QED Lagrangian lead to self-interaction?

[akhmeteli]

... until those experiments are done, and until there is yet another LCHV phenomenological model or (even better) physical theory that can account for these currently undone experiments as well as all the other quantum predictions, I think the situation is still somewhat in favor of standard QM.

I agree that the standard QM deserves our full respect. I think QM unitary evolution reflects some deep truth. On the other hand, the projection postulate both contradicts unitary evolution (as it introduces irreversibility) and is necessary to prove that there are VBI in QM. I guess this contadiction may be crucial for correct understanding of the status of VBI in QM.

... Also, I should point out that some people have suggested (and I agree with this view) giving up the causality assumption in Bell's or GHZ's theorems. If you do this, then you can easily keep locality and there is in principle no obstacle to violating the Bell or GHZ inequalities. In fact, a causally symmetric Bohm model does exist which does precisely this AND reproduces all the other quantum predictions. It was developed by Rod Sutherland:

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

I don't know, I'm somewhat skeptical, but I have not read this preprint in detail yet.

 

[Maaneli]

I agree that the standard QM deserves our full respect. I think QM unitary evolution reflects some deep truth. On the other hand, the projection postulate both contradicts unitary evolution (as it introduces irreversibility) and is necessary to prove that there are VBI in QM. I guess this contadiction may be crucial for correct understanding of the status of VBI in QM.



I don't know, I'm somewhat skeptical, but I have not read this preprint in detail yet.

<< On the other hand, the projection postulate both contradicts unitary evolution (as it introduces irreversibility) and is necessary to prove that there are VBI in QM. >>

Agreed the projection postulate in standard QM or GRW QM (which are empirically inequivalent theories by the way) contradict unitary evolution and introduce irreversibility. But an irreversible projection postulate is not actually necessary for VBI in QM. Even in standard QM, the projection postulate is not the cause of the nonlocal correlations - it is the entanglement of wavefunctions in configuration space. The deBB plus decoherence theory is a sharper counterexample since there is no irreversible projection postulate. Evolution of entangled statevectors are always unitary. Decoherence of the entangled two-particle superposition is a result of the measurement interaction (given by the tensor product between the system entangled wavefunction and the separate wavefunctions of the two separate apparatus pointers), but this is still a unitary interaction and evolution. What leads to the appearance of a single realized eigenstate (and the appearance of an irreversible wavefunction collapse) is that each of the two point particles (whose trajectories are instantaneously codependent and determined by a guiding equation defined in terms of the system wavefunction) ends up in only one of those two decohered eigenstates. But the entire particle and Schroedinger evolution is still unitary. Now it turns out that as long as the measured particle position distribution is restricted to rho = |psi(x,t)|^2, there can be no superluminal signalling. However, if the Born rule does not hold, then superluminal signalling is possible, as Valentini and Pearle have shown. To that extent, we could say that the reason equilibrium deBB QM and standard QM (both of which are always empirically equivalent) are as nonlocal as they are, and not more nonlocal so as to allow superluminal signalling, is because of the probability density distribution of the particles. In other words the nonlocality of QM (meaning the VBI) has nothing really to do with the projection postulate. If SFED is fundamentally a locally causal theory, I do not believe this would be any contradiction to making a pilot wave version of it, simply because one could always still define the guiding equations of the two particles in terms of the local currents of the two particles. That's all that would be necessary.


<< I don't know, I'm somewhat skeptical, but I have not read this preprint in detail yet >>

For a more general philosophical discussion and justification of this point of view, please have a look at Bell's paper "Free Variables and Local Causality" in Speakable and Unspeakable in QM. Also have a look at the following paper of the philosopher of physics Huw Price:

Backward causation, hidden variables, and the meaning of completeness. PRAMANA - Journal of Physics (Indian Academy of Sciences), 56(2001) 199—209.
http://www.usyd.edu.au/time/price/preprints/QT7.pdf

 

[Maaneli]

He was explicitely talking about two identical particles. See the reference in my post #18 in this thread. A.O. Barut, "Foundations of Self-Field Quantumelectrodynamics", in: "New Frontiers in Quantum Electrodynamics and Quantum Optics", Ed. by A.O. Barut, NATO ASI Series V.232, 1991, p. 358



Sorry, I just have no idea how to discuss some hybrid between SFED and the standard quantum theory without any rationale. There are just no wavefunctions in the configuration space in SFED other than in some approximation (what nightlight calls "Barut's ansatz"). SFED is a relatively consistent and nonlinear theory. There is no superposition principle there, for example. You cannot just take whatever you want from the standard quantum theory, any quantum state, such as a wavefunction in the configuration space, describing a singlet state, and shove into SFED.

Andy,

I just uncovered that the configuration space formalism is indeed used in the Barut SFED for two entangled electrons. And there is no contradiction between this and the use of the nonlinear Hartree-Fock equations. So I am now quite certain there are indeed nonlocal entanglement correlations in SFED, and therefore VBI. I also read nightlight's posts on this subject, and I'm not sure he properly understood the Barut ansatz or the variational principle argument Barut used, in relation to the issue of entanglement nonlocality (he also seemed to improperly mix-up SED and SO with SFED). For a clear explication of this, see Barut's section 3.5 "QED of the relativistic two-body system" in The Electron:

The Electron: New Theory and Experiment
http://books.google.com/books?id=7w...&oi=book_result&resnum=10&ct=result#PPT143,M1

Also see "Relativistic two body QED" in section 4 of Barut's paper "QED based on self energy":

http://streaming.ictp.trieste.it/preprints/P/87/248.pdf

On page 10 of that section, you will see that Barut says,

<< We must now specify a variational principle. We could vary the action W with
respect to individual fields psi_1 and psi_2 separately. This results in non-linear
coupled Hartree-type equations for thse fields. Instead, we propose a
relativistic configuration space formalism to take into account the long-range
quantum correlations. >>

He then goes on to discuss how one can equivalently rewrite the SFED Lagrangian in terms of a 16-component composite wavefunction field. In the nonlinear Hartree-fock representation, you'll notice that there is still interaction between the two particles, and I found out that the Hartree-fock method is also frequently used in applied QM to solve many-body systems of entangled electrons. See also these two discussions of the Hartree-Fock method:

2.3 Hartree Fock theory
http://www.physics.uc.edu/~pkent/thesis/pkthnode13.html

Hartree-Fock Theory
http://www.fyslab.hut.fi/~asf/physics/thesis1/node27.html

All this seems pretty conclusive to me. What say you?

~Maaneli

 

[Maaneli]

<< and I found out that the Hartree-fock method is also frequently used in applied QM to solve many-body systems of entangled electrons. >>

Sorry I meant separable but weakly interacting electrons.

 

[akhmeteli]

<< On the other hand, the projection postulate both contradicts unitary evolution (as it introduces irreversibility) and is necessary to prove that there are VBI in QM. >>

Agreed the projection postulate in standard QM or GRW QM (which are empirically inequivalent theories by the way) contradict unitary evolution and introduce irreversibility. But an irreversible projection postulate is not actually necessary for VBI in QM. Even in standard QM, the projection postulate is not the cause of the nonlocal correlations - it is the entanglement of wavefunctions in configuration space. The deBB plus decoherence theory is a sharper counterexample since there is no irreversible projection postulate.

I was not discussing dBB in this case, and I was not talking about nonlocal correlations, whatever they are. I was talking about VBI in QM. Do you believe it is possible to prove theoretically that there are VBI in QM without using the projection postulate or something similar?

I haven'had time to reply to your later post yet.

 

[Maaneli]

<< I was not discussing dBB in this case, and I was not talking about nonlocal correlations, whatever they are. I was talking about VBI in QM. >>

But that's the point. VBI in QM and nonlocality go hand in hand. If a VBI ever occurred, it would be conclusive evidence of nonlocal correlations. Even Santos and Marshall say that, and admit that any *genuine* VBI would rule out ALL locally causal hidden variable theories.


<< Do you believe it is possible to prove theoretically that there are VBI in QM without using the projection postulate or something similar? >>

Yes, absolutely, that was the point of my post. The deBB pilot wave theory is a perfectly rigorous example of a QM theory that produces VBI's without the projection postulate.

 

[akhmeteli]

<< I was not discussing dBB in this case, and I was not talking about nonlocal correlations, whatever they are. I was talking about VBI in QM. >>

But that's the point. VBI in QM and nonlocality go hand in hand. If a VBI ever occurred, it would be conclusive evidence of nonlocal correlations. Even Santos and Marshall say that, and admit that any *genuine* VBI would rule out ALL locally causal hidden variable theories.

Nevertheless, I prefer to talk about VBI, not about nonlocal correlations right now, as the latter term seems much more vague than the former.

<< << Do you believe it is possible to prove theoretically that there are VBI in QM without using the projection postulate or something similar? >>

Yes, absolutely, that was the point of my post. The deBB pilot wave theory is a perfectly rigorous example of a QM theory that produces VBI's without the projection postulate.

That is not what I asked. By QM I meant the standard quantum mechanics. I don't quite see how what you said about dBB can be translated into a proof of VBI for the standard quantum mechanics. So, to make sure I got it right, let me rephrase my question: Do you believe it is possible to prove theoretically that there are VBI in the standard QM without using the projection postulate or something similar?

 

[Maaneli]

Nevertheless, I prefer to talk about VBI, not about nonlocal correlations right now, as the latter term seems much more vague than the former.

OK, but strictly from Bell's inequality, VBI necessarily implies nonlocal correlations. Nonlocal correlations are not mysterious (at least mathematically). It just means, for example in Bell's theorem, that the measurement outcome A at detector a is instantaneously dependent on the measurement setting at detector b, even when the two detectors and measurement events are space-like separated.

By QM I meant the standard quantum mechanics. I don't quite see how what you said about dBB can be translated into a proof of VBI for the standard quantum mechanics.

The reason I mention deBB theory as an example that indeed translates into a proof of VBI in the standard QM is because standard QM (projection postulates and all) is the prediction of deBB theory. And, yes, that has been mathematically proven.

So, to make sure I got it right, let me rephrase my question: Do you believe it is possible to prove theoretically that there are VBI in the standard QM without using the projection postulate or something similar?

Well the "standard QM" by definition includes the measurement postulates. If you don't have the projection postulate in standard QM, then it is impossible to make single or statistical predictions for the outcomes of experiments. Then you just have a linear Schroedinger dynamics (or Eherenfest dynamics or path integral dynamics or whatever) and no means by which to make any empirical predictions (this is related to the so-called problem of definite outcomes). So, no, you would need a projection postulate in standard QM to get VBI. By the way, this is true even if you include decoherence theory in "standard QM".

 

[akhmeteli]

The reason I mention deBB theory as an example that indeed translates into a proof of VBI in the standard QM is because standard QM (projection postulates and all) is the prediction of deBB theory. And, yes, that has been mathematically proven.

I wonder if there is some subtlety here. If dBB implies both the unitary evolution and the projection postulate, which conradict each other, dBB also contains mutually contradictory elements. I guess such elements appear when you assume decoherence.

Well the "standard QM" by definition includes the measurement postulates. If you don't have the projection postulate in standard QM, then it is impossible to make single or statistical predictions for the outcomes of experiments. Then you just have a linear Schroedinger dynamics (or Eherenfest dynamics or path integral dynamics or whatever) and no means by which to make any empirical predictions (this is related to the so-called problem of definite outcomes). So, no, you would need a projection postulate in standard QM to get VBI. By the way, this is true even if you include decoherence theory in "standard QM".

That's what I mean. To get VBI in the standard QM, you need to use the projection postulate, which clearly contradicts the unitary evolution. So if we take unitary evolution seriously, we cannot get VBI in quantum mechanics. So maybe we should just take unitary evolution seriously?

 

[Maaneli]

I wonder if there is some subtlety here. If dBB implies both the unitary evolution and the projection postulate, which conradict each other, dBB also contains mutually contradictory elements. I guess such elements appear when you assume decoherence.

Let me be more precise. deBB preserves unitary evolution and yet shows how wavefunctions appear to collapse in measurement processes (it is called "effective collapse" in deBB), and therefore also explains why the measurement postulates, and the whole statistical operator formalism in standard QM works to begin with. So there is no contradiction. Sure, you could also easily incorporate decoherence, but that is not really necessary or relevant for this purpose.

That's what I mean. To get VBI in the standard QM, you need to use the projection postulate, which clearly contradicts the unitary evolution. So if we take unitary evolution seriously, we cannot get VBI in quantum mechanics. So maybe we should just take unitary evolution seriously?

Well, here's the thing. If you decide to take unitary evolution seriously and reject the projection postulate, then you are no longer talking about standard QM. Then you are talking about a truly unitary QM theory such as deBB or MWI.

There are three statements which are mutually inconsistent:

A. The wavefunction of a system is complete, i.e. the wavefunction specifies (directly or indirectly) all of the physical properties of a system.

B. The wavefunction always evolves in accord with a linear dynamical equation (e.q. Schroedinger equation).

C. Measurements of e.g. the spin fo an electron always (or at least usually) have determinate outcomes.

If you take A + B, then that is incompatible with C. If you take B + C, then that is incompatible with A. If you take A + C, then that is incompatible with B. The resolution to A + B, is something like MWI. The resolution to B + C is linear hidden variables. The resolution to A + C is a stochastic or nonlinear QM theory like GRW stochastic collapse or nonlinear hidden variable theories.

Hope this helps.

 

[akhmeteli]

Well, here's the thing. If you decide to take unitary evolution seriously and reject the projection postulate, then you are no longer talking about standard QM. Then you are talking about a truly unitary QM theory such as deBB or MWI.

There are three statements which are mutually inconsistent:

A. The wavefunction of a system is complete, i.e. the wavefunction specifies (directly or indirectly) all of the physical properties of a system.

B. The wavefunction always evolves in accord with a linear dynamical equation (e.q. Schroedinger equation).

C. Measurements of e.g. the spin fo an electron always (or at least usually) have determinate outcomes.

If you take A + B, then that is incompatible with C. If you take B + C, then that is incompatible with A. If you take A + C, then that is incompatible with B. The resolution to A + B, is something like MWI. The resolution to B + C is linear hidden variables. The resolution to A + C is a stochastic or nonlinear QM theory like GRW stochastic collapse or nonlinear hidden variable theories.

Hope this helps.

I won't discuss A and B now, as it may take a long time, but I certainly don't need C, as it seems to contradict the Poincare recurrence theorem.

 

[Maaneli]

I certainly don't need C, as it seems to contradict the Poincare recurrence theorem.

Poincare's recurrence theorem doesn't really apply to QM measurements in this way.

What is your response to my previous post about VBI in SFED?

 

[akhmeteli]

Poincare's recurrence theorem doesn't really apply to QM measurements in this way./QUOTE]
I think the quantum recurrence theorem (Phys. Rev. V.107 #2, pp.337-338, 1957), maybe somewhat modified, does apply to QM measurements. Why not? No measurement is ever final, if you accept the theorem.

What is your response to my previous post about VBI in SFED?

I do remember that post, but I do need time to sort it out.

 

[Maaneli]

Poincare's recurrence theorem doesn't really apply to QM measurements in this way./QUOTE]
I think the quantum recurrence theorem (Phys. Rev. V.107 #2, pp.337-338, 1957), maybe somewhat modified, does apply to QM measurements. Why not? No measurement is ever final, if you accept the theorem.


I do remember that post, but I do need time to sort it out.

<< I think the quantum recurrence theorem (Phys. Rev. V.107 #2, pp.337-338, 1957), maybe somewhat modified, does apply to QM measurements. Why not? No measurement is ever final, if you accept the theorem. >>

Perhaps the recurrence theorem is applicable in some way - but I don't think it is relevant to the treatment of measurement processes in short time intervals.

 

[akhmeteli]

<< I think the quantum recurrence theorem (Phys. Rev. V.107 #2, pp.337-338, 1957), maybe somewhat modified, does apply to QM measurements. Why not? No measurement is ever final, if you accept the theorem. >>

Perhaps the recurrence theorem is applicable in some way - but I don't think it is relevant to the treatment of measurement processes in short time intervals.

In this case it does not matter whether it is relevant to the treatment of measurement processes in short time intervals. The way you formulated C, it does seem relevant (no time scales defined there). And it is certainly relevant to the projection postulate (actually, it seems incompatible with the latter). I also tend to believe that it is relevant to the Bell theorem.

 

[Maaneli]

In this case it does not matter whether it is relevant to the treatment of measurement processes in short time intervals. The way you formulated C, it does seem relevant (no time scales defined there). And it is certainly relevant to the projection postulate (actually, it seems incompatible with the latter). I also tend to believe that it is relevant to the Bell theorem.

Why does it seem so relevant to Bell's theorem or incompatible with the projection postulate? The recurrence theorem would just say something to the effect that given a long enough time, a quantum system will eventually return back to its original coherent state. That's just because a system can in principle still be put back into an approximately coherent state by human experimenters or by some complex and improbable series of natural events in the world. But it would take an extremely long time for this to happen. I don't see how this is very relevant to Bell's theorem (unless you want to take seriously something like the common past hypothesis), or how it is incompatible with the projection postulate, anymore than it is incompatible with Boltzmann's typicality argument in statistical mechanics (which it isn't).

 

[akhmeteli]

Why does it seem so relevant to Bell's theorem or incompatible with the projection postulate? The recurrence theorem would just say something to the effect that given a long enough time, a quantum system will eventually return back to its original coherent state. That's just because a system can in principle still be put back into an approximately coherent state by human experimenters or by some complex and improbable series of natural events in the world.

No, if the system has discrete energy eigenvalues, it will happen in the absence of any external interference, and with certainty. Actually, external interference can prevent recurrence.

But it would take an extremely long time for this to happen. I don't see how this is very relevant to Bell's theorem (unless you want to take seriously something like the common past hypothesis), or how it is incompatible with the projection postulate, anymore than it is incompatible with Boltzmann's typicality argument in statistical mechanics (which it isn't).

It is incompatible with the projection postulate because a particle, strictly speaking, does not stay in the eigenstate after measurement (so the projection postulate may be a good approximation or a bad approximation, but it is just an approximation). It is relevant to the Bell's theorem because the projection postulate is an essential assumption of the theorem.

 

[Maaneli]

No, if the system has discrete energy eigenvalues, it will happen in the absence of any external interference, and with certainty.

What will happen with certainty in the absence of any external interference?

It is incompatible with the projection postulate because a particle, strictly speaking, does not stay in the eigenstate after measurement (so the projection postulate may be a good approximation or a bad approximation, but it is just an approximation).

Well it depends. Perhaps you could infer that in the standard QM, it is only an approximation; but certainly not so in GRW theories.

By the way, this is why I think it is not very productive to stick with thinking about the projection postulate in standard QM, since it is already obvious that it cannot be a fundamental description of measurement processes.

 

[akhmeteli]

What will happen with certainty in the absence of any external interference?

The state vector will get arbitrarily close to the initial one (Phys. Rev. V.107 #2, pp.337-338, 1957).

Well it depends. Perhaps you could infer that in the standard QM, it is only an approximation; but certainly not so in GRW theories.

I was discussing the standard QM.

By the way, this is why I think it is not very productive to stick with thinking about the projection postulate in standard QM, since it is already obvious that it cannot be a fundamental description of measurement processes.

If we reject the projection postulate (PP), we can reject the Bell theorem, as it cannot be proven without PP.

 

[Maaneli]

The state vector will get arbitrarily close to the initial one (Phys. Rev. V.107 #2, pp.337-338, 1957).

I'll have a look but I'm skeptical of how relevant it is.

If we reject the projection postulate (PP), we can reject the Bell theorem, as it cannot be proven without PP.

No you can't just reject Bell's theorem by rejecting the projection postulate - the derivation of the Bell inequality has nothing to do with the projection postulate, and the Bell theorem (which says if an LCHV model is compatible with QM, then here is an inequality that QM correlations must satisfy) does not specifically require the projection postulate, just a means by which the QM formalism can make empirical predictions. That is why deBB theory and stochastic mechanics, which have no need for a projection postulate in their measurement theories, can also violate the Bell inequality and thus be applied to Bell's theorem. If you reject the projection postulate, you have to replace it with some other mechanism for your quantum theory to make empirical predictions (some measurement theory in other words). Otherwise, your theory can't make any predictions and is therefore totally useless.

 

[akhmeteli]

No you can't just reject Bell's theorem by rejecting the projection postulate - the derivation of the Bell inequality has nothing to do with the projection postulate,

I agree, the derivation of the Bell inequality does not require PP.

and the Bell theorem (which says if an LCHV model is compatible with QM, then here is an inequality that QM correlations must satisfy)

The Bell theorem also states that the inequality can be violated in QM, and you need PP to prove that. Maybe you use some form of the Bell theorem that does not include this statement, but that does not really matter. I think you appreciate that if this statement is wrong, the Bell inequality, although correct, loses most of its thrust, as genuine VBI will never be demonstrated (assuming QM is correct).

does not specifically require the projection postulate, just a means by which the QM formalism can make empirical predictions. That is why deBB theory and stochastic mechanics, which have no need for a projection postulate in their measurement theories, can also violate the Bell inequality and thus be applied to Bell's theorem. If you reject the projection postulate, you have to replace it with some other mechanism for your quantum theory to make empirical predictions (some measurement theory in other words). Otherwise, your theory can't make any predictions and is therefore totally useless.

I could agree that we may need some other mechanism for quantum theory to make empirical predictions. But how can we be sure that no matter how we choose that mechanism, we'll have VBI in QM? I tend to believe that PP is the real source of nonlocality, as it states that immediately after we measure a spin projection of one particle of a singlet, the system will be in an eigenstate of that spin projection. That means that the spin projection of the second particle immediately becomes definite (assuming angular momentum conservation), no matter how far the second particle is.

 

[Maaneli]

The Bell theorem also states that the inequality can be violated in QM, and you need PP to prove that. I think you appreciate that if this statement is wrong, the Bell inequality, although correct, loses most of its thrust, as genuine VBI will never be demonstrated (assuming QM is correct).

I think you're still missing the point. Bell's theorem doesn't say that the inequality can be violated in QM. Again, Bell's theorem is just the statement that if QM can be embedded into a locally causal theory, it must satisfy a certain inequality derived from that locally causal theory. QM (and this applies not just to standard QM) just violates that inequality.

I could agree that we may need some other mechanism for quantum theory to make empirical predictions. But how can we be sure that no matter how we choose that mechanism, we'll have VBI in QM?

If that other mechanism for QM measurements still involves wavefunctions (with their nonlocal configuration spaces) and Bell's causality assumption (like deBB or GRW theory), then it will always violate Bell inequalities. If you give up causality, or modify Kolmogorov's probability axioms, you can keep locality and still violate the Bell inequality. All this has been exhaustively demonstrated.

I tend to believe that PP is the real source of nonlocality, as it states that immediately after we measure a spin projection of one particle of a singlet, the system will be in an eigenstate of that spin projection.

Sorry but there are counterexamples to your belief. deBB theory and stochastic mechanics, neither of which require the PP, make explicit the fact that the entanglement of wavefunctions in configuration space is the real source of nonlocality. The PP is only an approximation. And don't forget that those alternative formulations of QM are empirically equivalent to standard QM and QED. So you have no reason to regard standard QM as primary over those alternative formulations.

 

[akhmeteli]

I think you're still missing the point. Bell's theorem doesn't say that the inequality can be violated in QM.

Some forms of BT do include that, at least implicitely. For example, in http://plato.stanford.edu/entries/bell-theorem/#2 :

"In the present section the pattern of Bell's 1964 paper will be followed: formulation of a framework, derivation of an Inequality, demonstration of a discrepancy between certain quantum mechanical expectation values and this Inequality." A discrepancy arises when VBI occur in QM.

Or in http://en.wikipedia.org/wiki/Bell's_theorem :
"No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics." Again, to prove it, you have to prove that there are VBI in QM.

Again, Bell's theorem is just the statement that if QM can be embedded into a locally causal theory, it must satisfy a certain inequality derived from that locally causal theory.

Again, it does not matter whether you formally include the statement that there are VBI in QM in the Bell theorem. If this statement is wrong, the Bell Theorem (BT) loses most of its importance.

QM (and this applies not just to standard QM) just violates that inequality.

Again, you need PP or something similar to prove this "just violates" for the standard QM. Unitary evolution is not enough.

If that other mechanism for QM measurements still involves wavefunctions (with their nonlocal configuration spaces) and Bell's causality assumption (like deBB or GRW theory), then it will always violate Bell inequalities.

I don't know that other mechanism, so I don't know if these "ifs" are true for it. All I know is the current mechanism contradicts unitary evolution.

Sorry but there are counterexamples to your belief. deBB theory and stochastic mechanics, neither of which require the PP, make explicit the fact that the entanglement of wavefunctions in configuration space is the real source of nonlocality. The PP is only an approximation. That don't forget that those alternative formulations of QM are empirically equivalent to standard QM and QED.

If entanglement of wavefunctions in configuration space is the real source of nonlocality in deBB theory and stochastic mechanics (I don't know it for sure and unfortunately don't have time and motivation to check), it does not mean this is also true for QM. These theories may be empirically equivalent to QM only after you include PP in the latter. I don't know how one can get VBI in standard QM without PP or something similar.

 

[Maaneli]

Some forms of BT do include that, at least implicitely. For example, in http://plato.stanford.edu/entries/bell-theorem/#2 :

Fair enough. Maybe I was parsing a little too much.

Again, it does not matter whether you formally include the statement that there are VBI in QM in the Bell theorem. If this statement is wrong, the Bell Theorem (BT) loses most of its importance.

If Bell's theorem is wrong, that's just as important as if it's right. That means QM can be embedded into a locally causal theory.

I don't know that other mechanism, so I don't know if these "ifs" are true for it. All I know is the current mechanism contradicts unitary evolution.

As I said, those scenarios have been exhaustively considered. They are true, as you would find out if you make the effort to study them for yourself. Of course, there are phenomenological models like stochastic optics that prevent a VBI from happening in the first place (for example with light). You are welcome to try and formulate a locally causal theory of the electron or other massive particles for which VBI appears to occur only when the locality condition has not been met, which is the current status of such experiments with massive particles. Oh and you should also try to reproduce all the other QM predictions with that locally causal theory of the electron. But ultimately, you'll have to deal with the time when a Bell or GHZ test is done with massive particles and which also implements the locality condition. If that turns out to produce VBI (which is likely), then I really see no more wiggle room. Anyway, hopefully you can see how serious of an uphill battle it is, and all the odds against it.

If entanglement of wavefunctions in configuration space is the real source of nonlocality in deBB theory and stochastic mechanics (I don't know it for sure and unfortunately don't have time and motivation to check), it does not mean this is also true for QM. These theories may be empirically equivalent to QM only after you include PP in the latter.

Actually it is. It is not the projection postulate per se that produces the correlations that violate the VBI, as indicated by the fact that the projection postulate applies even to separable wavefunctions in standard QM. If two wavefunctions were not entangled in configuration space, then the correlations between two "particles" would not VBI, even with PP, since they would be separable quantum systems.

I don't know how one can get VBI in standard QM without PP or something similar

Well you're conflating standard QM with another theory that doesn't have PP. As I said before, if you remove PP from textbook QM, then you have to replace it with a measurement theory to make predictions. The moment you do that, you have a different formulation of QM.

I see no point in dwelling on the PP from standard QM without considering the alternative formulations. It really isn't getting us anywhere. And besides, you already agreed that the PP is only an approximation, and that there must be some more fundamental measurement. So let's talk about those superior quantum measurement theories. Or at least can we get back to the argument in my previous post about VBI in SFED?

 

[Maaneli]

And besides, you already agreed that the PP is only an approximation, and that there must be some more fundamental measurement.

Some more fundamental measurement theories*.

 

[akhmeteli]

As I said, those scenarios have been exhaustively considered. They are true, as you would find out if you make the effort to study them for yourself.

Maybe you misunderstood me or I was not clear enough. I meant that this hypothetical mechanism does not have to "involve wavefunctions (with their nonlocal configuration spaces)".

Anyway, hopefully you can see how serious of an uphill battle it is, and all the odds against it.

I am not making any commitments to battle anything. All I'm trying to say can be formulated as follows. 1) The theoretical proof of VBI in the standard QM is based on assumptions that contradict each other. 2) Genuine VBI have not been demostrated experimentally.

Actually it is. It is not the projection postulate per se that produces the correlations that violate the VBI, as indicated by the fact that the projection postulate applies even to separable wavefunctions in standard QM. If two wavefunctions were not entangled in configuration space, then the correlations between two "particles" would not VBI, even with PP, since they would be separable quantum systems.

This argument does not seem conclusive. If PP does not always result in VBI, it does not mean PP is not the culprit.

Well you're conflating standard QM with another theory that doesn't have PP. As I said before, if you remove PP from textbook QM, then you have to replace it with a measurement theory to make predictions. The moment you do that, you have a different formulation of QM.

I see no point in dwelling on the PP from standard QM without considering the alternative formulations. It really isn't getting us anywhere. And besides, you already agreed that the PP is only an approximation, and that there must be some more fundamental measurement. So let's talk about those superior quantum measurement theories. Or at least can we get back to the argument in my previous post about VBI in SFED?

I have no alternative mechanism to offer. Again, what I'm trying to tell is limited to the two points above. As for VBI in SFED, I am not sure I'll be able to offer a final conclusion within a reasonable time frame, so I'll just try to share a preliminary opinion today or tomorrow.

 

[Maaneli]

Andy,

Maybe you misunderstood me or I was not clear enough. I meant that this hypothetical mechanism does not have to "involve wavefunctions (with their nonlocal configuration spaces)".

I didn't misunderstand you. I said before that IF your hypothetical alternative measurement mechanism involves wavefunctions plus the causality assumption, then it will necessarily VBI. If your alternative mechanism involves the causality assumption but does not involves wavefunctions, then it will not VBI.


I am not making any commitments to battle anything. All I'm trying to say can be formulated as follows. 1) The theoretical proof of VBI in the standard QM is based on assumptions that contradict each other. 2) Genuine VBI have not been demostrated experimentally.

But as I pointed out, 1) is trivial because a) the PP is not the direct cause of VBI, and b) the PP is not a uniquely valid measurement theory (in fact it is not even a measurement theory), as there are other superior one's that do not require PP and still VBI. So I don't think 1) has any substance with all do respect. And of course I agree with 2), but the situation is still in favor of nonlocal or causally symmetric formulations of QM, as I explained before.


This argument does not seem conclusive. If PP does not always result in VBI, it does not mean PP is not the culprit.


I disagree. Think about the example I provided earlier, if a wavefunction psi(x1, x2, t) is not factorizable (it is entanglement in configuration space), then add in the PP and you get VBI. However, if a wavefunction psi(x1, x2, t) is factorizable (there is no entanglement in configuration space), then add in the PP (because you still have reduction of the state vector) and you do not get VBI. So it is obvious that in the first case, entanglement of wavefunctions plus PP necessarily implies VBI, and in the second case, there are factorizable wavefunctions plus PP, and no VBI is possible. The same is also true of GRW collapse QM. So which do you think is more directly relevant to the cause of VBI in standard QM? Entangled wavefunctions in configuration space or the PP? Also throw in the fact that you can eliminate PP with deBB, keep unitary evolution, and still get VBI. There is no doubt that PP is not the culprit of VBI. The PP is actually a deceptive, red herring.


I have no alternative mechanism to offer. Again, what I'm trying to tell is limited to the two points above. As for VBI in SFED, I am not sure I'll be able to offer a final conclusion within a reasonable time frame, so I'll just try to share a preliminary opinion today or tomorrow.

OK.

 

[akhmeteli]

Andy,

I just uncovered that the configuration space formalism is indeed used in the Barut SFED for two entangled electrons. And there is no contradiction between this and the use of the nonlinear Hartree-Fock equations. So I am now quite certain there are indeed nonlocal entanglement correlations in SFED, and therefore VBI. I also read nightlight's posts on this subject, and I'm not sure he properly understood the Barut ansatz or the variational principle argument Barut used, in relation to the issue of entanglement nonlocality (he also seemed to improperly mix-up SED and SO with SFED). For a clear explication of this, see Barut's section 3.5 "QED of the relativistic two-body system" in The Electron:

The Electron: New Theory and Experiment
http://books.google.com/books?id=7w...&oi=book_result&resnum=10&ct=result#PPT143,M1

Also see "Relativistic two body QED" in section 4 of Barut's paper "QED based on self energy":

http://streaming.ictp.trieste.it/preprints/P/87/248.pdf

On page 10 of that section, you will see that Barut says,

<< We must now specify a variational principle. We could vary the action W with
respect to individual fields psi_1 and psi_2 separately. This results in non-linear
coupled Hartree-type equations for thse fields. Instead, we propose a
relativistic configuration space formalism to take into account the long-range
quantum correlations. >>

He then goes on to discuss how one can equivalently rewrite the SFED Lagrangian in terms of a 16-component composite wavefunction field.
~Maaneli

Sorry for the late reply. As I said, the situation does not seem clear to me. I don't know what was Barut's take on his own ansatz, whether this is just a computational trick or a new theory. In fact, what he does is he "underoptimizes" action and radically expands the set of functions under consideration. It is not clear at all whether this is necessary. nightlight's take is that this is just an artifact of linearization, and I tend to agree. If you believe that this is part and parcel of the Barut's theory, then it's another place where he "smuggles in" 2nd quantization, at least as far as contents, rather than form, is concerned.

Actually, my problem is I don't know why we need entangled wavefunctions in the Barut's theory, in the first place.

 

[Maaneli]

Sorry for the late reply. As I said, the situation does not seem clear to me. I don't know what was Barut's take on his own ansatz, whether this is just a computational trick or a new theory. In fact, what he does is he "underoptimizes" action and radically expands the set of functions under consideration. It is not clear at all whether this is necessary. nightlight's take is that this is just an artifact of linearization, and I tend to agree. If you believe that this is part and parcel of the Barut's theory, then it's another place where he "smuggles in" 2nd quantization, at least as far as contents, rather than form, is concerned.

Actually, my problem is I don't know why we need entangled wavefunctions in the Barut's theory, in the first place.

Andy,

Did you read any of those links? Barut does say what he thinks about the configuration space formulation. That's why I posted them for you. He also says it is necessary for accounting for nonlocal correlations. Mathematically, this is no different from what is done in standard QM for entangled wavefunctions. So nothing really changes there except now you have the self-field interaction which makes the wave equation nonlinear. In fact, he is not at all linearizing the Dirac equation by constructing that 16-component nonlocal wavefunction. The Dirac equation is still a nonlinear integro-differential equation, but now with a nonlocal self-field. In fact, what Barut does here is exactly what I proposed one would do in constructing the SFED version of the singlet state in an earlier post. Nightlight's comments seem misguided to me. He was incorrectly mixing up the Hartree-Fock approximation for separable wavefunctions, with nonlocality in Barut's SFED.


<< my problem is I don't know why we need entangled wavefunctions in the Barut's theory, in the first place. >>

How can you still not see it? We've just been over the fact that entangled wavefunctions are not only possible in SFED, but that it would be necessary to consistently predict the current quantum entanglement correlations for electrons, even though none of them VBI quite yet (because the seperability condition hasn't been implemented yet). Otherwise, the theory wouldn't even be able to match these nonideal correlations. You would have to construct some additional ad-hoc mechanism to do this. And you couldn't use stochastic optics to do it, since there are no ZPF fields in SFED. So I don't know what else would be availabe. And, honestly, what seems more natural, using the entanglement of the wavefunctions in configuration space which the theory permits or something entirely new and ad-hoc?

 

[akhmeteli]

Andy,

Did you read any of those links? Barut does say what he thinks about the configuration space formulation. That's why I posted them for you.

I did read the links, and what Barut says, does not make clear what he thinks, sorry.

He also says it is necessary for accounting for nonlocal correlations.

I have not found the word "nonlocal". He does mention "long-range quantum correlations". I'm not sure this is the same thing.

Mathematically, this is no different from what is done in standard QM for entangled wavefunctions. So nothing really changes there except now you have the self-field interaction which makes the wave equation nonlinear. In fact, he is not at all linearizing the Dirac equation by constructing that 16-component nonlocal wavefunction. The Dirac equation is still a nonlinear integro-differential equation, but now with a nonlocal self-field. In fact, what Barut does here is exactly what I proposed one would do in constructing the SFED version of the singlet state in an earlier post. Nightlight's comments seem misguided to me. He was incorrectly mixing up the Hartree-Fock approximation for separable wavefunctions, with nonlocality in Barut's SFED.

When I was talking about linearization, I did not mean that specific equation. I meant that "underoptimization" and the configuration space in general may appear as a result of linearization. nightlight cites the results from K. Kowalski and W.-H. Steeb, Nonlinear Dynamical Systems and Carleman Linearization (World Scientific, Singapore, 1991) (brief outline in http://arxiv.org/abs/hep-th/9212031 ): if we have a nonlinear differential equation in an (s+1)-dimensional space-time {\partial_t}u(x,t) = F(u,{D^\alpha}u) , where {D^\beta}={\partial^{|\beta|}}/\partial x_1^{\beta_1}\ldots<br /> \partial<br /> x_s^{\beta_s}, |\beta|=\sum\limits_{i=1}^{s}\beta_i , we can introduce a normalized functional
coherent state |u\rangle =\exp\left(-\frac{1}{2}\int<br /> d^sx|u|^2\right)\exp\left(\int<br /> d^sxu(x)a^\dagger(x)\right)|0\rangle (so a(x)|u\rangle =u(x)|u\rangle, where {a^\dagger}(x) and a(x) are the standard Bose operators of creation and annihilation) and a boson operator M = \int {d^s}x{a^\dagger}(x)F(a(x),{D^\alpha}a(x)) , and then we have a linear evolution equation in Hilbert
space \frac{d}{dt}|u,t\rangle = M|u,t\rangle, where |u,t\rangle = \exp\left[\frac{1}{2}\left(\int {d^s}xu^2<br /> -\int {d^s}xu_0^2\right)\right]|u\rangle and \qquad<br /> |u,0\rangle=|u_0\rangle (I did cut some corners; you can find the details in the Kowalski's work). Thus, a less than exciting nonlinear differential equation can be linearized using 2nd quantization. If we did not know the equation for what it was, we could start talking about the configuration space, entangled wavefunctions, and so on. Are you sure we should do just that? I am not. I am not trying to convince you that entangled wavefunctions are just an artifact of linearization, but I believe this is a possibility.

How can you still not see it? We've just been over the fact that entangled wavefunctions are not only possible in SFED, but that it would be necessary to consistently predict the current quantum entanglement correlations for electrons, even though none of them VBI quite yet (because the seperability condition hasn't been implemented yet). Otherwise, the theory wouldn't even be able to match these nonideal correlations. You would have to construct some additional ad-hoc mechanism to do this. And you couldn't use stochastic optics to do it, since there are no ZPF fields in SFED. So I don't know what else would be availabe. And, honestly, what seems more natural, using the entanglement of the wavefunctions in configuration space which the theory permits or something entirely new and ad-hoc?

Frankly, a straight-forward nonlinear differential equation seems much more natural. Whether such a minimalist theory is possible, I don't know, but so far I don't see any fundamental difficulties, theoretical or experimental.

Just a few more words. I can live without locality. I can live without reality. I can live without causality. But not until I am absolutely sure I do have to go to such extremes.