

Bell's words, not mine: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." Quoted from one of my previous posts. So I am not sure I follow the 30 seconds thing.

I think he knew why this definition - which is PI and is as identical to my (7) as I could make it - was the weakest possible definition that would be convincing. I would have formulated a weaker version if I could have and gotten away with it, but I also think this is the minimal definition that works. If Alice's measurement apparatus is not affecting Bob's results (and vice versa), and I am correlating Alice and Bob's outcomes, I assert I have a valid test. I do not claim there is no relationship between the outcomes of Alice and Bob; the nature of the relationship is the very thing I determine for use with my Inequality.

 

[ttn]

Bell's words, not mine: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." Quoted from one of my previous posts. So I am not sure I follow the 30 seconds thing.

I think he knew why this definition - which is PI and is as identical to my (7) as I could make it - was the weakest possible definition that would be convincing. I would have formulated a weaker version if I could have and gotten away with it, but I also think this is the minimal definition that works. If Alice's measurement apparatus is not affecting Bob's results (and vice versa), and I am correlating Alice and Bob's outcomes, I assert I have a valid test. I do not claim there is no relationship between the outcomes of Alice and Bob; the nature of the relationship is the very thing I determine for use with my Inequality.

Yes, in the paper you have in mind, Bell says what you say he says -- that the outcomes on each side can't depend on the distant setting. But this is *not* what is technically known in the literature as PI (parameter independence). You have to be extremely careful about what all these things mean precisely, mathematically -- in particular, you have to be careful about what the probabilities involved are conditionalized on. To say something like "the outcome here doesn't depend on the parameter there" is indeed a kind of "parameter independence". But it simply is *not* the same as the "PI" satisfying "PI + OI = Bell Locality".

These things are very subtle and you can't just plow through them at light speed. For example, you say: "If Alice's measurement apparatus is not affecting Bob's results..." Well what do you mean exactly that Bob's results aren't affected? That in a given run of the experiment (i.e., for a given particle pair) the outcome is the same as it would otherwise have been? That the probabilities for different outcomes are the same as they would have been? Or that the long-time-average of Bob's results over many runs are the same as they would have been? Or that the correlation coefficient for Alice's and Bob's outcomes are independent of Alice's settings? etc. The point is, there are a ton of subtly different things that might plausibly be thought of as a kind of parameter independence. Being clear about which is which and which is justified/relevant in a given context, however, is crucial to this discussion.

I still think you need to read La Nouvelle Cuisine. Is there something preventing you from doing this? Or maybe you read it and didn't find it clarifying?