Bell Locality: New Paper Clarifies Arguments

[Tez]

And let me nip something in the bud: The hidden variable models Bell gave in those two papers were not epistemic models - the ontic state space included the full information about the quantum state as well as a hidden parameter. However in Kochen and Specker's 67 paper they give what I would call an epsitemic model (which also happens to be non-contextual) for a spin-1/2 system...

 

[ttn]

However I have something stronger in mind than what you maybe think I do when I say "treat the quantum states as no more than classcal ignorance. For instance, in Bohmian mechanics the wavefunction is not a purely epistemic object. As far as I know, in BM there is no isomorphism induced from the quantum state |\psi\rangle to probablity densities P_\psi(\lambda) d\lambda over some hidden variable space \Lambda. Thus the interpretation of the wavefunction in BM is not purely epistemic - some parts of it "touch the world" (through the quantum potential). In the gaussian world the Wigner distributions are isomorphic to the states and yet do not "touch the world", so I would call them "purely epistemic". They can be understod as merely encapsulations of an observers "state of knowledge" about the world.

Yes, you're right, I didn't appreciate your intended emphasis on *no more than* classical ignorance. And you're of course right about Bohm's theory. In that theory, the wf is not merely a statement about our knowledge. It refers to a real "wave" out there in the world (from which we can infer something about the probability distribution of particles according to the quantum equilibrium hypothesis).

Note that this gaussian model is deterministic - the point of the particle in phase space determines what outcome it will give to any particular measurement - and this is a feature I like and generally presume.

Hmmm. But if you're regarding this distribution as purely epistemic, doesn't that mean it's implicit in the model that there exists a real particle which has some definite (but of course unknown) values for position and momentum? (Otherwise I just don't know what you mean by "purely epistemic" -- that knowledge has to be knowledge about some real state of affairs, or it isn't really knowledge.) But then I wonder: is the model deterministic in the sense that the Wigner distributions at different times are consistent (in the sense of "equivariance" in Bohm's theory -- that is, does the x,p probability distribution at one time flow, via the underlying Schroedinger dynamics, into the same new probability distribution you'd get by evolving it forward using the implied particle-with-definite-position-and-momentum ontology?

Maybe that isn't clear. What I'm getting at is that there seem to be two aspects to the dynamics: the measurement part, and the non-measurement part. You claimed that the model is deterministic in the sense that there is a definite phase space point which determines what the outcome will be for either an x-measurement or a p-measurement. No problem there. The question is: what about the other half of the dynamics, the non-measurement part? If there is an actual phase space point, what controls its evolution from one moment to the next, and is this consistent with the Schroedinger type evolution which lies behind the time evolution of the Wigner distributions? I suspect the answer is that these aren't consistent, which seems like a serious problem. But I'm not really sure.

So let's call "epistemic models" the deterministic hidden variable theories of the form I just briefly described. The gaussian world is formed in Hilbert space, but can be understood in terms of a local epistemic model. Quantum mechanics cannot be understood in terms of a local epistemic model, but perhaps it can in terms of a nonlocal one (i.e. one in which the ontic states \lambda\in\Lambda are nonlocal).

I don't understand this. The model you described above does have some "ontic" commitments, right? It says there's a definite (but unknown) phase space point for the particle. Maybe you want to deny that, and just take the phase space probability distribution (the wigner dist) as elementary. But if a theory is purely epistemic in that sense -- if it makes no ontic claims whatever -- then I literally don't know what there is to talk about in regard to the locality/nonlocality of the model. Indeed, it ceases to be a model or theory in the sense I'm used to -- it ceases to say *anything* about the external world. So then what is left of the question of whether or not what it says about the world is consistent with relativity's causal prohibitions?

I absolutely agree that no local hidden variable theory (epsitemic or otherwise) is going to work.

Well we know a non-local hvt can work, because there's an example: Bohm's theory. The question that most interests me is: what do you have to give up to get rid of the nonlocality? Everybody has been saying for decades that you can have a local model so long as it isn't deterministic, or so long as it isn't "realistic", or so long as it doesn't have hidden variables, etc. But as far as I can tell, all these claims are wrong. Nonlocality is not a price paid for introducing determinism/hv's/etc. I think you indicated that you agree with me here. So I'm still confused about what exactly we're arguing about...

I hope that's clear form what I wrote above. I was challenging you to prove that no epsitemic model whatsoever is going to work.

I guess I'm objecting to the phrase "epistemic model." If what you mean by "epistemic" is that the model makes zero ontic claims -- i.e., doesn't purport to be *about* anything, i.e., doesn't say anything about a really-existing external world -- then (a) I don't know why you're calling it a "model" (since it's not then a model *of* anything) and (b) I don't know what it even means to assess its locality.

 

[Tez]

Maybe that isn't clear. What I'm getting at is that there seem to be two aspects to the dynamics: the measurement part, and the non-measurement part. You claimed that the model is deterministic in the sense that there is a definite phase space point which determines what the outcome will be for either an x-measurement or a p-measurement. No problem there. The question is: what about the other half of the dynamics, the non-measurement part? If there is an actual phase space point, what controls its evolution from one moment to the next, and is this consistent with the Schroedinger type evolution which lies behind the time evolution of the Wigner distributions? I suspect the answer is that these aren't consistent, which seems like a serious problem. But I'm not really sure.

No, it is consistent - in fact this is what underpins various results in quantum information to do with being able to classically simulate quantum computers built only out of such gaussian operations. In fact these simulations are nearly always done by following the covariance matrix (fourier transform of the Wigner distribution). The Hamiltonian evolution induces exactly the same symplectic transform on the canonical variables as it would in the classical case, while on the states it induces standard unitary evolution. The closest paper I have in front of me at hand I see discussing the evolution is quant-ph/0402004, though they may not prove it just assume it! Ah - I also just noticed in quant-ph/0204052 in the second paragraph on page 2 they state what I said above without proof! I don't think it'd be too hard to prove, but if you'd like to see it I'll try.

I don't understand this. The model you described above does have some "ontic" commitments, right? It says there's a definite (but unknown) phase space point for the particle. Maybe you want to deny that, and just take the phase space probability distribution (the wigner dist) as elementary. But if a theory is purely epistemic in that sense -- if it makes no ontic claims whatever -- then I literally don't know what there is to talk about in regard to the locality/nonlocality of the model. Indeed, it ceases to be a model or theory in the sense I'm used to -- it ceases to say *anything* about the external world. So then what is left of the question of whether or not what it says about the world is consistent with relativity's causal prohibitions?

I don't understand what you don't understand! But let me try and help by saying yes, the gaussian model does have ontic commitments which are represented by the points of phae space which in turn describe the position and momentum (or quadrature value in optics) of the system; no, I don't want to take the phase space distribution as ontic, that's the last thing I want to do!

I'm simply imagining the ontic entities out there are nonlocal - in some way or another they disrespect our precious notions of locality. I see quantum theory as a probabilistic theory about these Unidentified Ontic Objects. (UOO's)

Well we know a non-local hvt can work, because there's an example: Bohm's theory. The question that most interests me is: what do you have to give up to get rid of the nonlocality? Everybody has been saying for decades that you can have a local model so long as it isn't deterministic, or so long as it isn't "realistic", or so long as it doesn't have hidden variables, etc. But as far as I can tell, all these claims are wrong. Nonlocality is not a price paid for introducing determinism/hv's/etc. I think you indicated that you agree with me here. So I'm still confused about what exactly we're arguing about...

As you said, we have no disagreement on those points.

I guess I'm objecting to the phrase "epistemic model." If what you mean by "epistemic" is that the model makes zero ontic claims -- i.e., doesn't purport to be *about* anything, i.e., doesn't say anything about a really-existing external world -- then (a) I don't know why you're calling it a "model" (since it's not then a model *of* anything) and (b) I don't know what it even means to assess its locality.

No - an epistemic model makes all sorts of ontic claims (once one identifies the ontic state space!) The epsitemic part refers only to the fact that the quantum states are interpreted epistemically.

More simply, by epsitemic model I mean only this: Quantum states are to the (nonlocal) UOO's as the probability distributions in statistical mechanics are to the points in phase space of atoms.

In the big picture I look to what Jaynes did in '48 when he showed how many of the laws of thermodynamics could be understood as not truly fundamental, but rather must follow from how any rational being must calculate given coarse grained information (pressure, temp etc) about an underlying reality. I suspect that many features of QM - collapse and linearity being the main two - also follow not from something truly fundamental, but rather from similar such principles.

 

[vanesch]

Hmmm. But if you're regarding this distribution as purely epistemic, doesn't that mean it's implicit in the model that there exists a real particle which has some definite (but of course unknown) values for position and momentum? (Otherwise I just don't know what you mean by "purely epistemic" -- that knowledge has to be knowledge about some real state of affairs, or it isn't really knowledge.) But then I wonder: is the model deterministic in the sense that the Wigner distributions at different times are consistent (in the sense of "equivariance" in Bohm's theory -- that is, does the x,p probability distribution at one time flow, via the underlying Schroedinger dynamics, into the same new probability distribution you'd get by evolving it forward using the implied particle-with-definite-position-and-momentum ontology?

Yes, that's also the objection I had, even with the limited positive definite Wigner states.

It isn't sufficient to say that we can just have, at each moment in time, a positive-definite probability function over some state space. One also needs to define a dynamics that gouverns the flow of this probability distribution in such a way that it really is a flow of independent points, ea that the final distribution is the convolution of the initial distribution and a "dynamic Kernel function" ; where this dynamic kernel function is independent of the initial distribution, of course.
That Kernel function then describes the true dynamics of each individual state (point in phase space) independent of how we (epistemologically) had a distribution of probability over the different points. This is what Bohmian mechanics does, if I'm not mistaking. But this dynamics is then assuredly non-local (a flow in phase space can be local, or not, depending on whether we can split the phase space into a direct sum of sub-phase space points corresponding to remote systems, and whether the flow also splits correspondingly).

 

[Tez]

A note on what I mean by epistemic models, plus the qubit model of Kochen and Specker:

http://www.physicsnerd.com/NotesForPhysicsForums.pdf

 

[ttn]

Yes, that's also the objection I had, even with the limited positive definite Wigner states.

It isn't sufficient to say that we can just have, at each moment in time, a positive-definite probability function over some state space. One also needs to define a dynamics that gouverns the flow of this probability distribution in such a way that it really is a flow of independent points, ea that the final distribution is the convolution of the initial distribution and a "dynamic Kernel function" ; where this dynamic kernel function is independent of the initial distribution, of course.
That Kernel function then describes the true dynamics of each individual state (point in phase space) independent of how we (epistemologically) had a distribution of probability over the different points. This is what Bohmian mechanics does, if I'm not mistaking. But this dynamics is then assuredly non-local (a flow in phase space can be local, or not, depending on whether we can split the phase space into a direct sum of sub-phase space points corresponding to remote systems, and whether the flow also splits correspondingly).

Yes, exactly. That's precisely what I was trying to say. And you also get to the reason I was worried about this: Bohmian mechanics does do this, but with a first-order dynamics, where the "phase space" is just the configuration (position) space. Momentum then becomes something like a contextual variable -- yes, the particle always has a definite rate-of-change-of-position (which I guess you could define as proportional to the "momentum") but this *isn't* what one gets as the outcome of a "momentum measurement". (That's why I say it's something like a contextual variable -- the outcome doesn't reflect the pre-existing value. But unlike a genuinely contextual property, the momentum measurement outcome will be uniquely determined. But I don't think that makes any difference here.)

And then too there is the fact that Bohmian Mechanics is nonlocal, and *has* to be in order to give the right answers. I'm quite certain you can't take Bohmian Mechanics and make it local and still have a theory that is consistent with experiment. And it sounded like Tez was making an even stronger claim than this -- that one can localize Bohmian mechanics *and* un-contextualize momentum. If that were true, it would be truly shocking!

 

[vanesch]

And it sounded like Tez was making an even stronger claim than this -- that one can localize Bohmian mechanics *and* un-contextualize momentum. If that were true, it would be truly shocking!

No, I understood that he accepts non-locality and tries to prove that there then exists such a model... But I thought that Bohmian mechanics IS exactly such a model he was looking for. What seems to disturb him is that there is still this wavefunction floating around, but that is then just to be taken as PART of the phase space and you HAVE a phase space (= product of the configuration space of particles, and the hilbert space of the wavefunction), no ? Ok, this looks probably too clumsy for Tez, but if he's looking for an existence proof, then having a concrete example should do the thing, no ?

 

[Tez]

Sorry for slow responses guys - I have a visitor for a week and then have to travel so I'll be here infrequently.

Bohmian mechanics is certainly nonlocal, but it does not have an epistemic interpretation of the wavefunction, in the sense that I indicated I'm looking for in those notes I linked to. I believe I can find such a formulation, but its quite ugly and not intuitive - plus for silly technical reasons I am not confident in my proof that it is completely epistemic (in the sense that a system in some state \lambda should not be able to "know" that its actually in quantum state \psi, as in the qubit model).

Travis I hope you realize I never claimed anything like "that one can localize Bohmian mechanics *and* un-contextualize momentum". In case it has not been clear, though I have stated it several times: I am not talking about a theory that is equivalent to quantum mechanics. Thus comparing it directly to Bohmian mechanics, which is equivalent to QM, is a bit of a mugs game. The Gaussian world is a subset of quantum mechanics that incorporates many of the things which are often taken to be puzzling about the larger theory, but which remains local (although it has wavefunction collapse on distant systems which some may call nonlocality, but which in this model is no different to the classical case of updating your information about a remote system). It is a useful pedagogical tool. No more, no less. In the context of this discussion I brought it up to illustrate that a theory in a complex Hilbert space with both a "measurement problem" and an EPR paradox (in its orginal form!) is not necessarily nonlocal, nor does it have to have a weird non-classical ontology.

I did have an interesting thought: I think (though haven't checked) that the Bohmian description of the Gaussian world is nonlocal (unless the quantum potential vanished for gaussian states and quadratic Hamiltonians). In this sense Bohmian mechanics is more nonlocal than it needs to be. Since the gaussian world hidden variable model is formulated in phase space, not configuration space, I am wondering if there is a phase space version of Bohmian mechanics which has the feature that when restricted to gaussian states the theory becomes local? Or perhaps a new version of BM in configuration space (which I personally find more intuitive) can be formulated with this feature?

 

[DrChinese]

I've argued here in the past (with dr chinese and others) about what, exactly, is proved by Bell's Theorem. Here is a new paper which addresses
and clarifies many of those points:

http://www.arxiv.org/abs/quant-ph/0601205

OK, I'm ready to talk about the paper (even though I am still working on some parts).

a. The basic assertion is that "No Bell Local Theory can be consistent with relevant experiments on entangled particles." And some pretty good logic is presented to support that view. (In my opinion, the main result is dependent on the exact definition of locality given.)

b. However, I wish to demonstrate that another view is equally reasonable. My assertion is "No Realistic Theory can be consistent with relevant experiments on entangled particles." My definition of realisitic is very simple: One in which the Heisenberg Uncertainty Relations can be beaten - just as envisioned in EPR. Thus, a theory which provides a more complete specification of the state of the system than oQM does (the wave function) is by definition "realistic". And I believe this definition is consistent with Bell.

c. I think we would all agree that if a. is true as a consequence of Bell's Theorem, then b. cannot be. And vice versa. I mean, the whole point of Bell's Theorem is to rule out the entire class of local realistic theories. Of course, a. and b. can both be true, but we cannot deduce both from Bell's Theorem.

So now I simply say: there are currently no theories which provide a more complete specification of the system than does oQM. By my definition, Bohmian Mechanics does not qualify because there is no more complete specification of the system experimentally possible - i.e. no one has ever provided such greater specification even though it is claimed it is "possible". For any such theory to qualify, we need to beat the HUP which still never happens. Thus, I conclude b. is demonstrably true and therefore a. is not necessarily true (by c.). QED.

My point is that conclusion a. is not justified from Bell's Theorem. We need to know more to distinguish between a. and b. - if indeed one is true and the other is not.

 

[ttn]

b. However, I wish to demonstrate that another view is equally reasonable. My assertion is "No Realistic Theory can be consistent with relevant experiments on entangled particles." My definition of realisitic is very simple: One in which the Heisenberg Uncertainty Relations can be beaten - just as envisioned in EPR. Thus, a theory which provides a more complete specification of the state of the system than oQM does (the wave function) is by definition "realistic".

This is definitely not true. I can prove it by constructing a counter-example.

Here's my theory, call it Theory X. Let's suppose we're only talking about the kind of experiment covered in the paper -- three possible measurement directions (which are the same on the two sides). According to Theory X, each particle in the pair possesses simultaneous definite values for spin along all three of these axes. And (this part is arbitrary and need not be this way, but) what we call "preparing a singlet state" is really (according to Theory X) a way of producing one of the following two definite pair states:

A1=+, A2=+, A3=+, B1=+, B2=+, B3=+

or

A1=-, A2=-, A3=-, B1=-, B2=-, B3=-

So, before any measurements are made, each particle has a definite value for all 3 spin components. This violates the HUP since the qm spin operators for these three directions don't commute. Well, nevermind, because mine is a hidden variable theory. OK so far? So if I can get this theory to agree with the QM predictions, then I'll have a counterexample to your claim above, right?

Well it's easy to do that if I introduce some nonlocality into the theory. Suppose Alice's particle gets to Alice first, so she makes the first measurement (with "first" defined in the ether frame) and she randomly picks from among the 3 measurement directions. So she measures either A1, A2, or A3 at random, and gets whatever pre-existing value is assigned to that observable by whichever of the two states happens to have been produced on that run. So she gets either + or -, with 50/50 probability.

But Theory X also includes the following nonlocal mechanism. Once Alice makes this measurement, her particle "radios" the other particle and "tells" it which axis Alice measured along. Then I think it is obvious that there can be a pre-existing set of rules which Bob's particle uses to re-adjust its state (by some stochastic process) such that the joint outcomes will, in the long run, agree with QM. If that's not obvious I can make it explicit, but I think it's obvious so I won't bother. But for example: if Alice's particle "tells" Bob's particle that Alice measured along direction 1, then Bob's particle will (a) flip its value of B1 with probability 100%, (b) flip its value of B2 with a probability depending on the angle between directions 1 and 2, and (c) flip its value of B3 with a probability depending on the angle between directions 1 and 3.

You get the idea? The point is, if you're going to allow non-locality, it is *easy* to always reproduce the QM predictions. I can do it *even* with a theory that is (as you defined it) "realistic". So where does that leave things? Let's catalogue whether or not the following types of theories can agree with experiment:

Non-Realistic and Non-Bell-Local? Yes (i.e., yes, such a theory can agree with experiment, e.g., orthodox QM)

Realistic and Non-Bell-Local? Yes (e.g., Theory X)

Non-Realisitic and Bell Local? No (as proved in the paper)

Realistic and Bell Local? No (as proved by Bell's theorem)

So I don't think it's possible to deny the logic. The realistic vs. non-realistic "axis" doesn't correlate the right way with being vs. not being able to make the right predictions. Bell Local vs. not Bell Local *does* correlate the right way. This is all just an overly fancy and cumbersome way of saying that no Bell Local theory (whether "realistic" or not) can agree with experiment.

I mean, the whole point of Bell's Theorem is to rule out the entire class of local realistic theories.

That's the conventional wisdom maybe, but repeating it as a mantra doesn't make it true. And frankly it's a mystery to me how it even got to be the conventional wisdom in the first place since Bell himself so clearly repudiated this view. He says repeatedly that "the whole point" is that there is a conflict between quantum theory (in any interpretation) and relativity. "Realism" just doesn't enter into it.

...unless you switch from a narrow definition of realism that basically means hidden variables, to some kind of broad metaphysical sense, according to which "anti-realism" means you don't believe there's a real world out there. But if your "theory" is "anti-realist" in *that* sense, you're hardly in a position to claim that the theory is local! "There's no such thing as external reality, but the causal processes in the world, as described by my theory, respect relativity's prohibition on superluminal causation." That's just flat out contradictory nonsense, right?

So now I simply say: there are currently no theories which provide a more complete specification of the system than does oQM. By my definition, Bohmian Mechanics does not qualify because there is no more complete specification of the system experimentally possible - i.e. no one has ever provided such greater specification even though it is claimed it is "possible".

I don't follow this. *Clearly* Bohmian Mechanics proposes a more detailed specification than OQM. It has *definite particle positions* in *addition* to the wave function!

Is your phrase about "experimentally possible" some kind of qualification of what you mean by "providing a more complete specification"? You better be careful, though, not to define things in such a way that what you mean by a more complete specification turns into "makes different empirical predictions than OQM". *That* is a different issue entirely.

For any such theory to qualify, we need to beat the HUP which still never happens.

What do you mean by "beat"? According to Bohm, particles have definite positions and follow definite trajectories (hence have definite velocities and hence definite p=m*v). Does that count as "beating" the uncertainty principle? If what you mean is: provide a more detailed specification of the state of things such that variables which are "fuzzy" according to OQM (as quantified by the HUP) are "sharp", then this obviously does that. Again, though, if what you really mean is only that we should be able to "beat" the HUP *in practice* (i.e., *measure* x and p simultaneously, say) then that is a totally different issue. To insist on that is (roughly) to insist that any alternative to OQM make different empirical predictions from OQM. But this is simply to misunderstand what the completeness controversy is all about. The whole question is whether one can tell a more detailed story that makes some physical sense and isn't inherently fuzzy in the ways that OQM is fuzzy, and still get the experimentally correct answers. If you define things in such a way that you're no longer talking about that issue, but something else entirely, then you are just changing the subject instead of addressing the issue.

My point is that conclusion a. is not justified from Bell's Theorem.

That's probably right. But since "Bell's theorem" wasn't the proposed argument for it in the first place, who cares?

 

[DrChinese]

This is definitely not true. I can prove it by constructing a counter-example.

Here's my theory, call it Theory X. Let's suppose we're only talking about the kind of experiment covered in the paper -- three possible measurement directions (which are the same on the two sides). According to Theory X, each particle in the pair possesses simultaneous definite values for spin along all three of these axes. And (this part is arbitrary and need not be this way, but) what we call "preparing a singlet state" is really (according to Theory X) a way of producing one of the following two definite pair states:

A1=+, A2=+, A3=+, B1=+, B2=+, B3=+

or

A1=-, A2=-, A3=-, B1=-, B2=-, B3=-

So, before any measurements are made, each particle has a definite value for all 3 spin components. This violates the HUP since the qm spin operators for these three directions don't commute. Well, nevermind, because mine is a hidden variable theory. OK so far? So if I can get this theory to agree with the QM predictions, then I'll have a counterexample to your claim above, right?

You have to "beat" the HUP *first* to win your prize. You can't simply say it has these hidden values but lacks a way to unlock them. That would be like me saying I have a local theory that agrees with oQM even though it acts as if it is non-local. (For instance, Vanesch might say MWI qualifies in that regard, thus presenting a counterexample to your main argument.)

So: no, I don't agree.

 

[DrChinese]

What do you mean by "beat"? According to Bohm, particles have definite positions and follow definite trajectories (hence have definite velocities and hence definite p=m*v). Does that count as "beating" the uncertainty principle? If what you mean is: provide a more detailed specification of the state of things such that variables which are "fuzzy" according to OQM (as quantified by the HUP) are "sharp", then this obviously does that. Again, though, if what you really mean is only that we should be able to "beat" the HUP *in practice* (i.e., *measure* x and p simultaneously, say) then that is a totally different issue. To insist on that is (roughly) to insist that any alternative to OQM make different empirical predictions from OQM. But this is simply to misunderstand what the completeness controversy is all about.

Yes, by "beat" or "more complete" I mean that the theory not only posits a greater specification of the WF, but shows us how to observe it.

With an extra wave of the hand, you could say that your same theory explains the origin of the big bang too. But that won't be very persuasive to many people.

 

[ttn]

Yes, by "beat" or "more complete" I mean that the theory not only posits a greater specification of the WF, but shows us how to observe it.

With an extra wave of the hand, you could say that your same theory explains the origin of the big bang too. But that won't be very persuasive to many people.

So... you insist that any "beables" postulated by a theory be directly observable? I don't think that's a good standard. But even leaving that aside, I'd have to note that OQM is disqualified on this same basis. After all, you can't directly observe the wave function (in the sense of figuring out what the wf is for a system someone hands you). In fact, by this standard, one could never have a theory of microscopic phenomena at all.

I really have no idea what you're trying to say with the last comment about "the origin of the big bang." Do you think the claim that Bohmian Mechanics reproduces the quantum mechanical predictions is somehow made up out of thin air and hence meaningless? Nothing could be further from the truth. That Bohm's theory agrees with the QM predictions is an actual *theorem* (which applies so long as what we call "measurements" are always registered configurationally). What we have is two perfectly well-defined theories, with radically different ontologies, which nevertheless agree about what the outcomes of experiments should be. Your attitude seems to be: well, everybody already accepts theory 1 and it agrees with experiment, so why change? Well even leaving aside that there is a good reason to change (namely the measurement problem) it's totally bogus to think that one theory is better than another just because lots of people believe it. If the two are equally good at explaining the observed data, then *on that criterion* there is no valid basis for preferring one to the other.

 

[DrChinese]

So... you insist that any "beables" postulated by a theory be directly observable?

I am asking as follows: If a theory claims to have a greater predictive ability (i.e. BM versus oQM), then it should offer that to us. Otherwise, I cannot give it credit for what is claimed but not demonstrated. So my specific requirement is, coming straight from EPR:

Alice measures attribute A on her particle, while Bob measures attribute B on his particle. Then Alice measures attribute B on her particle, while Bob next measures attribute A on his particle. The respective measurements give results that violate the HUP. When we can do this, we have a more complete specification of the system. Until then, we have nothing but unsubstantiated claims; and certainly nothing useful to distinguish one theory from the other.

 

[ttn]

I am asking as follows: If a theory claims to have a greater predictive ability (i.e. BM versus oQM), then it should offer that to us. Otherwise, I cannot give it credit for what is claimed but not demonstrated.

What are you talking about? Who ever made any claim about one theory "having greater predictive ability" than another? If you think that that's what the completeness vs. hidden variables debate is about, you're so far off base I'm wasting my time talking to you.

Sigh.

Look, you made a very specific claim -- namely, that no "realistic" theory could agree with the observed EPR-Bell correlation data, with a perfectly definite meaning of "realistic" that amounted to the existence of hidden variables. I then provided a counterexample: a hidden variable theory that did agree with the data. Now you're twisting and contorting trying to redefine what you meant by "realistic". I can't hit a moving target.

So my specific requirement is, coming straight from EPR:

Alice measures attribute A on her particle, while Bob measures attribute B on his particle. Then Alice measures attribute B on her particle, while Bob next measures attribute A on his particle. The respective measurements give results that violate the HUP. When we can do this, we have a more complete specification of the system. Until then, we have nothing but unsubstantiated claims; and certainly nothing useful to distinguish one theory from the other.

What the heck is this supposed to be a requirement *for*? This is now your new definition of "realistic"? Or what? I honestly have no idea what you're even trying to say here. Is there any theory in which Alice *can't* measure attribute A on her particle, and then measure attribute B on her particle? And what exactly does it mean for those two measured values to violate the HUP? I mean, you can do this according to OQM for god's sake. Measure sigma_x and then sigma_y on some spin 1/2 particle. You get definite outcomes (with no uncertainty). So the product of the uncertainties is zero, in violation of HUP. I'm sure this isn't what you meant, but it's what you said. So you better clarify.

Presumably you have something in mind like: Alice's results for A and B agree with some values that Bob could infer (about Alice's results) based on his own measurements of A and B. Or perhaps you mean that Alice should measure A, then B, then A again -- and always get the same answer for A both times. Or something like that. But then the point is: what you are requiring is tantamount to a disagreement with the QM predictions!

And so look at what you're saying: no realistic theory can agree with the QM predictions -- where "realistic" is defined as disagreeing with the QM predictions.

I bow down before this amazing and illuminating new theorem!

And anyway, isn't this thread supposed to be about the claim (which you said you were ready to discuss) that no Bell Local theory can agree with the QM predictions? You started your contribution to the thread by saying that you thought this was wrong, and that what was really true was that no realistic theory can agree with the QM predictions. That has been blasted to high heaven. So why don't we return to the main issue. If you think that initial claim of mine is wrong, presumably you can provide a counterexample to it -- i.e., an example of a theory which is Bell Local (as defined in the paper) but which agrees with the QM predictions for these spin correlations. I'll bet you can't.

 

[DrChinese]

Look, you made a very specific claim -- namely, that no "realistic" theory could agree with the observed EPR-Bell correlation data, with a perfectly definite meaning of "realistic" that amounted to the existence of hidden variables. I then provided a counterexample: a hidden variable theory that did agree with the data. Now you're twisting and contorting trying to redefine what you meant by "realistic". I can't hit a moving target.

...

And anyway, isn't this thread supposed to be about the claim (which you said you were ready to discuss) that no Bell Local theory can agree with the QM predictions? You started your contribution to the thread by saying that you thought this was wrong, and that what was really true was that no realistic theory can agree with the QM predictions. That has been blasted to high heaven. So why don't we return to the main issue. If you think that initial claim of mine is wrong, presumably you can provide a counterexample to it -- i.e., an example of a theory which is Bell Local (as defined in the paper) but which agrees with the QM predictions for these spin correlations. I'll bet you can't.

My point is quite simple: every argument you have made in favor of the idea that "Bell Locality cannot be respected by any theory whose predictions match oQM" can be turned around to prove my contention. Which, to me, demostrates neither can be correct. You can no more produce a valid theory that beats the HUP than I can produce a valid theory that does not appear non-local from some viewpoint.

Defining "realism": There is no moving target, we can use the definition of EPR, which is that there is simultaneous reality to non-commuting observables - thus holding out the prospect of a more complete specification of the system (which I am fairly skeptical of).

As to completeness: You hypothesize the existence of hidden variables that just happen to disappear right around the point that the HUP kicks in - and leaving us no better off than before (i.e. with old-fashioned oQM). If you can give me simultaneous values for non-commuting variables that step over that edge, now that would be interesting.

As to the counterexample: Vanesch has provided such over and over - but you happen to prefer BM over MWI and so you seem not to take it seriously. MWI is local non-realistic (since there is branching whenever an observation occurs). There is not one lick of experimental support for one over the other. I ask: What is the point of fabricating theories which cannot in principle be tested? I assume you have seen Weinberg's view of BM, which was not particularly kind in exactly that regard...

So I stand my ground: it is still either/or. I respect your preference for non-local solutions but your argument swings both ways. If we follow your logic, my argument is just as reasonable - or as unreasonable - as yours.

 

[ttn]

My point is quite simple: every argument you have made in favor of the idea that "Bell Locality cannot be respected by any theory whose predictions match oQM" can be turned around to prove my contention.

What contention is that? That no "realist" theory can agree with experiment? But this has been demonstrated to be false. There exist realist theories that do agree with experiment, e.g., theory X from several posts above, and Bohm's theory.

Defining "realism": There is no moving target, we can use the definition of EPR, which is that there is simultaneous reality to non-commuting observables - thus holding out the prospect of a more complete specification of the system (which I am fairly skeptical of).

I've given two examples of theories which posit "simultaneous reality to non-commuting observbles" and which agree with the relevant experiments.

Your rejection of those as counterexamples involves a change to a new definition of "realism" that is totally vague and stupid, and seems to have something to do with disagreeing with the QM predictions. That's a moving target.

As to completeness: You hypothesize the existence of hidden variables that just happen to disappear right around the point that the HUP kicks in - and leaving us no better off than before (i.e. with old-fashioned oQM). If you can give me simultaneous values for non-commuting variables that step over that edge, now that would be interesting.

What disappears? Do you mean that the values of some of the variables sometimes change when the system interacts with things? Are you seriously requiring that a realist theory cannot have any dynamics? Give me a break.

As to the counterexample: Vanesch has provided such over and over - but you happen to prefer BM over MWI and so you seem not to take it seriously. MWI is local non-realistic (since there is branching whenever an observation occurs). There is not one lick of experimental support for one over the other. I ask: What is the point of fabricating theories which cannot in principle be tested? I assume you have seen Weinberg's view of BM, which was not particularly kind in exactly that regard...

Actually, MWI doesn't agree with the predictions of QM. QM says that pointers point. MWI says they don't (but that we are deluded into thinking they do). They agree about some things -- namely, what some human consciousness will believe -- but not about others (namely, what the actual state of certain macroscopic objects will be). In particular, they don't agree about the *outcomes* of the measurements made by Alice and Bob. QM says there are outcomes (with certain correlations) and MWI says there aren't outcomes. So this is not a counterexample.

So I stand my ground: it is still either/or. I respect your preference for non-local solutions but your argument swings both ways. If we follow your logic, my argument is just as reasonable - or as unreasonable - as yours.

First off, I don't have a "preference" for non-local solutions. I have a preference for identifying clearly what is required by the facts. Second, what are you talking about when you say your argument is just as reasonable... What argument? You just arbitrarily claimed that "no realist theory can agree with experiment" and then refuse to define what you mean or provide any kind of argument or proof for the claim. (The closest you come is to define "realist" as "disagreeing with the QM predictions", which of course renders your alternative theorem an empty tautology.)

Based on our previous conversations, I thought you'd be interested to really confront the issues raised by this paper. But now it's you who is coming off as closed-minded and evasive. I have no interest in an extended fight-fest; if you want to discuss the paper seriously, that would be cool. If not, let's agree to not waste our time.

 

[ttn]

I assume you have seen Weinberg's view of BM, which was not particularly kind in exactly that regard...

You mean the view that develops here?

http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/weingold.htm

 

[DrChinese]

You mean the view that develops here?

http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/weingold.htm

Yes, exactly. Clearly, there is a wide range of opinions on the subject and emotions tend to get into the matter fairly quickly.

I thought you might see that your argument (that no Bell Local theory can agree with oQM) is no stronger than the counter-argument (that no Realistic theory can agree with QM).

Further: If you say you have a theory that is non-local and thus disproves my counter-argument, then I simply answer I have a theory that is non-realistic and that disproves your argument.

And there is not a single experimental fact that proves you right or me right. It is all words.

So if you are convinced you won the war of words, then fine. I was interested in learning more about your views and why you hold them so strongly. But if you can't answer some simple questions that anyone else is bound to ask (i.e. why non-locality over non-reality), then I would agree: let's stop it here.

 

[ttn]

Yes, exactly. Clearly, there is a wide range of opinions on the subject and emotions tend to get into the matter fairly quickly.

No doubt.

I thought you might see that your argument (that no Bell Local theory can agree with oQM) is no stronger than the counter-argument (that no Realistic theory can agree with QM).

But it *is* stronger -- in (at least!) an empirically measurable sense: I provided a counter-example to your claim (that no realistic theory can agree with QM), whereas you have not (and, I dare say, will never) provide a counter-example to my claim (that no Bell Local theory can agree with the predictions of QM for these measurement outcomes).

Further: If you say you have a theory that is non-local and thus disproves my counter-argument, then I simply answer I have a theory that is non-realistic and that disproves your argument.

Um, yeah, you can "simply answer" that way... but it's not particularly convincing unless you actually *have* and actually *share* this theory. So... would you be willing to share it? Tell us about this Bell Local (but not "realistic") theory which agrees with the predictions of QM.

 

[DrChinese]

Um, yeah, you can "simply answer" that way... but it's not particularly convincing unless you actually *have* and actually *share* this theory. So... would you be willing to share it? Tell us about this Bell Local (but not "realistic") theory which agrees with the predictions of QM.

Sure, I'll give you two:

1. MWI. That does not make me an advocate of it.

2. Here is another one, a personal invention, and again I am not advocating it.

There are no avenues of influence or communication which are superluminal*. However, the future influences the past with a limiting velocity of c, respecting relativity. The influence from the future to the past is limited to signalling the nature of the measurement which Alice (or Bob) is making. Of course, this signalling goes from the future to the past and so it appears to us as an influence coming from nowhere - ie. random. This would allow a way for Alice's measurement setting to be communicated to Bob, as the backward influence of her measurement setting is communicated to a point in the past which can affect Bob's soon-to-be future. This theory is *not* realistic, because there is no greater specification of the wave function possible and particles do not have well defined attributes independent of the act of measurement. All other elements of the theory match oQM.

Now, as far fetched as this may sound, I don't see how it is any more far fetched than postulating superluminal pilot waves that are individually undetectable.

*It is possible you might say this violates Bell Locality, and in a way you are correct. But collapse of the wave function is local, which is not a feature of oQM as many see it.

 

[ttn]

1. MWI. That does not make me an advocate of it.

Already addressed in a previous post.

2. Here is another one, a personal invention, and again I am not advocating it.

There are no avenues of influence or communication which are superluminal*. However, the future influences the past with a limiting velocity of c, respecting relativity...

"The future" is definitely not in the past light cone of an event. So this violates Bell Locality.

To hear about some other problems with this kind of idea, check out Tim Maudlin's comments on Cramer's "Transactional Interpretation" (in Maudlin's book, Quantum Nonlocality and Relativity... highly recommended.)

Now, as far fetched as this may sound, I don't see how it is any more far fetched than postulating superluminal pilot waves that are individually undetectable.

Positing Bohm's theory is a different issue. One doesn't have to like Bohmian Mechanics to recognize that viable theories have to violate Bell Locality.

*It is possible you might say this violates Bell Locality, and in a way you are correct. But collapse of the wave function is local, which is not a feature of oQM as many see it.

I don't know what you mean by saying "collapse of the wf is local". You mean in OQM? Or in your funny reverse-temporal causation model? Or what?

 

[DrChinese]

I don't know what you mean by saying "collapse of the wf is local". You mean in OQM? Or in your funny reverse-temporal causation model? Or what?

In my funny model...

Look, don't take things so seriously. Your ideas have plenty of merit, but they need some polishing. If you can't convince me (I'm easy), then they need more work. How are you going to convince someone serious?

 

[ttn]

In my funny model...

But as I pointed out before, your funny model violates Bell Locality.

 

[selfAdjoint]

But as I pointed out before, your funny model violates Bell Locality.

Please, not another megillah on the semantics of "Bell Locality"!

 

[ttn]

Please, not another megillah on the semantics of "Bell Locality"!

Yeah, I'm sick of it too. Some people just refuse to see what's there in front of them.

But hey, some good came of it -- I learned the new word "megillah"!

 

[Sherlock]

Ok, I've read the paper, and I agree with the conclusion that no Bell Local theory can be empirically viable.

Does this mean that nonlocality is a fact of nature? Yes, but only in the sense that no Bell Local theory can be empirically viable. (At least for the foreseeable future.)

This means that if you are going to construct a realistic (ie., a metaphysical rendition) theory of an underlying quantum world, then that theory is going to have to be nonlocally causal in order to account for certain quantum experimental correlations.

This doesn't mean that it is a physical fact that nonlocal causal transmissions or propagations or evolutions, or whatever, exist in whatever might constitute the reality of an underlying quantum world, because there's simply no way to ascertain that. If, in fact, there are no such nonlocal causal agents in nature, then you have a theory which is a bad heuristic vision of the underlying reality and in unnecessary conflict with relativity.

You write:
"Since the empirical predictions of quantum theory respect Signal Locality, there is no way to 'exhibit' any nonlocality at the level of 'our observations'. It simply cannot be done. But if, motivated by the orthodox quantum philosophy, one excludes from the beginning any talk about the 'features of a putative underlying reality', then there is literally nothing else -- that is, no other sense of locality -- to discuss. The vague anti-realism of the orthodox quantum philosophy thus seems to rule out the very kind of talk that is absolutely required to show that nature violates some locality condition -- namely, talk of nature."

It only rules out taking talk of the underlying reality of nature as necessarily corresponding to what that underlying reality actually is.

You continue:
"But orthodox quantum theory better commit to a realistic description of something. Otherwise -- that is, if one retreats to an exclusively epistemological interpretation of quantum theory in general and the wave function in particular -- one simply no longer has a theory in the sense defined in Section II. It is then meaningless to discuss whether the causal processes posited by the 'theory' respect relativity's prohibition on superluminal causation. A formalism which is not about any such processes is neither local nor nonlocal. Both terms are simply inapplicable."

Well, that's it, isn't it ? Orthodox quantum theory doesn't commit to a realistic description of an underlying reality.

The orthodox quantum philosophy is "vague and ambiguous" because our knowledge of the underlying reality is vague and ambiguous.

You can construct a clear, realistic, metaphysical (and of course nonlocal) theory of underlying reality. But it's quite possible that such clarity will cost you something far more valuable -- namely, the truth.

For all anybody knows, Bohmian Mechanics is the correct approach. But, for all anybody knows, it isn't. That's why I think it's best to stick with the orthodox interpretation (even with all its fuzziness) for the foreseeable future.

 

[ttn]

Does this mean that nonlocality is a fact of nature? Yes, but only in the sense that no Bell Local theory can be empirically viable. (At least for the foreseeable future.)

You make it sound like that's some kind of qualification of the thesis. But it isn't, right?

This means that if you are going to construct a realistic (ie., a metaphysical rendition) theory of an underlying quantum world, then that theory is going to have to be nonlocally causal in order to account for certain quantum experimental correlations.

Sure, you can avoid the nonlocality if you don't talk about the relevant part of the physical world (but instead, say, restrict your attention to peanut butter sandwiches). But that *in no way* undermines the fact that reality is not Bell Local. Just like: you can't qualify or contradict or undermine the thesis "all tigers have stripes" by changing the subject and talking about elephant toenails.

This doesn't mean that it is a physical fact that nonlocal causal transmissions or propagations or evolutions, or whatever, exist in whatever might constitute the reality of an underlying quantum world, because there's simply no way to ascertain that.

Um, yes it does, and yes there is. Bell's two part argument proves that "it is a physical fact..." As I suggested just above, changing the subject (or simply refusing to talk about that subject) doesn't make that fact go away.

Well, that's it, isn't it ? Orthodox quantum theory doesn't commit to a realistic description of an underlying reality.

Well, some people think it does, and it is a natural reading of the "completeness" doctrine to take it as committing to a description of an underlying reality. If it does, it violates Bell Locality. That isn't (or shouldn't be) controversial.

And if you're right (or: in regard to the purely epistemic version of the orthodoxy) that doesn't change anything. There *is* a reality, and that reality is not Bell Local. Refusing to talk about reality doesn't change that.

You can construct a clear, realistic, metaphysical (and of course nonlocal) theory of underlying reality. But it's quite possible that such clarity will cost you something far more valuable -- namely, the truth.

Only if "the truth" is that there is no underlying reality. But it's unscientific, irrational, and downright stupid in the extreme to even entertain that possibility for a second.

For all anybody knows, Bohmian Mechanics is the correct approach. But, for all anybody knows, it isn't. That's why I think it's best to stick with the orthodox interpretation (even with all its fuzziness) for the foreseeable future.

I would have a bit of sympathy if you said we should stick to the mathematics that works. But the orthodox interpretation includes the ridiculous and totally arbitrary completeness doctrine, all of the convoluted measurement axioms, a special dynamical role for "the observer", and so forth. This is all just crap -- crap that should never have received respect from serious scientists.

Bohm's theory is better not because some random person "likes" its "picture" of reality better. It's better *as a scientific theory*. It's better because of its simplicity, plausibility, physical clarity, and success in accounting for experimental results. As I said before, I'm the first to admit that this isn't yet sufficient for claiming it's true. But if you are going to go beyond the equations and commit to a particular interpretation for some reason, you'd have to be crazy to pick Copenhagen over Bohm.

(somewhere mr. vanesch is rolling his eyes because I always forget to mention his baby MWI... )

 

[DrChinese]

Only if "the truth" is that there is no underlying reality. But it's unscientific, irrational, and downright stupid in the extreme to even entertain that possibility for a second.

Stupid? This is where you go off the deep end. You keep assuming that which you want to prove! Mainly, that there is a realistic theory in which particle attributes are well-defined at all times. Considering the wide array of evidence to the contrary (i.e. all tests confirming the HUP), I would think this particular statement should be proven rather than assumed. There is not one scintilla of evidence that the HUP is *not* an complete description of reality.

Out of all of your discussions, you fail to grasp that no matter how you slice it, there is NO GREATER SPECIFICATION of the wave function present in any theory. Because even BM - correct me if I'm wrong here - requires such a vast array of knowledge of particle positions that you come back to where we started in predictive capability: oQM. Because apparently it is axiomatic that the non-local pilot waves are themselves not observable.

I have certainly never seen a serious proposal to observe such a wave. I have certainly never seen a proposal to "beat" the HUP using an enhanced wave function. Am I mistaken on this?

 

[ttn]

Stupid? This is where you go off the deep end. You keep assuming that which you want to prove! Mainly, that there is a realistic theory in which particle attributes are well-defined at all times. Considering the wide array of evidence to the contrary (i.e. all tests confirming the HUP), I would think this particular statement should be proven rather than assumed. There is not one scintilla of evidence that the HUP is *not* an complete description of reality.

No, it's you who is assuming what you want to prove. The fact is, there are several different theories which give different accounts of quantum reality and which are all equally consistent with the empirical facts (because the theories all make the same predictions about what those empirical facts should be). You say there is evidence "confirming the HUP" (by which I assume you mean confirming orthodox QM and/or its completeness doctrine). But this is completely and totally false. There is ZERO evidence showing that OQM is right and (say) Bohm (or, say, GRW) is wrong. None. Zip. Any evidence that you point to and say "See, this is consistent with OQM, so it confirms it" I can equally well point to and say "It's consistent with Bohm and GRW too, so it confirms those." The right question is: is there "one scintilla of evidence" that the HUP *is* a complete description of reality? And since there exist empirically viable theories according to which the HUP is merely epistemic, the answer is clearly, unambiguously NO.

Out of all of your discussions, you fail to grasp that no matter how you slice it, there is NO GREATER SPECIFICATION of the wave function present in any theory.

You mean "greater specification *than* the wf"? If so, this is just factually incorrect. There *do exist* empirically viable theories according to which the wave function does *not* provide a complete description of reality. Bohmian mechanics being the prime example. I don't understand why this is so hard for you to understand or accept.

Because even BM - correct me if I'm wrong here - requires such a vast array of knowledge of particle positions that you come back to where we started in predictive capability: oQM. Because apparently it is axiomatic that the non-local pilot waves are themselves not observable.

You're running together a bunch of completely different issues here. The central point is that BM and OQM make the same empirical predictions, so there is no possibility that you could point to some empirical fact that supports on as opposed to the other. Once you understand that, there's really nothing else to argue about -- except the question of which of the several empirically viable theories is the *best* theory.

I have no idea what you're talking about when you say BM "requires such a vast array of knowledge of particle positions..." BM is a *theory*. It doesn't "require" knowledge of anything, any more than OQM requires its advocates to know the exact wave function for every electron in Pluto.

You are also running together "OQM" with the class of predictions made by OQM. Those aren't the same thing. There are several theories which make the same class of predictions. You can't just pick your favorite theory, identify it with the predictions, and then dismiss the alternatives on the grounds that they "merely" reproduce the predictions of your favorite one. The reason this is bogus (in case it isn't obvious) is that I could do the same thing. I could say "BM is my favorite theory, and you're stupid for believing in OQM because it merely reproduces the predictions of BM -- and at the cost of introducing all sorts of fuzziness and measurement problems and such." This is why I said above that it's *you* who is simply assuming what you want to prove.

I have certainly never seen a serious proposal to observe such a wave. I have certainly never seen a proposal to "beat" the HUP using an enhanced wave function. Am I mistaken on this?

Paraphrasing Pauli, you're "not even mistaken." You're so completely confused about what the issues even are, that you haven't yet risen to the level of being merely "mistaken" about some technical detail.