What Is an Element of Reality?

[vanesch]

Though true, if you want to derive a general Bell inequality, valid for imperfect detectors, it is necessary, I think, to do as Clauser and Horne (and Bell, in 1971) did and treat the important (type I) components of the HV in a logically different manner from unimportant (type II) ones. The "type I" ones are those such as polarisation direction and signal amplitude that are set at the source and are relevant when the particles reach the analysers. These really do play a logically different role in the experiments from the "type II" components concerned with, for instance, the microstate of the detector. The type I components are responsible for any correlation, while the type II ones are assumed to be independent on the two sides -- just random "noise".
Cat

This is true, but amounts to postulating (again) a deterministic theory. My claim is that the relationship between what is called "Bell locality" (a factorisation condition joint probabilities have to satisfy and from which one can deduce the Bell inequalities) and any kind of "physical locality of interaction" only makes sense in the framework of an essentially deterministic HV theory. It is _that_ deterministic mechanism (hidden or not) which, if required to give rise to probabilities and to be based on local interactions, that gives rise to Bell locality.
But "Bell locality" doesn't make any sense for fundamentally stochastic theories, because there is no supposed hidden mechanism of interaction which is to be local or not. A fundamentally stochastic theory just tells you what are the probabilities for "single events" and for "joint events" (correlations) WITHOUT being generated by an underlying deterministic mechanism.
The only locality condition we can then require is that probabilities of observations can only depend on what is in the past lightcone of those observations, and this then gives:

P(A|a,b,L) can only be function of a because only the setting a is in the past lightcone of event A.
P(B|a,b,L) can only be function of b, because only the setting b is in the past lightcone of event B.

But:
P(A,B|a,b,L) can be function of a and b, because this correlation can only be established when we get news from A AND from B, and at that moment, a and b are in the past lightcone of a and b. Or otherwise formulated: a and b are in the past lightcones of the events A and B.

The first two conditions impose an INTEGRAL condition on the third expression, but do not require that P(A,B) factorizes. That factorization only comes about when P(A,B) is _constructed_ from an underlying deterministic model.

The objection seemed to be: hey, but I can think of hidden variable theories which are _stochastic_. And I tried to point out that that's tricking the audience, because it can trivially be transformed into a deterministic hidden variable theory. BTW, I don't understand what the purpose could be of constructing a truly stochastic hidden variable theory to explain a stochastic "no hidden variable" theory (such as QM).

cheers,
Patrick.

 

[ttn]

This is true, but amounts to postulating (again) a deterministic theory. My claim is that the relationship between what is called "Bell locality" (a factorisation condition joint probabilities have to satisfy and from which one can deduce the Bell inequalities) and any kind of "physical locality of interaction" only makes sense in the framework of an essentially deterministic HV theory. It is _that_ deterministic mechanism (hidden or not) which, if required to give rise to probabilities and to be based on local interactions, that gives rise to Bell locality.
But "Bell locality" doesn't make any sense for fundamentally stochastic theories, because there is no supposed hidden mechanism of interaction which is to be local or not. A fundamentally stochastic theory just tells you what are the probabilities for "single events" and for "joint events" (correlations) WITHOUT being generated by an underlying deterministic mechanism.

I'm sorry, but this really is just playing semantic word games to make the answer appear to come out the way you want. First you define "nonlocality" in terms of "underlying deterministic mechanisms", then you shrug and say: since QM has no such mechanisms, it isn't nonlocal.

The beauty of Bell's locality condition is that it doesn't require any of this loose talk about "underlying mechanisms" and "communication of information" and all these other things that lead to endless debates. And despite what you say above, Bell Locality *does* apply perfectly well to stochastic theories. The condition is, after all, stated exclusively in terms of probabilities, so the applicability is really rather obvious.

The only locality condition we can then require is that probabilities of observations can only depend on what is in the past lightcone of those observations, and this then gives:

P(A|a,b,L) can only be function of a because only the setting a is in the past lightcone of event A.
P(B|a,b,L) can only be function of b, because only the setting b is in the past lightcone of event B.

But:
P(A,B|a,b,L) can be function of a and b, because this correlation can only be established when we get news from A AND from B, and at that moment, a and b are in the past lightcone of a and b. Or otherwise formulated: a and b are in the past lightcones of the events A and B.

Here you are simply forgetting an important rule of probability calculus. I believe it is sometimes called "Bayes theorem" or something to that effect. It says:

P(A,B) = P(A|B) * P(B)

that is, you can *always* write a joint probability as a product so long as you conditionalize one of the probabilities on the other event.

If we are interested in something of the form P(A,B|a,b,L), we may write this as

P(A,B|a,b,L) = P(A|B,a,b,L) * P(B|a,b,L)

But then Bell Locality enters and says:

P(A|B,a,b,L) = P(A|a,L)

and

P(B|a,b,L) = P(B|b,L)

on the grounds of locality: neither event (A or B) may depend stochastically on occurrences outside of their past light cones. Specifically, the probability distribution of events A cannot be affected by conditionalizing on space-like separated events B and b, since we have already conditionalized on a complete description of the world in the past light cone of A, namely L. And likewise for B. There is no determinism built in here, no requirement that the probabilities P(A|a,L), etc., be zero or unity.

Bottom line: Bell Locality *does* completely justify the factorization condition that is (a) required to demonstrate the Bell Theorem and (b) violated by orthodox QM when we identify L with the QM wave function (as surely Bohr invites us to do).

The first two conditions impose an INTEGRAL condition on the third expression, but do not require that P(A,B) factorizes. That factorization only comes about when P(A,B) is _constructed_ from an underlying deterministic model.

No, this is just wrong. I got from the joint probability to the factored, Bell Local expression, by using "Bayes Theorem" (I'm not actually sure it's called that...) and Bell Locality and that's it. No mention of determinism.

 

[vanesch]

P(A,B|a,b,L) = P(A|B,a,b,L) * P(B|a,b,L)

But then Bell Locality enters and says:

P(A|B,a,b,L) = P(A|a,L)

No ! Because B enters in the condition on the left hand side, this may depend upon b. There is no way to talk about "upon condition B" without having information about B. So the conditional probability on the left hand side talks about A and B, and so can depend on a and b. Now, you can *require* that the conditional probability P(A|B) = P(A), in which case you call A and B statistically independent events. But that's a property that you can call "zork" or "Bell beauty" or "Bell locality" or "Bell desire". It isn't required for a stochastic theory that only claims that probabilities of events only depend on conditions in their past lightcones ; THIS is what is required by locality as specified by relativity. From the moment you mention A AND B in a probability (whether joint or conditional), they may depend on everything about A and everything about B.

So, again: QM probabilities do not satisfy "zork"
QM probabilities do satisfy locality as specified by relativity.

However, what I'm trying to make clear as a point, is that IF YOU WANT THOSE PROBABILITIES TO BE GENERATED FROM A DETERMINISTIC THEORY which has hidden variables (that will give you the "stochastic appearance" because of their hidden character) and YOU REQUIRE THAT ALL INTERACTIONS ARE LOCAL including those concerning the change, transfer etc... of the hidden variables, THEN YOU OBTAIN A CONDITION WHICH IS ZORK (also called Bell locality).

And from the zork condition follows the Bell inequality.

You cannot PROVE me the necessity of Bell Locality (which I call zork) without going to a deterministic model (or a pseudo-deterministic model, that can be transformed into a deterministic one by adding variables).
Try to prove me somehow (not DEFINE) that factorization is necessary for locality without using an underlying deterministic model !

However, I can PROVE you the requirement of locality specified by relativity on the basis of information theory. Now, since the concept of locality plays an eminent role only because of relativity, my point is that that is the only sensible requirement for locality given a stochastic theory. We only switch to a more severe one (zork) because we want "extra stuff" such as an underlying deterministic mechanics.

cheers,
Patrick.

 

[vanesch]

Specifically, the probability distribution of events A cannot be affected by conditionalizing on space-like separated events B and b, since we have already conditionalized on a complete description of the world in the past light cone of A, namely L.

It is in this phrase that is catched exactly the deterministic character of an underlying mechanism ! (the "complete description" part)

Why ? Because you seem to claim that "whatever happens to B and whatever choice I make for b, it can not be "signalled " to A. (by the underlying mechanism). But careful: the choice of b will of course affect the result B. So you shouldn't be surprised that P(A|B) can a priori depend on b ; as long as it is done in such a way, that P(A) doesn't depend on b. (that's the integral condition)

So my claim is: P(A|B) does not need to be equal to P(A). I wish you could pove me its necessity. (it is, as you point out, equivalent to factorizing P(A,B) = P(A) P(B) )

But of course if you want to invent a machinery that generates these probabilities, you will have a hard time sending a hidden variable messenger from B to A, and THEN of course, you can claim that any machinery that will determine things at B, as a function of b, can never send a message to A in order to do anything there.

cheers,
Patrick.

 

[ttn]

No ! Because B enters in the condition on the left hand side, this may depend upon b. There is no way to talk about "upon condition B" without having information about B. So the conditional probability on the left hand side talks about A and B, and so can depend on a and b. Now, you can *require* that the conditional probability P(A|B) = P(A), in which case you call A and B statistically independent events. But that's a property that you can call "zork" or "Bell beauty" or "Bell locality" or "Bell desire". It isn't required for a stochastic theory that only claims that probabilities of events only depend on conditions in their past lightcones ; THIS is what is required by locality as specified by relativity. From the moment you mention A AND B in a probability (whether joint or conditional), they may depend on everything about A and everything about B.

So... let me see if I get your position. You are willing to allow that

P(B|a,b,L) = P(B|b,L)

as a perfectly reasonable requirement of locality. But you are unwilling to allow that

P(B|A,b,L) = P(B|b,L)

is a reasonable requirement.

Do I have that straight? You think: Locality forbids the outcome B from depending on the setting (a) of the distant apparatus, but does not forbid B from depending on the *outcome* of that distant measurement (A). Is that it?

Try to prove me somehow (not DEFINE) that factorization is necessary for locality without using an underlying deterministic model !

I'm not sure what kind of thing you would take as a proof. I think Bell Locality is an extremely natural way of expressing the requirement of local causality. Bell thought so too. But there is no way to "prove" this. One has to simply accept it as a way of defining what it means for a theory to be local; then people can choose to accept or reject that definition. What bothers me is when people accept it in regard to hv theories, but reject it in regard to QM. That's just inconsistent.

However, I can PROVE you the requirement of locality specified by relativity on the basis of information theory.

Not really, although surely the statement "humans should never be able to communicate, i.e., transmit information, faster than light" is another somewhat reasonable definition of locality. The problem is, if you are going to define locality that way in order to prove that QM is local, Bohm's theory turns out to be local, too -- despite the fact that, in some *other* senses of "locality", Bohm's theory is rather blatantly *nonlocal*.

Again, I only really care here about consistency. If you're going to define locality in terms of "information", then you shouldn't say that Bohm's theory is nonlocal. And if you're going to define locality as Bell did, then you shouldn't say that orthodox QM is local.

 

[ttn]

It is in this phrase that is catched exactly the deterministic character of an underlying mechanism ! (the "complete description" part)

Why ? Because you seem to claim that "whatever happens to B and whatever choice I make for b, it can not be "signalled " to A. (by the underlying mechanism). But careful: the choice of b will of course affect the result B. So you shouldn't be surprised that P(A|B) can a priori depend on b ; as long as it is done in such a way, that P(A) doesn't depend on b. (that's the integral condition)

I agree with this much: P(B) depends on b. But that's precisely why I find it so silly to argue that locality requires

P(A|B,a,b,L) = P(A|B,a,L)

but not

P(A|B,a,b,L) = P(A|a,L)

If the point is that, in a local theory, P(A|a,L) should not change when you specify the distant setting b, then shouldn't it also not change if you specify the distant outcome B? If you allow the latter sort of dependence, you are in effect smuggling in the previously-eliminated dependence on "b" for just the sort of reason you elaborate above.

So my claim is: P(A|B) does not need to be equal to P(A). I wish you could pove me its necessity. (it is, as you point out, equivalent to factorizing P(A,B) = P(A) P(B) )

Well, I certainly can't prove that P(A|B) = P(A). That would be a preposterous requirement. It would basically just assert that there is no correlation between A and B. But locality doesn't forbid correlations. It merely forbids correlations which cannot be in some way accounted for by information in the past of the two events in question. That is, the condition only makes sense if you conditionalize all probabilities involved on some complete specification of the state of the system at some prior time(slice), and if you add in possible local dependencies on things like apparatus settings:

P(A,B|a,b,L) = P(A|B,a,b,L) * P(B|a,b,L) = P(A|a,L) * P(B|b,L)

where the first equality is pure unobjectionable math, and the second involves application of Bell Locality.

I'm sure you will now say "Aha!" and assert that by "accounted for" above I really mean "deterministically accounted for". But I just don't. I am perfectly happy to allow non-deterministic laws. In fact, that's one of the nice things about this probability-based notation for expressing Bell locality. Some of Bell's papers use a notation like A(a,L) where now A is the (evidently one and only) outcome consistent with setting "a" and prior-joint-state L. That notation does imply determinism, and hence a statement of Bell Locality couched in that language would *not* be able to be applied to orthodox QM (which is stochastic). But a fairly straightforward change of notation gives the statement of Bell Locality we've been discussing, the one that is couched explicitly in stochastic terms and which therefore is entirely applicable to stochastic theories like orthodox QM.

 

[vanesch]

We're getting closer

Not really, although surely the statement "humans should never be able to communicate, i.e., transmit information, faster than light" is another somewhat reasonable definition of locality.

Well, in order to satisfy relativity, replace "humans" by "anything that can send out information" (because that's the relativity paradox you want to avoid: that you receive your own information before sending it ; on which you could base a decision to send out OTHER information, hence the paradox)

The problem is, if you are going to define locality that way in order to prove that QM is local, Bohm's theory turns out to be local, too -- despite the fact that, in some *other* senses of "locality", Bohm's theory is rather blatantly *nonlocal*.

The problem with locality is that the definition is different according to whether you work with a stochastic theory or with a deterministic theory.
In a purely stochastic theory, the only definition we can have concerning locality is of course based upon information theory.
In that sense, QM and of course Bohm's theory considered as a stochatical theory (which gives the same stochastic predictions) is local.

Next, we can talk about the locality of mechanisms, whether or not they lead to a deterministic or stochastic theory ; and in the latter case, independent of whether the stochastic theory is local in the information theory sense.

For instance, the "collapse of the wavefunction" in QM is blatantly non local, because it affects the internal description at B when doing something at A.
However, the MWI approach gives us a local mechanism, in a very subtle way: you can only talk about a correlation when the events at A and B are in the past lightcone and you deny the individual existence of events at A and B until at the moment where you can observe the correlations. At most you can observe one of both.

The *hidden* variables are also subject to a non-local mechanism in Bohm's theory.

Theories which have a non-local mechanism but give rise to a stochastic theory which IS local (in the relativistic sense) are said to "conspire": they have all the gutwork to NOT respect the locality requirement of relativity, but they simply don't take advantage of it. Bohm's theory, and QM in the Copenhagen view are in that case (that's why I don't like them).
MWI QM doesn't have such a non-local mechanism

Of course a stochastic theory without any underlying mechanism cannot be analysed for their underlying mechanism!

What's now the room for Bell Locality ? It turns out that any stochastic theory generated by a deterministic theory which respects a local mechanism, satisfies Bell locality.

Amen.

cheers,
Patrick.

 

[selfAdjoint]

Theories which have a non-local mechanism but give rise to a stochastic theory which IS local (in the relativistic sense) are said to "conspire": they have all the gutwork to NOT respect the locality requirement of relativity, but they simply don't take advantage of it. Bohm's theory, and QM in the Copenhagen view are in that case (that's why I don't like them).
MWI QM doesn't have such a non-local mechanism

Two questions on this. First, do you have any links to discussions where this technical term "conspire" is introduced? And second, does this resolution of nonlocality exist in the weaker relative interpretation of MWI or do you require the literal multiple worlds?

 

[vanesch]

Two questions on this. First, do you have any links to discussions where this technical term "conspire" is introduced? And second, does this resolution of nonlocality exist in the weaker relative interpretation of MWI or do you require the literal multiple worlds?

I have to say that I use the term "conspire" as I intuitively thought it was typically used, namely that a strict principle should be obeyed, but that the underlying mechanism (whatever it is) doesn't obey it, but in such a way that it doesn't show. I don't know if there is a rigorous definition for the term.
An example that comes to mind is the "naive" QFT mass-energy of the 1/2 hbar omega terms (which is HUGE) and a corresponding cosmological constant which happens to exactly (or almost so) compensate this. So, or there is a principle that says that the effective cosmological constant must be small, or there is a "conspiracy" so that these two unconstrained contributions cancel.

Concerning your second point, I guess one can discuss about it, depending on exactly what one defines as a "local mechanism". If it is sufficient to say that the correlations only make sense to an observer when the corresponding events are already in the past lightcone, such as is the case in _any_ MWI like scheme, then I would think that that is sufficient to call the mechanism "local". If, however, you require a totally local state description, then there is a problem with the Schroedinger picture, where there is one, holistic wavefunction of the universe. However, Rubin has written a few articles showing that - if I understood it well - you can get rid of that problem in the Heisenberg picture. The price to pay is that you carry with you a lot of indices which indicate your whole "entanglement history". But you carry them with you at sub lightspeed.

I may have used words and definitions in my arguments here which are not 100% correct. The whole thing is of course discussable, but the intuition - to me - is clear: local means: there's no obvious way you see how to use the mechanism to make an FTL phone. Non-local means: highly suggestive of how to make an FTL phone.
The projection postulate collapses wave functions at a distance. You would think immediately that somehow you can exploit that ! It is only after doing some calculations that you find out that you can't.
We know that the stochastic predictions of QM do not allow you to make an FTL phone. That's good enough for me to call it a "local" theory. But the underlying wheels and gears can or cannot suggest that FTL phones are possible (even if we know, at the end of the day, that they aren't). In such cases, I call the mechanism "non-local".

cheers,
Patrick.

 

[DrChinese]

[/INDENT]
I had a look at this and was shocked to find that they said they'd infringed the CHSH inequality but did not even mention the main "loophole" that bugs this -- the "fair sampling" one. Of course, if their detecters were perfect then it would have been irrelevant, but since it was an ordinary optical experiment this cannot have been so.

How can they justify quoting the results of this test without so much as a mention of the efficiencies involved? They say their results "cannot be described by a local realist model". If they have not closed the detection loophole they have not proved this!

Cat

Per the Rowe et al citation previously given, a lot of folks think this "loophole" is closed. Once the rest of us close a loophole, it is not necessary to repeat something that no longer applies. They also don't mention what day of the week the test was performed on because that doesn't matter either.

On the other hand, there are "certain" local realists out there who deny nearly every aspect (pun intended) of Bell tests. Some of us have come to the conclusion that a debate on the matter is a waste of time and effort.

BTW, I don't have a subscription to PRL. I could not find a link anywhere to the Walther article. Anyone find such?

 

[vanesch]

If the point is that, in a local theory, P(A|a,L) should not change when you specify the distant setting b, then shouldn't it also not change if you specify the distant outcome B?

I would like to add something here. Note that these discussions help me too clearing up my ideas, I hope it is also your case ! It brings up things I didn't think about before.

So the point you raise is an interesting one, and probably comes from the fact that I consider A and B as "coming out of the system" while a and b are input, because somehow "arbitrary determined by free will at A and B". So "a" and "b" are sources of information, while A and B are information receivers.
A is a local receiver at a, so if any statistic of A would depend on b, I would have an information channel. But in order for A|B to be an information channel, I have to know A and B, so in any way I have to solve another communication problem between A and B. At that moment I shouldn't have difficulties using sources from a and b.

There is a difference in meaning between P(A|B ; a,b,...) and P(A ; B, a, b...)
The first one is a probability that is defined as P(A,B)/P(B), so it is a derived quantity from the correlation function P(A,B). The second one has no meaning, because B is an event, and no parameter describing the distribution, as are a and b.

P(A,B)/P(B) has the frequentist interpretation of "the relative frequency of the events A in the subsample where we had B". A priori, it is somehow clear to me that this can depend on all that has to do with A and with B, because in order to _measure_ this quantity I have to have a coincidence counter, wired up with A and with B.

cheers,
Patrick.

 

[Haelfix]

I don't quite agree, there are several loopholes to Bell's theorem that are known. Usually they are easily dismissed by contriving a counter example that exploits local symmetry principles (isospin and things like that). However it could be the case that those local symmetries are broken at fundamental levels (see Planckian regimes). T'Hooft and several String theorists (Vafa etc) have exploited this in devising hidden variable theories that gets by the usual objections. The former has to resort to information loss, the latter in general through quasi local variables found in stringy physics.

The usual problem there is retrieving completely unbroken unitarity and managing to get a bounded hamiltonian.

All those programs have amounted to more or less zero, as the dynamics of any such theory is atrociously complicated, but the idea or possibility is there.

 

[Cat]

Note that these discussions help me too clearing up my ideas, I hope it is also your case ! It brings up things I didn't think about before.

Me too!

One thing I've been thinking about is how much easier life would be if one simply accepted the two sides as being independent (once L is fixed) and treated the matter of their coincidence probability just as you would treat the problem of achieving two 6's, say, with a pair of dice. With dice, it surely would not occur to you to do the operation in two stages, using conditional probabilities? You'd simply multiply the two separate probabilities.

I've begun to work on an analogy based on this idea. I don't think the actual Bell test experiments can be modeled without making some allowance for the geometry -- the fact that we are dealing with angles, so that the addition of 2 pi to every "setting" makes no difference. Instead of a dice we'd need one of those little hexagonal tops, with the sectors numbered consecutively. The "hidden variables" might be little weights attached to particular segments (the same for each -- it makes things easier and does not affect the final logic to assume the same rather than "opposite" or "orthogonal") and the "detector settings" could correspond to specified ranges of results. We could have, for example, (1 or 2) scoring + for A, while (2 or 3) scores + for B. If the little weight is fixed at 2, we can have a fully deterministic experiment if is it so heavy that the tops always stops at 2 ... [to be continued]

Cat

 

[ttn]

Well, in order to satisfy relativity, replace "humans" by "anything that can send out information" (because that's the relativity paradox you want to avoid: that you receive your own information before sending it ; on which you could base a decision to send out OTHER information, hence the paradox)

As I said before, there is something to be gained from analyzing "locality" in terms of information transfer. But it is also a dangerous game, mostly because "information" is a dangerously fuzzy, human-centered concept. Here's is Bell's comment:

"Do we then have to fall back on 'no signalling faster than light' as the expression of the fundamental causal structure of contemporary theoretical physics? That is hard for me to accept. For one thing we have lost the idea that correlations can be explained, or at least this idea awaits reformulation. More importantly, the 'no signalling' notion rests on concepts which are desperately vague, or vaguely applicable. The assertion that 'we cannot signal faster than light' immediately provokes the question:
Who do we think *we* are?
*We* who can make 'measurements,' *we* who can manipulate 'external fields', *we* who can 'signal' at all, even if not faster than light? Do *we* include chemists, or only physicists, plants, or only animals, pocket calculators, or only mainframe computers?"

I'm sure you get the point. Bohmian mechanics is, yet again, a clarifying example here. Part of Bell's point, surely, is that what relativity really requires, if you are going to take it seriously, is *more* than a mere no-signalling condition. *That's* why people are unwilling to accept Bohm's theory as consistent with relativity, even though it too doesn't permit signalling -- the behind-the-scenes nonlocality is just too obvious. But then, exactly the same thing is true in orthodox QM. If you take the wf seriously as a complete description of reality, the collapse of the wf is just as nonlocal as anything in Bohm's theory. And both violate the cleanly-formulated "Bell Locality" test.

The problem with locality is that the definition is different according to whether you work with a stochastic theory or with a deterministic theory.
In a purely stochastic theory, the only definition we can have concerning locality is of course based upon information theory.
In that sense, QM and of course Bohm's theory considered as a stochatical theory (which gives the same stochastic predictions) is local.

I still don't understand why you think there's an important distinction here. I thought of a perhaps clarifying example to discuss, though maybe you beat me to the punch with your comment about Bohm's theory "considered as a stochastical theory". But I don't understand exactly what you're getting at there, so I'll throw my example out and see what happens.

Consider Bohm's theory: Sch's equation plus a "guidance formula" specifying particle velocities in terms of the wf. Now add a small random noise term to the guidance formula -- on average, particles will still go where Bohm's theory says they should, only now they'll occasionally deviate by just a little bit. This noise is meant to be completely random (but Gaussian about zero and pretty narrow so it keeps deviations from well-tested QM predictions below the level at which they could be detected). Make sense?

The question is: for this modified Bohm theory, does anything really change in regard to its locality? The theory is now fundamentally stochastic instead of deterministic. Yet it seems to still blatantly violate our notions of local causality -- in particular, the particle velocities still depend on the simultaneous positions of other (entangled) particles. So the theory will still violate "Bell Locality" and I think anyone who looked at it would have no trouble seeing that it was (in pretty much any sense other than "signalling") quite blatantly nonlocal.

Do you agree that this would be an example of a stochastic theory to which the notion of Bell Locality is perfectly applicable?

Next, we can talk about the locality of mechanisms, whether or not they lead to a deterministic or stochastic theory ; and in the latter case, independent of whether the stochastic theory is local in the information theory sense.

Sure, you can talk about that. But when you come to QM, you'll end up playing the same semantic games as before, I suspect. QM has no underlying mechanism (I suspect you'll want to say), hence there is no nonlocality in its underlying mechanism.

But this is just trading on fuzziness over what is meant by "mechanism". Sure, QM lacks a clear detailed ontology that allows you to understand what's going on behind the scenes, i.e., you might say, it lacks a mechanism. But in another sense, QM is perfectly clear. It says: there is nothing going on behind the scenes; the wf is the whole story, a complete description of the state of a system at any moment. And when you make a measurement, the wf -- i.e., the state of the system -- suddenly and randomly jumps into an eigenstate of the operator measured.

My question is: why not just take QM at its word and accept *this* as its mechanism?? It is, after all, what QM says the mechanism is! I mean, it's a pretty strange and fuzzy and non-mechanical mechanism, but if that bothers you you should reject the story on that grounds, not turn it into a point in QM's favor, a get-out-of-jail-free card.

For instance, the "collapse of the wavefunction" in QM is blatantly non local, because it affects the internal description at B when doing something at A.
However, the MWI approach gives us a local mechanism, in a very subtle way: you can only talk about a correlation when the events at A and B are in the past lightcone and you deny the individual existence of events at A and B until at the moment where you can observe the correlations. At most you can observe one of both.

Yes, according to your MWI, the only things that really exist are in your mind -- so in fact there aren't any spatially separated physical objects to interact nonlocally (or locally for that matter) in the first place. So, um, sure, I guess that counts as local.

The *hidden* variables are also subject to a non-local mechanism in Bohm's theory.

No doubt. As shown most cleanly by the fact that Bohm's theory violates Bell Locality. (See? Bell Locality really is a nice litmus test for whether a theory is "locally causal." Bohm's theory isn't.) But then, as you're probably all tired of hearing me say, orthodox QM violates Bell Locality too.

Theories which have a non-local mechanism but give rise to a stochastic theory which IS local (in the relativistic sense) are said to "conspire": they have all the gutwork to NOT respect the locality requirement of relativity, but they simply don't take advantage of it. Bohm's theory, and QM in the Copenhagen view are in that case (that's why I don't like them).
MWI QM doesn't have such a non-local mechanism

OK, I think we're in agreement here. Bohm's theory and orthodox QM both "conspire" in some sense -- there is a non-local mechanism which is somehow washed out by uncertainty or randomness to prevent that nonlocal mechanism from being used to transmit information.

Of course a stochastic theory without any underlying mechanism cannot be analysed for their underlying mechanism!

But you can still ask if such a theory violates Bell Locality.

Perhaps it's the word "underlying" that is causing (err, spontaneously and inexplicably correlating with?) trouble. In Bohm's theory, there is a pretty clear distinction of "levels" between the level of prediction and the "underlying" level of definite particle trajectories, etc. In QM, the level of prediction and the level of "exact and complete specification of the state of the world" are pretty much one and the same. But again, it's just cheap semantics to insist on a clean difference between two levels, in order to then dismiss Bell Locality as inapplicable to (say) QM on the grounds that it has no "underlying" levels. Bell Locality is stated/defined in terms of an "exact and complete specification of the state of the system" -- the thing we've been calling "L" that all the relevant probabilities are conditioned on. There is no requirement that that "L" be "underlying" or anything like that. So again, I would advocate just taking QM straight (e.g., letting the wf play the role of "L"), and taking Bell Locality straight. Don't twist words and make subtle distinctions that are not made in or required by these ideas.

Then you won't have to worry about distractions like deterministic vs. stochastic and "underlying".

 

[Cat]

... Bell Locality is stated/defined in terms of an "exact and complete specification of the state of the system" -- the thing we've been calling "L" that all the relevant probabilities are conditioned on. There is no requirement that that "L" be "underlying" or anything like that. So again, I would advocate just taking QM straight (e.g., letting the wf play the role of "L"), and taking Bell Locality straight. Don't twist words and make subtle distinctions that are not made in or required by these ideas.

That won't quite work, though, since the wave function applies to an ensemble of particles and L applies to one particular one (or, in our case, two, both having arisen from the one source in state L).

Then you won't have to worry about distractions like deterministic vs. stochastic and "underlying".

To continue my analogy, this little hexagonal top can be made either fully deterministic (if the biasing weight is heavy) or stochastic, if it is lighter. Attaching the weight at the "2" position may, if it is heavy, cause the top always to come to rest with the 2 down, but if it is light then it will merely cause bias, the degree depending on the actual weight. There will be the highest probality of a 2, lesser chance of a 1 or 3, and very little chance of the other scores.

And clearly if we have two such tops, coming from the same factory and with the same fault but spun independently, and define detector settings as I suggested, we have your "Bell locality" and can multiply the individual probabilities of success to get the joint probability.

If I persevere, I think I'll be able to demonstrate that the "coincidences" don't form a "fair sample" ... I'll have to define what I mean by '-' results, though, as well as '+':

If, as in the previous message, the values 1 or 2 count as '+' for A, then the opposite sectors (which will be 4 and 5, since we number them sequentially) I define as counting '-'. Under this scheme, if I've got it right, when B is set "parallel" to A (i.e. it also scores either + or - when the top lands with 1, 2, 4 or 5 down, but fails to score anything when it lands on 3 or 6), you get a lot more coincidences than when they are set one unit apart (effectively the only other option in this simple scheme). In the deterministic version, there would (I think) be twice as many coincidences in the parallel case as compared to other orientations.

Perhaps I'm getting carried away, though!

Questions:

(a) Is the variation of coincidence probability in itself sufficient to show that we have not got a fair sample?

(b) Is this a convincing analogy for a Bell setup?

(c) Can we squeeze a "Bell inequality" out of it that can be compared with any QM prediction?

Ah well, probably not, so the exercise was a waste of time from that point of view. I think it might be helpful, though, for illustrating stochastic v deterministic models and for helping us to escape from the use of conditional probabilities.

Cat

 

[ttn]

That won't quite work, though, since the wave function applies to an ensemble of particles and L applies to one particular one (or, in our case, two, both having arisen from the one source in state L).

Well, it's true that identifying Bell's "L" with the QM wf requires the assumption that the QM wf is a complete description of the relevant part of the world. So when I say things like "QM violates Bell Locality" what I mean is "QM, so long as one accepts Bohr's completeness doctrine and hence regards the wf as a complete description of a system, violates Bell Locality."

If, on the other hand, one wishes to reject the completeness assumption and regard psi as merely an average or collective description of an ensemble of similar but not identical systems, then you're right, this identification doesn't work. Two things follow: 1, one needs a *different* (and in fact much less trivial) argument to show that a hidden variable theory (i.e., the kind of theory one is led to when one rejects completeness) must also violate Bell Locality. This argument is of course Bell's theorem. and 2, EPR were exactly correct. They didn't prove that QM was incomplete, and they didn't prove that it violated locality; but they did prove it was *either* nonlocal or incomplete.

(b) Is this a convincing analogy for a Bell setup?

(c) Can we squeeze a "Bell inequality" out of it that can be compared with any QM prediction?

I don't think so. The results of two dice rolls will always be statistically independent unless there is some "mechanism" by which the result of one roll can affect the result of the other. Merely making one or the other "biased" in some way isn't at all the same as "linking" them. So, as long as they are independent, you will never find that the correlations violate a Bell inequality.

 

[vanesch]

I still don't understand why you think there's an important distinction here. I thought of a perhaps clarifying example to discuss, though maybe you beat me to the punch with your comment about Bohm's theory "considered as a stochastical theory". But I don't understand exactly what you're getting at there, so I'll throw my example out and see what happens.

A quick reaction (I don't have much time right now): I may have expressed myself badly, conducting you in misunderstanding what I tried to say.

When I say "Bohm's theory considered as a stochastic theory" I mean Bohm's theory, as a black box, out of which come probabilities for observation P(A), P(A,B) etc... I didn't mean "turn Bohm into a stochastic theory". It IS, at the end of the day, exactly the same stochastic theory as quantum theory (also seen as a black box out of which come probabilities P(A), P(A,B)...) or so I understood, if it is 100% equivalent.

Any qualifier based upon the probabilities must then be of course exactly the same for both theories. For example I call them "relativistically local" and you call them Bell-non-local. We agree upon that point.

To me, a stochastic theory is a black box out of which come prescriptions for calculating probabilities of events. Nothing is said about how these probabilities come about.

So, given the "description of the experiment", we have the function:
P(A,B ; a, b)
(out of which all other probabilities can be derived).
Note that we cannot include an explicit "state description" in these probabilities, because it is inside the black box. The only thing we can specify is the "description of the experiment": a laser beam here, a PDC xtal there, etce... You already see a difficulty in specifying "Bell Locality" here without "opening the black box", but I have no problem defining my "relativity locality".

We can now open the black box and look at the formalism that gives us these probabilities. If somehow it is assumed that parts of the formalism correspond to a physical reality, then we have a MECHANISM.
It can also be that the formalism does not correspond to something describing a physical reality. In that case the black box remains black. Some people see QM as such. There's nothing to say something against it (except that it is a bit deceiving for a physical theory).

A deterministic theory gives us an underlying mechanics, such that, if we were to know all the internal degrees of freedom, only probabilities 1 and 0 would come out.
There are different ways to make shortcuts here: we can use these internal degrees of freedom to specify non-trivial probability distributions, and we can "hide" internal degrees of freedom. If we hide internal degrees of freedom, then we can always ADD others to generate the non-trivial probability distributions. So I do not see what is the point in making non-deterministic hidden-variable theories, because they are always equivalent to another, deterministic one.
However, there are good reasons to have non-hidden variable stochastic theories with a mechanism. In fact our big black box then becomes a structure containing "smaller black boxes" which are by themselves generators of probabilities without any underlying mechanism. Quantum theory, with a physical interpretation of the wave function, is in that case.

The locality or non-locality of a mechanism is harder to define in all generality because of the variety of mechanisms. But if something "happening here" does something to the physical description "over there" then it is non-local.
As you point out, the collapse of the wave function in Copenhagen QM is non-local if you attach a physical reality to the wavefunction. Also the HV in Bohm is non-local if you attach a physical reality to the HV (and honestly, what's the point of introducing HV if you do not attach a physical reality to them ?)

cheers,
patrick.

 

[ttn]

When I say "Bohm's theory considered as a stochastic theory" I mean Bohm's theory, as a black box, out of which come probabilities for observation P(A), P(A,B) etc... I didn't mean "turn Bohm into a stochastic theory". It IS, at the end of the day, exactly the same stochastic theory as quantum theory (also seen as a black box out of which come probabilities P(A), P(A,B)...) or so I understood, if it is 100% equivalent.

Any qualifier based upon the probabilities must then be of course exactly the same for both theories. For example I call them "relativistically local" and you call them Bell-non-local. We agree upon that point.

Yup.

To me, a stochastic theory is a black box out of which come prescriptions for calculating probabilities of events. Nothing is said about how these probabilities come about.

So, given the "description of the experiment", we have the function:
P(A,B ; a, b)
(out of which all other probabilities can be derived).
Note that we cannot include an explicit "state description" in these probabilities, because it is inside the black box. The only thing we can specify is the "description of the experiment": a laser beam here, a PDC xtal there, etc... You already see a difficulty in specifying "Bell Locality" here without "opening the black box", but I have no problem defining my "relativity locality".

I don't think this is right. You say you treat the theory as a black box and that there's really no way to include an explicit 'state description' in the probabilities. But surely you know that you must do that, in QM, in order for the probabilities to be defined. You don't/can't just calculate "P(A,B|a,b)" in QM -- rather, you calculate P(A,B|a,b,psi). If nobody tells you what state the system is prepared in, there is no way to predict using QM what the probabilities of various measurement outcomes are. QM may be a black box, but it isn't as much of one as you imply here. It *does* contain "state descriptions" and these play an absolutely essential role in its abililty to predict (probabilities for) outcomes of experiments.

We can now open the black box and look at the formalism that gives us these probabilities. If somehow it is assumed that parts of the formalism correspond to a physical reality, then we have a MECHANISM.
It can also be that the formalism does not correspond to something describing a physical reality. In that case the black box remains black. Some people see QM as such. There's nothing to say something against it (except that it is a bit deceiving for a physical theory).

I thought what I said against it before was pretty good.

EPR asked: Can the quantum-mechanical description of reality be considered complete? They said no, Bohr said yes. I don't think there was any debate about whether quantum state descriptions refer to something in reality (though nowadays one can find people arguing for any nonsense, even this). What does the completeness doctrine even *mean*, if it isn't that the wave function alone provides a complete description of reality?

So in the sense you are talking about "mechanisms" in the above paragraph, QM has just as much mechanism as Bohm's theory. They both claim to provide a complete picture of what is real at any given moment. And on that basis they have some rule for calculating probabilities of various things.

So again I see no fundamental difference. Both the mechanisms violate Bell Locality, yet this underlying nonlocal causality is washed out by uncertainty (in the case of Bohm) and irreducible indeterminism (in the case of QM) at the level of measurement results, thus preventing its being used for superluminal telephones.

There are different ways to make shortcuts here: we can use these internal degrees of freedom to specify non-trivial probability distributions, and we can "hide" internal degrees of freedom. If we hide internal degrees of freedom, then we can always ADD others to generate the non-trivial probability distributions. So I do not see what is the point in making non-deterministic hidden-variable theories, because they are always equivalent to another, deterministic one.

Maybe you're right; I'm not sure. But your point is only that it would be silly to construct a stochastic hv theory, not that it is really impossible in principle. But I wasn't seriously advocating that one ought to construct such a theory; I was just pointing out that it was possible to build one, and that the mere addition of randomness in the theory doesn't in any way preclude one from identifying the resulting theory as nonlocal.

However, there are good reasons to have non-hidden variable stochastic theories with a mechanism. In fact our big black box then becomes a structure containing "smaller black boxes" which are by themselves generators of probabilities without any underlying mechanism. Quantum theory, with a physical interpretation of the wave function, is in that case.

Is there a quantum theory without a physical interpretation of the wf? I know people (e.g., the Fuchs and Peres "opinion" article that appeared in Physics Today a few years ago) talk about the wf as purely/merely epistemological, but this is blatantly in contradiction with the completeness doctrine (that such people also tend to advocate), isn't it?

The locality or non-locality of a mechanism is harder to define in all generality because of the variety of mechanisms. But if something "happening here" does something to the physical description "over there" then it is non-local.
As you point out, the collapse of the wave function in Copenhagen QM is non-local if you attach a physical reality to the wavefunction.

Precisely. And if you don't "attach a physical reality to the wf" -- i.e., if you think the wf represents mere knowledge of some state that is, in physical reality, perfectly definite -- then you have abandoned completeness. And that means you believe in a hidden variable theory instead of QM. And that means (because of Bell's theorem) that you haven't successfully gotten around quantum nonlocality! ...which is really the point I want to stress: the choice between orthodox QM and (say) Bohmian mechanics is a choice between two equally-nonlocal theories. The nonlocality cannot be escaped, and is hence no reason to support QM as against Bohm.

Also the HV in Bohm is non-local if you attach a physical reality to the HV (and honestly, what's the point of introducing HV if you do not attach a physical reality to them ?)

I certainly can't think of any!

 

[vanesch]

I don't think this is right. You say you treat the theory as a black box and that there's really no way to include an explicit 'state description' in the probabilities. But surely you know that you must do that, in QM, in order for the probabilities to be defined. You don't/can't just calculate "P(A,B|a,b)" in QM -- rather, you calculate P(A,B|a,b,psi). If nobody tells you what state the system is prepared in, there is no way to predict using QM what the probabilities of various measurement outcomes are. QM may be a black box, but it isn't as much of one as you imply here. It *does* contain "state descriptions" and these play an absolutely essential role in its abililty to predict (probabilities for) outcomes of experiments.

Ah, I think the real issue here is the term "completeness" ,and not "locality". I have to say I don't know what it means, except "a potentially deterministic underlying mechanics".
Because what stops me from giving the precise description of the experiment as "complete" ? A laser here, a PDC there etc... In "complete" I include everything I'm potentially allowed to know, but I don't include things that I cannot, in principle, know, such as hidden variables. You can write it down on 20 pages of text, but the quantummechanical wavefunction does exactly that: it is the unique state of which I'm supposed to know everything I can know (complete set of commuting observables determine it).

If out of such a description comes still a series of probabilities, different from 0 or 1, I call such a theory fundamentally stochastic, because there is no way, in principle, to reduce the randomness here. But *this* seems to be what one objects to when one requires "completeness".

EPR asked: Can the quantum-mechanical description of reality be considered complete? They said no, Bohr said yes. I don't think there was any debate about whether quantum state descriptions refer to something in reality (though nowadays one can find people arguing for any nonsense, even this). What does the completeness doctrine even *mean*, if it isn't that the wave function alone provides a complete description of reality?

Yes, I agree that the wavefunction is supposed to give a complete description of reality in QM. Such as would be those 20 pages of text describing in detail the experimental setup. The wavefunction is the translation, in the mathematical formalism, of those 20 pages.

You are free to say that that 20 page text is "an element of reality". Personally, I also think that there must be something "real" to it (and hence want to tell a story = interpretation), but many people just see it as a "generator of statistics". In that view, I don't know how you apply Bell locality for example, because obviously:

P(A,B| a, b, 20 pages) is not equal to P(A|a, 20 pages) x P(B|b, 20 pages)

Indeed, that wouldn't even allow you to have classical correlations! Nevertheless those 20 pages are a full, complete description of what we are supposed to know about the experiment.

So in the sense you are talking about "mechanisms" in the above paragraph, QM has just as much mechanism as Bohm's theory. They both claim to provide a complete picture of what is real at any given moment. And on that basis they have some rule for calculating probabilities of various things.

So again I see no fundamental difference. Both the mechanisms violate Bell Locality, yet this underlying nonlocal causality is washed out by uncertainty (in the case of Bohm) and irreducible indeterminism (in the case of QM) at the level of measurement results, thus preventing its being used for superluminal telephones.

Well, what I wanted to show, in an MWI story that goes with QM, is that there is no underlying nonlocal causal mechanism. There is maybe a kind of "holistic description" (such as the wavefunction of the universe), but it is the OBSERVER which, on each of his observations, has to make a choice between branches (and hence introduces the apparent randomness in his observations). As the observer is essentially "local" to itself, there is no way for him to influence what so ever remotely. If he travels from A to B, then first he only knows about A, and so determines a probability P(A) at that moment and "registers" the entanglement branch which he chose, but B is "still in the air", in that the measurement apparatus at B just got into entanglement with B and is in the two possible states it can be. It is only when that event B gets in the past lightcone of the observer that he has a chance of reading the apparatus, meaning looking at THAT branch of the apparatus which corresponds to his registering of his branch at A. Now OR the apparatus is in a pointer state (which means that we had equal settings a and b), or the apparatus is still in a superposition within that branch, upon which he makes again a choice, and now registers again a second branching.

It is important to notice that nothing "happened" to the apparatus, or B in all these cases. It is just the *observer* who made choices. And when you look at it this way, you're NOT tempted to make FTL phones. You maybe also see my insistance upon the fact that P(A,B) shouldn't be constrained so as to be factorisable: indeed, at the moment where P(A,B) makes sense, namely when the observer has to make his choice for the result of B, he has already everything in his pocket about A and now about B.

Maybe you're right; I'm not sure. But your point is only that it would be silly to construct a stochastic hv theory, not that it is really impossible in principle. But I wasn't seriously advocating that one ought to construct such a theory; I was just pointing out that it was possible to build one, and that the mere addition of randomness in the theory doesn't in any way preclude one from identifying the resulting theory as nonlocal.

As I said, a stochastic theory CAN have structure, and then you can analyse that structure for locality. But you can, if you wish, just see it as a generator of statistics too.
I don't see the point however, to go and postulate hidden variables (that by itself is ugly, no ?) and to keep randomness. The original reason for introducing hidden variables was, I thought, to _explain_ randomness.
But of course you're free to do so.

Is there a quantum theory without a physical interpretation of the wf? I know people (e.g., the Fuchs and Peres "opinion" article that appeared in Physics Today a few years ago) talk about the wf as purely/merely epistemological, but this is blatantly in contradiction with the completeness doctrine (that such people also tend to advocate), isn't it?

Precisely. And if you don't "attach a physical reality to the wf" -- i.e., if you think the wf represents mere knowledge of some state that is, in physical reality, perfectly definite -- then you have abandoned completeness. And that means you believe in a hidden variable theory instead of QM. And that means (because of Bell's theorem) that you haven't successfully gotten around quantum nonlocality! ...which is really the point I want to stress: the choice between orthodox QM and (say) Bohmian mechanics is a choice between two equally-nonlocal theories. The nonlocality cannot be escaped, and is hence no reason to support QM as against Bohm.

Ah, this "completeness" looks more and more to be a "realist" condition.
And yes, QM in a MWI like setting is not very "realist" in that observations are not determining the external world, but the state of the observer in relationship to the external world (which is vastly more complex: we have ONE TERM in the wavefunction given by our observations, while they all "exist", whatever that may mean).

So it seems that the vague term (to me) is not locality but "completeness"...
I would naively think that a theory is "complete" if we can get out of it, as predictive properties (if it is stochastic: in the information - theoretic way) the maximum that we are fundamentally allowed to get out, so that you cannot do any better.
In that sense, I don't know how "completeness" of QM has anything to do with whether we consider the wavefunction as real. And Bohm and QM are the of course equally complete because they give us, as black boxes, the same probability functions upon the parameters we're allowed to choose freely, namely P(A,B ; a,b).
In Einstein's view, of course, there couldn't be any stochastic theory, so a complete theory, to him, had to mean a deterministic theory (and yes, then all probabilities are 0 or 1 and hence you get more information out ; but you then have the problem that the hidden variables cannot be hidden for ever).

But apparently, completeness means now something totally different, so can you enlighten me ?

cheers,
Patrick.

 

[vanesch]

P(A,B| a, b, 20 pages) is not equal to P(A|a, 20 pages) x P(B|b, 20 pages)

Indeed, that wouldn't even allow you to have classical correlations! Nevertheless those 20 pages are a full, complete description of what we are supposed to know about the experiment.

I would like to elaborate a bit more on this. I"ll try to give an example illustrating what is so different between a stochastic theory and a deterministic one. It hasn't got anything to do with EPR or QM, but I would like to "attack Bell locality".

Imagine that I have a system which sends two little balls to each detector ; upon emission they are blue, but due to an inherent reaction inside, they turn red or they turn black. Imagine now that it is IN PRINCIPLE impossible to know the details of this inherent reaction. You have to accept such a possibility in the framework of a stochastic theory ; however, in a deterministic theory you can object: indeed, something inside must "know" if the ball turns black or red.

But assuming that this is purely stochastic, this "inside" is not part of a complete description, because you have no access to it. The complete description is simply that out of the experiment come two blue balls. There is nothing more I can say. Those balls have been analysed in all possible ways, they turn out to be identical. There is no measurement I can perform to show me which ball will turn out to become black, and which one will become red.

Imagine now that my theory is such that this predicts that of two blue balls generated, one always turns red, and the other black. We don't know why, and it is simply in principle impossible to know why, but it is so. A basic axiom of my theory is that a generator of 2 blue balls always has one that turns black and the other turn red.
Then I have P(A,B ; 2 blue balls) has the following values (A = black or red, B = black or red).

P(black,black ; 2 blue balls) = 0
P(red, red ; 2 blue balls) = 0
P(black, red ; 2 blue balls) = 0.5
P(red, black ; 2 blue balls) = 0.5

P(A = black ; 2 blue balls) = P(A = red ; 2 blue balls) = P(B = black ; 2 blue balls) = P(B = red ; 2 blue balls) = 0.5

Clearly "2 blue balls" is a complete description of the setup in that I cannot know more.
Clearly, P(A,B) is not equal to P(A) x P(B)

And I didn't introduce any non-local mechanism !

There is no issue about relativistic locality, because there wasn't even a free choice that could send information !

So where does Bell locality indicate non-locality ?

Aren't you tempted to say that "there must be an underlying (deterministic?) mechanism that should show me what ball will turn red ?" But if no such mechanism is postulated, how do we conclude about non-locality ?

cheers,
Patrick.

 

[Cat]

EPR were exactly correct. They didn't prove that QM was incomplete, and they didn't prove that it violated locality; but they did prove it was *either* nonlocal or incomplete.

Agreed.

Re two dice (or, in my analogy, two spinning hexagons) being a reasonable analogy to illustrate entanglement, you say:

I don't think so. The results of two dice rolls will always be statistically independent unless there is some "mechanism" by which the result of one roll can affect the result of the other. Merely making one or the other "biased" in some way isn't at all the same as "linking" them. So, as long as they are independent, you will never find that the correlations violate a Bell inequality.

True, they will never violate a "genuine" Bell inequality, but I suspect that the fact that there are some "non-detections" means that they will violate the equivalent of the CHSH inequality, i.e. one in which the estimated test statistic is related to the detected pairs, not to the emitted ones.

When time, I'll work on this. Meantime I've having fun trying to produce a local realist model that will predict the outcome of one of the latest proposed "loophole-free" experiments -- that by Grangier's team, using PDC sources with "event-ready detectors" and balanced homodyne detection. Here, because, even without the event-ready detectors, we shall have (I think) some kind of record for every single emitted pair (i.e. no non-detections), I predict that the CHSH inequality will not be violated.

Cat

 

[vanesch]

Let us go for the strange world of Balls.

Imagine the following situation: in the world of Balls, we have a theory describing a curious experiment: a generator of pairs of blue balls sends one ball to a left observer, Alice, and another ball to the right observer, Bob.

It has been empirically verified that blue balls turn into red or black objects, piramids or cubes, smooth or hairy. However, it is only possible to observe one property: if you look at the color red or black, they become slimy balls ; if you look at the shape, they become blue, slimy shapes, and if you look at the surface quality, they become blue balls.
It has also been empirically verified that if we measure the same property of both balls coming out of the pair producer, they are always opposite.

For tens of years, people have tried to analyse these pairs of balls, but nothing seems to distinguish them until they change (about after half an hour or so) and we can do a measurement on them. So we've come to the conclusion that "pair of blue balls" completely describes the physical situation.
Even in a zargon-ray analysis, they give exactly the same diffraction patterns.

We have measured empirically since years the following probabilities for the pairs of blue balls measurements, and this has lead to the Stochastic Theory of Blue Ball Pairs (in Mathematica notation) which takes as fundamental postulate:

p[{hair, smooth}] = 1/2
p[{hair, hair}] = 0
p[{smooth, smooth}] = 0
p[{red, blue}] = 1/2
p[{red, red}] = 0
p[{blue, blue}] = 0
p[{piramid, cube}] = 1/2
p[{piramid, piramid}] = 0
p[{cube, cube}] = 0

p[{hair, blue}] = 1/2
p[{hair, red}] = 0
p[{smooth, blue}] = 0
p[{smooth, red}] = 1/2
p[{piramid, blue}] = 0
p[{piramid, red}] = 1/2
p[{cube, blue}] = 1/2
p[{cube, red}] = 0
p[{hair, cube}] = 1/2
p[{hair, piramid}] = 0
p[{smooth, cube}] = 0
p[{smooth, piramid}] = 1/2
p[{a_, b_}] := p[{b, a}]

the last equation indicating that the probabilities are symmetric.

It is interesting to note that from these 2-point correlations, we can deduce that the local probabilities of Alice, to find on a color measurement:
blue, has probability 1/2
red has probability 1/2

on a shape measurement:
cubes have probability 1/2
piramids have probability 1/2

on a surface aspect measurement:
hair has probability 1/2
smooth has probability 1/2

and this, independent on the choice of measurement Bob will make.

So Bob can not use its choice of measurement to send a message to Alice.

Is my stochastic theory local or not ?
Is in this theory P(B|A) equal to P(B)

Now compare it to the following theory, the theory of Blue Bells:

p[{hair, smooth}] = 1/2
p[{hair, hair}] = 0
p[{smooth, smooth}] = 0
p[{red, blue}] = 1/2
p[{red, red}] = 0
p[{blue, blue}] = 0
p[{piramid, cube}] = 1/2
p[{piramid, piramid}] = 0
p[{cube, cube}] = 0

p[{hair, blue}] = 0
p[{hair, red}] = 1/2
p[{smooth, blue}] = 1/2
p[{smooth, red}] = 0
p[{piramid, blue}] = 0
p[{piramid, red}] = 1/2
p[{cube, blue}] = 1/2
p[{cube, red}] = 0
p[{hair, cube}] = 1/2
p[{hair, piramid}] = 0
p[{smooth, cube}] = 0
p[{smooth, piramid}] = 1/2
p[{a_, b_}] := p[{b, a}]

Same questions...


cheers,
Patrick.

 

[Hans de Vries]

When time, I'll work on this. Meantime I've having fun trying to produce a local realist model that will predict the outcome of one of the latest proposed "loophole-free" experiments -- that by Grangier's team, using PDC sources with "event-ready detectors" and balanced homodyne detection. Here, because, even without the event-ready detectors, we shall have (I think) some kind of record for every single emitted pair (i.e. no non-detections), I predict that the CHSH inequality will not be violated.

I guess you are referring to this paper?
http://arxiv.org/abs/quant-ph/0403191

I also found a followup paper from a later data here:
http://arxiv.org/abs/quant-ph//0407181

The similar related papers from H. Nha and H.J. Carmichael:
http://arxiv.org/abs/quant-ph/0406101
http://arxiv.org/abs/quant-ph/0406102



If you are objecting to the Clauser, Horner, Shimony, Holt inequality
is it because the derrivation of the ≤ 2 assumes that the value E_b
is equal in both E_ab and E_a'b (see below) while in fact they are
generally selected subsets (~3%) after coincidence detection ?


|E_ab + E_a'b + E_ab' - E_a'b'| ≤ 2
≡
|(E_a + E_a')E_b + (E_a - E_a')E_b' | ≤ 2

(for individual measurements with outcome +1 or -1 either
(E_a+E_a')=0 or (E_a-E_a')=0 resulting in a maximum value of 2)


Regards, Hans

 

[ttn]

It is interesting to note that from these 2-point correlations, we can deduce that the local probabilities of Alice [...]
and this, independent on the choice of measurement Bob will make.

That's potentially misleading. The marginals (the probabilities for Alice gotten by summing
over the possible outcomes for Bob weighted by the appropriate probabilities) for alice to measure red/blue are indeed 50/50. But the conditional probability for Alice to measure red is *not* independent of the color of Bob's ball. ...e.g., the probability that Alice will find a blue ball when Bob's has already turned red, is 100%.

So, since you went out of your way to claim that there is no behind-the-scenes, local mechanism which can account for the correlations, i.e., that the description "two blue balls" is *complete*, there is a violation of Bell Locality here.

So Bob can not use its choice of measurement to send a message to Alice.

That's right. This example shows a violation of Bell Locality, but one that is washed out by randomness and so cannot be used to transmit information. Just like QM. Just like Bohm.

Is my stochastic theory local or not ?

Depends on what you mean. It's not Bell Local, but it is "information local".

Is in this theory P(B|A) equal to P(B)

No, definitely not. 100% =/= 50%.

 

[ttn]

Clearly "2 blue balls" is a complete description of the setup in that I cannot know more.

That is not clear at all. "Completeness" is not a statement merely about what can be known. Completeness is a shorthand for something like "complete description of reality." Einstein talked about it as requiring a one-to-one correspondence between physical states and state-descriptions in some theory. EPR of course urged that every "element of reality" must have a counterpart in the theoretical description. etc.

It is admittedly difficult if not impossible to know whether a given state description represents a complete description. Personally I think Bohr was off his rocker for making this kind of claim in the first place -- what in the world could have counted as evidence for it? The mere fact that the Heisenberg principle seems to prevent us from obtaining *knowledge* of certain things? That of course proves nothing. The little switch in the door prevents me from knowing whether or not the light in the refrigerator really goes off or not when I shut the door -- but that doesn't mean I stop believing that, in fact, the light is either on or off. In that case, there are obviously more facts out there in the external world than I can know about directly, so my description "I think there's about a 99% chance that the light does go out when I shut the door" is an admittedly incomplete one.

In the QM case, we can't take anything for granted. It is by no means "obvious" there that there are further facts of reality beyond what is contained in or described by the wave function. But that is why EPR-like arguments are so clever. They allow you to say something, not about the completeness alone, but about the relationship between completeness and locality. EPR showed that, if you hold fast to the locality principle, there must exist "elements of reality" for more quantities than are consistent with the uncertainty principle; hence QM, if local, is incomplete. I think Einstein's argument is even better: he argues that (a) you must be willing to inject the wave function collapse rule into the dynamics in order to get the right correlations and so (b) there is *not* a one-to-one correspondence between physical states and theoretical descriptions since when you collapse the wf for a distant system by making a measurement "here", the wf for that distant system changes in a situation where (by locality) its physical state can not have changed. That ruins any claim of one-to-one correspondence. I also like the Bell-Locality-based argument for this same conclusion: if you assume that the wf alone does provide a complete description of the system described, it is trivial to note that Bell Locality is violated.

Anyway, my point is just to reject in the strongest possible terms the idea that what "completeness" means is somehow purely epistemological, e.g., that it means we've learned all we can or have said all we can say. Completeness involves a comparison between knowledge and the facts, not just a comparison of knowledge to itself.

Of course, many people have tried to define completeness in a purely epistemological way, i.e., while dropping the assumption of realism. This (as with the attempt to define "locality" outside the context of realism) is literal nonsense. Tim Maudlin makes this point (about locality) very nicely in an article called "Space-time in the quantum world": "Physicists have been tremendously resistant to any claims of non-locality, mostly on the assumption (which is not a theorem) that non-locality is inconsistent with Relativity. The calculus seems to be that one ought to be willing to pay *any* price -- even the renunciation of pretensions to accurately describe the world -- to preserve the theory of Relativity. But the only possible view that would make sense of this obsessive attachment to Relativity is a thoroughly realistic one! These physicists seem to be so certain that Relativity is the last word in space-time structure that they are willing even to forego any coherent account of the entities that inhabit space-time." I believe parallel remarks apply as well to the concept of "completeness". Defenders of orthodox QM have been extremely resistant to any claims that QM might be incomplete... yet the only view that would make sense of this obsessive attachment to "completeness" is a thoroughly realistic one.

 

[vanesch]

...e.g., the probability that Alice will find a blue ball when Bob's has already turned red, is 100%.

So, since you went out of your way to claim that there is no behind-the-scenes, local mechanism which can account for the correlations, i.e., that the description "two blue balls" is *complete*, there is a violation of Bell Locality here.

And my second example ? The 2 Bells Theory ? Is it also violating Bell Locality ? The same example can be given about Alice's black ball and Bob's red ball...


cheers,
Patrick.

 

[ttn]

And my second example ? The 2 Bells Theory ? Is it also violating Bell Locality ? The same example can be given about Alice's black ball and Bob's red ball...

Maybe I'm just being dumb and/or not looking carefully enough, but I didn't see any difference between the two theories. Isn't the second just the same as the first with some of the (already
just meaningless, made-up) terms swapped around?

Any time you tell me there are persistent, law-like correlations between separated events and that there is *nothing* in the shared past of those events which made them be so correlated, I am going to say this violates Bell Locality. That kind of "magical" correlation between separated events is precisely what Bell Locality forbids.

I gather you are going to object to this, and say that my view is premised on a demand for explanation (which black box theories aren't intended to provide) or relies to heavily on realist commitments, or something to that effect. I guess I'm guilty as charged. By the way, you might enjoy the article "Do Correlations Need to be Explained" by Arthur Fine (in the Cushing/McMullin volume called "Philosophical Consequences of Quantum Theory"). He takes a position there that seems like the one you are evolving toward here -- namely, that if we are going to accept irreducible randomness at the individual-outcome-level, we should be equally willing to accept irreducible correlations between distant events. I don't agree with this position of course, but it's certainly out there.

Oh yeah, one other point I wanted to make that fits in nicely here. I was skimming through some of the other threads here, especially the ones on the "loopholes" in the Bell's Inequality experiments. Dr. Chinese made an excellent point there against the "local realism" people who refuse to admit that the experiments actually support the claim that Bell's Inequality is violated in nature. Paraphrasing, the point was: if you made these same sorts of objections on any other issue in science (e.g., claiming that different systematic errors in a bunch of different experiments all conspire magically to make those experiments give exactly the same results, claiming that the samples might be biased merely on the basis that the sample represents less than 100% of the population and without *any* statistical evidence to suggest a bias, etc.) you'd be branded a loony. Science would seriously grind to a complete and total halt if scientists were this willing, across the board, to consider conspiracy theories. It is relevant that the stakes are pretty high here -- one is talking about having to reject a premise (locality) that has been awfully important to physics for a long time. So there is *some* justification for a bit of extra skepticism, scrutiny, and thinking carefully about "loopholes", etc. But at some point you have to draw a line and say: enough. *All* of the evidence points to the QM predictions being correct, and *no* evidence suggests they are wrong. (And the lack of evidence against that proposition is not evidence for it!)

Anyway, I think similar comments apply to the question of whether we should try to explain correlations between distant events. The position of Arthur Fine in the article I mentioned (which I think Patrick would be symapthetic to?) amounts to shrugging and saying "well, some correlations can't be explained." But imagine that view being taken seriously by, say, the drug industry or biologists or chemists or anybody else in science. "Hmmm, people who live in these two widely separated towns all simultaneously came down with a rare disease that hasn't been observed anywhere else on Earth for 100 years... <shrug> oh well, coincidences happen all the time. When's lunch?" Or: "Well yes, your honor, there is a strong correlation between patients having undergone Medical Procedure X and, ahem, dying the next day -- but some correlations are just inexplicable." etc... you get the point.

 

[vanesch]

My claim is that this "completeness" requirement means: there is an underlying deterministic theory that can generate the probabilities in a classical statistical mechanical way. You are fighting like a devil to show me that I do not need that word "deterministic" but I will try to show you that THAT is what you want, and as long as you don't have it, you call a theory "incomplete". This is not surprising, because it was indeed Einstein's programme. But, although you won't admit it, it comes down to regard any fundamentally statistical theory as "incomplete".

I hope you do not mean by "complete" the "ultimate theory describing the true nature of reality" because that theory will change every century or so, and we will never have a 'true description of reality'. Newtonian theory wasn't, Maxwell's theory wasn't, we now know that general relativity isn't, quantum field theory isn't so I think it is clear by now that nothing we will ever have to put our hands on will be "the true description of reality".
EVERY theory we will ever have is an approximate formalism and with a totally different paradigm than the previous one giving sufficiently accurate results when compared with the experimental results available by the technology of the moment.
Maybe some day we will have to stop, because it all fits logically together and we cannot perform technologically any experiment anymore that could possibly challenge the theory. But that doesn't mean we "arrived".
So it is very simple: if you mean that, by completeness, you can just as well stop and say that every theory is incomplete.

That is not clear at all. "Completeness" is not a statement merely about what can be known. Completeness is a shorthand for something like "complete description of reality." Einstein talked about it as requiring a one-to-one correspondence between physical states and state-descriptions in some theory. EPR of course urged that every "element of reality" must have a counterpart in the theoretical description. etc.

Ok, so "element of reality" must mean: determines precisely every outcome, potentially with certainty. I'll try to show you.

It is admittedly difficult if not impossible to know whether a given state description represents a complete description.

No, once you have a determinisitic theory, you will be happy because there's nothing more to be added. What can be more "complete" than a deterministic theory which tells you individually, for each event, what will happen, with certainty ?

Personally I think Bohr was off his rocker for making this kind of claim in the first place -- what in the world could have counted as evidence for it? The mere fact that the Heisenberg principle seems to prevent us from obtaining *knowledge* of certain things? That of course proves nothing. The little switch in the door prevents me from knowing whether or not the light in the refrigerator really goes off or not when I shut the door -- but that doesn't mean I stop believing that, in fact, the light is either on or off. In that case, there are obviously more facts out there in the external world than I can know about directly, so my description "I think there's about a 99% chance that the light does go out when I shut the door" is an admittedly incomplete one.

Indeed, you want to talk about the switch, and the fact that it determines with certainty that the light goes off.

In the QM case, we can't take anything for granted. It is by no means "obvious" there that there are further facts of reality beyond what is contained in or described by the wave function. But that is why EPR-like arguments are so clever. They allow you to say something, not about the completeness alone, but about the relationship between completeness and locality. EPR showed that, if you hold fast to the locality principle, there must exist "elements of reality" for more quantities than are consistent with the uncertainty principle; hence QM, if local, is incomplete.

Again, in a deterministic case, when it is "in principle" possible to determine with certainty each individual outcome.

I think Einstein's argument is even better: he argues that (a) you must be willing to inject the wave function collapse rule into the dynamics in order to get the right correlations and so (b) there is *not* a one-to-one correspondence between physical states and theoretical descriptions since when you collapse the wf for a distant system by making a measurement "here", the wf for that distant system changes in a situation where (by locality) its physical state can not have changed. That ruins any claim of one-to-one correspondence. I also like the Bell-Locality-based argument for this same conclusion: if you assume that the wf alone does provide a complete description of the system described, it is trivial to note that Bell Locality is violated.

Bell locality is violated for EVERY stochastic theory which gives you correlations and which does not include a deterministic model for each individual outcome in its "state description". See my Blue Balls and my Blue Bells examples. It is only when you give a potentially deterministic state description that you can avoid Bell locality to be violated and have correlations in certain cases.

Anyway, my point is just to reject in the strongest possible terms the idea that what "completeness" means is somehow purely epistemological, e.g., that it means we've learned all we can or have said all we can say. Completeness involves a comparison between knowledge and the facts, not just a comparison of knowledge to itself.

Yes, and the facts "determine" every individual outcome. Again, there is no room for a purely stochastic theory which *postulates* probabilities as fundamental concepts.

Of course, many people have tried to define completeness in a purely epistemological way, i.e., while dropping the assumption of realism. This (as with the attempt to define "locality" outside the context of realism) is literal nonsense. Tim Maudlin makes this point (about locality) very nicely in an article called "Space-time in the quantum world": "Physicists have been tremendously resistant to any claims of non-locality, mostly on the assumption (which is not a theorem) that non-locality is inconsistent with Relativity. The calculus seems to be that one ought to be willing to pay *any* price -- even the renunciation of pretensions to accurately describe the world -- to preserve the theory of Relativity. But the only possible view that would make sense of this obsessive attachment to Relativity is a thoroughly realistic one! These physicists seem to be so certain that Relativity is the last word in space-time structure that they are willing even to forego any coherent account of the entities that inhabit space-time." I believe parallel remarks apply as well to the concept of "completeness". Defenders of orthodox QM have been extremely resistant to any claims that QM might be incomplete... yet the only view that would make sense of this obsessive attachment to "completeness" is a thoroughly realistic one.

That's why I think that the only reasonable definition of locality is the one that avoids the paradox in relativity, which is that you receive your own information before sending it so that you can decide to send something else.
If *that* requirement is satisfied, the stochastic predictions of a theory are local.

Bell-locality is a requirement that doesn't only depend upon the stochastic predictions a theory makes, but also upon what is considered as a state description, and can only avoid calling any correlation as non-local if that state description is potentially deterministic. But it will call ANY stochastic description 'non-local'. Bell locality has no meaning for theories which are inherently stochastic, meaning: out of which come simply rules to calculate probabilities.

There is more room for such stochastic theories than for deterministic theories with local mechanisms to make up probabilities which do not violate "information transfer" locality, and QM happens to hit in that extra room.

So you can redefine qualifiers such as "complete" or "realist" or whatever, what you really mean is "deterministic", or "potentially deterministic".

By "potentially deterministic" I mean partly deterministic and partly stochastic theories, of which the stochastic parts can trivially be converted in deterministic ones by adding (hidden) variables.

cheers,
Patrick.

 

[vanesch]

Maybe I'm just being dumb and/or not looking carefully enough, but I didn't see any difference between the two theories. Isn't the second just the same as the first with some of the (already
just meaningless, made-up) terms swapped around?

Hehe

The second theory (Blue Bells) HAS a hidden variable explanation:

you have a hairy, red cube going one side and a smooth blue piramid going the other way. So ADDING this deterministic hidden variable model will turn my Bell-locality violating theory into a Bell-respecting theory.

The first theory (Blue balls) hasn't such a potentially underlying model.

Please admire it for at least 3 seconds, it took me some puzzling to find it .

cheers,
Patrick.

 

[vanesch]

Any time you tell me there are persistent, law-like correlations between separated events and that there is *nothing* in the shared past of those events which made them be so correlated, I am going to say this violates Bell Locality. That kind of "magical" correlation between separated events is precisely what Bell Locality forbids.

And if the correlations are only born when the two events are already in the past, like in an MWI approach ? When the "remote measurement" didn't take place *until you got news of it because it is YOU who determined the outcome* ?

I gather you are going to object to this, and say that my view is premised on a demand for explanation (which black box theories aren't intended to provide) or relies to heavily on realist commitments, or something to that effect.

I go even further: what you call "realist" means deterministic, even if you don't want to admit it. But I'll find a way to make you talk

Dr. Chinese made an excellent point there against the "local realism" people who refuse to admit that the experiments actually support the claim that Bell's Inequality is violated in nature. Paraphrasing, the point was: if you made these same sorts of objections on any other issue in science (e.g., claiming that different systematic errors in a bunch of different experiments all conspire magically to make those experiments give exactly the same results, claiming that the samples might be biased merely on the basis that the sample represents less than 100% of the population and without *any* statistical evidence to suggest a bias, etc.) you'd be branded a loony. Science would seriously grind to a complete and total halt if scientists were this willing, across the board, to consider conspiracy theories. It is relevant that the stakes are pretty high here -- one is talking about having to reject a premise (locality) that has been awfully important to physics for a long time. So there is *some* justification for a bit of extra skepticism, scrutiny, and thinking carefully about "loopholes", etc. But at some point you have to draw a line and say: enough. *All* of the evidence points to the QM predictions being correct, and *no* evidence suggests they are wrong. (And the lack of evidence against that proposition is not evidence for it!)

I don't think locality (in the relativity sense) is the issue, I think it is a certain form of realism (which you call somehow complete, and which I'm sure means "determinisitic"). I think that at the moment, we cannot give up on the first (and happily QM DOESN'T violate locality in the relativity sense in generating an information paradox). But I easily give up on the second condition.

Anyway, I think similar comments apply to the question of whether we should try to explain correlations between distant events. The position of Arthur Fine in the article I mentioned (which I think Patrick would be symapthetic to?) amounts to shrugging and saying "well, some correlations can't be explained." But imagine that view being taken seriously by, say, the drug industry or biologists or chemists or anybody else in science. "Hmmm, people who live in these two widely separated towns all simultaneously came down with a rare disease that hasn't been observed anywhere else on Earth for 100 years... <shrug> oh well, coincidences happen all the time. When's lunch?" Or: "Well yes, your honor, there is a strong correlation between patients having undergone Medical Procedure X and, ahem, dying the next day -- but some correlations are just inexplicable." etc... you get the point.

If I were the judge, I'd try to send information through the patients, by given certain days the drug to the people, and certain days not. The receiver which would be the grand jury, and should then try to decode my message by looking at how people die. My message would be: "Cut this guy his head off - stop - repeat - cut this guy his head off" coded in ASCII 7 bit. Bit one: I give them the drug, and they die. Bit 0, they get a placebo and they live.
Hmm, if my phrase contains 80 characters, that means 560 bits to send, with at least 10 people per bit ; ok but half of them will have bit 0 and live, so I'll need to kill 2800 people for this message to be sent...
If they can read my message, I'd say that there is a causal link

cheers,
Patrick.

 

[DrChinese]

That is not clear at all. "Completeness" is not a statement merely about what can be known. Completeness is a shorthand for something like "complete description of reality." Einstein talked about it as requiring a one-to-one correspondence between physical states and state-descriptions in some theory. EPR of course urged that every "element of reality" must have a counterpart in the theoretical description. etc.

It is admittedly difficult if not impossible to know whether a given state description represents a complete description. Personally I think Bohr was off his rocker for making this kind of claim in the first place -- what in the world could have counted as evidence for it? The mere fact that the Heisenberg principle seems to prevent us from obtaining *knowledge* of certain things? That of course proves nothing.

Probably you are right that Bohr should not have asserted QM was complete. I think that statement carries too much baggage with it.

EPR thought they had a pretty clever argument by throwing the singlet state into the equation along with the HUP. They argued that at least a "more complete" specification of the system was possible, even if you accepted QM's predictions. They tried, in other words, to use the logic of the HUP against the idea that QM was complete.

Bell said that EPR's argument - which also tried to define what an element of reality was - did not actually work as they had pictured it. The problem being that their assumption - elements of reality exist independent of the measurement - was flawed. As we now know, Bell's Inequality shows that these elements of reality cannot have predetermined values and still yield experimental results consistent with QM. This is true - in my opinion - whether the theory is local or non-local: unmeasured quantum properties do not correspond to elements of reality. This conclusion is diametrically opposed to the closing words of EPR. However, I do not think this is semantically equivalent to the statement that QM is complete.

 

[DrChinese]

Hehe

The second theory (Blue Bells) HAS a hidden variable explanation:

you have a hairy, red cube going one side and a smooth blue piramid going the other way. So ADDING this deterministic hidden variable model will turn my Bell-locality violating theory into a Bell-respecting theory.

The first theory (Blue balls) hasn't such a potentially underlying model.

Please admire it for at least 3 seconds, it took me some puzzling to find it .

cheers,
Patrick.

You have a lot of balls (sorry couldn't resist).

The only detail I would comment on is this: you can construct a local hidden variable theory as you have above which appears to provide certain correspondence to the Bell model, but that correspondence is superficial. You can't do it AND give the same predictions as QM. That is the essence of Bell! There is no \theta in your formula. Functions exist which respect the Bell Inequality as \theta varies; but they will not match the cos^2\theta predictions of QM.

 

[DrChinese]

1. Any time you tell me there are persistent, law-like correlations between separated events and that there is *nothing* in the shared past of those events which made them be so correlated, I am going to say this violates Bell Locality. That kind of "magical" correlation between separated events is precisely what Bell Locality forbids.

...

2. But imagine that view being taken seriously by, say, the drug industry or biologists or chemists or anybody else in science. "Hmmm, people who live in these two widely separated towns all simultaneously came down with a rare disease that hasn't been observed anywhere else on Earth for 100 years... <shrug> oh well, coincidences happen all the time. When's lunch?" Or: "Well yes, your honor, there is a strong correlation between patients having undergone Medical Procedure X and, ahem, dying the next day -- but some correlations are just inexplicable." etc... you get the point.

1. I guess you could use this as an operating definition of Bell Locality. But there is yet one more item to consider: who is saying that there is no connection between these events? I say there is a connection between the events. But I deny that there are more "elements of reality" than actually measured.

2. Good point. Would you bet your life that there is no causality to the correlation? If you wouldn't - as a strategy - then you believe the correlation is not spurious.

I don't believe the connection between the correlations is spurious, but I don't know what is the cause and what is the effect. Presumably, causes must precede effects but maybe that does not apply. If you see time as symmetric then maybe causes only precede effects in some frames.

 

[Cat]

My claim is that this "completeness" requirement means: there is an underlying deterministic theory that can generate the probabilities in a classical statistical mechanical way.

Yes, in any case this is what I would mean, but this does not lead necessarily to the requirement that every "elements of reality" has to determine outcomes in a Bell test completely. Any given element of reality may need (as explained by Bell and by Clauser and Horne) the company of other elements of reality, mostly local to the detectors, before it yields a definite outcome. Without this extra input, our element of reality set at the source may determine only the probability of each possible outcome.

Ok, so "element of reality" must mean: determines precisely every outcome, potentially with certainty. I'll try to show you.

This is the actual statement that I'm challenging. It is probably not essential to your point but it's as well to be clear what is meant.

Yes, and the facts "determine" every individual outcome. Again, there is no room for a purely stochastic theory which *postulates* probabilities as fundamental concepts.

Ah yes, that's a more correct way of saying it. The "facts" can include more than one element of reality.

Bell locality has no meaning for theories which are inherently stochastic, meaning: out of which come simply rules to calculate probabilities.

There is more room for such stochastic theories than for deterministic theories with local mechanisms to make up probabilities which do not violate "information transfer" locality, and QM happens to hit in that extra room.

But doesn't that imply that QM operates by magic?

By "potentially deterministic" I mean partly deterministic and partly stochastic theories, of which the stochastic parts can trivially be converted in deterministic ones by adding (hidden) variables.

This sounds reasonable.

The interesting question now is whether or not experiments have in fact ruled out such "potentially deterministic" theories. Isn't the fact that they [e.g. Grangier's team, and Nha and Carmichael -- see Hans de Vries post earlier] are still looking for "loophole-free" tests an indication that the evidence against such theories is, to date, not conclusive? Of course, by Bell's theorem, if this kind of theory really does underly everything it means that QM is not quite correct, but it's probably nearly correct, or perhaps sufficiently near to correctness that the various applications of entanglement are effectively valid.

Cat

 

[DrChinese]

Isn't the fact that they [e.g. Grangier's team, and Nha and Carmichael -- see Hans de Vries post earlier] are still looking for "loophole-free" tests an indication that the evidence against such theories is, to date, not conclusive?

That is a logical flaw. You want it both ways. You refuse to accept it as conclusive evidence when folks stop looking; and you see it as supporting your position when they are looking! From your logic, it makes no sense to repeat an experiment, either! (Presumably that would mean that the experimented does not accept the initial results.) There are a lot of reasons to do experiments, even ones in which the essential results are not in question.

 

[ttn]

I hope you do not mean by "complete" the "ultimate theory describing the true nature of reality" because that theory will change every century or so, and we will never have a 'true description of reality'. Newtonian theory wasn't, Maxwell's theory wasn't, we now know that general relativity isn't, quantum field theory isn't so I think it is clear by now that nothing we will ever have to put our hands on will be "the true description of reality".
EVERY theory we will ever have is an approximate formalism and with a totally different paradigm than the previous one giving sufficiently accurate results when compared with the experimental results available by the technology of the moment.
Maybe some day we will have to stop, because it all fits logically together and we cannot perform technologically any experiment anymore that could possibly challenge the theory. But that doesn't mean we "arrived".
So it is very simple: if you mean that, by completeness, you can just as well stop and say that every theory is incomplete.

Good point, I totally agree. This is exactly why I think Bohr should never have been taken seriously when he claimed QM was complete.

Perhaps, then, what really makes you uncomfortable with all of this is not that the EPR-type argument against Bohr's claim is unsound, but that it is totally unnecessary. Why work so hard to refute something that is preposterous on its face? There is no grounds whatsoever for thinking QM is complete, so just forget about the whole issue and get on with life. Einstein et al were *obviously* right to reject the completeness doctrine, and they shouldn't have opened unnecessary cans of worms arguing against it. Is this more or less what you think?

No, once you have a determinisitic theory, you will be happy because there's nothing more to be added. What can be more "complete" than a deterministic theory which tells you individually, for each event, what will happen, with certainty ?

It's true; if you have a deterministic theory that explains everything, you'd at least have some evidence that maybe the theory is complete. On the other hand, any time you have a stochastic theory, it's always possible to wonder if the randomness is merely due to incomplete information, i.e., if an underlying deterministic theory could give rise to the stochastic theory already in hand.

But that doesn't mean I simply equate "complete" with "deterministic". Perhaps nature really is not deterministic. Who knows. (Actually, as someone who believes in free will, I'm really pretty open to this possibility.) My only point is: if you have a stochastic theory that predicts correlations which cannot be locally explained (with the usual stochastic sense of "explained"), you should admit that your stochastic theory is nonlocal. And, say, if it is possible to remove that nonlocality (i.e., construct a local theory that makes the same predictions) by filling in the description a bit (maybe leaving you with a deterministic underlying theory, or maybe a still-stochastic but more detailed underlying theory) you should be open to that possibility.

Indeed, you want to talk about the switch, and the fact that it determines with certainty that the light goes off.

It's not so much that I *want* to talk about this stuff. But if talking about this stuff allows me to get around a shocking and troublesome problem (which would be that thinking my stochastic statement about the fridge light was a complete description, led to my fridge theory being nonlocal -- which makes no sense in this example, but oh well) then I should be open to the possibility.

That's my only point. It's totally simple. People who claim QM is complete should admit that their theory is nonlocal. (...and they should therefore quit dismissing, out of hand, theories like Bohm's because of their nonlocality.)

Bell locality is violated for EVERY stochastic theory which gives you correlations and which does not include a deterministic model for each individual outcome in its "state description". See my Blue Balls and my Blue Bells examples.

That's not true. You yourself revealed that there exists a local, stochastic theory that can explain all the observational results you catalogued for the Blue Bells example. (It's stochastic because it's random which of the two goobers goes which way -- and for all I know, maybe it's *really*, irreducibly random.)

That's why I think that the only reasonable definition of locality is the one that avoids the paradox in relativity, which is that you receive your own information before sending it so that you can decide to send something else.
If *that* requirement is satisfied, the stochastic predictions of a theory are local.

We've been here before. I agree this is an important and interesting definition of locality, definitely worth considering. The problem is that "information" is a very high level idea, and it's possible for theories to be local in this "no info transfer" sense while being fundamentally, in their guts, quite blatantly nonlocal. Bohm's theory is the obvious non-controversial example. Orthodox QM is another obvious example that is, for reasons I frankly don't understand, controversial. (I guess, the reason it's controversial is that people are happy to emblazon Bohm's theory with the scarlet letter "NL" based on its violating Bell Locality, then they like to switch to the "no info transfer" definition so that QM gets the label "Local". But as I've said several times, that's just stupid naked inconsistency and shouldn't be tolerated by serious thinkers.)

 

[vanesch]

You have a lot of balls (sorry couldn't resist).

I hope you realize that the names have been carefully choosen
The Blue Balls theory is very preposterous, and violates Bell's inequalities much more than QM (hence Balls ) - at least if I didn't make an error.

The Bells theory is compatible with a local hidden variable model and hence will satisfy Bell's inequalities.

I took on purpose NOT a cover-up of a prediction of QM because that would be seen as too cheap. In fact, I tried to make the two correlation functions as much alike as I could, with similar values of correlations, but in different cases.

Note that what ttn defined as Bell Locality is not the Bell's inequalities (but they can be derived from it). He defines Bell Locality as the fact that if you take into account a "complete state description", then the correlation P(A,B) factorizes in P(A) x P(B).

I wanted to show how inevident it is to apply this to a stochastical theory, by showing two very similar stochastical theories.

The only detail I would comment on is this: you can construct a local hidden variable theory as you have above which appears to provide certain correspondence to the Bell model, but that correspondence is superficial. You can't do it AND give the same predictions as QM. That is the essence of Bell! There is no \theta in your formula. Functions exist which respect the Bell Inequality as \theta varies; but they will not match the cos^2\theta predictions of QM.

The only "theta" I have is discrete: colors, shapes and surface type. 3 values is sufficient.

cheers,
Patrick.

 

[ttn]

Hehe

The second theory (Blue Bells) HAS a hidden variable explanation:

you have a hairy, red cube going one side and a smooth blue piramid going the other way. So ADDING this deterministic hidden variable model will turn my Bell-locality violating theory into a Bell-respecting theory.

The first theory (Blue balls) hasn't such a potentially underlying model.

Please admire it for at least 3 seconds, it took me some puzzling to find it .

It's a nice example, no doubt. But I still think you are missing my point. In fact, your example helps me make my point even stronger, so thank you.

My claim was that the Blue Bells theory violated Bell Locality -- ***if*** you asserted that the theory is complete. It's just like EPR: the conclusion is not a blanket claim for in-completeness or non-locality, but a dilemma: if you want to believe the theory is complete, you must admit that it violates locality. Or: if you insist on avoiding nonlocality, you must admit that the theory is incomplete.

So your example is helpful in that it illustrates this dilemma very clearly. Regarded as a complete specification of the system, the Blue Bells model is nonlocal. The probabilities violate Bell Locality. Of course, you can get around this conclusion easily, by admitting that maybe, after all, the theory was not complete, and considering the very local-hv account you provided.

Really, this is exactly like the coin-in-two-hands or Einstein's Boxes example I mentioned a while back. Put a particle in a box, split the box in two so half the wf goes each way, separate the halves, and then look in one to see if the particle is there. If you *insist* on regarding the wf as a complete description of the state of the particle prior to looking in the boxes, you can then identify the wf with Bell's "L" and infer that Bell Locality is violated. QM, if complete, is nonlocal. But in this example there is, just like in yours, a rather obvious local way to understand the probabilities involved (specifically, that the joint probability for finding the particle in *both* boxes is not simply the product of the individual probabilities for the two boxes = 50% * 50% = 25%) as arising from a deeper level of description -- namely, one in which the particle just is in one of the two boxes the whole time, prior to measurement. Then opening the boxes merely reveals the pre-existing location of the particle. *Obviously* local. But -- and this is the whole point -- the price of *doing* this is regarding the original wf-only description as *incomplete*. QM, if local, must be incomplete. Or equivalently: QM, if complete, is nonlocal. All of that follows from this trivial example.

Of course, less trivial examples (involving spin correlations along several distinct axes, or the equivalent of the case of the Blue Balls -- which, by the way, is not a sherlock holmes story I'd particularly like to read) yield different results. Sometimes it is *not* possible to elude the apparent nonlocality of the quantum predictions merely by giving up the idea that the wf provides a complete description. That is Bell's theorem. But that doesn't undo what we already showed with the simpler example, namely, that QM, if complete, is nonlocal.

And that's really all I'm interested in claiming. The nonlocality that is *apparent* in the QM predictions is actually *real* -- it cannot be escaped by dropping the completeness assumption or anything else. Nature is nonlocal (in the Bell sense, though, yes, possibly local in some other senses). You're going to be stuck with a Bell-Nonlocal theory whether you regard QM as complete or not. This is not a proof that QM *isn't* complete. Duh. But it is a proof that the people who dismiss theories like Bohmian mechanics out of hand (on the grounds of their violating Bell Locality) should shut up.

 

[vanesch]

That's not true. You yourself revealed that there exists a local, stochastic theory that can explain all the observational results you catalogued for the Blue Bells example. (It's stochastic because it's random which of the two goobers goes which way -- and for all I know, maybe it's *really*, irreducibly random.)

That's where we differ.
IF you consider this theory as "Bell Local" it is obviously deterministic, in that for each pair of bells emitted, you are in case A (cube left, piramid right) or you are in case B (cube right, piramid left). If you are in case A, all the probabilities are 1 or 0, and if you are in case B, idem. So if the case is determined, everything is deterministic. Now, if you think you have the right to put the "case" into the "complete description of nature" then I have also the right to say that this complete description of nature determines all outcomes with certainty, and that's what I call a deterministic theory.
Whether this CASE information is accessible in principle to us, observers, or not (in which case it is a "hidden variable") doesn't change anything: if you consider it part of a complete description, it "is there".
It is our lack of information about the CASE variable, so that we have to consider an ensemble of these variables, that gives us the ONLY randomness in the outcomes. Now, or (as in the case of statistical mechanics) this is just a problem in practice, or somehow it is "fundamentally hidden", so whatever we do, we'll never find out. In that last case you could maybe try to claim that your theory is fundamentally stochastic, but then I can claim that your variable is so well hidden that it shouldn't be part of a state description in the first place ! But if you do that, your Bell locality condition falls on its face again...
As I said elsewhere, you could pro forma introduce some finite probabilities in such hidden variable theories to make em look like a stochastic theory, but by adding a few more variables, you easily turn them in fully deterministic theories out of which (when including them in the "complete state description") come only 1 and 0 as probabilities.

cheers,
Patrick.

 

[vanesch]

And that's really all I'm interested in claiming. The nonlocality that is *apparent* in the QM predictions is actually *real* -- it cannot be escaped by dropping the completeness assumption or anything else. Nature is nonlocal (in the Bell sense, though, yes, possibly local in some other senses). You're going to be stuck with a Bell-Nonlocal theory whether you regard QM as complete or not. This is not a proof that QM *isn't* complete. Duh. But it is a proof that the people who dismiss theories like Bohmian mechanics out of hand (on the grounds of their violating Bell Locality) should shut up.

I had the impression (but I can be wrong) that if you take the hidden variables in Bohm for real (and you have to, if you consider them part of the reality description), that LOCAL probability distributions of these hidden variables can have expectation values which change according to what happens elsewhere, so that these probability distributions of these hidden variables are not local in the sense of relativity (in that we can send information that way, if only we had local access to these hidden variables).
It is in *that* sense that I thought that Bohm was non-local.

I honestly don't care about Bell locality itself which is, in my opinion, just a statement about probabilities generated by deterministic, local theories. So I agree with you that I wouldn't mind Bohm only to violate Bell Locality. The same rules have to count for everybody.

cheers,
Patrick.

 

[ttn]

I had the impression (but I can be wrong) that if you take the hidden variables in Bohm for real (and you have to, if you consider them part of the reality description), that LOCAL probability distributions of these hidden variables can have expectation values which change according to what happens elsewhere, so that these probability distributions of these hidden variables are not local in the sense of relativity (in that we can send information that way, if only we had local access to these hidden variables).
It is in *that* sense that I thought that Bohm was non-local.

Yes, that's exactly right. But (and this is becoming something of an anthem on my part..) it's just the same for QM. If you could actually discover somehow what the wave function for some entity next to you was, you would be able to use this information to send messages. Send your friend one of the boxes with "half a particle" in it. The value of the wf over by your friend is 1/sqrt(2). [or something like that... technically I'm talking about the mod of the wf integrated over the volume of the box, but who cares about that detail.] But as soon as you open your box and either find or don't find the particle there, the value of the wf over by your friend will immediately change to either zero or one (respectively). And if he had access to that change -- if he knew that the value of the wf in his box had suddenly jumped, he'd know that you had just opened your box. Hence, information transfer.

Of course, everybody knows that you can't just "learn the value of the wf at some point". So you can't actually use this underlying non-locality in orthodox QM to transmit information. But if this kind of argument gets QM off the hook, it ought to get bohmian mechanics off the hook too. They're really equivalent -- both are theories about some quantity/quantities (wave functions only for QM, wf's plus particle positions for Bohm) which are affected nonlocally by various fiddling that can be done at distant locations. And if only you had access to the exact local state (as indicated by the local values for the quantities your theory is *about*) you could use this nonlocality to transmit information and thus get into all sorts of hot water with relativity. But, in both theories, you *don't* have access to the exact local state, so you are *prevented* from using the nonlocality to transmit information, and hence (by the "info" type definition of locality) both theories turn out to be *local*. But this has a very uncomfortable, conspiratorial feel to it, which people have no trouble expressing when it comes to Bohm. They all say more or less what you said above: "come on, the underlying *physics* in Bohm's theory is blatantly nonlocal -- so the fact that this nonlocality is washed out and can't be put to use is irrelevant." For some reason people aren't as willing to say what is, I think, obviously and equally true of QM: "the underlying *physics* of QM is blatantly nonlocal [specifically, the collapse postulate] -- the fact that this is washed out and can't be put to use is irrelevant."

By the way, the kind of statements you are making here about Bohm's theory -- that it is obviously nonlocal if you take it seriously -- is exactly what bothered Bell about Bohm's theory at first. It is, I suspect, part of why he was motivated to come up with clean mathematical condition by which one could judge deep/fundamental locality [or what he called "local causality"]. Remember, Bohm's theory is *local* by the standard of info transfer, so *some* clean way of expressing its "obvious" nonlocality is needed. What he came up with -- "Bell Locality" -- does the job beautifully. It's because Bohmian mechanics violates this condition that we all feel good about saying: "ahh, OK, so despite the fact that you can't send messages FTL in Bohm's theory, it really is nonlocal behind the scenes." But then you notice that orthodox QM violates this same condition -- something which people remain far less comfortable about, but which is painfully obvious nevertheless.

 

[ttn]

That's where we differ.
IF you consider this theory as "Bell Local" it is obviously deterministic, in that for each pair of bells emitted, you are in case A (cube left, piramid right) or you are in case B (cube right, piramid left). If you are in case A, all the probabilities are 1 or 0, and if you are in case B, idem. So if the case is determined, everything is deterministic. Now, if you think you have the right to put the "case" into the "complete description of nature" then I have also the right to say that this complete description of nature determines all outcomes with certainty, and that's what I call a deterministic theory.
Whether this CASE information is accessible in principle to us, observers, or not (in which case it is a "hidden variable") doesn't change anything: if you consider it part of a complete description, it "is there".

Yes, you're entirely right about this. My mistake. I shouldn't have said that picking between cases A and B in some "irreducibly stochastic" way made the theory genuinely stochastic. It doesn't, for just the reasons you give.

I don't think this changes anything significant, though. I still maintain that it's possible to have a genuinely stochastic theory that either does or does not satisfy Bell Locality -- i.e., the Bell Locality condition makes perfect sense applied to genuinely stochastic theories -- i.e., that condition isn't somehow uniquely applicable to deterministic theories.

We already have on the table an example of a genuinely stochastic theory that, I think, we've agreed violates Bell Locality. (namely, QM) So maybe it would help to make up an example of a genuinely stochastic theory that is Bell Local. Would that help?? I'm actually a bit confused now about what you're even claiming, so maybe this won't help at all. In fact, I'm pretty sure it won't since it's so damn trivial. But, for what it's worth, here's an example of a genuinely stochastic theory that is consistent with Bell Locality:

Alice and Bob shake hands, walk to opposite sides of the room, and then each flips a fair coin (or some other event we're willing to pretend is irreducibly random). The joint probability for Alice and Bob both getting heads factors: 50% for Bob times 50% for Alice = 25% for two heads. Bell Locality is respected.

Stupid, huh? Admittedly so, but it's an example of applying Bell Locality to a stochastic situation. Maybe you'll think what's special about this example is that there are actually no correlations at all between the two sides. If so, modify the scenario in another admittedly stupid way: say Alice and Bob each have two coins in their pockets, a two-headed coin and a regular heads/tails coin. After separating, Alice and Bob each independently decide, with irreducibly random probability, whether to flip their H/H coin or their H/T coin. Say there is a 99% chance each time that they'll choose the H/H coin, and only a 1% chance that they'll decide to flip the regular H/T coin. So... a large fraction of the time, Alice and Bob both end up with a "heads" outcome.

I think it is obvious that Bell Locality is still 100% respected. Yet the correlation coefficient

P(H,H) + P(T,T) - P(H,T) - P(T,H)

is not zero.

So it isn't merely the lack of correlations between separated events that permits one to apply Bell Locality to stochastic situations.

I dunno, somehow I doubt any of this will help move the conversation forward. Maybe you could remind me/us what exactly you object to in applying Bell Locality to stochastic theories (in particular, what precisely you object to in my claim that QM, so long as you believe that the wf is a complete description of the system, violates Bell Locality)...

 

[ttn]

Bell said that EPR's argument - which also tried to define what an element of reality was - did not actually work as they had pictured it.

That is *definitely* not true! Bell was emphatic that the EPR argument *had indeed* established that, if complete, QM itself was nonlocal. This was the first part of his two-part argument that nature violates Bell-Locality. (The second part is, of course Bell's Theorem: you can't get rid of the apparent nonlocality of QM by rejecting the completeness doctrine, i.e., by building a hidden variable theory.)

Perhaps you are confusing the proposition that EPR actually argued for (QM is either incomplete or nonlocal) with the conclusion they (naturally, at the time) drew from this: since locality is true, QM must be incomplete. That is, EPR showed that, for QM, locality --> incompleteness. Then as a separate premise, they postulated: locality. Combining these obviously gives the conclusion: incompleteness.

Bell's later work undermines the "separate premise: locality" but in no way undermines the important dilemma that EPR argued for, namely, "locality --> incompleteness." Indeed, as I said, Bell continued to cite EPR as having provided the first half of the argument which proves that locality fails, period (whether or not one subscribes to completeness).

The problem being that their assumption - elements of reality exist independent of the measurement - was flawed.

This was hardly an *assumption* of EPR! They proved (under the assumption of locality) that these pre-measurement elements of reality must exist.

 

[DrChinese]

That is *definitely* not true! Bell was emphatic that the EPR argument *had indeed* established that, if complete, QM itself was nonlocal. This was the first part of his two-part argument that nature violates Bell-Locality. (The second part is, of course Bell's Theorem: you can't get rid of the apparent nonlocality of QM by rejecting the completeness doctrine, i.e., by building a hidden variable theory.)

Perhaps you are confusing the proposition that EPR actually argued for (QM is either incomplete or nonlocal) with the conclusion they (naturally, at the time) drew from this: since locality is true, QM must be incomplete. That is, EPR showed that, for QM, locality --> incompleteness. Then as a separate premise, they postulated: locality. Combining these obviously gives the conclusion: incompleteness.

...

This was hardly an *assumption* of EPR! They proved (under the assumption of locality) that these pre-measurement elements of reality must exist.

No, not so! Bell may have said various things, same Einstein, but their work speaks for itself. Bell's Theorem does not rest upon locality, and neither does EPR, and in both of these papers locality is barely mentioned. Replace the word "locality" with "causality" (which is I think is close to your Bell locality) and we are in the same ballpark.

EPR claimed that if the result of a measurement could be predicted in advance, then the observable must correspond to an element of reality and that that observable was in fact predetermined. Bell explored this idea too.

While you are talking about the locality of the observable, I am talking about the reality of the observable. EPR said: "Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted."

Bell showed that we should insist on the more restrictive definition of reality; i.e. that quantum attributes are not objectively real if we can't measure or predict them. Bell represented the reality condition within his theorem explicitly - see his (2) with \lambda. Under this criteria, then, EPR does not prove that QM is incomplete by admission of EPR because they assumed that these elements of reality existed.

EPR never claimed that they proved that QM was non-local if complete, although I can see why that would be a logical deduction IF you didn't know about Bell. After all, they considered predetermined "elements of reality" to be a given. Now that we know this is questionable, evertyhing looks different.

 

[ttn]

No, not so! Bell may have said various things, same Einstein, but their work speaks for itself. Bell's Theorem does not rest upon locality, and neither does EPR, and in both of these papers locality is barely mentioned.

Bell's Theorem does not rest upon locality? Are you kidding? Read any of Bell's papers -- I think you'll find (a) that the theorem assumes that the theories the theorem is about satisfy the Bell Locality condition and (b) Bell spends a lot of time and energy arguing for this condition. See especially the article "La Nouvelle Cuisine", re-printed as the final chapter in the new 2nd edition of Speakable and Unspeakable.

Re: Einstein, you are right in one sense: the actual EPR paper barely mentions the locality issue. But Podolsky wrote that paper, and Einstein wrote in a letter (later in '35) to Schroedinger that he thought the point he considered crucial (namely, the completeness-locality dilemma) had been "smothered by the formalism" in Podolsky's paper!

Here are Einstein's words from the "Reply to Criticisms" essay in the Schilpp volume:

"By this way of looking at the matter it becomes evident that the paradox [EPR] forces us to relinquish one of the following two assertions:
1. the description by means of the \psi-function is complete.
2. the real states of spatially separated objects are independent of each other."

For more detail on this point, see the first few chapter of Arthur Fine's wonderful book, "The Shaky Game." One notable line: "It is important to notice that the conclusion Einstein draws from EPR is not a categorical claim for the incompleteness of quantum theory. It is rather that the theory poses a dilemma between completeness and separation; both cannot be true." The paper "Einstein's Boxes" in the Feb. '05 American Journal of Physics also discusses this issue in some detail.

Bell showed that we should insist on the more restrictive definition of reality; i.e. that quantum attributes are not objectively real if we can't measure or predict them.

This sounds nothing like the Bell I know and love.

Under this criteria, then, EPR does not prove that QM is incomplete by admission of EPR because they assumed that these elements of reality existed.

EPR proved that QM, if complete, is nonlocal.
Bell proved that if QM is *not* complete, the resulting hidden variable theory has to be nonlocal.
Combined, these two arguments prove that nature is nonlocal. *That* is what Bell proved -- at least, it is what I think he proved... which wouldn't count for much except that this matches what Bell himself thought he proved.

EPR never claimed that they proved that QM was non-local if complete, although I can see why that would be a logical deduction IF you didn't know about Bell. After all, they considered predetermined "elements of reality" to be a given. Now that we know this is questionable, evertyhing looks different.

Yes, the actual EPR paper obscured the importance of the locality issue, and generally failed to make clear what Einstein (later) did -- that the real point of EPR was (supposed to be!) that there is a dilemma, for QM, between completeness and locality. You seem to think EPR just *assumed* the existence of the elements of reality they needed to show that QM was incomplete. Wouldn't that make their argument trivially circular/empty? I don't think it was empty at all. They didn't just assume the desired conclusion; they showed that it followed from the locality assumption -- an assumption which was indeed, as you say, a logical one until/unless one knows about Bell. After Bell, you realize that you're stuck with a nonlocal theory regardless of your position re: completeness. See quant-ph/0408105 for further details on this.

 

[DrChinese]

Bell's Theorem does not rest upon locality? Are you kidding? Read any of Bell's papers -- I think you'll find (a) that the theorem assumes that the theories the theorem is about satisfy the Bell Locality condition and (b) Bell spends a lot of time and energy arguing for this condition. See especially the article "La Nouvelle Cuisine", re-printed as the final chapter in the new 2nd edition of Speakable and Unspeakable.

Re: Einstein, you are right in one sense: the actual EPR paper barely mentions the locality issue. But Podolsky wrote that paper, and Einstein wrote in a letter (later in '35) to Schroedinger that he thought the point he considered crucial (namely, the completeness-locality dilemma) had been "smothered by the formalism" in Podolsky's paper!

Here are Einstein's words from the "Reply to Criticisms" essay in the Schilpp volume:

"By this way of looking at the matter it becomes evident that the paradox [EPR] forces us to relinquish one of the following two assertions:
1. the description by means of the \psi-function is complete.
2. the real states of spatially separated objects are independent of each other."

The EPR paper and Bell's 1964 follow up say it all:

I. EPR proves: "...either (1) the quantum-mechanical description given by the wave function is not complete or (2) when the operaters corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality".

II. Bell proves both cannot be true: (1) QM is incomplete (as represented by the \lambda in his formulas; and (2) the predictions of QM are correct. To quote: "The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics was not complete but should be supplemented by additional parameters... In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics."

III. Accepting both EPR and Bell as correct (as I do), as well as Aspect, you must conclude that:

a) Aspect et al proves that the predictions of QM are correct (please Cat stay out of this discussion as we are not interested in debating this).
b) If QM is correct, then Bell (2) is true; therefore Bell (1) is false.
c) If Bell (1) is false, then EPR (1) is also false as they are equivalent by design.
d) If EPR (1) is false, then EPR (2) is true.

IV. Ergo: Aspect + Bell + EPR -> Reality fails ("when the operates corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality"). This is the logical result of the chain, and you can clearly see that locality is not a factor by examining the formalisms.

A close look at the arguments of EPR (as you have seen) and Bell, you will see that whether QM is local or non-local is not a factor in any way. The only requirement Bell mentions is that "the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past." However, this requirement is not actually represented in any way in Bell's formalism (that I can see - perhaps you can find a *formula* which embodies this). The only assumption Bell actually makes is that there is an A, B and C when we can measure only 2 at a time. In other words, his conclusion is correct and his derivation is correct; but his description strays a bit in ways that do not affect his work in any way.

Put another way in my own words: so what if there are hidden variables across the universe when t=0? There still cannot be an A, B and C which are simultaneously real at t=0. Therefore, it is the measurement at t=T which creates the reality. The location of the hidden variables is not a factor, there is no A, B and C regardless.

 

[ttn]

A close look at the arguments of EPR (as you have seen) and Bell, you will see that whether QM is local or non-local is not a factor in any way. The only requirement Bell mentions is that "the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past." However, this requirement is not actually represented in any way in Bell's formalism (that I can see - perhaps you can find a *formula* which embodies this).

Are you kidding?? How about the requirement that the joint probabilities factor, as expressed, e.g., in Bell's equation (14) [of "On the E-P-R paradox"]. The discussion in his later papers is much clearer: check out, e.g., section 4 of "Bertlmann's socks...", or the very extensive and detailed discusison in "La Nouvelle Cuisine."

Here is a nice statement (from "Bertlmann's socks...", one of his later papers, after he had had lots of time to get his thinking straight on exactly what he had proved):

"Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of QM. So we *cannot* dismiss intervention on one side as a causal influence on the other." (pg 149-50 of Speakable...)

I don't see any possible way of interpreting this, other than the one I have been advocating here. Bell is saying: under the assumption of locality ("if we do not accept the intervention on one side as a causal influence on the other") we are led to conclude that there exist local hidden variables determining the outcomes. [that is the EPR argument!] But as he goes on to point out, this assumption (that there exist local hv's) leads to a contradiction with the experimentally observed results. [that is Bell's theorem.]

In other words, the only way of trying to interpret QM as a local theory (namely, by dropping the completeness assumption and trying for a local hidden variable theory) does not work. You cannot get rid of the nonlocality.


I'd like to keep this as positive as possible, but your anti-realist comments are really inexcusable. There is just no reasonable way of believing that somehow the upshot of EPR/Bell is that it's impossible to believe in realism or elements of reality or whatever. Bohmian mechanics exists. It is an unambiguous counterexample to any such claims.

 

[DrChinese]

I don't see any possible way of interpreting this, other than the one I have been advocating here. Bell is saying: under the assumption of locality ("if we do not accept the intervention on one side as a causal influence on the other") we are led to conclude that there exist local hidden variables determining the outcomes. [that is the EPR argument!] [1]But as he goes on to point out, this assumption (that there exist local hv's) leads to a contradiction with the experimentally observed results. [that is Bell's theorem.]

In other words, the only way of trying to interpret QM as a local theory (namely, by dropping the completeness assumption and trying for a local hidden variable theory) does not work. You cannot get rid of the nonlocality.

I'd like to keep this as positive as possible, but your anti-realist comments are really inexcusable. There is just no reasonable way of believing that somehow the upshot of EPR/Bell is that it's impossible to believe in realism or elements of reality or whatever. Bohmian mechanics exists. It is an unambiguous counterexample to any such claims.

Anti-realist comments are "inexcusable"? Say that to Einstein and Bell, not me. I am quoting him (EPR): "...either (1) the quantum-mechanical description given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality". That is what the paper is all about, and Einstein clearly took it - as obviously you do - that (2) is false. (That, by the way, is not the same as your EPR argument above.) I realize your opinion is different than mine, but these are the actual relevant words from the actual paper, and not an out of context comment made later. The fact is, Einstein didn't miss a trick as his actual words allowed for him to be wrong about (1) and right about (2) and therefore right - again - in the end when it mattered. He publicly supported the (1) position and yet - here is it again - (2) is the anti-realist position you disdain.

Bell (14): P(a,b)=-\int d\lambda p(\lambda) A(a,\lambda) A(b,\lambda)

Perhaps you can explain how this has anything to do with the location of the hidden variables. On the other hand, Bell's realist assumption follows on the very next line... "It follows that c is another unit vector" and thereafter there is a, b and c. This is the explicit labeling of attributes that do not commute; and that we now know does not have simultaneous reality. In his paper, Bell states: "the quantum mechanical expectation value cannot be represented, either accurately or arbitrarily closely, in the form (2)" which is

P(a,b)=\int d\lambda p(\lambda) A(a,\lambda) B(b,\lambda)

That means to me that there are NO hidden variables ANYWHERE. So how could *you* argue otherwise? I am sure that in most ways our position is more alike than different.

I agree with your deduction [reference 1 above] that an observation on one side is causally connected to the results on the other. And the reason I believe that has nothing to do with whether QM is local or non-local! I believe that because I believe in the QM formalism and that is what it says is the most complete specification of the system possible. Therefore, I agree with the conclusion (2) of EPR, and I specifically deny (1). That conclusion is 100% in keeping with EPR, Bell and Aspect and I would challenge you to deny that is a logical deduction from the facts (see again III my preceding post for a recap).

So if you want to say that "proves" QM is non-local, then I say fine. If someone else says that conclusion is not part of the formalism of QM, then I say fine to that too. But if you try to tell me that there is simultaneous reality to non-commuting quantum attributes, I say... prove it by experiment. (You can't.)

 

[vanesch]

Yes, that's exactly right. But (and this is becoming something of an anthem on my part..) it's just the same for QM. If you could actually discover somehow what the wave function for some entity next to you was, you would be able to use this information to send messages. Send your friend one of the boxes with "half a particle" in it. The value of the wf over by your friend is 1/sqrt(2). [or something like that... technically I'm talking about the mod of the wf integrated over the volume of the box, but who cares about that detail.] But as soon as you open your box and either find or don't find the particle there, the value of the wf over by your friend will immediately change to either zero or one (respectively).

Ah we're home
You think of "collapse of the wavefunction". Well, let me tell you something: EVERYBODY AGREES that collapse of the wavefunction in this way would be bluntly non-local. So I fully agree with you that such a thing is just as ugly non-local as Bohm ! And it is one of the reasons many people don't like it. ( (There is also another reason that I find even more severe: that is that we don't know what physical process could ever lead to such a collapse)
But in an MWI-like view of QM THERE IS NO SUCH COLLAPSE AT A DISTANCE.
So if Bob "could locally look at your part of the wavefunction" nothing special would happen when Alice "looks at her part of the wavefunction"
And if they see the wavefunction, they wouldn't see any result of a measurement. It is only because of a property of observers that apparently they have to choose a result that they 1) obtain a result and 2) experience some randomness in that result. But the wavefunction itself nicely continues to evolve in all its splendor, whether you have looked or not (well, except for your OWN part of the wavefunction, which gets smoothly entangled, locally, with what you are measuring and of which you have to pick one branch).

That's what I've been trying to tell you.
In the "internal information sense":

Bohm is non-local
Copenhagen QM is non-local
MWI QM is local

In the "external information sense"
Bohm is local
Copenhagen and MWI QM are local

In the "Bell local sense"
Bohm is nonlocal
Copenhagen and MWI QM are non local

cheers,
Patrick.

 

[vanesch]

I dunno, somehow I doubt any of this will help move the conversation forward. Maybe you could remind me/us what exactly you object to in applying Bell Locality to stochastic theories

I do not object to applying Bell locality to stochastic theories, I tell you that it is a criterium *designed* on the basis of deterministic theories, and that stochastic theories that by coincidence obey it, can (that's exactly the MEANING of Bell Locality) simply be turned into deterministic local hidden variable theories, so that ALL the randomness comes about from the lack of knowledge of local variables, which, if we would know them, determine all outcomes with certainty.

Bell Locality is a criterion that says: from *this* theory, it is possible to make a local, deterministic hidden variable theory.

That's why I consider it as a too severe criterion to judge locality on.


cheers,
Patrick.