A Paradox: Do LHV Theories Need the HUP?

[DrChinese]

Here is one I am having trouble following. Can anyone help me through my confusion?

Our setup is a normal Bell test using entangled photons created using spontaneous parametric down conversion (PDC). Such a setup uses 2 BBO crystals oriented a 90 degrees relative to each other. See for example Dehlinger and Mitchell's http://users.icfo.es/Morgan.Mitchell/QOQI2005/DehlingerMitchellAJP2002EntangledPhotonsNonlocalityAndBellInequalitiesInTheUndergraduateLaboratory.pdf .

1. Say we have Alice and Bob set their polarizers at identical settings, at +45 degrees relative to the vertical. Once the individual results of Alice and Bob are examined, it will be seen (in the ideal case) that they always match (either ++ or --). According to the local realist or local hidden variables (LHV) advocate, this is "easily" explained: if you measure the same attribute of two separated particles sharing such a common origin, you will naturally always get the same answer. There is no continuing entanglement or spooky action at a distance, and conservation rules are sufficient to provide a suitable explanation. I.e. in LHV theories there is no continuing connection between spacelike separated particles that interacted in the past. The results will be 100% correlation.

But that explanation does not seem reasonable to me, even in the case above in which Alice and Bob have identical settings. Here is the paradox as I see it. The source of the photon pairs is the 2 crystals. They achieve an EPR entangled state for testing by preparing a superposition of states as follows:

|\psi_e_p_r\rangle = \frac {1} {\sqrt{2}} (|V\rangle _s|V\rangle _i + |H\rangle _s|H\rangle _i)

This is the standard description per QM. We already know this leads to the cos^2 \theta relationship and the results will be 100% correlation.

The local realist presumably would not accept this description as accurate because it is not complete, and violates the basic premise of any LHV theory. He has an alternate explanation, and the Heisenberg Uncertainty Principle (HUP) is not part of it. So now it appears that our experimental results are compatible with the expectations of both QM and LHV (at least when Alice and Bob have matching settings); however, they have different ways of obtaining identical predictions. But let's look deeper, because I think there is a paradox in the LHV side.

2. Suppose I remove one of the BBO crystals, say the one which produces pairs that are horizontally polarized. I have removed an element of uncertainty of the output stream, as we will now know which crystal was the source of the photon pair. Now the results of Alice and Bob no longer match in all cases, and such is predicted by the application of QM: Alice and Bob will now have matched results only 50% of the time. This follows because the resulting photon pairs emerge from the remaining BBO crystal with a vertical orientation. Each photon has a 50-50 chance of passing through the polarizer at Alice and Bob. But since there is no longer a superposition of states, Alice and Bob do not end up with correlated results.

But what about our LHV theory? We should still get matching results for Alice and Bob because we are still measuring the same attribute on both photons and the conservation rule remains in effect! Yet the actual results are now matches only 50% of the time, no better than even odds. What happened to our explanation that "measuring the same attribute" gives identical results? It seems to me that the only way for a LHV to avoid the paradox is to incorporate the HUP - and maybe the projection postulate too - as a fundamental part of the theory so that it can give the same predictions as QM.

I mean, if the LHV advocate denies there is superposition in case 1 (such denial is essentially a requirement of any LHV, right?), how does the greater knowledge of the state change anything in case 2?

 

[ZapperZ]

Hum... but is this really a sufficient set of measurements? The whole purpose of measuring the observable at various angles is to distinguish between QM and LHV, per Bell's theorem. This is especially crucial based on the EPR paper of what happens with regards to the non-commuting observable, which in this case, is the "perpendicular" component of the detected angular momentum.

The superposition aspect of QM is what makes this different than, let's say, the fragmentation of an object with zero angular momentum into 2 pieces going in opposite direction, where one knows immediately the angular momentum of the other piece upon the measurement of the angular momentum of the first piece. This is pure conservation law, but without any superposition of angular momentum before a measurement.

Zz.

 

[vanesch]

Now the results of Alice and Bob no longer match in all cases, and such is predicted by the application of QM: Alice and Bob will now have matched results only 50% of the time. This follows because the resulting photon pairs emerge from the remaining BBO crystal with a vertical orientation. Each photon has a 50-50 chance of passing through the polarizer at Alice and Bob.

The LR adept will probably tell you that this changed the setup of the source, and as such, the "measuring the same attribute" result can change.
I think you have to make a distinction between two classes of LR theories: Maxwellian field theories (which are of course LR) in which we have a more or less clear model of the physics that is happening (+ detector model) - eventually with modifications, such as SED, and "abstract LR theories" where no specific model is given (the kind of thing that is considered by Bell).
I guess that the first category is what you are adressing your criticism against. This kind of theory has extreme difficulties explaining the 100% correlation that happens when the two polarizers are parallel, but make an angle with the polarization of the beam. I'm not expert enough in SED with the added noise and "detector background subtraction" to know whether it can talk itself out of this, but *classical* optics certainly can't.
On the other hand, the abstract kind of LR theories, where photons walk around with entire books of prescriptions of what to do when they encounter which detector have the easy way out of saying that you simply change the contents of the books when you change the setup of the source.

cheers,
Patrick.

 

[DrChinese]

The whole purpose of measuring the observable at various angles is to distinguish between QM and LHV, per Bell's theorem. ... where one knows immediately the angular momentum of the other piece upon the measurement of the angular momentum of the first piece. This is pure conservation law, but without any superposition of angular momentum before a measurement.

Zz.

Ya, we have the advantage today of Bell's Theorem. And that is quite an advantage. IF Einstein had that, well... who knows.

But Bell figured out that something about the EPR argument didn't make sense. In retrospect, there must be more things about the local realistic argument that don't make sense. One thing I notice very clearly in dealing with the "crackpots" (you know who you are) is that they never come up with their own predictions! You can't pin them down to any particular formula. I have concluded that in addition to Bell's Inequality, there must actually be a number of critical relationships that hold true to constrain LHV theories. I would like to document these. I think if we documented them, we would see that constructing LHV theories that are even remotely close to experiment is impossible. Even more impossible than the Bell Inequalities might otherwise imply.

 

[DrChinese]

I guess that the first category is what you are adressing your criticism against. This kind of theory has extreme difficulties explaining the 100% correlation that happens when the two polarizers are parallel, but make an angle with the polarization of the beam.

Yes, and of course you know how I like Bell. But the LR folks keep trying to attack Bell tests by arguing that there is experimental error present. I, of course, don't agree with that logic and I don't believe there are any more loopholes in Bell tests than I believe there are loopholes in measuring the value of c.

But I believe that if one advances any particular mechanism for local reality, one will quickly see that it fails on more fronts than a violation of a Bell Inequality. You can't make sense of any LR theory that makes specific predictions as regards a PDC setup. There are always angles that can't be explained.

The norm is to say that QM and LR agree at 0 and 90 degrees. But I don't think that an LR theory can be constructed that works at those angles AND makes consistent sense within the context of PDC optics. And I think "naive" LR theories that match the Bell Inequality (i.e. as close as you can come to QM without crossing the line) become circular immediately. I.e. you have to assume that which you are trying to prove.

 

[vanesch]

But I don't think that an LR theory can be constructed that works at those angles AND makes consistent sense within the context of PDC optics. And I think "naive" LR theories that match the Bell Inequality (i.e. as close as you can come to QM without crossing the line) become circular immediately. I.e. you have to assume that which you are trying to prove.

Well, you should check out nightlight's posts on s.p.r. where he claims that Stochastic Electrodynamics (by Santos and co) do exactly that. There are indeed some peer-reviewed articles by him on the subject, and Santos claims that he has constructed a model of PDC which has identical predictions with quantum optics in all cases (up to some redefinition of what is a detection event). I have to say, I tried to read the paper, I think I understand more or less the gist of it, but I'm not enough of a quantum optician to be able to critically read it and understand it.
What I understand of it is the following: the EM field is classical, except that the field in vacuum is not empty, but has 1/2 hbar omega intensity in each mode (and this is then responsable for all "zero point energy" in quantum theory, also for electrons and so on). When we have a photodetector, it DOES respond to this classical noise, and does "click" a lot, only, we call that noise, or background, and subtract it off the "real" signal.
The PDC receives the pump laser, but also the "noise", and the outgoing beams (classical beams) also have "noise". He then claims that this system gives exactly the same correlation function as quantum optics.
But you will see that the paper is quite complicated and I just couldn't bring myself in spending weeks in digging out all the details.

cheers,
Patrick.

 

[DrChinese]

Well, you should check out nightlight's posts on s.p.r. where he claims that Stochastic Electrodynamics (by Santos and co) do exactly that. There are indeed some peer-reviewed articles by him on the subject, and Santos claims that he has constructed a model of PDC which has identical predictions with quantum optics in all cases (up to some redefinition of what is a detection event). I have to say, I tried to read the paper, I think I understand more or less the gist of it, but I'm not enough of a quantum optician to be able to critically read it and understand it.
What I understand of it is the following: the EM field is classical, except that the field in vacuum is not empty, but has 1/2 hbar omega intensity in each mode (and this is then responsable for all "zero point energy" in quantum theory, also for electrons and so on). When we have a photodetector, it DOES respond to this classical noise, and does "click" a lot, only, we call that noise, or background, and subtract it off the "real" signal.
The PDC receives the pump laser, but also the "noise", and the outgoing beams (classical beams) also have "noise". He then claims that this system gives exactly the same correlation function as quantum optics.
But you will see that the paper is quite complicated and I just couldn't bring myself in spending weeks in digging out all the details.

cheers,
Patrick.

Thanks for the reference, and I will check it out. What I am looking for is if the Santos theory can explain the results with both crystals, and just one as well. I realize that his approach must fail to Bell's Inequality anyway, but it seems to me that there must be other serious flaws in any LR theory being put forth as well. There are too many references to optics experiments nowadays for it not to fail victim to one or the other!

 

[vanesch]

Thanks for the reference, and I will check it out. What I am looking for is if the Santos theory can explain the results with both crystals, and just one as well. I realize that his approach must fail to Bell's Inequality anyway, but it seems to me that there must be other serious flaws in any LR theory being put forth as well. There are too many references to optics experiments nowadays for it not to fail victim to one or the other!

Also have a look at:

http://www.qols.ph.ic.ac.uk/~kinsle/e-docs/kinsler-1996-arXiv.pdf

cheers,
Patrick.

 

[ZapperZ]

Hey DrChinese, I'm not sure if this will address your question, but I should have pointed this out to you. You MAY want to read it:

Research on hidden variable theories: A review of recent progresses, M. Genovese, Phys. Rep. v.413, p.319 (2005).

It is 77 pages long! However, I think this is a worthwhile read.

Zz.

 

[DrChinese]

Also have a look at:

http://www.qols.ph.ic.ac.uk/~kinsle/e-docs/kinsler-1996-arXiv.pdf

cheers,
Patrick.

Wow, this is great, almost like like he read my mind (9 years in advance LOL).

 

[DrChinese]

Hey DrChinese, I'm not sure if this will address your question, but I should have pointed this out to you. You MAY want to read it:

Research on hidden variable theories: A review of recent progresses, M. Genovese, Phys. Rep. v.413, p.319 (2005).

It is 77 pages long! However, I think this is a worthwhile read.

Zz.

Looks great, I guess it may keep me busy as with Vanesch's ref. Good stuff guys!

 

[ttn]

But Bell figured out that something about the EPR argument didn't make sense.

No, no, no. The EPR argument is not the same thing as the kind of theory that that argument argued for. The *argument* was that, if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side. That argument was, is, and always will be completely valid.
Now a separate point: Einstein (and others) believed that the premise of the EPR argument (namely, locality) was true. Hence they thought, based on the argument, that QM wasn't complete (since it didn't contain those outcome-determining variables) and that we should be looking for a hidden variable theory to complete it.
Now what did Bell prove? He proved that no local hidden variable theory can agree with the QM predictions / experiment. That is, he proved that the kind of theory Einstein was hoping for (on the basis of (1) his belief in locality and (2) the EPR type argument) can't exist.
That is simply not the same thing as proving that the EPR argument was wrong, that "something about it didn't make sense." It makes perfect sense, and Bell was one of the few people who has been able to rise above all the Copenhagenish obfuscation and see this clearly. If you read Bell's papers, you'll find that there is no room for doubt on this. Bell himself was 100% convinced that the EPR argument was perfectly valid.
I'm not one of the LHV people you (rightly) criticize. LHV theories are ruled out by experiment, by any reasonable standard. As you say in another post, there are no more "loopholes" in the Bell tests than there are in such mundane experiments as measuring the speed of light. Yes, in principle there are loopholes, but you basically have to be a nut at this point to think those loopholes are of any relevance.
My point is: one doesn't have to be a nut to insist on getting the logic of EPR and Bell straight. It's really not that complicated, and it undercuts your position when you say things like "Bell figured out that the EPR argument didn't make sense."

 

[DrChinese]

No, no, no. The EPR argument is not the same thing as the kind of theory that that argument argued for. The *argument* was that, if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side. That argument was, is, and always will be completely valid.
Now a separate point: Einstein (and others) believed that the premise of the EPR argument (namely, locality) was true. Hence they thought, based on the argument, that QM wasn't complete (since it didn't contain those outcome-determining variables) and that we should be looking for a hidden variable theory to complete it.
Now what did Bell prove? He proved that no local hidden variable theory can agree with the QM predictions / experiment. That is, he proved that the kind of theory Einstein was hoping for (on the basis of (1) his belief in locality and (2) the EPR type argument) can't exist.
That is simply not the same thing as proving that the EPR argument was wrong, that "something about it didn't make sense." It makes perfect sense, and Bell was one of the few people who has been able to rise above all the Copenhagenish obfuscation and see this clearly. If you read Bell's papers, you'll find that there is no room for doubt on this. Bell himself was 100% convinced that the EPR argument was perfectly valid.
I'm not one of the LHV people you (rightly) criticize. LHV theories are ruled out by experiment, by any reasonable standard. As you say in another post, there are no more "loopholes" in the Bell tests than there are in such mundane experiments as measuring the speed of light. Yes, in principle there are loopholes, but you basically have to be a nut at this point to think those loopholes are of any relevance.
My point is: one doesn't have to be a nut to insist on getting the logic of EPR and Bell straight. It's really not that complicated, and it undercuts your position when you say things like "Bell figured out that the EPR argument didn't make sense."

Well, I agree with some of what you say but disagree with other parts.

I like what you have to say about "if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side". That is a great way to frame the argument about local reality. And I agree about the importance of getting EPR and Bell straight, which is why I try to stay close to their words on the subject where possible.

But I disagree about Bell not finding something wrong with EPR. There is something wrong with EPR, and Bell showed it to us! EPR said both of the following:

a) Either QM is incomplete, or there is not simultaneous reality to non-commuting observables.
b) They believed that there IS simultaneous reality to non-commuting observables because a more complete specification of the system is possible.

a) was supported by the logic presented. Clearly, b) was not rigorously supported and was an ad hoc assumption. Some people never accepted b) anyway, so it may not be material to them. Maybe that is your opinion too. On the other hand, some people did accept b) - but Bell saw a problem with that. He formulated his paper ("On the EPR Paradox") mathematicially assuming there WAS simultaneous reality to such observables, and found that was incompatible with QM itself. Hardly a result that EPR envisioned.

I would definitely say that EPR took locality as an axiom. Bell definitely did not, as he was explicit in this regard.

FYI: I do not believe people who believe in local reality are nuts. I think any scientist is a nut who says there is no scientific evidence for something when there is a lot of scientific evidence for it.

 

[DrChinese]

The superposition aspect of QM is what makes this different than, let's say, the fragmentation of an object with zero angular momentum into 2 pieces going in opposite direction, where one knows immediately the angular momentum of the other piece upon the measurement of the angular momentum of the first piece. This is pure conservation law, but without any superposition of angular momentum before a measurement.
Zz.

Yeah, that is what I was wanting to say but somehow you said it a lot better. That is, that the superposition of states is central to QM and is not a feature of LHV theories. And in fact, the results are radically different when you look at the H and V streams independently than when you look at them combined. I don't think you can make any sense of the results if you postulate hidden mechanisms. (I.e. How can you get more matches at +45 degrees with the HV combined stream than with the H or V streams independently unless the superposition of states is real?)

 

[Sherlock]

The EPR argument is not the same thing as the kind of theory that that argument argued for. The *argument* was that, if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side.

He [Bell] formulated his paper ("On the EPR Paradox") mathematicially assuming there WAS simultaneous reality to such [non-commuting] observables, and found that was incompatible with QM itself.

... that the superposition of states is central to QM and is not a feature of LHV theories. And in fact, the results are radically different when you look at the H and V streams independently than when you look at them combined. I don't think you can make any sense of the results if you postulate hidden mechanisms. (I.e. How can you get more matches at +45 degrees with the HV combined stream than with the H or V streams independently unless the superposition of states is real?)

My current understanding is that the EPR and Bell arguments and experimental results, taken together, aren't necessarily telling us anything about locality. That is, locality-nonlocality isn't *necessarily* an issue. Rather, the issue might have to do with the way hidden variables can be modeled (which is what DrChinese seems to be getting at) which has to do with what can be ascertained about an *underlying reality* (ie., what it is that is incident on, say, the polarizers in an optical Bell test) from experimental results.

Might one conclude that the *observables* are not in one to one correspondence with the underlying reality, and therefore that the qm form and experimental tests aren't revealing that nonlocal phenomena exist (or that they don't exist)?

 

[ZapperZ]

Might one conclude that the *observables* are not in one to one correspondence with the underlying reality, and therefore that the qm form and experimental tests aren't revealing that nonlocal phenomena exist (or that they don't exist)?

No, one might not. By making such a statement, you are already making a HUGE assumption that there is (i) an underlying reality and that (ii) it is inaccessible via ANY measurement since, after all, it is, then we would have detected a deviation from QM's predictions.

This isn't obvious, nor automatic.

Zz.

 

[vanesch]

That is, locality-nonlocality isn't *necessarily* an issue. Rather, the issue might have to do with the way hidden variables can be modeled (which is what DrChinese seems to be getting at) which has to do with what can be ascertained about an *underlying reality* (ie., what it is that is incident on, say, the polarizers in an optical Bell test) from experimental results.
Might one conclude that the *observables* are not in one to one correspondence with the underlying reality, and therefore that the qm form and experimental tests aren't revealing that nonlocal phenomena exist (or that they don't exist)?

Sherlock, I never understood fully what you wanted to say when you wrote about Bell.
Bell's theorem tells us that it is impossible to construct a theory which:
1) has a deterministic mechanism in it that determines (not that is 1-1, but that determines) all the outcomes of potential experiments (whether or not we perform them!)
2) that this deterministic mechanism obeys local dynamics
3) can generate exactly the same probabilities for outcomes as quantum theory does (the only randomness being a distribution of certain uncontrolled parameters in the source and in the detectors which have statistically INDEPENDENT distributions)

 

[Sherlock]

No, one might not. By making such a statement, you are already making a HUGE assumption that there is (i) an underlying reality and that (ii) it is inaccessible via ANY measurement since, after all, it is, then we would have detected a deviation from QM's predictions.
This isn't obvious, nor automatic.
Zz.

The main assumptions are that reality exists independent of measurement, and that the results of probings of reality so far don't allow a complete assessment of what reality *is*.

I would think that a physicist would embrace this view, if only for reasons of job security. :-)

By 'underlying reality' I'm just referring to the exact qualitative form of what (which presumably came from the same oscillator) is incident on the polarizers during a coincidence interval . Or, for that matter, what is incident on a polarizer in an individual measurement. (One might assume that there is *no* qualitative physical form, but that doesn't make sense to me.)

Obviously *some* aspect of this isn't inaccessible to measurement. But it isn't (to me at least) readily apparent what the form of the *incident* disturbance is. The polarization model that would seem to fit ok with individual measurements does not fit joint measurements.

So, either the polarization model is not in one to one correspondence with what the incident disturbance is, or joint measurements are measuring something different than individual measurements, or both.

In any case, the individual measurements are unpredictable, which indicates that the models involved are not in one to one correspondence with reality. That is, the results of polarization measurements don't necessarily tell us anything about the polarization of the incident disturbance prior to filtration or, in the case of joint measurements of entangled particles, if polarization is the applicable model.

 

[Sherlock]

Sherlock, I never understood fully what you wanted to say when you wrote about Bell.
Bell's theorem tells us that it is impossible to construct a theory which:
1) has a deterministic mechanism in it that determines (not that is 1-1, but that determines) all the outcomes of potential experiments (whether or not we perform them!)
2) that this deterministic mechanism obeys local dynamics
3) can generate exactly the same probabilities for outcomes as quantum theory does (the only randomness being a distribution of certain uncontrolled parameters in the source and in the detectors which have statistically INDEPENDENT distributions)

I'm assuming that there is a physical mechanism which determines, qualitatively, the outcomes of Bell tests -- and that it is so far unknown.

Since quantum theory doesn't deal explicitly with this mechanism, then the form of qm calculations can't be taken to mean that there exist nonlocal phenomena in nature. It is of course certain that there exist, in some more artificial sense, nonlocal 'phenomena' in qm.

 

[ZapperZ]

By 'underlying reality' I'm just referring to the exact qualitative form of what (which presumably came from the same oscillator) is incident on the polarizers during a coincidence interval . Or, for that matter, what is incident on a polarizer in an individual measurement.
Obviously *some* aspect of this isn't inaccessible to measurement. But it isn't (to me at least) readily apparent what the form of the *incident* disturbance is. The polarization model that would seem to fit ok with individual measurements does not fit joint measurements.
So, either the polarization model is not in one to one correspondence with what the incident disturbance, or joint measurements are measuring something different than individual measurements, or both.
In any case, the individual measurements are unpredictable which indicates that the models involved are not in one to one correspondence with reality.

Which again emphasized my previous message, that you ARE making an a priori assumption of something beyond that can be measured. I can easily make a similar assumption, that there's no such thing, and you can't dispute that since I will only put validity on what I can measure. Everything else is speculation.

Zz.

 

[ZapperZ]

I'm assuming that there is a physical mechanism which determines, qualitatively, the outcomes of Bell tests -- and that it is so far unknown.
Since quantum theory doesn't deal explicitly with this mechanism, then the form of qm calculations can't be taken to mean that there exist nonlocal phenomena in nature. It is of course certain that there exist, in some more artificial sense, nonlocal 'phenomena' in qm.

Again, as I've said in my first response to DrChinese posting, that in many instances, people do not realize that this has a lot to do with the superposition principle than anything else. The difference between the classical "conservation" principle, and the QM superposition phoenomenon, is what makes this a very different event. One cannot simply attempt to understand EPR-type phenomenon without understanding what superposition is, and why it is as valid as anything we know (re: the Stony Brook and Delft experiments).

Until you can clarify the "underlying reality" of those experiments, I suggest you hold off from applying your underlying reality to the EPR-type experiments.

Zz.

 

[Sherlock]

Which again emphasized my previous message, that you ARE making an a priori assumption of something beyond that can be measured. I can easily make a similar assumption, that there's no such thing, and you can't dispute that since I will only put validity on what I can measure. Everything else is speculation.
Zz.

The main assumptions are that reality exists independent of measurement, and that the results of probings of reality so far don't allow a complete assessment of what reality *is*.

I would think that a physicist would embrace this view, if only for reasons of job security. :-)

One might assume that what is incident on a polarizer has *no* qualitative physical form, but that would seem to be an apriori sort of assumption that's as untenable as you say its converse is.

In fact, the assumption that there is an underlying physical reality *depends* on experimental results.

 

[Sherlock]

Again, as I've said in my first response to DrChinese posting, that in many instances, people do not realize that this has a lot to do with the superposition principle than anything else. The difference between the classical "conservation" principle, and the QM superposition phoenomenon, is what makes this a very different event. One cannot simply attempt to understand EPR-type phenomenon without understanding what superposition is, and why it is as valid as anything we know (re: the Stony Brook and Delft experiments).
Until you can clarify the "underlying reality" of those experiments, I suggest you hold off from applying your underlying reality to the EPR-type experiments.
Zz.

I understand your point about superposition, but are you saying that conservation laws have nothing to do with entanglement?

Don't you view the exercise of modern physics as having everything to do with a collective attempt to "clarify the 'underlying reality'" of experiments?

 

[vanesch]

I'm assuming that there is a physical mechanism which determines, qualitatively, the outcomes of Bell tests -- and that it is so far unknown.

Yes, that's one of Bell's hypotheses in his theorem.
And a few others, like local dynamics. He doesn't make any explicit assumptions of a model, just that one exists that can, in principle, determine the outcomes of all measurements, and that the dynamics of that model is local. That is sufficient to be in contradiction with the predictions of QM.

Since quantum theory doesn't deal explicitly with this mechanism, then the form of qm calculations can't be taken to mean that there exist nonlocal phenomena in nature.

It is not the form of the calculations, it are the outcomes ! What Bell proved, is that a certain class of theories, which have very reasonable assumptions (and which Einstein supposed were underlying QM), WILL NEVER BE ABLE TO GET THE SAME RESULTS OUT AS QM.
This was the big surprise of Bell's theorem. We're not saying that the QM *calculations* are somehow non-local, we're saying that the predictions that come out of it cannot be also the result of a theory that satisfies the premisses of Bell's theorem.
As a (poor) analogy, I could think up the following:
Imagine that some Greek philosophers would find it "natural" that all lengths in geometry come in multiples of an "elementary length", and they simply say that Euclid's geometry is a nice theory, but doesn't describe the "underlying reality" of geometry. That all of its results are of course correct, but that one should look for the "realistic" theory of geometry, which starts with "elementary lengths".
Well, Pythagoras (Bell) could then say that such a theory, no matter what form it takes, cannot be right, because the diagonal of a square is related to the side by a non-rational number in Euclidean geometry. So no matter how you fiddle around with "elementary lengths" you'll never be able to obtain this ratio.
This has nothing to do with the specific axiom system of Euclid. The prediction is simply that the ratio of the diagonal over the side is sqrt(2), and this is an irrational number. This is something that *comes out of Euclid's system*. A theory that claims that all constructed lengths are multiples of an "elementary length" can never come to such a conclusion, hence can not be an "underlying reality" to Euclidean geometry.
cheers,
patrick.

 

[ZapperZ]

I understand your point about superposition, but are you saying that conservation laws have nothing to do with entanglement?

That was what I said in the very first posting in this thread, as in the example from an object that fragmented into two!

You need to address how your "reality" jive with the Stony Brook/Delft experiments. Till then, I truly believe all of this is meaningless.

Don't you view the exercise of modern physics as having everything to do with a collective attempt to "clarify the 'underlying reality'" of experiments?

No, we intend to "clarify" what we don't understand via verification of that understanding through a series of experiments. There's nothing to indicate what you claim to be a separate "underlying reality" is valid. Believing in such a thing dispite the lack of evidence isn't "modern physics".

Zz.

 

[Sherlock]

You need to address how your "reality" jive with the Stony Brook/Delft experiments. Till then, I truly believe all of this is meaningless.
... we intend to "clarify" what we don't understand via verification of that understanding through a series of experiments. There's nothing to indicate what you claim to be a separate "underlying reality" is valid. Believing in such a thing dispite the lack of evidence isn't "modern physics".
Zz.

The idea that conservation laws having nothing to do with entanglement doesn't make sense to me at this point. Maybe someday it will. In any case I don't want to take the thread any further off topic. If i get a chance to prepare some researched statements or questions on it, then I'll post them in a new thread. Until then, I'll take your word for it.

I also don't want to argue here about whether or not reality exists independent of measurement, although it seems pretty clear to me that it does, and that that's not what Bell tests are testing. It also seems clear to me that physics doesn't yet know everything that there is to know about a whole lot of experimental phenomena (quantum entanglement being just one example).

'Underlying reality' just refers to what isn't yet known about reality (like the behavior of the light incident on polarizers in a Bell test). Of course, we don't know yet what it is that we don't know (at least I don't :-) ) -- but what you seem to be saying is that it's ok to assume that we already know everything that there is to know about reality.

The experimental evidence isn't just the foundation for what can be said to be known, it's also an indicator that what is known isn't the whole story.

 

[ZapperZ]

The idea that conservation laws having nothing to do with entanglement doesn't make sense to me at this point. Maybe someday it will. In any case I don't want to take the thread any further off topic. If i get a chance to prepare some researched statements or questions on it, then I'll post them in a new thread. Until then, I'll take your word for it.

No, I'm saying the conservation laws when applied to classical system is DIFFERENT than that in the EPR type experiment. The system is under A SUPERPOSITION of states that have no particular state until it is measured! Once it is measured, then the "conservation" law that caused the entanglement in the first place kicks in! When this occurs, one can easily ask "So what's the difference between this and a classical system where we have conservation of angular momentum, for example?". This is there the measurement of non-commuting components will show the difference!

I also don't want to argue here about whether or not reality exists independent of measurement, although it seems pretty clear to me that it does, and that that's not what Bell tests are testing. It also seems clear to me that physics doesn't yet know everything that there is to know about a whole lot of experimental phenomena (quantum entanglement being just one example).
'Underlying reality' just refers to what isn't yet known about reality (like the behavior of the light incident on polarizers in a Bell test). Of course, we don't know yet what it is that we don't know (at least I don't :-) ) -- but what you seem to be saying is that it's ok to assume that we already know everything that there is to know about reality.
The experimental evidence isn't just the foundation for what can be said to be known, it's also an indicator that what is known isn't the whole story.

I NEVER said we know all there is to know. I simply refuse to play the speculation game, which is what you're doing. If we do that, I can speculate anything I want without bothering for any physical justification. So how would this solve anything and answer anything? I could speculate that some unseen angels are actually directing the polarization of each photon passing through the polarizers, and it would be no different than what you're doing. Would this make it better?

I'd rather stick to what we already know, and continue to LOOK for any violation of things we thought we understood already! I find those to be a more definitive indication of new and unknown things.

Zz.

 

[Sherlock]

... I'm saying the conservation laws when applied to classical system is DIFFERENT than that in the EPR type experiment. The system is under A SUPERPOSITION of states that have no particular state until it is measured! Once it is measured, then the "conservation" law that caused the entanglement in the first place kicks in! When this occurs, one can easily ask "So what's the difference between this and a classical system where we have conservation of angular momentum, for example?". This is there the measurement of non-commuting components will show the difference!

Ok, that's different than what you first wrote when I asked if you were saying that conservation laws have nothing to do with entanglement -- and you said yes. I still don't think I agree with the way you've put it above -- but that can be a topic for another thread.

I NEVER said we know all there is to know. I simply refuse to play the speculation game, which is what you're doing.

Where have I speculated? What I said, in effect, is that the results of optical Bell tests might be taken as an indication that we don't know all there is to know about the underlying reality, which in the case of optical Bell tests would include, among other things, what is commonly referred to as the electromagnetic field (and particular phenomena related to this field such as photons and polarization).

If we do that, I can speculate anything I want without bothering for any physical justification. So how would this solve anything and answer anything? I could speculate that some unseen angels are actually directing the polarization of each photon passing through the polarizers, and it would be no different than what you're doing.

Let's see what I'm doing:
I asked, "Might one conclude that the *observables* are not in one to one correspondence with the underlying reality, and therefore that the qm form and experimental tests aren't revealing that nonlocal phenomena exist (or that they don't exist)?"

And you answered, "No, one might not. By making such a statement, you are already making a HUGE assumption that there is (i) an underlying reality and that (ii) it is inaccessible via ANY measurement since, after all, it is, then we would have detected a deviation from QM's predictions.

And I clarified (or so I thought) what I was talking about in post 18 of this thread -- and none of it involved speculating about the underlying reality itself. (We can do that in another thread also.) The speculation is about the interpretation of Bell's analysis of lhv supplements to qm and the physical meaning of experimental violations of Bell inequalities.

By the way, the idea that the wavefunction isn't in one to one correspondence with reality came from my quantum theory textbook, which teaches a probability interpretation.

I'd rather stick to what we already know, and continue to LOOK for any violation of things we thought we understood already! I find those to be a more definitive indication of new and unknown things.

Yes of course. That's probably the most productive way that discoveries have been, and are going to continue to be, made -- along with advances in the hardware.

But, I'm not speculating specifically about hitherto unknown physical phenomena. This is just one possible avenue of inquiry regarding the physical meaning of Bell tests, and the essence of quantum entanglement. But such speculation will probably turn out to be unnecessary, imo -- since the essence of entanglement has been known since Schroedinger first talked about it, and partly due to this it can be inferred that Bell's theorem and Bell tests aren't telling us anything about local realism.

 

[Sherlock]

Sherlock, I never understood fully what you wanted to say when you wrote about Bell.

Neither did I. :-) I just have this nagging feeling that people are focusing on irrelevant stuff wrt some statements that are made regarding the meaning of Bell's theorem and experimental violations of inequalities. The basic datum in Bell tests is nonseparable. So is the instrumental variable. They can't be analyzed into component parts. Bell discussed situations in which lhv supplements to qm would be ok. So the results don't rule out all lhv supplements for all situations -- just a certain form wrt entangled states.

Since quantum theory doesn't deal explicitly with this mechanism, then the form of qm calculations can't be taken to mean that there exist nonlocal phenomena in nature.

That's the way I've learned to think about it, but some people seem to think that the qm formalism itself indicates the existence of nonlocal phenomena in nature.

It is not the form of the calculations, it is the outcomes! What Bell proved, is that a certain class of theories, which have very reasonable assumptions (and which Einstein supposed were underlying QM), WILL NEVER BE ABLE TO GET THE SAME RESULTS OUT AS QM.
This was the big surprise of Bell's theorem. We're not saying that the QM *calculations* are somehow non-local, we're saying that the predictions that come out of it cannot be also the result of a theory that satisfies the premises of Bell's theorem.

It depends on what premises are being considered. There are more assumptions involved than local realism. In any case, we certainly can't conclude from Bell tests that there's no physical reality between emitters and detectors. We can, however, be pretty sure that extant models aren't in one to one correspondence with what is happening between emitters and detectors. The idea that entanglement is *created* via common source or common interaction is a compelling one -- and, as far as my limited experience is concerned, this idea is the one held by most physicists.

As for locality, is it possible that the joint result can be nonseparable and still be partly dependent on a local common source or interaction? It would seem so. The joint result also depends on the variable joint setting of polarizers, but this joint setting is one nonanalyzable thing -- so when you change the setting of one polarizer, no matter the extent of their spatial separation, then the value of the variable that reveals predictable rates of coincidental detection is instantaneously changed. And, as far as I can tell, the instrumental variable is the only variable involved in determining coincidental detection (if whatever is happening between emitters and detectors is varying, it doesn't affect the results) -- so the search for a *hidden* variable wrt Bell test situations would seem to be wrongheaded.

Thus, the statement that Bell test *results* disallow lhv supplements is a bit off. Bell test *setups* disallow lhv supplements -- because such variables as might exist between emitters and detectors are simply not relevant to the results, and including them in the calculation screws it up.

 

[vanesch]

It depends on what premises are being considered. There are more assumptions involved than local realism.

Which ones ?

 

[ZapperZ]

Ok, that's different than what you first wrote when I asked if you were saying that conservation laws have nothing to do with entanglement -- and you said yes. I still don't think I agree with the way you've put it above -- but that can be a topic for another thread.

Well, no. Let's address it here.

Case 1: A blob with no net angular momentum. At some time, it fragmented into two pieces that flew off in opposite directions. When they are very far away, I measure Piece 1 and found its angular momentum. I immediately can say that I know the angular momentum of Piece 2.

Case 2: 2 entangled particle flew off in opposite direction. I perform an EPR-type measurement. Upon measurement of one of the paritcles, the entangled property of the other is immediately set.

Do you think those two cases are identical?

Let's see what I'm doing:
I asked, "Might one conclude that the *observables* are not in one to one correspondence with the underlying reality, and therefore that the qm form and experimental tests aren't revealing that nonlocal phenomena exist (or that they don't exist)?"
And you answered, "No, one might not. By making such a statement, you are already making a HUGE assumption that there is (i) an underlying reality and that (ii) it is inaccessible via ANY measurement since, after all, it is, then we would have detected a deviation from QM's predictions.
And I clarified (or so I thought) what I was talking about in post 18 of this thread -- and none of it involved speculating about the underlying reality itself. (We can do that in another thread also.) The speculation is about the interpretation of Bell's analysis of lhv supplements to qm and the physical meaning of experimental violations of Bell inequalities.

But what evidence do you have to be able to say:

"... *observables* are not in one to one correspondence with the underlying reality..."?

You made two explicit assumptions here: (i) the observables do not have a one-to-one correspondence with some reality and (ii) that there is an "underlying reality" that is DIFFERENT than what these observables are producing.

When you produce no such evidence, and we currently do not have one, I categorize that as speculation.

But, I'm not speculating specifically about hitherto unknown physical phenomena. This is just one possible avenue of inquiry regarding the physical meaning of Bell tests, and the essence of quantum entanglement. But such speculation will probably turn out to be unnecessary, imo -- since the essence of entanglement has been known since Schroedinger first talked about it, and partly due to this it can be inferred that Bell's theorem and Bell tests aren't telling us anything about local realism.

Then you owe the community a favor by rebutting all those papers that continually claim violation of local realism. If you believe in such a thing, then you have an obligation to correct the situation. Write a rebuttal with your arguments to make sure such a claim is never made.

Zz.

 

[Sherlock]

Which ones ?

One is the assumption that the hidden variables are relevant to the outcome. Bell tests are measuring entanglement. The entanglement is assumed to not vary from entangled pair to entangled pair. Experimenters tweak and calibrate everything to minimize untoward effects. Any variations in the entanglement should be in the results.

Another is the assumption that the separable formulation is applicable to entangled states, which apparently it isn't.

 

[ZapperZ]

One is the assumption that the hidden variables are relevant to the outcome. Bell tests are measuring entanglement. The entanglement is assumed to not vary from entangled pair to entangled pair. Experimenters tweak and calibrate everything to minimize untoward effects. Any variations in the entanglement should be in the results.

But this is making a slanderous implication that experimenters deliberately manipulate their instruments so as to only produce results that will only verify a prevailing idea. Are you willing to stand by such an accusation?

Zz.

 

[vanesch]

One is the assumption that the hidden variables are relevant to the outcome.

What does it mean, "relevant" ?
The idea of a local realist theory is that the local hidden variables is THE ONLY MECHANISM of inducing correlations. You are free NOT to use that mechanism but then OF COURSE you will not find any correlation, so you better use it.

Bell tests are measuring entanglement.

No, entanglement is a theoretical property proper to quantum theory, while Bell's inequalities apply to ANOTHER class of theories which does NOT have the mechanism of entanglement, but only of (hidden or not) local quantities which can have a common origin (or not).

Bell's tests are testing CORRELATIONS of measurements (that's not the same as "entanglement").

Local quantities which have common origin produce correlations between outcomes, and quantum entanglement produces correlations between outcomes. Bell's inequalities put limits on the amount of correlation you can obtain with the first kind of mechanism, and quantum entanglement can produce correlations which go beyond these limits (exactly because it is not a "common origin of local quantities" kind of mechanism)

Another is the assumption that the separable formulation is applicable to entangled states, which apparently it isn't.

But that's exactly what "local realism" means, no ? That each individual particle has a well-defined state which will from that point on, determine all what can be measured on that particle. This well-defined state can have a common origin with another particle (that's the "common origin of hidden variables" = state of the local particle) but that's the only allowed mechanism to generate correlations.

Clearly the quantum description doesn't allow that: the quantum state of an entangled pair does NOT split into two individual states of the individual particles (and THAT is the exact reason that quantum theory is NOT a local realist theory, and hence does not have to satisfy Bell's inequalities - which indeed it doesn't). But the Local Realist wants to see an individual state assigned to each particle, which will entirely determine what will be measured.
Bell's theorem just states that such a theory must satisfy certain conditions on the correlations that can be observed (Bell's inequalities), which are NOT satisfied by QM, and hence that such a theory can never be the "underlying mechanism" of QM.

 

[DrChinese]

Thus, the statement that Bell test *results* disallow lhv supplements is a bit off. Bell test *setups* disallow lhv supplements -- because such variables as might exist between emitters and detectors are simply not relevant to the results, and including them in the calculation screws it up.

This is definitely not the case. Plenty of experiments have been performed in which the detector settings are changed mid-flight. As a a result, there is no possibility that any kind of equilibrium state (between the emitter and the detector) affects the outcome.

 

[ttn]

I like what you have to say about "if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side". That is a great way to frame the argument about local reality. And I agree about the importance of getting EPR and Bell straight, which is why I try to stay close to their words on the subject where possible.
But I disagree about Bell not finding something wrong with EPR. There is something wrong with EPR, and Bell showed it to us!

The thing I said that you liked ("if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side") is simply a summary of the EPR conclusion. So I don't see how/why you claim to like this statement, given that you think "there is something wrong with EPR."

EPR said both of the following:
a) Either QM is incomplete, or there is not simultaneous reality to non-commuting observables.

In other words, either QM is incomplete, or it is complete. (Either the two quantities whose simultaneous values are restricted by the HUP are both simultaneously real, or they aren't. If they are real, orthodox QM is incomplete; if they aren't simultaneously real, QM is complete, at least in so far as those two variables are concerned.)

b) They believed that there IS simultaneous reality to non-commuting observables because a more complete specification of the system is possible.

Yes, they argued that there "IS simultaneous reality to non-commuting observables"... but not merely because they felt a more complete specification of the system is possible. That's not a *reason* to believe in the simultaneous reality of those two properties, it's just another way of saying that one believes in the simultaneous reality of those two properties. To believe that a more complete specification of the system is possible is simply to deny the completeness doctrine, specifically, to deny the orthodox view that the uncertainty principle is ontological rather than epistemic.

The *actual reason* EPR believed in the simultaneous reality of these properties is because he saw that to *not* believe in them would violate the assumption of reality. If you think that x and p are not simultaneously real for the distant particle, then, in order to explain the perfect correlations between the particle here and the one there, you *must* posit some kind of non-local mechanism by which the measurement here *causes* the particle there to assume the appropriate, correlated value for the property in question. Completeness entails non-locality (given the predicted correlations). Or equivalently, locality entails in-completeness. Specifically, locality entails that both x and p for that distant particle were already (simultaneously) definite/real before any measurement was made here.

a) was supported by the logic presented. Clearly, b) was not rigorously supported and was an ad hoc assumption. Some people never accepted b) anyway, so it may not be material to them. Maybe that is your opinion too.

Hogwash. You can't be analyzing what's wrong with their argument until you've understood it.

On the other hand, some people did accept b) - but Bell saw a problem with that. He formulated his paper ("On the EPR Paradox") mathematicially assuming there WAS simultaneous reality to such observables, and found that was incompatible with QM itself.

Fine, but you miss what's essential if you just say "some people did accept b)". That's true, but what's important is that people accepted "b)" (which as I noted above is just equivalent to your "a)") *because it was a requirement of locality. The whole point of EPR in so far as it relates to Bell's Theorem is this: given the perfect correlations predicted by QM, the *only* way to respect locality is to deny the completeness doctrine and add local hidden variables to account (locally, duh) for the outcomes. That's the only way you can possibly have a local theory.

Bell later proved that even this way of trying to have a local theory couldn't work. You can't reproduce the QM predictions with a hidden variable theory that respects locality. But this isn't "too bad for hidden variables". To say that is to simply *forget* why we should have believed in hidden variables in the first place, namely: because having them is the only way to have a local theory. That's what EPR showed.

Think of it this way: EPR and Bell both showed that a certain theory (or class of theories) was non-local. EPR pointed out the orthodox QM was nonlocal, and noted what, in principle, would have to be done to construct a local theory. Bell showed that the kind of theory needed to respect locality in the face of the EPR argument, also doesn't work -- such a theory cannot be made to agree with QM/experiment. Conclusion: locality is false. The only way to save it doesn't work.

Hardly a result that EPR envisioned.

No doubt. But that doesn't mean their *argument* is wrong. It means one of the premises of that argument turns out to be untenable. This is elementary logic. "Locality" and "Locality --> InCompleteness" are not the same proposition. EPR accepted the first and proved the second, and hence believed in the conclusion "InCompletness".

Later, Bell proved that this conclusion "InCompleteness" plus the original "Locality" premise entails a contradiction with experiment. So, just considering Bell, either "Incompleteness" or "Locality" must fail. But if "InCompleteness" fails, that means we are upholding the orthodox Completeness doctrine, and that means, per EPR, that we are denying "Locality". So... again... you can't save "locality" by denying "InCompleteness". The two arguments together prove absolutely that "Locality" is false.

(Well, not absolutely... You could always say something completely bonkers, like that we're all deluded when we think that the experiments in question even had definite outcomes. Of course, that would be even crazier than clinging to the various "loopholes" in those experiments that are clung to by fans of local hidden variable theories.)

I would definitely say that EPR took locality as an axiom.

You mean, they took it as a premise in their argument for "InCompleteness"? No doubt. Yet you seem ignorant of the role this premise actually played in the argument.

Bell definitely did not, as he was explicit in this regard.

Excuse me? Are you saying that you don't think "Locality" is a premise of Bell's Theorem? The whole point of the theorem is to show that a certain class of LOCAL theories are inconsistent with the QM predictions.

Or maybe you just mean that, in a broader sense, Bell was willing to consider that possibly "Locality" might be false. That's certain true, although he only thought that because his theorem, combined with the EPR argument, *proved* that "Locality" is untenable.

 

[Sherlock]

But this is making a slanderous implication that experimenters deliberately manipulate their instruments so as to only produce results that will only verify a prevailing idea. Are you willing to stand by such an accusation?
Zz.

Oh come now ZapperZ. Look at what I wrote.

"Bell tests are measuring entanglement. The entanglement is assumed to not vary from entangled pair to entangled pair. Experimenters tweak and calibrate everything to minimize untoward effects. Any variations in the entanglement should be in the results."

What this means is that experimenters do everything they possibly can to ensure that the hardware is working as it should, and that the entanglement preparation is actually producing entangled results.

What are you saying ... that experimenters who conduct Bell tests are *not* trying to produce entangled pairs?

 

[ZapperZ]

Oh come now ZapperZ. Look at what I wrote.
"Bell tests are measuring entanglement. The entanglement is assumed to not vary from entangled pair to entangled pair. Experimenters tweak and calibrate everything to minimize untoward effects. Any variations in the entanglement should be in the results."
What this means is that experimenters do everything they possibly can to ensure that the hardware is working as it should, and that the entanglement preparation is actually producing entangled results.
What are you saying ... that experimenters who conduct Bell tests are *not* trying to produce entangled pairs?

I didn't say anything. I was asking if you're implying that experimenters tweak their equipment to only produce what they think it should. That was how I understood from reading what you said.

And oh, unless I again misunderstood what you are saying, the measurement itself produce only a detection of the component of the entangled variable - it does NOT measure "entanglement". It is only when you look at the whole collection of the measured data can one deduce such such correlation. Other experiments are a lot more convincing in detecting entanglement than the EPR-type experiments (example: the defeat of the diffraction limit by entangled particles).

I'm confused as to why entanglement is the issue here. Even those who are sticking with local realism isn't debating the reality of entanglement. EPR wasn't addressing such a thing, but the non-local nature of entanglement.

Zz.

 

[DrChinese]

The thing I said that you liked ("if locality is true, there must exist a certain kind of hidden variables which determine the outcomes on each side") is simply a summary of the EPR conclusion. So I don't see how/why you claim to like this statement, given that you think "there is something wrong with EPR."
In other words, either QM is incomplete, or it is complete. (Either the two quantities whose simultaneous values are restricted by the HUP are both simultaneously real, or they aren't. If they are real, orthodox QM is incomplete; if they aren't simultaneously real, QM is complete, at least in so far as those two variables are concerned.)
Yes, they argued that there "IS simultaneous reality to non-commuting observables"... but not merely because they felt a more complete specification of the system is possible. That's not a *reason* to believe in the simultaneous reality of those two properties, it's just another way of saying that one believes in the simultaneous reality of those two properties. To believe that a more complete specification of the system is possible is simply to deny the completeness doctrine, specifically, to deny the orthodox view that the uncertainty principle is ontological rather than epistemic.
The *actual reason* EPR believed in the simultaneous reality of these properties is because he saw that to *not* believe in them would violate the assumption of reality. If you think that x and p are not simultaneously real for the distant particle, then, in order to explain the perfect correlations between the particle here and the one there, you *must* posit some kind of non-local mechanism by which the measurement here *causes* the particle there to assume the appropriate, correlated value for the property in question. Completeness entails non-locality (given the predicted correlations). Or equivalently, locality entails in-completeness. Specifically, locality entails that both x and p for that distant particle were already (simultaneously) definite/real before any measurement was made here.
Hogwash. You can't be analyzing what's wrong with their argument until you've understood it.

Fine, but you miss what's essential if you just say "some people did accept b)". That's true, but what's important is that people accepted "b)" (which as I noted above is just equivalent to your "a)") *because it was a requirement of locality. The whole point of EPR in so far as it relates to Bell's Theorem is this: given the perfect correlations predicted by QM, the *only* way to respect locality is to deny the completeness doctrine and add local hidden variables to account (locally, duh) for the outcomes. That's the only way you can possibly have a local theory.
Bell later proved that even this way of trying to have a local theory couldn't work. You can't reproduce the QM predictions with a hidden variable theory that respects locality. But this isn't "too bad for hidden variables". To say that is to simply *forget* why we should have believed in hidden variables in the first place, namely: because having them is the only way to have a local theory. That's what EPR showed.
Think of it this way: EPR and Bell both showed that a certain theory (or class of theories) was non-local. EPR pointed out the orthodox QM was nonlocal, and noted what, in principle, would have to be done to construct a local theory. Bell showed that the kind of theory needed to respect locality in the face of the EPR argument, also doesn't work -- such a theory cannot be made to agree with QM/experiment. Conclusion: locality is false. The only way to save it doesn't work.
No doubt. But that doesn't mean their *argument* is wrong. It means one of the premises of that argument turns out to be untenable. This is elementary logic. "Locality" and "Locality --> InCompleteness" are not the same proposition. EPR accepted the first and proved the second, and hence believed in the conclusion "InCompletness".
Later, Bell proved that this conclusion "InCompleteness" plus the original "Locality" premise entails a contradiction with experiment. So, just considering Bell, either "Incompleteness" or "Locality" must fail. But if "InCompleteness" fails, that means we are upholding the orthodox Completeness doctrine, and that means, per EPR, that we are denying "Locality". So... again... you can't save "locality" by denying "InCompleteness". The two arguments together prove absolutely that "Locality" is false.
(Well, not absolutely... You could always say something completely bonkers, like that we're all deluded when we think that the experiments in question even had definite outcomes. Of course, that would be even crazier than clinging to the various "loopholes" in those experiments that are clung to by fans of local hidden variable theories.)
You mean, they took it as a premise in their argument for "InCompleteness"? No doubt. Yet you seem ignorant of the role this premise actually played in the argument.
Excuse me? Are you saying that you don't think "Locality" is a premise of Bell's Theorem? The whole point of the theorem is to show that a certain class of LOCAL theories are inconsistent with the QM predictions.
Or maybe you just mean that, in a broader sense, Bell was willing to consider that possibly "Locality" might be false. That's certain true, although he only thought that because his theorem, combined with the EPR argument, *proved* that "Locality" is untenable.

I can't really debate what you are saying, as I don't really get your points.

EPR was not about locality: it really isn't discussed and is more a tacit assumption ("... after which time we suppose that there is no longer any interaction between the two parts..."). It was about the completeness of QM. They felt they demonstrated that QM was incomplete. I don't feel they demonstrated that. I feel they DID demonstrate that if QM was complete, then there is not simultaneous reality to non-commuting observables. Do we disagree about this? Or maybe you read the last 2 paragraphs of EPR differently than I do.

Bell discusses locality explicitly ("... the signal involved must propagate instantaneously" ...), as I say. His primary argument, however, has nothing to do with locality and everything to do with reality (i.e. hidden variables) - that is what the math is all about ("It follows that c is another unit vector..."). After then proving that hidden variables are inconsistent with the predictions of QM, he concludes that hidden variables can only be "rescued" within a non-local theory. Do we disagree on this?

It is patently false that EPR+Bell excludes locality. It is also possible that reality is both local and observer dependent (i.e. there is no unit vector c). I am merely stating that QM, per Copenhagen, can be interpreted several different ways and often is.

 

[Sherlock]

I didn't say anything. I was asking if you're implying that experimenters tweak their equipment to only produce what they think it should. That was how I understood from reading what you said.
And oh, unless I again misunderstood what you are saying, the measurement itself produce only a detection of the component of the entangled variable - it does NOT measure "entanglement". It is only when you look at the whole collection of the measured data can one deduce such such correlation. Other experiments are a lot more convincing in detecting entanglement than the EPR-type experiments (example: the defeat of the diffraction limit by entangled particles).
I'm confused as to why entanglement is the issue here. Even those who are sticking with local realism isn't debating the reality of entanglement. EPR wasn't addressing such a thing, but the non-local nature of entanglement.
Zz.

So called "Bell states" are maximally entangled states. Bell inequalities are entanglement 'witnesses'. Violations of Bell inequalities are an indication of the presence of entanglement. Hence, my statement that Bell tests measure entanglement, which, if experimenters have prepared things correctly, is not a *variable* property. The only thing that is varying in the Bell tests (that has anything to do with the outcome) is the joint setting of the polarizers.

Therefore, the application of a hidden variable supplement to the qm formulation is just a *mis*application -- since the variable properties of entangled pairs don't affect the rate of coincidental detection.

The relevant hidden parameter is the entanglement itself, and it isn't varying from pair to pair. So, we can still assume that the entanglement is locally produced at emission.

 

[Sherlock]

Originally Posted by Sherlock
Thus, the statement that Bell test *results* disallow lhv supplements is a bit off. Bell test *setups* disallow lhv supplements -- because such variables as might exist between emitters and detectors are simply not relevant to the results, and including them in the calculation screws it up.

This is definitely not the case. Plenty of experiments have been performed in which the detector settings are changed mid-flight. As a a result, there is no possibility that any kind of equilibrium state (between the emitter and the detector) affects the outcome.

I wasn't talking about any kind of equilibrium state between emitter and detector. Just that the exact properties of each entangled pair will vary somewhat from pair to pair. But this variability will not affect the outcome, as long as the pairs being jointly analyzed are entangled.

Change the joint setting as much as you want while the particles are in flight. It's still that case that for any given pair that's analyzed in a given coincidence interval there is one and only one joint setting that is analyzing the pair -- and a given joint setting that is analyzing entangled pairs will produce a certain predictable rate of coincidental detections.

The point of my statement is that whatever variability there is from pair to pair, this variability isn't relevant to the results. This is one thing that varying the joint analyzer setting randomly while the particles are in flight ensures. But whether the analyzers are varied randomly while the particles are in flight or not, you get the same average results for a given setting -- which is a pretty solid indication that the variable properties of the incident disturbances aren't what is producing the variable results.

So, I take the *entanglement*, per se, as a nonvarying property of the jointly analyzed particles, and then the only variable in the setup is the joint analyzer setting. Hence my statement that the *setup* itself is what disallows a hidden variable supplement to the qm formulation.

 

[vanesch]

It is patently false that EPR+Bell excludes locality. It is also possible that reality is both local and observer dependent (i.e. there is no unit vector c). I am merely stating that QM, per Copenhagen, can be interpreted several different ways and often is.

But nevertheless, it makes us make the rather unconfortable choice between non-locality, and (observed) reality is observer-dependent.
Bohmians (such as, I presume, ttn) and make the first choice, MWIers (like me) make the second choice. Copenhageners do something in between...

 

[vanesch]

Therefore, the application of a hidden variable supplement to the qm formulation is just a *mis*application -- since the variable properties of entangled pairs don't affect the rate of coincidental detection.
The relevant hidden parameter is the entanglement itself, and it isn't varying from pair to pair. So, we can still assume that the entanglement is locally produced at emission.

Yes, of course entanglement is locally produced at emission, that is entirely correct. I'm sorry, and no offense, but I think you never got the "click" of what Bell is all about.
Entanglement is a special kind of state description entirely proper to the formalism of quantum theory, and simply means that the way states of systems are described are, eh, well, entangled, meaning, you cannot disentangle the state description as "the state of A" and "the state of B". I don't know if you realize how revolutionary a concept that is. Never this occurred before in physics. In classical physics, if you have two systems which are in DIFFERENT LOCATIONS, it is always possible to describe the state of the TOTAL SYSTEM as "the state of A" and "the state of B". Of course there can be interactions between these states, and of course these states can have a "common origin" even if they are not interacting, because the systems interacted before.
But "the state of the sun-Betelgeuse system" can always be written as "the state of the sun" and "the state of Betelgeuse". All you can measure about the sun will depend ONLY on "the state of the sun" and all you can measure about Betelgeuse will depend only on "the state of Betelgeuse".
THAT DOESN'T MEAN that there cannot be correlations between both. Indeed, it could be that the sun and Betelgeuse had some interaction long ago, and the correlations of our measurements only measure that "common part" induced by that interaction long ago.
But, as Bell showed, when you have such a separate "this is the state of A" and "this is the state of B" state description EVEN IF THERE WAS A COMMON PART, the correlations you can obtain in such a way have to satisfy certain properties.
This is what is violated in QM. And it is (after the fact) not surprising because the states in QM are NOT of the form "the state of A" and "the state of B". There is only the state of AB.
Again, don't think that this is "simply because they have common origin". Classical systems can have "common origin", but that doesn't deny a reality both to the "state of A" and "the state of B". Measurements on A and B will show statistical correlations, but these correlations WILL SATISFY CERTAIN RULES (like Bell's inequalities). Quantum entanglement goes further and DENIES the existence of a state of A and a state of B.
But people feel uneasy about the fact that there is "no state of A" and "no state of B", and only a "state of AB", because we're used to thinking that what is right here, should have its own 'reality' (state). That's what local reality is all about.
Now it could be that you find it very normal for something NOT to have a state of its own (a reality of its own) just because it is confined to some space. You might have the intuition that "reality is holistic". But it is a very special way of thinking in physics, because VERY MANY USEFUL laws are based upon the locality principle. This is why people like Einstein thought that QM had an UNDERLYING theory which had identical predictions, but which had a (totally different) state description for A and for B. He called those state descriptions "hidden variables".
But Bell's theorem shows that this is not possible.
What is possible is that A and B DO have an individual state description ON THE CONDITION THAT they keep constantly in immediate interaction over long distances. Then, of course, the measurement of one can immediately change the STATE of the other, thus mimicking the quantum result. This is Bohmian mechanics.

 

[DrChinese]

But nevertheless, it makes us make the rather unconfortable choice between non-locality, and (observed) reality is observer-dependent.
Bohmians (such as, I presume, ttn) and make the first choice, MWIers (like me) make the second choice. Copenhageners do something in between...

I hoped you would like my little defense of reality.

I think all the interpretations are uncomfortable at least in some way. And that keeps us on our collective toes!

 

[ZapperZ]

So called "Bell states" are maximally entangled states. Bell inequalities are entanglement 'witnesses'. Violations of Bell inequalities are an indication of the presence of entanglement. Hence, my statement that Bell tests measure entanglement, which, if experimenters have prepared things correctly, is not a *variable* property. The only thing that is varying in the Bell tests (that has anything to do with the outcome) is the joint setting of the polarizers.

Therefore, the application of a hidden variable supplement to the qm formulation is just a *mis*application -- since the variable properties of entangled pairs don't affect the rate of coincidental detection.

The relevant hidden parameter is the entanglement itself, and it isn't varying from pair to pair. So, we can still assume that the entanglement is locally produced at emission.

Then I will await your rebuttal letters to all those experiments that claim that their experiments negate local realism.

Zz.

 

[DrChinese]

Quantum entanglement goes further and DENIES the existence of a state of A and a state of B.

What is possible is that A and B DO have an individual state description ON THE CONDITION THAT they keep constantly in immediate interaction over long distances. Then, of course, the measurement of one can immediately change the STATE of the other, thus mimicking the quantum result. This is Bohmian mechanics.

As you say, a lot of people get tripped up over this point.

If there are non-local hidden variables (in Bell's terms: there is a unit vector c), then there must be a hitherto unknown non-local mechanism in existence as well. After all, you are taking a classical idea - that there are separate A and B systems rather than a combined AB system - and trying to make it give identical predictions to QM. You will need the new hypothetical non-local mechanism to make this happen. Of course, this mechanism must elsewhere be dormant! (Since this mechanism is not explained by QM, QM would necessarily be incomplete if this actually exists. It would also violate special relativity.)

If you believe QM, there is no need (requirement) to postulate Bell's unit vector c. That is because the superposition of states explains it already. So in that limited respect, QM is complete. And since the superposition principle explains everything observed, there is no need for a new non-local mechanism.

(Of course, here I am talking of local and non-local in terms of Bell locality.)

 

[ttn]

I can't really debate what you are saying, as I don't really get your points.

Was something unclear? Or you just don't believe me, despite the logic being clear, or what? I honestly don't understand how you could fail to "get" what I'm saying.

EPR was not about locality: it really isn't discussed and is more a tacit assumption ("... after which time we suppose that there is no longer any interaction between the two parts..."). It was about the completeness of QM. They felt they demonstrated that QM was incomplete. I don't feel they demonstrated that. I feel they DID demonstrate that if QM was complete, then there is not simultaneous reality to non-commuting observables. Do we disagree about this? Or maybe you read the last 2 paragraphs of EPR differently than I do.

Yes, we disagree. First of all, what you are saying makes no sense. "EPR was not about locality... it was about the completeness of QM." The whole point of the EPR argument is to show that ***if*** you assume that QM is complete, the theory violates locality. Completeness entails non-locality.
You say that EPR did succeed in demonstrating that "if QM was complete, then there is not simultaneous reality to non-commuting observables." Do you even understand what you are saying here? There can be no "demonstration" of this statement. It's simply a tautology. The formalism of QM simply doesn't *permit* one to write down a state that attributes simultaneous definite values to non-commuting observables. So if the theory is complete, then those observables really fail to have simultaneous definite values (as opposed to: they have values, but we don't know them).
So, it seems that you think that all EPR proved was an empty tautology -- that if QM is incomplete, then it's incomplete. But that just means you have failed to grasp the actual EPR argument. Now, in your defense, it seems you are overly focused on the EPR paper itself. And that does lead to confusion about this point, because the EPR paper was written by Podolsky and Einstein was rather pissed off about how confusing it was. But we needn't be bothered by any of this, and we needn't remain unnecessarily confused. Einstein made quite clear, many times, later in his life, what the real point of the EPR paper was supposed to have been.

Bell discusses locality explicitly ("... the signal involved must propagate instantaneously" ...), as I say. His primary argument, however, has nothing to do with locality and everything to do with reality (i.e. hidden variables) - that is what the math is all about ("It follows that c is another unit vector..."). After then proving that hidden variables are inconsistent with the predictions of QM, he concludes that hidden variables can only be "rescued" within a non-local theory. Do we disagree on this?

Yes, I don't think you understand Bell's derivation. Look at his paper, "On the EPR Paradox." Right after equation (1) he states openly: "The vital assumption is that the result B ... does not depend on the setting a ... nor A on b." (Check out the footnote, too.) This is the locality assumption. It's only because of the locality assumption that we *forbid* A to depend on b, and vice versa. And without that assumption, the derivation (obviously) does not go through. Bell's inequality is a bound that applies to *local* theories only. So... how you can say "his primary argument...has nothing to do with locality", I have no idea. Again, all I can conclude is that you simply don't understand either EPR or Bell's Theorem. *Both* of these *crucially* involve locality.

It is patently false that EPR+Bell excludes locality.

I can see now how you might think so, since evidently you think that neither EPR or Bell's Theorem has anything to do with locality in the first place!

It is also possible that reality is both local and observer dependent (i.e. there is no unit vector c).

You will have to flesh this out. What, exactly, is "observer dependent"? And please note: if your "observer dependence" includes a dependence of the A-side outcome on the B-side observation, your theory is *nonlocal*. Which means it isn't "both local and observer dependent."
Or was your point that regular old Copenhagen-ish QM is "both local and observer dependent"? That is just patently false. Orthodox QM violates Bell's Locality condition (not the inequality, but the definition of locality that he applies to hidden variable theories in the derivation of the inequality) -- i.e., "regular old Copenhagen QM" is nonlocal. So it isn't an example of a theory that is "local and observer dependent."
In fact, I challenge you to provide any example of a theory that is local, predicts that experiments have definite outcomes, and consistent with the QM predictions. You can include "observer dependence" or anything else you want in the theory as long as it is consistent with Bell Locality. I will be delighted to put my money where my mouth is and make this interesting, if you are game.

 

[ttn]

If there are non-local hidden variables (in Bell's terms: there is a unit vector c), ...

Huh? If you mean the "unit vector c" that appears in Bell's derivation of his inequality, that is not a non-local hidden variable. First off, the lowercase letters in Bell's derivation (in almost all his papers) refer to unit vectors denoting the orientation of Stern-Gerlach devices. The hidden variables are the "lambdas" or, if you prefer (and in the deterministic case), the spin component values A(a,lambda), B(b,lambda), etc.
But my real issue is that, even leaving aside the question of whether you meant lowercase "c" or uppercase "c" or *whatever*, it just doesn't make any sense to talk about non-local hidden variables and cite *anything* from Bell's derivation. The derivation is always talking *exclusively* about *local* theories. If there were non-local hidden variables involved in Bell's derivation of the inequality, it wouldn't exactly be a bound on local hidden variable theories, now would it?

(Since this mechanism is not explained by QM, QM would necessarily be incomplete if this actually exists. It would also violate special relativity.)

But orthodox QM already violates special relativity. The collapse postulate tells us that the quantum state of distant systems can change simultaneously with a nearby measurement. And that "simultaneously" is meaningless according to SR.

If you believe QM, there is no need (requirement) to postulate Bell's unit vector c.

If you believe in locality, you *must* postulate these local hidden variables to account for the correlations.

That is because the superposition of states explains it already. So in that limited respect, QM is complete. And since the superposition principle explains everything observed, there is no need for a new non-local mechanism.

Yes, orthodox QM explains the correlations, but it explains them using a non-local mechanism. The collapse postulate violates relativity.
Of course, you can get around this conclusion if you deny the orthodox completeness doctrine. ...or so it seems until you learn about Bell's Theorem.

 

[DrChinese]

If you believe in locality, you *must* postulate these local hidden variables to account for the correlations.

Yes, orthodox QM explains the correlations, but it explains them using a non-local mechanism. The collapse postulate violates relativity.

I guess I could insult you back, but that wouldn't be nice.

First, assuming "unit vector c" is equivalent to assuming a hidden variable. You can believe in locality and reject the existence of "unit vector c". This is basic logic and is fully compatible with Bell's Theorem. Despite the fact that Bell mentions locality, he did not include it explicitly in his mathematical proof as he did the hidden variable assumption.

Second, QM is as local or non-local as you interpret it to be. This too is basic and why folks argue about Copenhagen vs. Many Worlds vs. Bohmian Mechanics vs. Transactional Interpretation etc. Many scientists feel that QM's collapse postulate is not "non-local" in the sense that no signalling mechanism is violated. So I disagree with you that relativity is violated.

 

[ttn]

I guess I could insult you back, but that wouldn't be nice.

If you think I've misunderstood something, then by all means "insult" me by pointing it out. I won't take it as an insult (as I hope you don't), but as an opportunity to get to the truth on this important issue.

First, assuming "unit vector c" is equivalent to assuming a hidden variable.

Maybe you should clarify your notation, but if it means what I think it means, then you are confused: the unit vector c isn't a hidden variable, it's the direction a certain person measures the spin of a certain particle along. The hidden variable is the "lambda" (Bell's notation) which determines what the *outcome* of that measurement will be.

You can believe in locality and reject the existence of "unit vector c".

Your claim was that the "unit vector c" was a *non-local* hidden variable. Even leaving aside the question of whether it's a hidden variable at all, it isn't non-local. No non-local hidden variables appear in Bell's derivation.

This is basic logic and is fully compatible with Bell's Theorem. Despite the fact that Bell mentions locality, he did not include it explicitly in his mathematical proof as he did the hidden variable assumption.

Look, with all due respect, you have just missed something that is incredibly important. Bell *did* include locality in the proof. See equation (1) of "On the EPR paradox", and the subsequent sentence. Or better yet, see one of his later papers where he makes all of this increasingly clear. I urge you, for example, to read the paper "La nouvelle cuisine" (chapter 24 of the new 2nd edition of Speakable and Unspeakable). Just to give you a taste, here are the titles of the sections from this paper: Introduction, What cannot go faster than light?, Local beables, No signals faster than light, Local commutativity, Who could ask for anything more, Principle of local causality, Ordinary quantum mechanics is not locally causal, Locally explicable correlations, Quantum mechanics cannot be embedded in a locally causal theory, But still we cannot signal faster than light, Conclusion.
Don't you think that suggests that locality was a rather important issue for Bell? But don't believe me -- read the paper.

Second, QM is as local or non-local as you interpret it to be. This too is basic and why folks argue about Copenhagen vs. Many Worlds vs. Bohmian Mechanics vs. Transactional Interpretation etc. Many scientists feel that QM's collapse postulate is not "non-local" in the sense that no signalling mechanism is violated. So I disagree with you that relativity is violated.

I'm sorry, but isn't this just silly naked subjectivism? Would you say that Bohmian Mechanics "is as local or non-local as you interpret it to be"? No way! Bohmian Mechanics is a definite theory, defined by certain equations. If you want to find out if the theory is local or non-local, you just examine the theory carefully and see how it works and assess whether or not it includes non-local physics. There's nothing subjective about this. You don't just close your eyes and inhale incense and wait for a mystical experience to tell you whether it's nonlocal. You just look. And in the case of Bohmian Mechanics, there is no controversy or ambiguity: it's non-local. Specifically, it violates Bell Locality (though it is consistent with "signal locality" -- you can't transmit a message faster than light).
It's the same story with orthodox Copenhagen QM. There's nothing open or unclear. Whether the theory is local or nonlocal isn't a matter of feelings or mystical revelation. You just look at the theory and test: is it consistent with Bell locality? Is it consistent with signal locality? The answers are respectively: no, yes. Same as Bohmian Mechanics. So if you think Bohm's theory violates relativity, you have to think that orthodox QM also violates relativity (on pain of inconsistency). There is nothing to debate here -- just something that needs to be grasped clearly.