Exploring Non-Locality in dBB Theory: Insights from EPR and Bell's Inequalities

[zenith8]

The Holland's paper
http://xxx.lanl.gov/abs/quant-ph/0305175
does not discuss the many-particle case at all.

A many-particle case (for spin 1/2) is studied in
http://xxx.lanl.gov/abs/quant-ph/9801070
where it was found necessary to introduce a preferred foliation of spacetime, which is certainly not unique.

The only (currently known) way to avoid preferred foliation is the evolution with respect to a scalar parameter s. But then, as I explained, the natural probabilistic interpretation does not seem compatible with the idea of dynamical relaxation towards the equilibrium. A typicality approach works much better.

For the many-particle case see section 10.5 of Bohm and Hiley's book or, for example, Timko and Vrscay's 'spin-dependent Bohmian electronic trajectories for helium' available at Found. Phys. 39, 1055 (2009) or on the usual web page.

Anyway, what's wrong with preferred foliations? Perfectly compatible with all known experimental results - it's just the neo-Lorentzian interpretation of relativity, no?

 

[Demystifier]

Anyway, what's wrong with preferred foliations? Perfectly compatible with all known experimental results - it's just the neo-Lorentzian interpretation of relativity, no?

Perhaps there is nothing wrong with it, but looks ugly. Too many possibilities are allowed, so how to know which foliation is the right one? In the absence of direct experimental evidence for a theory, simplicity and mathematical elegance should be the main guiding principles.

Besides, a preferred foliation is certainly not in the spirit of the Holland's approach that was first mentioned by you.

 

[Maaneli]

What about Holland's result that, if you consider the non-relativistic spin 1/2 theory as the limiting case of the relativistic Dirac theory, then this fixes the guidance equation uniquely (recalling there is a 'gauge freedom' in the standard one) and that this unique equation has a 'spin term' in addition to the gradient of the phase? With such a guidance equation, the electrons are no longer at rest in the stationary wave function case.

Btw, Holland wasn't the first to recognize this in the literature. Hestenes and Gurtler did way back in the 70's:

Consistency in the formulation of the Dirac, Pauli, and Schroedinger theories
Journal of Mathematical Physics, 16 573–584 (1975).
http://geocalc.clas.asu.edu/pdf/Consistency.pdf

Also, I independently derived this result as an undergrad, which suggests that it's been independently rediscovered by others countless times.

 

[Maaneli]

Perhaps there is nothing wrong with it, but looks ugly. Too many possibilities are allowed, so how to know which foliation is the right one? In the absence of direct experimental evidence for a theory, simplicity and mathematical elegance should be the main guiding principles.

But if you take the possibility of quantum nonequilibrium seriously, then there's nothing fundamentally problematic about that underdetermination of foliations - we just happen to be stuck in a special state (the quantum equilibrium state) that prevents us from observing the correct foliation.

 

[Maaneli]

The only (currently known) way to avoid preferred foliation is the evolution with respect to a scalar parameter s.

Though it isn't popular among deBB theorists, another logical possibility is to introduce retrocausation a la Sutherland's model:

Causally Symmetric Bohm Model
Rod Sutherland
http://arxiv.org/abs/quant-ph/0601095

 

[Demystifier]

But if you take the possibility of quantum nonequilibrium seriously, then there's nothing fundamentally problematic about that underdetermination of foliations - we just happen to be stuck in a special state (the quantum equilibrium state) that prevents us from observing the correct foliation.

I completely agree. Yet, it does not change the fact that the theory itself is ugly. It's hard to take seriously a theory that looks ugly, unless there is a direct experimental evidence supporting the theory.

For example, there are many alternatives to the classical Einstein theory of gravity, compatible with existing experimental data. Yet, the Einstein theory is the most popular. Why? Because neither of the alternatives is so elegant.

Another example is the Standard Model of elementary particles. It is in perfect agreement with all experiments. Yet, many physicists search for alternatives (GUTs, supersymmetries, strings, ...). Why? Because the Standard Model is terribly ugly.

 

[Maaneli]

I agree. And I would be very happy if I were not the only guy who is actually doing it (thinks hard about that).

Yeah, I'm thinking about it. One possibility I have in mind is to allow that a nonequilibrium version of your relativistic psi does initially depend on s, and then a stochastic Markov process dynamically relaxes the wavefunction to an equilibrium state with respect to s (much like in the Parisi-Wu approach to stochastic quantization). Then, it is only in this stochastic equilibrium state that your relativistic psi appears to be independent of s, and thus not allow for relativistic nonequilibrium states thereafter.

On the other hand, if you want to insist on deterministic dynamics, you might insist that your relativistic psi should always depend on s, in which case, your relativistic deBB theory becomes a deBB version of the Stueckelberg proper time formulation of relativistic QM.

 

[Demystifier]

Though it isn't popular among deBB theorists, another logical possibility is to introduce retrocausation, a la Sutherland's model:

Causally Symmetric Bohm Model
Rod Sutherland
http://arxiv.org/abs/quant-ph/0601095

Thanks, I didn't know about this. But it also seem to require a preferred frame [Eq. (60)].

 

[Demystifier]

Yeah, I'm thinking about it. One possibility I have in mind is to allow that a nonequilibrium version of your relativistic psi does initially depend on s, and then a stochastic Markov process dynamically relaxes the wavefunction to an equilibrium state with respect to s (much like in the Parisi-Wu approach to stochastic quantization). Then, it is only in this stochastic equilibrium state that your relativistic psi appears to be independent of s, and thus not allow for relativistic nonequilibrium states thereafter.

That seems interesting, but I don't like the idea that I must add a stochastic process by hand.

On the other hand, if you want to insist on deterministic dynamics, you might insist that your relativistic psi should always depend on s, in which case, your relativistic deBB theory becomes a deBB version of the Stueckelberg proper time formulation of relativistic QM.

Irrespective of dBB, the Stueckelberg equation does not seem to be in agreement with observations. In particular, we do not observe a continuous mass spectrum. (See however
http://xxx.lanl.gov/abs/0801.4471 )

 

[Maaneli]

I completely agree. Yet, it does not change the fact that the theory itself is ugly. It's hard to take seriously a theory that looks ugly, unless there is a direct experimental evidence supporting the theory.

For example, there are many alternatives to the classical Einstein theory of gravity, compatible with existing experimental data. Yet, the Einstein theory is the most popular. Why? Because neither of the alternatives is so elegant.

Another example is the Standard Model of elementary particles. It is in perfect agreement with all experiments. Yet, many physicists search for alternatives (GUTs, supersymmetries, strings, ...). Why? Because the Standard Model is terribly ugly.

I would agree that it is reasonable to take more seriously alternative models, if those alternative models can make all the same predictions as the standard theory, but with fewer and more physically plausible assumptions. However, I still think it's dubious to say that the standard deBB theory is hard to take seriously because it has this feature which seems "ugly" (or even fugly) to you.

In the 19th century, positivistic physicists like Mach criticized Boltzmann's statistical mechanics on similar grounds, saying for example that for molecules in thermal equilibrium, one could double the number of particles composing a gas, but halve their volume and masses (or something like that), and make all the same predictions. Of course, we now know that Mach's criticism is wrong because we understand (and can empirically observe) that equilibrium dynamics masks important microscopic details of particle dynamics, and that equilibrium dynamics is only a special case of a more general nonequilibrium dynamics. So even though Boltzmann's statistical mechanics has this feature which would probably seem ugly to you if you were living in that time, we can see that nature can still conform to such ugly features.

 

[Demystifier]

Thanks, I didn't know about this. But it also seem to require a preferred frame [Eq. (60)].

Perhaps I'm wrong, but the theory of quantum measurements in that paper also seems fishy to me.

 

[zenith8]

Perhaps there is nothing wrong with [a preferred foliation], but looks ugly. Too many possibilities are allowed, so how to know which foliation is the right one? In the absence of direct experimental evidence for a theory, simplicity and mathematical elegance should be the main guiding principles.

Does it really look ugly? But if you insist that all reference frames are equivalent, then:

(1) you get causal paradoxes over who measured things first (like someone was moaning about earlier in relation to the EPR experiment). These don't appear if you have a preferred frame.

(2) either (in Minkowski spacetime) there is no 'temporal becoming' since everything exists simultaneously as a 4d worldtube, or (in Einstein 3+1 spacetime) things pop in and out of reality as you switch reference frames (uh??) and objects undergo (reciprocal!) physical length contraction just because they are in relative motion for no readily apparent reason.

Those sound pretty ugly to me - at least philosphically.

In the Lorentzian interpretation with a preferred frame you have a causal explanation for length contraction/time dilation, you have temporal becoming, you don't get the causal paradoxes, and you have complete agreement with experiment..

I accept that historically people have thought preferred frames unnecessary (because that our condition of being in quantum equilibrium means we can't detect it..) but that viewpoint was developed for a local physics. With our new non-local universe, it might be worth looking again at preferred frames (since the `ether' or absolute space or whatever you want to call it is presumably the medium in which the nonlocal interactions are absolutely simultaneous..)

 

[Demystifier]

I would agree that it is reasonable to take more seriously alternative models, if those alternative models can make all the same predictions as the standard theory, but with fewer and more physically plausible assumptions. However, I still think it's dubious to say that the standard deBB theory is hard to take seriously because it has this feature which seems "ugly" (or even fugly) to you.

In the 19th century, positivistic physicists like Mach criticized Boltzmann's statistical mechanics on similar grounds, saying for example that for molecules in thermal equilibrium, one could double the number of particles composing a gas, but halve their volume and masses (or something like that), and make all the same predictions. Of course, we now know that Mach's criticism is wrong because we understand (and can empirically observe) that equilibrium dynamics masks important microscopic details of particle dynamics, and that equilibrium dynamics is only a special case of a more general nonequilibrium dynamics. So even though Boltzmann's statistical mechanics has this feature which would probably seem ugly to you if you were living in that time, we can see that nature can still conform to such ugly features.

Again I agree, and I am certainly not strictly against the idea of a preferred frame. After all, I have published a lot of papers with a preferred frame by myself. Yet, the idea that the preferred frame can be eliminated seems even more attractive to me. Besides, I find it very challenging as a research direction. In any case, we can certainly make consensus that various different approaches should be studied.

 

[inflector]

The only (currently known) way to avoid preferred foliation is the evolution with respect to a scalar parameter s.

What does "preferred foliation" mean? I've seen the term used here quite a bit but never explained. I tried googling it but didn't find any definitions just plenty of usage.

I have a very very rough idea what a foliation means but don't understand the term "preferred foliation."

 

[Demystifier]

Does it really look ugly? But if you insist that all reference frames are equivalent, then:

(1) you get causal paradoxes over who measured things first (like someone was moaning about earlier in relation to the EPR experiment). These don't appear if you have a preferred frame.

(2) either (in Minkowski spacetime) there is no 'temporal becoming' since everything exists simultaneously as a 4d worldtube, or (in Einstein 3+1 spacetime) things pop in and out of reality as you switch reference frames (uh??) and objects undergo (reciprocal!) physical length contraction just because they are in relative motion for no readily apparent reason.

Those sound pretty ugly to me - at least philosphically.

In the Lorentzian interpretation with a preferred frame you have a causal explanation for length contraction/time dilation, you have temporal becoming, you don't get the causal paradoxes, and you have complete agreement with experiment..

I accept that historically people have thought preferred frames unnecessary (because that our condition of being in quantum equilibrium means we can't detect it..) but that viewpoint was developed for a local physics. With our new non-local universe, it might be worth looking again at preferred frames (since the `ether' or absolute space or whatever you want to call it is presumably the medium in which the nonlocal interactions are absolutely simultaneous..)

I would say that the unpleasent features you discuss are counterintuitive, not ugly. But of course, this is all subjective, and I am not trying to change your opinion. I am just trying to explain to you the way I think.

 

[Maaneli]

Thanks, I didn't know about this. But it also seem to require a preferred frame [Eq. (60)].

You're welcome. I don't see why equation 60 implies a preferred frame. The psi^bar_f is not the complex conjugate of the psi_i.

 

[Maaneli]

Again I agree, and I am certainly not strictly against the idea of a preferred frame. After all, I have published a lot of papers with a preferred frame by myself. Yet, the idea that the preferred frame can be eliminated seems even more attractive to me. Besides, I find it very challenging as a research direction. In any case, we can certainly make consensus that various different approaches should be studied.

OK, fair enough.

 

[Maaneli]

Perhaps I'm wrong, but the theory of quantum measurements in that paper also seems fishy to me.

Which parts?

 

[Maaneli]

That seems interesting, but I don't like the idea that I must add a stochastic process by hand.

Well if there is no other way to do it, then the assumption of a stochastic process would be well-justified, I think.

Irrespective of dBB, the Stueckelberg equation does not seem to be in agreement with observations. In particular, we do not observe a continuous mass spectrum. (See however
http://xxx.lanl.gov/abs/0801.4471 )

Interesting, I wasn't aware of this. Can you give a ref. about the Stueckelberg equation predicting a continuous mass spectrum?

 

[Demystifier]

Interesting, I wasn't aware of this. Can you give a ref. about the Stueckelberg equation predicting a continuous mass spectrum?

It's trivial, you can easily show it by yourself. Just recall that mass^2 are eigenvalues of the operator \partial^{\mu}\partial_{mu} and consider solutions with the dependence on s of the form exp(i const s).

I don't want to comment the Sutherland's paper any more, because I have not yet studied it carefully. I hope I will find time to do it properly in the near future.

 

[Demystifier]

Well if there is no other way to do it, then the assumption of a stochastic process would be well-justified, I think.

As usual, It's hard to disagree with your well balanced statements.

 

[Demystifier]

OK, I have finished a more careful reading of the Shaterland's paper, so let me make some comments.

First, I have some inessential "technical" objections:
1) Contrary to the statement in the paper, Eq. (37) is NOT correct in standard QM. (A correct version would involve density matrices which generalize the notion of wave functions.)
2) Negative probabilities, as such, do not make sense.

Now to the point. Even if some details are incorrect (which I think they are), it seems that the main idea MIGHT WORK. But how exactly is that possible? Well, the idea is just an attempt to exploit a well-known loophole of the Bell theorem: the SUPERDETERMINISM loophole. Namely, if everything, including our "free" decisions, is actually determined by physical laws, then, AT LEAST IN PRINCIPLE, it is possible to get Bell correlations without nonlocality. The standard Bohm interpretation is also superdeterministic, but it still does not contain sufficiently many hidden-variables to avoid nonlocality. To overcome this, Shaterland adds ADDITIONAL hidden variables, the wave functions psi_f. There is no doubt that you can avoid nonlocality by adding a sufficient number of superdeterministic hidden variables. The difficult part is to do it in a relatively simple way, and that's what Shaterland attempts to do. His attempt can be seen as a combination of transactional and Bohmian interpretation.

This approach can be compared with that of 't Hooft, who is trying to construct local superdeterministic hidden variables that, at first sight, do not even resemble QM.

 

[Demystifier]

You're welcome. I don't see why equation 60 implies a preferred frame. The psi^bar_f is not the complex conjugate of the psi_i.

You are right, the equation is covariant, but his notation (the use of label 0) is very confusing.

Nevertheless, he does not give a covariant version of (42).

In addition, (42) does not look "causally symmetric", but I guess it can be justified by the thermodynamic arrow of time.

 

[zonde]

Does it really look ugly? But if you insist that all reference frames are equivalent, then:

(1) you get causal paradoxes over who measured things first (like someone was moaning about earlier in relation to the EPR experiment). These don't appear if you have a preferred frame.

(2) either (in Minkowski spacetime) there is no 'temporal becoming' since everything exists simultaneously as a 4d worldtube, or (in Einstein 3+1 spacetime) things pop in and out of reality as you switch reference frames (uh??) and objects undergo (reciprocal!) physical length contraction just because they are in relative motion for no readily apparent reason.

Those sound pretty ugly to me - at least philosphically.

In the Lorentzian interpretation with a preferred frame you have a causal explanation for length contraction/time dilation, you have temporal becoming, you don't get the causal paradoxes, and you have complete agreement with experiment..

Neo-Lorentzian interpretation makes exactly the same predictions as special relativity at least as long as you do not invoke some FTL stuff. So if you have paradoxes in SR (actually you don't) then you have exactly the same paradoxes in Neo-Lorentzian interpretation. The only difference is that Neo-Lorentzian interpretation is more intuitive then SR.

 

[Demystifier]

The only difference is that Neo-Lorentzian interpretation is more intuitive then SR.

This is not the only difference. The other difference is that it is also mathematically less elegant than SR. And this is indeed why the SR view is more popular, because in modern theoretical physics mathematical elegance is more appreciated than intuitivity.

 

[zonde]

This is not the only difference. The other difference is that it is also mathematically less elegant than SR. And this is indeed why the SR view is more popular, because in modern theoretical physics mathematical elegance is more appreciated than intuitivity.

Can you explain?
Do you mean that with Neo-Lorentzian interpretation you should always stick to one preferred reference frame?
Because as I see once you have established transformation in certain group of different reference frames that is intrinsically symmetric it afterwards does not matter (mathematically) how you have done that.
It's like that the way you prove theorem does not change the theorem itself.

 

[Maaneli]

It's trivial, you can easily show it by yourself. Just recall that mass^2 are eigenvalues of the operator \partial^{\mu}\partial_{mu} and consider solutions with the dependence on s of the form exp(i const s).

Right, I see. My reading indicates though that proponents of Stueckelberg such as Kyprianidis, Horwitz and Piron, etc., don't think that this creates problems for the empirical predictions of such theories.

 

[Maaneli]

First, I have some inessential "technical" objections:
1) Contrary to the statement in the paper, Eq. (37) is NOT correct in standard QM. (A correct version would involve density matrices which generalize the notion of wave functions.)

Eq. (37) is not true even for ideal measurements?

Negative probabilities, as such, do not make sense.

Formally, I don't see anything wrong with negative probabilities in the context of Sutherland's theory. Also, negative probabilities exist in classical statistical physics as well. See for example the backwards Kolmogorov equation.

to the point. Even if some details are incorrect (which I think they are), it seems that the main idea MIGHT WORK. But how exactly is that possible? Well, the idea is just an attempt to exploit a well-known loophole of the Bell theorem: the SUPERDETERMINISM loophole. Namely, if everything, including our "free" decisions, is actually determined by physical laws, then, AT LEAST IN PRINCIPLE, it is possible to get Bell correlations without nonlocality. The standard Bohm interpretation is also superdeterministic, but it still does not contain sufficiently many hidden-variables to avoid nonlocality. To overcome this, Shaterland adds ADDITIONAL hidden variables, the wave functions psi_f. There is no doubt that you can avoid nonlocality by adding a sufficient number of superdeterministic hidden variables. The difficult part is to do it in a relatively simple way, and that's what Shaterland attempts to do. His attempt can be seen as a combination of transactional and Bohmian interpretation.

This approach can be compared with that of 't Hooft, who is trying to construct local superdeterministic hidden variables that, at first sight, do not even resemble QM.

I think your characterization of Sutherland's theory is exactly right. So, if you think Sutherland's proposal works for the examples that he considers, then here you have an example of a hidden variables theory whose dynamics is relativistically covariant, and does not require a preferred frame or a synchronization parameter.

 

[Demystifier]

Eq. (37) is not true even for ideal measurements?

Not even then, but it is an inessential technicality.

Formally, I don't see anything wrong with negative probabilities in the context of Sutherland's theory. Also, negative probabilities exist in classical statistical physics as well. See for example the backwards Kolmogorov equation.

Maybe, but this is inessential technicality too.

I think your characterization of Sutherland's theory is exactly right. So, if you think Sutherland's proposal works for the examples that he considers, then here you have an example of a hidden variables theory whose dynamics is relativistically covariant, and does not require a preferred frame or a synchronization parameter.

I think that his proposal MIGHT work, provided that some details are better developed.
But I don't plan to do it. Instead, soon I will upload on the arXiv something similar but, I believe, even better: A local relativistic-covariant theory of particle trajectories that does not contain more hidden variables than my relativistic-covariant version of Bohm theory.

 

[Demystifier]

Right, I see. My reading indicates though that proponents of Stueckelberg such as Kyprianidis, Horwitz and Piron, etc., don't think that this creates problems for the empirical predictions of such theories.

That's true, but I never understood why do they think so.

 

[Maaneli]

I think that his proposal MIGHT work, provided that some details are better developed.
But I don't plan to do it. Instead, soon I will upload on the arXiv something similar but, I believe, even better: A local relativistic-covariant theory of particle trajectories that does not contain more hidden variables than my relativistic-covariant version of Bohm theory.

Cool, does your local relativistic-covariant theory also account for Bell nonlocality?

 

[Maaneli]

That's true, but I never understood why do they think so.

From one of Kyprianidis's papers, he writes:

"Horwitz and Piron [8] assign a definite mass only to non-interacting free particles while systems in presence of interaction are “off-mass shell” states. The latter approach has a profound physical meaning and it can be immediately associated with de Broglie’s “variable mass”, which is the rest mass additioned by the Quantum Potential. From this point of view, it is quite natural to seek for a description of quantum phenomena in terms of an indefinite mass theory, since quantum particles are never free but always submitted to the quantum potential. Therefore the Klein—Gordon theory must correspond to a specific restriction on the set of possible physical solutions, and consequently to a specific selection of processes out of the multiplicity of the processes described by the generalized Schrödinger equation."

Kyprianidis then goes on to suggest another way to deal with this indefinite mass problem.

 

[Demystifier]

Cool, does your local relativistic-covariant theory also account for Bell nonlocality?

Here it is:
http://xxx.lanl.gov/abs/1010.2082

It reproduces all predictions of QM. However, it is not completely local; it requires initial nonlocal correlations between the particle positions. Yet, it is much more local than standard Bohmian mechanics in the sense that nonlocal forces can be eliminated by appropriate choice of parameterization of the particle trajectories. ALL nonlocality is encoded in the initial conditions.

 

[unusualname]

aren't simplistic particle trajectories ruled out by bell type inequalities?

eg http://arxiv.org/abs/0903.3878

and

This subject [Bohmian Mechanics] was assessed by the NSF of the USA as follows [Cushing, J. T., review of Bohm, D., and Hiley, B., The Undivided Universe, Foundations of Physics, 25, 507, 1995.] "...The causal interpretation [of Bohm] is inconsistent with experiments which test Bell's inequalities. Consequently...funding...a research programme in this area would be unwise"..

and don't you have to chuck in a spin component to make it (more) consistent? (and hence use a C^2 representation for the wavefunction)

quote pasted from:
http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XI

 

[zenith8]

aren't simplistic particle trajectories ruled out by bell type inequalities?

eg http://arxiv.org/abs/0903.3878

and

and don't you have to chuck in a spin component to make it (more) consistent? (and hence use a C^2 representation for the wavefunction)

quote pasted from:
http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XI

Both Streater and the NSF are just wrong. Streater isn't usually wrong when he can be bothered to make an effort but he's just completely lazy here. It's clear that he's read about two paragraphs worth of stuff about deBB then just unloads his prejudices about what he thinks the theory is about in order to amuse the undergraduate viewers of his website..

Ilja Schmelzer has a full rebuttal of the whole of Streater's 'lost causes' page http://ilja-schmelzer.de/realism/dBBarguments.php" .