QED Lagrangian lead to self-interaction?

[akhmeteli]

As far as how Barut decides what variational principle to apply, I think it is no different than in the variational formulation of standard QM. One would first write down the wavefunction of the physical system; if it is the wavefunction describing a singlet state, then that is the wavefunction with respect to which you apply the variational principle, as it is not factorizable. I don't see any confusion here.

Cannot say the same about myself:-(

Let us summarize. If I understand you correctly, you believe that, in Barut's opinion (and in your opinion), the configuration space and entangled wavefunctions are an integral part of SFED (If I misunderstood you, please advise).

Maybe this is indeed his opinion. Then thank you for indicating this to me (I had a different idea of what SFED is). I should reiterate then that this is another point where he smuggles in the physical contents of 2nd quantization (not the form, I'm ready to admit). I should also reiterate that maybe the configuration space should arise in the "final" theory as a result of KSP, not as a new postulate.

Sorry, it is simply not accurate to call a c-numbered wavefunction in configuration space satisfying the proper permutation symmetries, "second quantized". Furthermore, just because second quantization can be introduced when particle numbers are fixed, doesn't mean that the 1st-quantized wavefunction is also "second quantized", especially because the operator wavefunction form allows for the POSSIBILITY of variable particle number. This is why the Fock space is not something you can just dispense with, if you are going to call a matter theory second quantized.

Again, I tend to believe that your reasoning is almost entirely about the form, not contents. I also stand by my initial statement that Barut smuggles in the physical contents of 2nd quantization in his theory (not the form, I admit).

Then you are just not using the terminology of second-quantization properly. By your logic, the original Dirac equation with the Dirac sea mechanism to allow for variable fermion numbers, is also a second quantized theory "for all intents and purposes". But this is just not true. The "form" of the theory does indeed matter in the definition of whether it is 1st or 2nd quantized.

No, I just stated that the Dirac sea introduces some elements of 2nd quantization in the original one-particle theory, because the Pauli principle is not a part of one-particle theory.

But in the DM Lagrangian, you already have self-field interactions and entanglement. How does KSP linearize this self-interaction?

I don't think there is any entanglement in the DM Lagrangian (defined in (3+1) dimensions). If you disagree, please advise.

In the same way it linearizes any NDE.

Also, it sounds like you are admitting that KSP is just a form of second quantization (otherwise I don't see why you would use it).

I could admit it only as far as the form, not physical contents, is concerned.

Why would I use it? This is a really good question. I would use it to prove that one can transform some NDE in (3+1)D space into QED using KSP. That would suggest that that NDE is the "final theory", and entanglement and the Fock space are the artifacts of KSP. Again, nobody has done anything like that and maybe it'll never be done. At the moment, though, KSP seems important to me as it describes a natural mechanism generating the Fock space from a banal NDE.

Also, just because there are solutions to the linear equation that are not solutions to the nonlinear equation, doesn't mean those new solutions to the linear equation are artifacts.

It does not. But this is a possibility.

There is however a way I discovered to transform between the linear Schroedinger equation and a nonlinear Burger's equation (using the Nagasawa-Schroedinger and Cole-Hopf substitutions), and both equations describe the same physics. I have sent you my paper where I do this.

Thank you. I'll look at it.

I'll try to reply to other points of your post later.

 

[akhmeteli]

See my comments in the previous post.

So you don't think KSP "is relevant for describing entanglement nonlocality in Barut's SFED". I understand your arguments as follows: entanglement has already been introduced in SFED without any KSP, so the latter is not relevant. I think however that it can be relevant, as we cannot be sure the entanglement was introduced correctly, and maybe in the "final" theory it is an artifact of KSP. That would seem more natural to me. I don't have more convincing arguments, and of course I may be dead wrong.

I think the point is that the first variational principle can only be applied to physical systems whose wavefunctions can be factorized (the variational principle does not determine whether a wavefunction can be factorizable). For the second variational principle, it can only be applied to physical systems whose wavefunctions are not factorizable (like the singlet state). That's all.

Again, the situation seems obvious for you and it does not seem obvious for me. If you believe that the configuration space is an integral part of SFED, let it be so.

You could also start from a Schroedinger equation with a nonlinear term proportional to the quantum potential. Such an equation describes soliton waves in classical fluid dynamics. But if you do not include either self-field interactions or else zero-point fields in your nonlinear theory, then I don't see how your theory could produce radiative effects like the Lamb shift or spontaneous emission.

I don't quite see how "a Schroedinger equation with a nonlinear term proportional to the quantum potential" is relevant. I just meant that the standard term A^\mu j_\mu in DM Lagrangian is a source of self-field (after you eliminate the electromagnetic fiield).

Again, you just keep on missing the point. Even though no genuine experimental demonstration of nonlocality has been demonstrated so far, your local alternative theory must still be able to predict, within experimental limits, the empirically observed nonideal statistical correlations for both electrons and photons. That within itself is still a nontrivial problem.

I fully agree. However, accepting nonlocality or noncausality is even less trivial problem for me. I just don't see compelling reasons to accept one of these radical ideas. I appreciate that you feel different. So we disagree. I don't think this is a problem for you or me.

Really? So the wavefunction on Fock space doesn't have different content than the wavefunction on configuration space? Then it sounds to me like you have not understood 2nd quantization.

In general, it may have a different content, though the difference is not very profound (it's just about varying numbers of particles). However, if its projections on all configuration spaces but one are zero (if the number of particles is definite), I don't see how it has a different content.

This is a semantic distinction without a physical difference. Honestly, what is the difference in your mind between the "appearance" of entanglement nonlocality in the mathematics of a theory, and the "possibility" of entanglement nonlocality in the mathematics of a theory?

I meant the following. We know that a typical NDE in (3+1) dimensions does not contain any entanglement nonlocality. If you apply KSP to this NDE, it certainly introduces "appearance" of entanglement nonlocality. And it certainly does not introduce a possibility that the entanglement nonlocality is immanent to the NDE.

Does it introduce the Fock space for the linearize equation and allow for variable particle numbers? Is the wavefunction solution a c-number field or an operator field? If so, then it has to be a second-quantized theory.

In form - yes. In essence - no. I tried to explain that typically second quantization changes the physics contents. What is second quantization? You just declare that fields do not commute anymore. This introduces new physics content, such as Pauli principle (for fermions), among other things. This physics contents was not present in the 1st-quantized theory. On the other hand, KSP does not introduce any new physical contents, as far as the solutions of NDE are concerned.

Aha, so then it does introduce the Fock space! Then why isn't it second quantization?

See the previous reply.

What doesn't it have that the second-quantized Schroedinger theory does have.

It does not have any new physical contents compared to the relevant 1st quantized theory, as far as the solutions of the latter are concerned. I'd say a different question is more interesting: What does it have that the second-quantized Schroedinger theory does not? And the answer is it has a locally causal interpretation, however 2nd-quantized it may look. Namely, we can just state that the original NDE is the genuine theory, which is enough to fully describe nature, and the post-KSTP is just its linearized form.


I'll try to reply to other points of your post later.

 

[Maaneli]

Cannot say the same about myself:-(

Let us summarize. If I understand you correctly, you believe that, in Barut's opinion (and in your opinion), the configuration space and entangled wavefunctions are an integral part of SFED (If I misunderstood you, please advise).

Yes, and it is also Dowling's opinion.

Maybe this is indeed his opinion. Then thank you for indicating this to me (I had a different idea of what SFED is). I should reiterate then that this is another point where he smuggles in the physical contents of 2nd quantization (not the form, I'm ready to admit). I should also reiterate that maybe the configuration space should arise in the "final" theory as a result of KSP, not as a new postulate.

I'm sorry but this just false. Entanglement nonlocality is definitely not a property of 2nd quantization (either in content or form) any more than it is a property of 1st quantization. You seem to have forgotten that configuration space and entanglement nonlocality are already properties of the standard 1st quantized linear Schroedinger equation for N particles.

Again, I tend to believe that your reasoning is almost entirely about the form, not contents. I also stand by my initial statement that Barut smuggles in the physical contents of 2nd quantization in his theory (not the form, I admit).

No, my reasoning is also about contents, and I still disagree with you that Barut's theory smuggles in 2nd quantization for the wavefunction. As I pointed out before, the Barut wavefunction is a c-number field, and the Pauli exclusion principle is already a property of the 1st quanitzed linear Dirac equation. The ONLY place where you may be able to say he smuggles in elements of "2nd quantization" is in the introduction of the complex-valued Green's function propagator in the self-field. But that's it.

I don't think there is any entanglement in the DM Lagrangian (defined in (3+1) dimensions). If you disagree, please advise.

. First of all, the DM Lagrangian is only defined in (3+1) dimensions for a SINGLE particle, NOT for N particles (then it is in configuration space). Furthermore, if you already admit (reluctantly) that there is entanglement in the Barut-Dirac equation (which is in fact derived from the DM Lagrangian), then you have absolutely no reason to think the situation it is different in the DM Lagrangian. Indeed, the DM equation is just the description of how the EM field couples to the Dirac wavefunctions, and it is well-known that entanglement is already a property of the DM equation for N particles. Otherwise, it wouldn't exist in the standard Dirac equation. If your idea of starting from the DM equation and applying KSP to it is based on the premise that the DM equation is not defined in configuration space for N particles, then you are simply incorrect. Unless you are talking about only the 1 particle DM equation? In that case, applying KSP to it would only yield a 1 particle 2nd quantized theory, not an N particle theory.

Why would I use it? This is a really good question. I would use it to prove that one can transform some NDE in (3+1)D space into QED using KSP. That would suggest that that NDE is the "final theory", and entanglement and the Fock space are the artifacts of KSP.

Sorry to disappoint you but if you apply KSP to an NDE like the 1-particle DM equation, you simply will not get entanglement in the resultant KSP form. You would need to apply it to the 2 or N particle DM equation, in which you already have entanglement in the NDE to start with.

Again, nobody has done anything like that and maybe it'll never be done. At the moment, though, KSP seems important to me as it describes a natural mechanism generating the Fock space from a banal NDE.

It may be a way of introducing the Fock space, and therefore is a novel way of transforming from a nonlinear 1st quantized theory like SFED (or the DM theory), to a linear 2nd quantized QED-type of theory. And I think that could be very interesting. But this transformation definitely will not show that entanglement is an "artifact".

 

[Maaneli]

So you don't think KSP "is relevant for describing entanglement nonlocality in Barut's SFED". I understand your arguments as follows: entanglement has already been introduced in SFED without any KSP, so the latter is not relevant. I think however that it can be relevant, as we cannot be sure the entanglement was introduced correctly, and maybe in the "final" theory it is an artifact of KSP. That would seem more natural to me. I don't have more convincing arguments, and of course I may be dead wrong.

Sorry but this particular approach sounds to me like not much more than wishful thinking.

Again, the situation seems obvious for you and it does not seem obvious for me. If you believe that the configuration space is an integral part of SFED, let it be so.

OK, I will.

I don't quite see how "a Schroedinger equation with a nonlinear term proportional to the quantum potential" is relevant. I just meant that the standard term A^\mu j_\mu in DM Lagrangian is a source of self-field (after you eliminate the electromagnetic fiield).

Then you are talking about SFED again, even though you said before that you didn't have SFED in mind to apply KSP to. So you sound like you're contradicting yourself again.

I fully agree. However, accepting nonlocality or noncausality is even less trivial problem for me. I just don't see compelling reasons to accept one of these radical ideas.

I think you misunderstood me yet again. I didn't say you SHOULD accept nonlocality or noncausality (not even I do yet!). I just simply said that EVEN if you don't accept nonlocality or noncausality, you still have the nontrivial challenge of trying to predict the already nonideal EPR correlations within a locally causal theory.

In general, it may have a different content, though the difference is not very profound (it's just about varying numbers of particles).

I think that is a pretty significant physical difference!

However, if its projections on all configuration spaces but one are zero (if the number of particles is definite), I don't see how it has a different content.

Well of course if you're only considering low-energy (nonrelativistic), few-body problems, then I agree with you.

I meant the following. We know that a typical NDE in (3+1) dimensions does not contain any entanglement nonlocality.

I don't know what "typical" means here. But if you're thinking of the DM equation, then as I explained, your statement is clearly false.

If you apply KSP to this NDE, it certainly introduces "appearance" of entanglement nonlocality. And it certainly does not introduce a possibility that the entanglement nonlocality is immanent to the NDE.

So, no.

In form - yes. In essence - no. I tried to explain that typically second quantization changes the physics contents. What is second quantization? You just declare that fields do not commute anymore. This introduces new physics content, such as Pauli principle (for fermions), among other things. This physics contents was not present in the 1st-quantized theory.

Again, the Pauli principle is already present in the 1st quantized Dirac theory with the Dirac sea mechanism.

On the other hand, KSP does not introduce any new physical contents, as far as the solutions of NDE are concerned.

You have no way of knowing that unless you can show that the extra solutions created by the KSP (that Steeb talks about) are unphysical, which you certainly have not yet done.

It does not have any new physical contents compared to the relevant 1st quantized theory, as far as the solutions of the latter are concerned. I'd say a different question is more interesting: What does it have that the second-quantized Schroedinger theory does not? And the answer is it has a locally causal interpretation, however 2nd-quantized it may look. Namely, we can just state that the original NDE is the genuine theory, which is enough to fully describe nature, and the post-KSTP is just its linearized form.

So, no.

 

[akhmeteli]

Your example here indicates that you did bother to read or understand my example from earlier. Honestly, I'm baffled that you still don't understand this very basic point. And this isn't a matter of opinion at all; the nonlocality from the instantaneous collapse of the wavefunction is already present in the single particle version of SQM, but single particle SQM doesn't display VBI because the Bell theorem requires correlations between TWO particles. Also, the nonlocality from the instantaneous collapse of the wavefunction is already present in two particle SQM for separate wavefunctions - for example, if you make 100 spin measurements in the z-direction for a single electron on earth, and then someone makes 100 spin measurements in the z-direction for a single electron somewhere in the Andromeda galaxy, in both places there will be this instantaneous wavefunction collapse from the PP of SQM; but if someone then computes the correlations between these two spin measurements, they will clearly find NO VBI. On the other hand, if one makes 100 measurements on two electrons which originally came from a singlet state so that their wavefunctions are entangled in configuration space, then there clearly will be VBI. Therefore, it is entangelement in configuration space that is the source of VBI. If you do not bother to show me that you at least understand this example, then this is the last time I will discuss this with you because I am tired of having my words ignored.

Of course, you don't owe me anything, and it's your sacred right to enter or exit this discussion or any part of it whenever you wish. However, I respectfully disagree that I ignored your argument. I just disagreed with it, and I believe this is my sacred right. You downplayed, to put it mildly, the role of PP in nonlocality, and I tried to object to you in several posts, including ##65, 67, 69, 81, 83, 86. In particular, when you said that "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 replied in post 86: "This argument does not seem conclusive. If PP does not always result in VBI, it does not mean PP is not the culprit." Obviously, you ignored my reply, although formally you did reply. But your reply was just a reiteration of your reasoning. Therefore, let me try to rephrase my reply and offer you an example. It is well-known that hemophiliacs are almost exclusively men. It is also well-known that hemophiliacs' mothers are in most cases carriers of a certain defective genes. So, if I follow your logics, I should conclude that having a carrier mother is not a cause of a disease, because not all children of such mothers are hemophilic (for example, their daughters are almost entirely free from disease). Sorry, I just cannot accept such logics. And absolutely the same logics is used in the post I'm replying now. Sorry, you just cannot brow-beat me into accepting such reasoning. If PP does not always result in nonlocality, that does not mean it is not a cause of nonlocality. Maybe entanglement is also a cause of nonlocality, but that does not mean PP is not a cause of nonlocality. One indication that it is is the fact that it is impossible to prove VBI in SQM without using PP or something similar. To summarize, whether I am absolutely right or dead wrong on this point, I don't know, but I cannot agree that I ignored your argument.

It sounds like you are confused about a number of issues here. A word of advice: it will probably help you more immediately to study and understand the already well-developed nonlocal hidden variable theories like deBB and GRW to understand why PP is not the crux of the issue here, as opposed to banking on a locally causal theory that you only have the vaguest idea about it would work.

I see your point of view.

You didn't fail to give me your reasons. You gave them, but they just aren't well thought out at the moment or based on reliable premises, with all due respect. Sorry.

Look, of course you are under no obligation to accept anything I say. However, you accused me of being unscientific, lacking objectivity and being dishonest just for one phrase (which, by the way, started with the words "I understand", so this phrase described my understanding): there are no VBI in nature. I immediately said that I may be wrong. I gave a reason why I think so (no experimental demonstration in 45 years). You admit that I gave you my reasons. You don't like my reasons. I fully appreciate that. However, I don't think your strong words were "well thought out or based on reliable premises".

 

[akhmeteli]

I'm sorry but this just false. Entanglement nonlocality is definitely not a property of 2nd quantization (either in content or form) any more than it is a property of 1st quantization. You seem to have forgotten that configuration space and entanglement nonlocality are already properties of the standard 1st quantized linear Schroedinger equation for N particles.

What you call "the standard 1st quantized linear Schroedinger equation for N particles", already carries a lot of what is the content of 2nd quantization, such as configuration space.

No, my reasoning is also about contents, and I still disagree with you that Barut's theory smuggles in 2nd quantization for the wavefunction. As I pointed out before, the Barut wavefunction is a c-number field, and the Pauli exclusion principle is already a property of the 1st quanitzed linear Dirac equation. The ONLY place where you may be able to say he smuggles in elements of "2nd quantization" is in the introduction of the complex-valued Green's function propagator in the self-field. But that's it.

No, the Pauli principle is not a part of the 1st quantized linear Dirac equation (unless you mean Dirac equation for N particles:-) ). The 1st quantized linear Dirac equation is just the Dirac equation in (3+1) dimensions. If you believe the Dirac sea is a part of that equation, then you add a part of contents of the 2nd quantization to it.

First of all, the DM Lagrangian is only defined in (3+1) dimensions for a SINGLE particle, NOT for N particles (then it is in configuration space).

Now I see the source of your confusion. Indeed, what I have in mind is application of KSP to NDE relating to a single particle, an NDE in (3+1) dimensions. You are saying that "the DM Lagrangian is only defined in (3+1) dimensions for a SINGLE particle", but you should also appreciate that this "1-particle" Lagrangian includes (as implications) the Maxwell equations. How many particles can be described by the Maxwell equations? One? but, however powerful is a light beam, it is still successfully described by the Maxwell equations (barring nonlinear effects).

Furthermore, if you already admit (reluctantly) that there is entanglement in the Barut-Dirac equation (which is in fact derived from the DM Lagrangian), then you have absolutely no reason to think the situation it is different in the DM Lagrangian. Indeed, the DM equation is just the description of how the EM field couples to the Dirac wavefunctions, and it is well-known that entanglement is already a property of the DM equation for N particles. Otherwise, it wouldn't exist in the standard Dirac equation. If your idea of starting from the DM equation and applying KSP to it is based on the premise that the DM equation is not defined in configuration space for N particles, then you are simply incorrect. Unless you are talking about only the 1 particle DM equation? In that case, applying KSP to it would only yield a 1 particle 2nd quantized theory, not an N particle theory.

Indeed, I am talking about applying KSP to the "1 particle" DM equation (or something similar). Why do you think that would only yield a 1 particle theory? We will get a theory in the Fock space, won't we?

Sorry to disappoint you but if you apply KSP to an NDE like the 1-particle DM equation, you simply will not get entanglement in the resultant KSP form.

This is not quite obvious to me. Could you give me your reasons?

It may be a way of introducing the Fock space, and therefore is a novel way of transforming from a nonlinear 1st quantized theory like SFED (or the DM theory), to a linear 2nd quantized QED-type of theory. And I think that could be very interesting. But this transformation definitely will not show that entanglement is an "artifact".

Again, what are your reasons for this "definitely"?

 

[akhmeteli]

Sorry but this particular approach sounds to me like not much more than wishful thinking.

I agree, it is "not much more than wishful thinking". Are nonlocality, noncausality, experimental demonstration of genuine VBI much more than wishful thinking so far?

Then you are talking about SFED again, even though you said before that you didn't have SFED in mind to apply KSP to. So you sound like you're contradicting yourself again.

I'm not sure. Maybe I was not clear enough. I do have in mind application of KSP to DM or something similar. I was just trying to explain that such theory already implicitely includes self-field, so the latter does not have to be added manually.

I think you misunderstood me yet again. I didn't say you SHOULD accept nonlocality or noncausality (not even I do yet!). I just simply said that EVEN if you don't accept nonlocality or noncausality, you still have the nontrivial challenge of trying to predict the already nonideal EPR correlations within a locally causal theory.

I admitted that this is a challenge. However, I did not make any commitment to take such a challenge. I was just trying to say that even if I don't take this challenge, I won't feel obligated to accept some radical ideas until they find reliable confirmation.

I think that is a pretty significant physical difference!.

I don't think this difference is significant for our discussion though.

Well of course if you're only considering low-energy (nonrelativistic), few-body problems, then I agree with you.

Again, I am not sure the circumstances that make you qualify your agreement are important for our discussion.

I don't know what "typical" means here. But if you're thinking of the DM equation, then as I explained, your statement is clearly false.

Is it really false for DM in (3+1) dimensions (what you call a 1-particle theory)?

Again, the Pauli principle is already present in the 1st quantized Dirac theory with the Dirac sea mechanism.

Again, if there is the Pauli principle, there is a part of the contents of the 2nd quantization.

You have no way of knowing that unless you can show that the extra solutions created by the KSP (that Steeb talks about) are unphysical, which you certainly have not yet done.

I mean all solutions of the NDE are embedded in the post-KSPT, so the pre-KSPT and the post-KSTP are equivalent on the set of such solutions, so there is no new contents within this set. As for the exta solutions (and not just such as described by Steeb) being or not being physical, this is a very good question, but I think it will be eventually solved experimentally, not just theoretically. Let us imagine that somebody did find an NDE that, after KSP is applied to it, is equivalent to QED. If, for example, genuine VBI are nevertheless demonstrated experimentally, that would mean that such extra solutions are indeed physical.

 

[Maaneli]

Obviously, you ignored my reply, although formally you did reply.

No I didn't ignore your reply, get your facts straight.

But your reply was just a reiteration of your reasoning.

And my reasoning was a direct response to your one sentence reply.

Therefore, let me try to rephrase my reply and offer you an example. It is well-known that hemophiliacs are almost exclusively men. It is also well-known that hemophiliacs' mothers are in most cases carriers of a certain defective genes. So, if I follow your logics, I should conclude that having a carrier mother is not a cause of a disease, because not all children of such mothers are hemophilic (for example, their daughters are almost entirely free from disease). Sorry, I just cannot accept such logics.

Wow. Your logic is so confused it frightens me. That is a horrible analogy for the simple fact that you are yet again ignoring entirely the fact that there are measurement theories superior to the PP and that in fact do not even require any kind of PP.

If PP does not always result in nonlocality, that does not mean it is not a cause of nonlocality. Maybe entanglement is also a cause of nonlocality, but that does not mean PP is not a cause of nonlocality.

This is a horrible argument because 1) you are not distinguishing the nonlocality of PP from the nonlocality of entanglement (they are in fact quite different), and 2) you have not pointed out what particular aspect of my example you think is flawed. You have merely regurgitated your belief, which my example is a direct argument against.

One indication that it is is the fact that it is impossible to prove VBI in SQM without using PP or something similar.

How many times do I have to correct you? SQM IS NOT THE ONLY POSSIBILITY.

To summarize, whether I am absolutely right or dead wrong on this point, I don't know.

Then honestly I think your are just dead confused about standard undergraduate QM, and if you're not even willing to understand undergrad QM, then quite frankly I'm not sure I want to help you out anymore.

Look, of course you are under no obligation to accept anything I say.

Why do you waste so much time pointing out the obvious? So seem to be obsessed with reminding yourself of my right or your right to disagree.

However, you accused me of being unscientific, lacking objectivity and being dishonest just for one phrase (which, by the way, started with the words "I understand", so this phrase described my understanding): there are no VBI in nature.

Yes, and I stand by this accusation, and am further affirmed by the continuation of these discussions.

I immediately said that I may be wrong.

Unfortunately you have a bad habit of contradicting yourself. You say you may be wrong, but this contradicts what you say right before that VBI does not exist in nature, like you already know this to be true (and which you cannot possibly know to be true). And my guess is that you just say that you "may be wrong" to appease me, not because you really think so with regard to this issue. And that is how you are being disingenuous here.

 

[Maaneli]

What you call "the standard 1st quantized linear Schroedinger equation for N particles", already carries a lot of what is the content of 2nd quantization, such as configuration space.

Once again the configuration space is not part of the definition of 2nd quantization. If you don't understand that, then I'm afraid you are beyond help.

No, the Pauli principle is not a part of the 1st quantized linear Dirac equation (unless you mean Dirac equation for N particles:-) ). The 1st quantized linear Dirac equation is just the Dirac equation in (3+1) dimensions. If you believe the Dirac sea is a part of that equation, then you add a part of contents of the 2nd quantization to it.

No, wrong again. The Dirac sea was a part of the 1st quantized Dirac theory well before the development of quantum electrodynamics.

Now I see the source of your confusion. Indeed, what I have in mind is application of KSP to NDE relating to a single particle, an NDE in (3+1) dimensions. You are saying that "the DM Lagrangian is only defined in (3+1) dimensions for a SINGLE particle", but you should also appreciate that this "1-particle" Lagrangian includes (as implications) the Maxwell equations. How many particles can be described by the Maxwell equations?

Um, don't you understand that coupling to the Maxwell equations can occur even with the N-particle Dirac equation (in configuration space!)? And don't you understand that the self-field of SFED couples to N-particles as well? Seriously Andy, this is very basic stuff that you should know if you have a PhD in physics and are interested in the foundations of QM.

Indeed, I am talking about applying KSP to the "1 particle" DM equation (or something similar). Why do you think that would only yield a 1 particle theory? We will get a theory in the Fock space, won't we?

NO! If that's what you think then you clearly don't know what a Fock space is. Let me tell you what it is. The Fock space is the Hilbert space of comprised from the direct sum of tensor products of single-particle Hilbert spaces. For a single particle, you only have ONE Hilbert space, with the corresponding wavefunction evolving in 3+1 dimensions. To get a Fock space, you need to start with more than one particle. That's all there is to it.

This is not quite obvious to me. Could you give me your reasons?

Well it really should be obvious. I can't believe I am explaining this to you, but if you only quantize the one particle theory, then you simply can't describe (or even approximate) the most basic of entangled states, namely, the singlet-state, which requires TWO wavefunctions corresponding to TWO particles. Again, this is undergraduate QM.

 

[Maaneli]

I agree, it is "not much more than wishful thinking". Are nonlocality, noncausality, experimental demonstration of genuine VBI much more than wishful thinking so far?

Of couse not! The standard and alternative formulations of nonlocal QM are the most empirically well-confirmed theories in terms of all their other predictions. The nonlocal versions of QM are also the ONLY theories of electrons AND photons that correctly predict the currently nonideal EPR correlations; so it is quite plausible that nonlocal QM may be entirely correct with respect to VBI, and that this will be shown once the remaining loopholes are closed.

I'm not sure. Maybe I was not clear enough. I do have in mind application of KSP to DM or something similar. I was just trying to explain that such theory already implicitely includes self-field, so the latter does not have to be added manually.

Then it sounds like you're confused about you're own idea!

I admitted that this is a challenge. However, I did not make any commitment to take such a challenge.

What? Then why are you interested in applying KSP to DM or SFED and why are you arguing that this may show entanglement to be an artifact? Are you also confused about you're own motivations?

I don't think this difference is significant for our discussion though.

Actually it is, for it is directly relevant to the definition of what a Fock space is.

Again, I am not sure the circumstances that make you qualify your agreement are important for our discussion..

Again, yes they definitely are important.

Is it really false for DM in (3+1) dimensions (what you call a 1-particle theory)?.

YES!

Again, if there is the Pauli principle, there is a part of the contents of the 2nd quantization.

No.

As for the exta solutions (and not just such as described by Steeb) being or not being physical, this is a very good question, but I think it will be eventually solved experimentally, not just theoretically. Let us imagine that somebody did find an NDE that, after KSP is applied to it, is equivalent to QED. If, for example, genuine VBI are nevertheless demonstrated experimentally, that would mean that such extra solutions are indeed physical.

Good to see that you acknowledge this point.

 

[akhmeteli]

No I didn't ignore your reply, get your facts straight.

Sorry, I stand by my statement.

:And my reasoning was a direct response to your one sentence reply.

I did not notice that. It did not look like you bothered to read my "one sentence reply".

Wow. Your logic is so confused it frightens me. That is a horrible analogy for the simple fact that you are yet again ignoring entirely the fact that there are measurement theories superior to the PP and that in fact do not even require any kind of PP.

This is a legitimate analogy, as you argued that, as PP does not always result in nonlocality, it is a red herring as far as nonlocality is concerned. I cannot discuss all possible measurement theories. SQM includes PP, and I insist that the latter is a source of nonlocality. Therefore I definitely disagree with you on this point.

This is a horrible argument because 1) you are not distinguishing the nonlocality of PP from the nonlocality of entanglement (they are in fact quite different), and 2) you have not pointed out what particular aspect of my example you think is flawed. You have merely regurgitated your belief, which my example is a direct argument against.

First you stated that PP is a red herring as far as nonlocality is concerned, now you mention some "nonlocality of PP". If the latter exists, how come PP is a red herring? And I did point out what aspect of your example is flawed, in my opinion: if PP does not always result in nonlocality, it does not mean that it is not a cause of nonlocality.

How many times do I have to correct you? SQM IS NOT THE ONLY POSSIBILITY.

I cannot accept your correction. I don't know why I am obliged to care about any theory you choose to mention. I am talking about SQM, and I insist that PP is a source of nonlocality in SQM. If other theories have other sources of nonlocality, this does not make my statement incorrect.

:Then honestly I think your are just dead confused about standard undergraduate QM, and if you're not even willing to understand undergrad QM, then quite frankly I'm not sure I want to help you out anymore.

So we disagree on whether I know undergraduate QM or not. And I don't remember asking you for any help.

:Why do you waste so much time pointing out the obvious? So seem to be obsessed with reminding yourself of my right or your right to disagree.

Just because it seems my disagreement often causes your wrath.

Yes, and I stand by this accusation, and am further affirmed by the continuation of these discussions.

I see your point of view. However, I reject your accusations as baseless. In the future I'll just try to ignore any further accusations. I would like to discuss physics. If that's not what you want, each of us is quite able to decide whether he is interested in further discussion.

Unfortunately you have a bad habit of contradicting yourself. You say you may be wrong, but this contradicts what you say right before that VBI does not exist in nature, like you already know this to be true (and which you cannot possibly know to be true). And my guess is that you just say that you "may be wrong" to appease me, not because you really think so with regard to this issue. And that is how you are being disingenuous here.

I've tried, but I failed to find a contradiction here. I did say what I thought, and I did say that what I thought might be wrong, just because, as you say, I cannot be sure. And I cannot imagine any reason to appease you. I just have no reason at all to be afraid of your wrath.

 

[akhmeteli]

Of couse not! The standard and alternative formulations of nonlocal QM are the most empirically well-confirmed theories in terms of all their other predictions. The nonlocal versions of QM are also the ONLY theories of electrons AND photons that correctly predict the currently nonideal EPR correlations; so it is quite plausible that nonlocal QM may be entirely correct with respect to VBI, and that this will be shown once the remaining loopholes are closed.

So we disagree on this point.

Then it sounds like you're confused about you're own idea!

So what? This is just an idea, which I have not tried to realize yet. I readily admit that it is not crystal clear to me. I am just trying to explain how a banal NDE can generate the Fock space.

What? Then why are you interested in applying KSP to DM or SFED and why are you arguing that this may show entanglement to be an artifact? Are you also confused about you're own motivations?

Yes, I am interested in something, does it mean I made any commitment to anybody or myself? As anybody else, I am interested in many different things, and I realize that I cannot do everything I would like to do. What's your point?

Actually it is, for it is directly relevant to the definition of what a Fock space is.

I still don't think it is important for our discussion for the following reason. If configuration space is a part of the contents of the 2nd quantization in the case where the number of particles is constant, do you really think a change in the number of particles could change such a conclusion?

Again, yes they definitely are important.

Again, do you really think that if configuration space is a part of the contents of the 2nd quantization in the low energy limit, it stops to be a part of this content as energy increases?

YES!

Well, I had to get several posts back to reconstruct what your "yes" means, and, if I am not mistaken, this means that, in your opinion, DM equations in (3+1) dimensions contain entanglement nonlocality. If this is indeed your opinion, I don't quite understand it: they are just banal NDE (in the coordinate space, not in configuration space), how come they contain entanglement nonlocality?

No.

So we disagree on this point.

 

[Maaneli]

I did not notice that. It did not look like you bothered to read my "one sentence reply".

Well then you must be in denial.

This is a legitimate analogy, as you argued that, as PP does not always result in nonlocality, it is a red herring as far as nonlocality is concerned. I cannot discuss all possible measurement theories. SQM includes PP, and I insist that the latter is a source of nonlocality. Therefore I definitely disagree with you on this point.

No, I did not say PP does not always result in nonlocality, get your damn facts straight. I always said "the nonlocality of PP is a red herring with respect to VBI". If you cannot or are not willing to discuss QM with a measurement theory, and not just the PP, then you will always be confused about this.

First you stated that PP is a red herring as far as nonlocality is concerned, now you mention some "nonlocality of PP". If the latter exists, how come PP is a red herring? And I did point out what aspect of your example is flawed, in my opinion: if PP does not always result in nonlocality, it does not mean that it is not a cause of nonlocality.

You just don't bother to read carefully do you? I never said PP is not a source of nonlocality. I said many times that it is not a source of *VBI*, which is different from the nonlocality of instantaneous wavefunction collapse implied by the PP. Sadly, I doubt that you understand this distinction.

I cannot accept your correction. I don't know why I am obliged to care about any theory you choose to mention. I am talking about SQM, and I insist that PP is a source of nonlocality in SQM. If other theories have other sources of nonlocality, this does not make my statement incorrect.

Yes it does. The example I presented explains why your belief about SQM is incorrect.

I see your point of view. However, I reject your accusations as baseless. In the future I'll just try to ignore any further accusations. I would like to discuss physics. If that's not what you want, each of us is quite able to decide whether he is interested in further discussion.

There is a difference between discussing physics and discussing your ungrounded beliefs about how physics should be, and you seem interested only in the latter.

I've tried, but I failed to find a contradiction here. I did say what I thought, and I did say that what I thought might be wrong, just because, as you say, I cannot be sure. And I cannot imagine any reason to appease you. I just have no reason at all to be afraid of your wrath.

Maybe it's your poor English, as you once said.

 

[Maaneli]

So what? This is just an idea, which I have not tried to realize yet. I readily admit that it is not crystal clear to me. I am just trying to explain how a banal NDE can generate the Fock space.

And you seem to have not properly understood the very procedure (KSP) that you want to use to generate the Fock space from the "banal" NDE (which you also have not properly understood).

Yes, I am interested in something, does it mean I made any commitment to anybody or myself? As anybody else, I am interested in many different things, and I realize that I cannot do everything I would like to do. What's your point?

You just sound totally confused about yourself.

I still don't think it is important for our discussion for the following reason. If configuration space is a part of the contents of the 2nd quantization in the case where the number of particles is constant, do you really think a change in the number of particles could change such a conclusion?

You don't seem to understand KSP yourself. KSP applied to an NDE describing a single particle will only generate a 2nd quantized linear equation in 3+1 dimensions, not the Fock or configuration space.

Again, do you really think that if configuration space is a part of the contents of the 2nd quantization in the low energy limit, it stops to be a part of this content as energy increases?

The Fock space is a more appropriate description in that case.

Well, I had to get several posts back to reconstruct what your "yes" means, and, if I am not mistaken, this means that, in your opinion, DM equations in (3+1) dimensions contain entanglement nonlocality.

NO absolutely not. Your confusion is unbelievable. I said very clearly that DM equations in 3+1 dimensions (the single particle case) do not contain entangelment nonlocality. Only the DM equations for N-particles do. That's the last time I'll say it.

If this is indeed your opinion, I don't quite understand it: they are just banal NDE (in the coordinate space, not in configuration space), how come they contain entanglement nonlocality?

Do you understand that the Dirac equation contains the possibility of entanglement nonlocality for N-particles, and that the Dirac equation for a single particle does not? If not, then that is the source of your confusion.

 

[Maaneli]

Andy, if you want to help the situation out, why don't you define (as rigorously as possible) the Fock space of QFT as you understand it. Then try to explain (as clearly and rigorously as possible) why you think entanglement can occur in a single particle Fock space.

 

[akhmeteli]

Once again the configuration space is not part of the definition of 2nd quantization. If you don't understand that, then I'm afraid you are beyond help.

I believe you can see the difference between the following phrases: "the configuration space is a part of the definition of 2nd quantization" and "the configuration space carries a part of the contents of 2nd quantization".

No, wrong again. The Dirac sea was a part of the 1st quantized Dirac theory well before the development of quantum electrodynamics.

You may call "1st quantized" whatever you want, even SFED. However, the Dirac sea implies the Pauli principle, the Pauli principle implies anticommutation of the relevant operators, and such anticommutation makes a part of the contents of the second quantization. Therefore, the Dirac equation with the Dirac sea carries some of the contents of the second quantization.

Um, don't you understand that coupling to the Maxwell equations can occur even with the N-particle Dirac equation (in configuration space!)? And don't you understand that the self-field of SFED couples to N-particles as well? Seriously Andy, this is very basic stuff that you should know if you have a PhD in physics and are interested in the foundations of QM.

I do understand that. What I don't understand, is how it is relevant to what I said. And I said that I have in mind application of KSP to the DM equations (or something similar) in (3+1) dimensions (I guess you would call these equations a 1-particle theory). If I am interested in something, that does not mean that nothing else exists in physics, and you are trying to explain to me that there exist other theories, as if I did not know that.

NO! If that's what you think then you clearly don't know what a Fock space is. Let me tell you what it is. The Fock space is the Hilbert space of comprised from the direct sum of tensor products of single-particle Hilbert spaces. For a single particle, you only have ONE Hilbert space, with the corresponding wavefunction evolving in 3+1 dimensions. To get a Fock space, you need to start with more than one particle. That's all there is to it.

Maaneli, we certainly don’t disagree on what the Fock space is. I repeat, we don’t disagree on that, so there is no need for me to provide my definition of the Fock space, as you suggest in a later post. Just bear with me for a moment, I beg you. I also fully understand that in standard quantum mechanics “for a single particle, you only have ONE Hilbert space, with the corresponding wavefunction evolving in 3+1 dimensions”. BUT! I am talking about what happens AFTER the Kowalski-Steeb procedure is applied to such one-particle theory with wavefunction u(x,t) (in Kowalski’s notation). Please take a short moment for another look at my post #90 (where I give an outline of KSP) or directly at Kowalski’s work. What corresponds to this wavefunction after KSP is the coherent state |u> (or, more exactly, |u,t>, which is not important for the following). Please look at the definition of this state. Up to a certain factor, it’s the vacuum state multiplied by an exponent of a linear combination of creation operators. You can expand this exponent in an infinite series of products of creation operators. What is a vacuum state? It’s a 0-particle state. When you multiply the vacuum state by a creation operator, you get a 1-particle state. When you multiply the vacuum state by a product of n creation operators, you get an n-particle state in the 3n-dimensional configuration space. Thus, the unitary state is a linear combination of k-particle states, where k takes all values from zero to infinity. Therefore, the coherent state lies in the Fock state! Therefore, the 1-particle wavefunctions are embedded into the Fock space. You can repeat ad nauseam that KSP is second quantization, and I’ll repeat ad nauseam that post-KSPT is equivalent to pre-KSPT on the set of solution of the latter. What I want to emphasize is that as a result of KSP, the Fock space naturally arises for the “1-particle” theory. Thus , “to get a Fock space, you” don’t “need to start with more than one particle “, you can just apply KSP to a one-particle wavefunction.

Well it really should be obvious. I can't believe I am explaining this to you, but if you only quantize the one particle theory, then you simply can't describe (or even approximate) the most basic of entangled states, namely, the singlet-state, which requires TWO wavefunctions corresponding to TWO particles. Again, this is undergraduate QM.

As I tried to explain in the previous comment in this post, if you apply KSP to a “one-particle” wavefunction, you get a function in the Fock space. If you then project this function on the 2-particle configuration space (and this projection will not be zero in a general case), you may get an approximation of the singlet state. At least it does not seem obvious that you cannot get such an approximation in this way. I readily admit that I was not taught KSP in the undergraduate QM course.

 

[akhmeteli]

Well then you must be in denial.

So we disagree on who might be in denial.

No, I did not say PP does not always result in nonlocality, get your damn facts straight. I always said "the nonlocality of PP is a red herring with respect to VBI".

I have to admit I did not quote you literally. However, if I am not mistaken, neither did you. You did not say “the nonlocality of PP is a red herring with respect to VBI", at least I could not find this phrase, you said: “The PP is actually a deceptive, red herring.” I don’t remember you mentioning the nonlocality of PP until a very recent post. At least now I know that you do not deny the nonlocality of PP. And I am glad to know that. That makes life much easier:-)
Returning to the subject of the discussion, I believe my reasoning remains fully valid, I just need to replace “nonlocality” with "VBI". I should have said “This is a legitimate analogy, as you argued that, as PP does not always result in VBI, it is a red herring as far as VBI are concerned.” So I just cannot agree with the logics of your argument.

If you cannot or are not willing to discuss QM with a measurement theory, and not just the PP, then you will always be confused about this.

So far I don’t quite see the point of discussing “QM with a measurement theory” (QMMT) for the following reason. If such QMMT is empirically equivalent to SQM (do I understand correctly that it means that every thinkable experiment will produce the same results in both theories?), it obviously includes some postulate that is equivalent to PP, so all my reasoning would be equally valid for such theory. Remember, I often said “PP or something similar”. If, however, such QMMT is not empirically equivalent to SQM, why should I care about such a theory in the framework of a discussion of local causality? OK, I may say, so there is a theory without local causality, with VBI, and with a dubious experimental status. So what? Why should I care?

You just don't bother to read carefully do you? I never said PP is not a source of nonlocality. I said many times that it is not a source of *VBI*, which is different from the nonlocality of instantaneous wavefunction collapse implied by the PP. Sadly, I doubt that you understand this distinction.

As I said, I admit that I did not quote you literally, and a part of my text that you are replying to is indeed out of place (and I am glad that it is out of place because I did not look forward to trying to convince you that PP is indeed a source of nonlocality). However, the following statement (with appropriate corrections) still remains valid: “And I did point out what aspect of your example is flawed, in my opinion: if PP does not always result in VBI, it does not mean that it is not a cause of VBI.”

Yes it does. The example I presented explains why your belief about SQM is incorrect.

No, it does not. See above.

There is a difference between discussing physics and discussing your ungrounded beliefs about how physics should be, and you seem interested only in the latter.

What ungrounded beliefs? I am actually trying to say just two things: 1) local causality should not be dismissed without bullet-proof arguments; 2) there are no such bullet-proof arguments, either theoretical or experimental. For this reason I am not holding my breath for experimental demonstration of genuine VBI. So you disagree. That does not necessarily mean your beliefs are “grounded” and mine are “ungrounded”. If you don’t want to discuss this matter (the status of local causality), you can always exit the discussion; if you want to discuss something else, tell me what it is, and I’ll tell you whether I am willing to enter such a discussion or not. I guess we are both busy, and have to “choose our battles”. And if you remember, the issue of local causality arose in this thread because it may be crucial for defining the direction of further development of SFED.

 

[Maaneli]

I have to admit I did not quote you literally. However, if I am not mistaken, neither did you. You did not say “the nonlocality of PP is a red herring with respect to VBI", at least I could not find this phrase, you said: “The PP is actually a deceptive, red herring.” I don’t remember you mentioning the nonlocality of PP until a very recent post.

Actually I've mentioned several times that the nonlocality of PP is not the same as VBI. You just never recognized that distinction earlier.

Returning to the subject of the discussion, I believe my reasoning remains fully valid, I just need to replace “nonlocality” with "VBI".

Such a replacement is just simply wrong, as I have already explained.

I should have said “This is a legitimate analogy, as you argued that, as PP does not always result in VBI, it is a red herring as far as VBI are concerned.” So I just cannot agree with the logics of your argument.

Then you obviously didn't understand the argument.

So far I don’t quite see the point of discussing “QM with a measurement theory” (QMMT) for the following reason. If such QMMT is empirically equivalent to SQM (do I understand correctly that it means that every thinkable experiment will produce the same results in both theories?), it obviously includes some postulate that is equivalent to PP, so all my reasoning would be equally valid for such theory. Remember, I often said “PP or something similar”. If, however, such QMMT is not empirically equivalent to SQM, why should I care about such a theory in the framework of a discussion of local causality? OK, I may say, so there is a theory without local causality, with VBI, and with a dubious experimental status. So what? Why should I care?

Now you're just being disingenuous here. I never ever suggested considering a QMMT that is not empirically consistent with all current experiments (and all current experiments are really what one has any rational reason to care about, not every "thinkable" experiment). In fact I repeatedly said to consider a QMMT like deBB or GRW which are empirically equivalent to SQM, but are NOT based on ad hoc and imprecise postulates about "measurements". Yet, you simply still refuse to study those theories well enough to understand how they describe VBI. If you do not bother to understand why I propose deBB and GRW as counterexamples to your belief that "PP is a cause of VBI and that rejection of PP implies no VBI", then I will not bother to spend anymore time talking to you about this. It is simply an insult for you to suggest to me to read up on KSP, when you won't even take the time, at my suggestion, to read up on deBB and GRW approaches to VBI.

What ungrounded beliefs? I am actually trying to say just two things: 1) local causality should not be dismissed without bullet-proof arguments; 2) there are no such bullet-proof arguments, either theoretical or experimental. For this reason I am not holding my breath for experimental demonstration of genuine VBI. So you disagree. That does not necessarily mean your beliefs are “grounded” and mine are “ungrounded”.

I say they are ungrounded because you have no idea yet of a locally causal theory that would explain the nonideal EPRB correlations as accurately as the various QM formulations (or for that matter any of the other experimentally tested atomic, nuclear, and high energy physical phenomena that the QM formulations can describe), and yet you seem to think locally causal theories are more plausible or as plausible in correctness as the varoius QM formulations. That to me is an ungrounded belief.

And if you remember, the issue of local causality arose in this thread because it may be crucial for defining the direction of further development of SFED.

The issue of local causality arose in this thread because of your mistaken belief (which apparently was not based on any evidence) that SFED is fundamentally a locally causal theory. Certainly it has been established that KSP has no relevance to SFED, especially in the idea of making SFED into a locally causal theory.

 

[Maaneli]

I believe you can see the difference between the following phrases: "the configuration space is a part of the definition of 2nd quantization" and "the configuration space carries a part of the contents of 2nd quantization".

Yes, but you still seem be suggesting (falsely) that a configuration space implies a 2nd quantized theory, and not recognizing that configuration space is a part of 1st quantized QM, entirely independently of second quantization. So any argument you make for why VBI might occur as a result of applying KSP to a locally causal NDE, has no bearing on the nonlocality from the configuration space in QM formulations, including SFED.

You may call "1st quantized" whatever you want, even SFED. However, the Dirac sea implies the Pauli principle, the Pauli principle implies anticommutation of the relevant operators, and such anticommutation makes a part of the contents of the second quantization.

The wavefunctions are still c-number fields, so they are not second quantized.

Therefore, the Dirac equation with the Dirac sea carries some of the contents of the second quantization.

No more so than the configuration space of the Dirac equation. And that is why it is still a fallacy to call the introduction of the Pauli principle as a "second quantization".

Maaneli, we certainly don’t disagree on what the Fock space is. I repeat, we don’t disagree on that, so there is no need for me to provide my definition of the Fock space, as you suggest in a later post. Just bear with me for a moment, I beg you. I also fully understand that in standard quantum mechanics “for a single particle, you only have ONE Hilbert space, with the corresponding wavefunction evolving in 3+1 dimensions”. BUT! I am talking about what happens AFTER the Kowalski-Steeb procedure is applied to such one-particle theory with wavefunction u(x,t) (in Kowalski’s notation). Please take a short moment for another look at my post #90 (where I give an outline of KSP) or directly at Kowalski’s work. What corresponds to this wavefunction after KSP is the coherent state |u> (or, more exactly, |u,t>, which is not important for the following). Please look at the definition of this state. Up to a certain factor, it’s the vacuum state multiplied by an exponent of a linear combination of creation operators. You can expand this exponent in an infinite series of products of creation operators. What is a vacuum state? It’s a 0-particle state. When you multiply the vacuum state by a creation operator, you get a 1-particle state. When you multiply the vacuum state by a product of n creation operators, you get an n-particle state in the 3n-dimensional configuration space. Thus, the unitary state is a linear combination of k-particle states, where k takes all values from zero to infinity. Therefore, the coherent state lies in the Fock state! Therefore, the 1-particle wavefunctions are embedded into the Fock space. You can repeat ad nauseam that KSP is second quantization, and I’ll repeat ad nauseam that post-KSPT is equivalent to pre-KSPT on the set of solution of the latter. What I want to emphasize is that as a result of KSP, the Fock space naturally arises for the “1-particle” theory. Thus , “to get a Fock space, you” don’t “need to start with more than one particle “, you can just apply KSP to a one-particle wavefunction.

It is still not at all clear to me that the embedding of this coherent state into Fock space for 1-particle via KSP would actually imply an N-particle theory in configuration space. From your example, I don't see a linear combination of n creation operators acting on the vacuum state. Furthermore, it still seems that physically, particle-creation annihilation processes in the KSP theory only apply in relativistic cases. Entanglement nonlocality has nothing to do with that. So I still don't understand your argument.

As I tried to explain in the previous comment in this post, if you apply KSP to a “one-particle” wavefunction, you get a function in the Fock space. If you then project this function on the 2-particle configuration space (and this projection will not be zero in a general case), you may get an approximation of the singlet state. At least it does not seem obvious that you cannot get such an approximation in this way. I readily admit that I was not taught KSP in the undergraduate QM course.

Again, this "projection onto the 2-particle configuration space" seem entirely physically unmotivated.

 

[akhmeteli]

And you seem to have not properly understood the very procedure (KSP) that you want to use to generate the Fock space from the "banal" NDE (which you also have not properly understood).

KSP does generate the Fock space from the banal NDE, irrespective of what I want.

You don't seem to understand KSP yourself. KSP applied to an NDE describing a single particle will only generate a 2nd quantized linear equation in 3+1 dimensions, not the Fock or configuration space.)

I tried to explain in one of my recent posts that KSP applied to an NDE describing a single particle will indeed generate the Fock space. A wavefunction in 3+1 dimension is mapped by KSP to the vacuum state multiplied by an exponent of a linear combination of creation operators (there is also an additional factor, which is not important for our discussion). The exponent, when expanded, contains a sum of products of k creation operators (k takes all values from zero to infinity). A product of k creation operators, acting on the vacuum state, produces a k-particle state in the 3k-dimensional configuration space. Therefore, the entire state that the wavefunction is mapped to exists in the Fock space.

The Fock space is a more appropriate description in that case.

But that does not contradict the fact that the configuration space carries a part of contents of 2nd quantization.

NO absolutely not. Your confusion is unbelievable. I said very clearly that DM equations in 3+1 dimensions (the single particle case) do not contain entangelment nonlocality. Only the DM equations for N-particles do.

Glad to hear that. So we agree on this point.

Do you understand that the Dirac equation contains the possibility of entanglement nonlocality for N-particles, and that the Dirac equation for a single particle does not? If not, then that is the source of your confusion.

I understand that, as far as SQM is concerned. So we agree on that point, as I said. That does not contradict the fact that KSP applied to the DM equations in (3+1) dimensions generates the Fock space.

 

[akhmeteli]

Actually I've mentioned several times that the nonlocality of PP is not the same as VBI. You just never recognized that distinction earlier.

When you say such things as "I am in disbelief that you still try to cling to this idea that PP somehow is the cause of the appearance of nonlocality.", life seems rather tough. You cannot blame me for previously thinking that you flatly deny that PP is a source of nonlocality.

Such a replacement is just simply wrong, as I have already explained.

So we disagree on this point.

Then you obviously didn't understand the argument.

So we disagree on this point.

Now you're just being disingenuous here. I never ever suggested considering a QMMT that is not empirically consistent with all current experiments (and all current experiments are really what one has any rational reason to care about, not every "thinkable" experiment). In fact I repeatedly said to consider a QMMT like deBB or GRW which are empirically equivalent to SQM, but are NOT based on ad hoc and imprecise postulates about "measurements". Yet, you simply still refuse to study those theories well enough to understand how they describe VBI. If you do not bother to understand why I propose deBB and GRW as counterexamples to your belief that "PP is a cause of VBI and that rejection of PP implies no VBI", then I will not bother to spend anymore time talking to you about this. It is simply an insult for you to suggest to me to read up on KSP, when you won't even take the time, at my suggestion, to read up on deBB and GRW approaches to VBI.

With all due respect, complaining of insults, coming from you - that's pretty rich. And I guess there is a difference between "reading up" and looking at one paragraph in my post (that does not mean that you owe me anything, even reading this paragraph). As for dBB, I explained my position in post #69. Your reply (the beginning of post #70), where you somewhat modified the statement that I was doubtful about did not look relevant to VBI. My understanding is, to get VBI, say, in dBB, you need to add some postulate to unitary evolution. Or do you believe you can get VBI in dBB using just unitary evolution? You said that in the pilot wave theory "you can easily account for VBI due to the branching of wavefunctions after a measurement interaction", but is this compatible with unitary evolution?

As for GRW, I just don't have any motivation to study it, as its collapse postulate (or is it postulates?) seems extremely arbitrary.

I say they are ungrounded because you have no idea yet of a locally causal theory that would explain the nonideal EPRB correlations as accurately as the various QM formulations (or for that matter any of the other experimentally tested atomic, nuclear, and high energy physical phenomena that the QM formulations can describe), and yet you seem to think locally causal theories are more plausible or as plausible in correctness as the varoius QM formulations. That to me is an ungrounded belief.

OK, I outlined my position, so perhaps there is no point in reiterating it. So we disagree on what is grounded and what is ungrounded.

The issue of local causality arose in this thread because of your mistaken belief (which apparently was not based on any evidence) that SFED is fundamentally a locally causal theory. Certainly it has been established that KSP has no relevance to SFED, especially in the idea of making SFED into a locally causal theory.

I guess our discussion illustrates that the issue of local causality in the context of SFED is not trivial. I believe you also learned something new about this issue in the course of the discussion. So maybe the discussion was not useless.
And for me, the question remains whether Barut was right when he introduced configuration space in his theory.

 

[Maaneli]

When you say such things as "I am in disbelief that you still try to cling to this idea that PP somehow is the cause of the appearance of nonlocality.", life seems rather tough. You cannot blame me for previously thinking that you flatly deny that PP is a source of nonlocality.

Again, a disingenuous characterization. We were obviously talking about VBI, when referring to nonlocality, not about some other form of nonlocality. Perhaps you decided to start thinking about something else during that time, and to not inform me of it.

With all due respect, complaining of insults, coming from you - that's pretty rich.

Hey I'm just using your dislike of insults against you in this argument. Actually, I think you're just being inconsistent and hypocritical by not practicing what you preach.

And I guess there is a difference between "reading up" and looking at one paragraph in my post (that does not mean that you owe me anything, even reading this paragraph).

Ah, wrong again. It is not just looking at one paragraph, but rather reading the papers related KSP. It's a sad day in physics when a 22 year old with a B.S. has more integrity and willingness to learn a new subject than a 50+ year old Ph.D physicist (allegedly).

As for dBB, I explained my position in post #69. Your reply (the beginning of post #70), where you somewhat modified the statement that I was doubtful about did not look relevant to VBI. My understanding is, to get VBI, say, in dBB, you need to add some postulate to unitary evolution. Or do you believe you can get VBI in dBB using just unitary evolution? You said that in the pilot wave theory "you can easily account for VBI due to the branching of wavefunctions after a measurement interaction", but is this compatible with unitary evolution?

YES IT IS PERFECTLY COMPATIBLE WITH UNITARY EVOLUTION. That's the whole damn point that doesn't seem to sink into your head. And if you don't even know those basics, then it's safe to say that you probably don't understand much of anything about deBB theory, and which is why you're so confused about EPRB.

As for GRW, I just don't have any motivation to study it, as its collapse postulate (or is it postulates?) seems extremely arbitrary.

No, it is not a postulate like in SQM. You should really look at those references if you want to make any statements about GRW. Otherwise you're being disingenuous again.

I guess our discussion illustrates that the issue of local causality in the context of SFED is not trivial. I believe you also learned something new about this issue in the course of the discussion. So maybe the discussion was not useless.
And for me, the question remains whether Barut was right when he introduced configuration space in his theory.

The only thing I learned new from this discussion is the KSP method, and a better understanding about how configuration space is used in relativistic SFED. That's about all.

 

[akhmeteli]

Yes, but you still seem be suggesting (falsely) that a configuration space implies a 2nd quantized theory, and not recognizing that configuration space is a part of 1st quantized QM, entirely independently of second quantization.

Let me give you an example. Imagine that you have a standard Hamiltonian for N identical bosons (for example) with standard binary interaction (let us assume for simplicity that they are placed in a box with periodic boundary conditions). The Hamiltonian acts upon symmetric wavefunctions in the 3N-dimensional configuration space. It is well-known how to write the relevant second-quantized Hamiltonian built using operator wavefunctions and acting in the Fock space. This Hamiltonian commutes with the particle number operator (the number of particles is conserved), so you can define this Hamiltonian for the subspace of the Fock space defined by the condition: the number of particles equals N. Or, in other words, this is an eigenspace of the particle number operator with eigenvalue N. Then you can calculate the eigenvalues of this Hamiltonian (limited to the subspace). I hope you understand that they will coincide with the eigenvalues of the initial Hamiltonian acting in the 3N-dimensional configuration space. That means that both Hamiltonians describe pretty much the same physics. That's why I am saying that configuration space carries a part of the contents of second quantization. While the form does not look 2nd-quantized in the first case, the contents of the theory is the same. I may praise the first theory as 1st-quantized, but it is pretty much equivalent to the second-quantized theory. So the physical contents of 2nd quantization has already been smuggled in through imposition of the symmetry condition on the wavefunctions and the symmetry of the Hamiltonian.

So any argument you make for why VBI might occur as a result of applying KSP to a locally causal NDE, has no bearing on the nonlocality from the configuration space in QM formulations, including SFED.

I believe such argument can indeed be relevant, as configuration spaces arise (as parts of the Fock space) as a result of applying KSP to a locally causal NDE. Therefore, the nonlocality from the configuration space in QM formulations may be just a property of an approximation to the "real" theory, i.e. the locally causal NDE or its KSP-version.

The wavefunctions are still c-number fields, so they are not second quantized.

But a part of the physical contents of second quantization is already there.

No more so than the configuration space of the Dirac equation.

And no less.

And that is why it is still a fallacy to call the introduction of the Pauli principle as a "second quantization".

Nevertheless, the Pauli principle introduces a part of the contents of 2nd quantization.

It is still not at all clear to me that the embedding of this coherent state into Fock space for 1-particle via KSP would actually imply an N-particle theory in configuration space. From your example, I don't see a linear combination of n creation operators acting on the vacuum state.

I did not say "a linear combination of n creation operators acting on the vacuum state". What acts on the vacuum state is an exponent of a linear combination of creation operators (actually, this linear combination is an integral). The configuration spaces arise as follows: you can replace the exponent by its Taylor series, i.e. the sum of powers of its argument. The n-th power of its argument will be a linear combination of products of n creation operators. Acting on the vacuum state, each product of n creation operators generates an n-particle function. You can regard such function as a function in an n-particle configuration space. Thus, the embedding of this coherent state into Fock space for 1-particle via KSP will in general have nonvanishing projections on configuration spaces with any number of particles.

Furthermore, it still seems that physically, particle-creation annihilation processes in the KSP theory only apply in relativistic cases. Entanglement nonlocality has nothing to do with that. So I still don't understand your argument.

In the following, I am on a shaky ground, as I did not study this in detail. Let us assume for the moment that you are correct, and "physically, particle-creation annihilation processes in the KSP theory only apply in relativistic cases." The thing is electrodynamics is always relativistic as photons are massless, so you always have a hell of a lot of soft photons. Actually, one can speculate that an entangled state (say of two electrons) is maintained through exchange of photons between the particles.

Again, this "projection onto the 2-particle configuration space" seem entirely physically unmotivated.

Again, I am on a shaky ground, but the physical motivation may be to get a decent approximation.

 

[akhmeteli]

Again, a disingenuous characterization. We were obviously talking about VBI, when referring to nonlocality, not about some other form of nonlocality. Perhaps you decided to start thinking about something else during that time, and to not inform me of it.

I tend to read everything as it is written. I cannot read your thoughts.

Hey I'm just using your dislike of insults against you in this argument. Actually, I think you're just being inconsistent and hypocritical by not practicing what you preach.

Only the "insult" that you somehow found in my words is purely imaginary.

Ah, wrong again. It is not just looking at one paragraph, but rather reading the papers related KSP.

Why not Encyclopedia Britannica as well? Anyway, I asked you just to look at one paragraph. Furthermore, that was a request, not a demand, so you could grant it or deny it.

It's a sad day in physics when a 22 year old with a B.S. has more integrity and willingness to learn a new subject than a 50+ year old Ph.D physicist (allegedly).

You asked some time ago why I tend to repeat obvious things. Partly because sometimes it seems you need it. So let me tell you something obvious. You are not my boss, and you cannot order me what and when I must read or study. I have my fair share of responsibilities as it is, and we owe each other nothing.

Another thing. Next time you publicly disclose other people's personal information shared with you in e-mail, don't be surprised if your own integrity is questioned.

YES IT IS PERFECTLY COMPATIBLE WITH UNITARY EVOLUTION. That's the whole damn point that doesn't seem to sink into your head. And if you don't even know those basics, then it's safe to say that you probably don't understand much of anything about deBB theory, and which is why you're so confused about EPRB.

I am afraid I cannot trust you on your word about dBB. In your post #68 you confidently assured me of something you had to modify in post #70, when challenged. On the other hand, I have no time to check all your statements.

No, it is not a postulate like in SQM. You should really look at those references if you want to make any statements about GRW. Otherwise you're being disingenuous again.

Same as above.

The only thing I learned new from this discussion is the KSP method, and a better understanding about how configuration space is used in relativistic SFED. That's about all.

Very well. If you believe this discussion is a waste of time for you, you know what to do.

 

[Maaneli]

Let me give you an example. Imagine that you have a standard Hamiltonian for N identical bosons (for example) with standard binary interaction (let us assume for simplicity that they are placed in a box with periodic boundary conditions). The Hamiltonian acts upon symmetric wavefunctions in the 3N-dimensional configuration space. It is well-known how to write the relevant second-quantized Hamiltonian built using operator wavefunctions and acting in the Fock space. This Hamiltonian commutes with the particle number operator (the number of particles is conserved), so you can define this Hamiltonian for the subspace of the Fock space defined by the condition: the number of particles equals N. Or, in other words, this is an eigenspace of the particle number operator with eigenvalue N. Then you can calculate the eigenvalues of this Hamiltonian (limited to the subspace). I hope you understand that they will coincide with the eigenvalues of the initial Hamiltonian acting in the 3N-dimensional configuration space. That means that both Hamiltonians describe pretty much the same physics. That's why I am saying that configuration space carries a part of the contents of second quantization. While the form does not look 2nd-quantized in the first case, the contents of the theory is the same. I may praise the first theory as 1st-quantized, but it is pretty much equivalent to the second-quantized theory. So the physical contents of 2nd quantization has already been smuggled in through imposition of the symmetry condition on the wavefunctions and the symmetry of the Hamiltonian.

First off, I thought we were talking about fermions, not bosons. Indeed, when you proposed to consider KSP in the context of SFED or the DM equations, you can only talk about the Hamiltonian of fermions, not bosons. Remember that there are no photons in SFED or DM. Secondly, the obvious fallacy in your reasoning is that by using words like "smuggled", you are implicitly implying that somehow 2nd quantization is physically and conceptually prior to 1st quantization, and that, in this case, the Pauli principle is somehow borrowed from 2nd quantization in an ad-hoc way. This bias on your part is quite blatant, and has no logical basis, which is why it cannot be taken very seriously.

I believe such argument can indeed be relevant, as configuration spaces arise (as parts of the Fock space) as a result of applying KSP to a locally causal NDE. Therefore, the nonlocality from the configuration space in QM formulations may be just a property of an approximation to the "real" theory, i.e. the locally causal NDE or its KSP-version.

No. See below.

But a part of the physical contents of second quantization is already there.

Again, that doesn't mean it "smuggles" elements of 2nd quantization. You are again implicitly assuming that these physical contents are a natural property of 2nd quantization, and not a natural property of 1st quantization.

Nevertheless, the Pauli principle introduces a part of the contents of 2nd quantization.

No, wrong again. See above and below.

I did not say "a linear combination of n creation operators acting on the vacuum state". What acts on the vacuum state is an exponent of a linear combination of creation operators (actually, this linear combination is an integral). The configuration spaces arise as follows: you can replace the exponent by its Taylor series, i.e. the sum of powers of its argument. The n-th power of its argument will be a linear combination of products of n creation operators. Acting on the vacuum state, each product of n creation operators generates an n-particle function. You can regard such function as a function in an n-particle configuration space. Thus, the embedding of this coherent state into Fock space for 1-particle via KSP will in general have nonvanishing projections on configuration spaces with any number of particles.

Again, there is no physical reason to think that the "particles" in this KSP Fock space are the physically real particles that we manipulate in real EPRB experiments. Furthermore, based on your first comment above, I don't know if you have in mind bosons or fermions when you talk about the creation-annihilation operators or the word "particle". The situation is quite different for fermions and bosons. You should know that if you have studied QED and QM.

In the following, I am on a shaky ground, as I did not study this in detail. Let us assume for the moment that you are correct, and "physically, particle-creation annihilation processes in the KSP theory only apply in relativistic cases." The thing is electrodynamics is always relativistic as photons are massless, so you always have a hell of a lot of soft photons. Actually, one can speculate that an entangled state (say of two electrons) is maintained through exchange of photons between the particles.

Um, no, QED is not always relativistic. Indeed the description of "photons" are. But if you're talking about electrons, then they can certainly have a nonrelativistic wavefunction or path integral desciption that is quite independent of real or virtual photons. Furthermore, your speculation makes no sense because, again, the phenomenon of entanglement nonlocality for two electrons has absolutely no need for any element of relativitistic physics.

Again, I am on a shaky ground, but the physical motivation may be to get a decent approximation.

The physical motivation you speculate makes absolutely no physical sense. So more like senseless ground than shaky ground at this point. I think it would help you enormously to clear your mind about the difference between fermions and bosons, and the physical description of entanglement nonlocality in nonrelativistic QED and QM before you present me with any further half-baked speculations about this.

 

[Maaneli]

I tend to read everything as it is written. I cannot read your thoughts.

. If you actually do read everything as it is written (and I highly doubt it at this point), it would be immediately clear to you that we initially agreed to assume that VBI and nonlocality meant the same thing. Of course there are different forms of nonlocality, but if you want to start changing definitions without informing me about it, then go confuse someone else. I cannot read your thoughts.

Why not Encyclopedia Britannica as well? Anyway, I asked you just to look at one paragraph. Furthermore, that was a request, not a demand, so you could grant it or deny it..

You call "I beg you, please" a request? Sad. Anyway, my point was that I went above and beyond, and you haven't even lifted a finger even after my repeated requests (which later turned into demands because of your deaf ear). Let me give you a bit of advice about how to lead a productive discussion - when someone requests you to read into something, and you beg them to read into something, it is ALWAYS a good idea to heed their request as well, especially if it is critical to understanding their point of view. It's clear to me now that you never had any interest in understanding my point of view, but instead in just spewing your random speculations. And please, don't bother to try and give me advice in return.

You asked some time ago why I tend to repeat obvious things. Partly because sometimes it seems you need it.

. I guess the joke went over your head. I was pointing out your obvious insecurity with harsh criticism and your right to speak freely. Honestly, you're just wasting energy by constantly preaching your right to say what you want.

So let me tell you something obvious. You are not my boss, and you cannot order me what and when I must read or study. I have my fair share of responsibilities as it is, and we owe each other nothing.

I never said I was your boss and I never ordered you to do anything (that would require a threat, which I have never made). I merely expressed my opinion about your lack of knowledge and understanding, and my opinion about what you should do to address it. Of course, I don't care to have to always qualify everything I say by pointing out that they are my opinions (that should be obvious to you). If you feel easily threatened by that, then you have more serious personal issues to deal with.

Another thing. Next time you publicly disclose other people's personal information shared with you in e-mail, don't be surprised if your own integrity is questioned.

Did you feel uncomfortable with that? If so, then I apologize. If you don't have a problem with that, then get over it. Personal information is mentioned by members of this forum quite frequently and without much objection.


I

I am afraid I cannot trust you on your word about dBB. In your post #68 you confidently assured me of something you had to modify in post #70, when challenged. On the other hand, I have no time to check all your statements.

First off, I am not asking you to "trust" me on my word. I am asking you to read, learn, and understand for yourself - but you obviously don't want to and never wanted to. Secondly, you clearly did not understand a damn thing about what I said in #68 and #70. My "modification" in #70 was actually just an elaboration of what I said in #68. And there was absolutely no contradiction made. Again, you are being disingenuous. And, if you would like to know why I am being abrasive with you now, then think back to my first email to you where I explained my reasons for being abrasive in previous threads with certain other people. It seems, regrettably, that you are absolutely no different than those individuals in that regard.

Very well. If you believe this discussion is a waste of time for you, you know what to do.

I think you have wasted a lot of time and energy by your frequent lack of clear explanations, your unwillingness to have either intellectual or academic integrity in discussing these issues, and for your repeated misrepresentations of my views.

 

[akhmeteli]

First off, I thought we were talking about fermions, not bosons. Indeed, when you proposed to consider KSP in the context of SFED or the DM equations, you can only talk about the Hamiltonian of fermions, not bosons. Remember that there are no photons in SFED or DM.

Actually, I was talking about both bosons and fermions (for example, I specifically mentioned fermions in post #96). I could agree that there are no photons in SFED (they were eliminated there), but why do you say that there are no photons in DM (Dirac-Maxwell)?

Secondly, the obvious fallacy in your reasoning is that by using words like "smuggled", you are implicitly implying that somehow 2nd quantization is physically and conceptually prior to 1st quantization, and that, in this case, the Pauli principle is somehow borrowed from 2nd quantization in an ad-hoc way. This bias on your part is quite blatant, and has no logical basis, which is why it cannot be taken very seriously.

I am not trying to decide what was physically and conceptually prior and what was not. In the framework of our discussion, however, we are actually trying to compare SFED with QED. The latter is second-quantized (as far as its contents is concerned – the form may be very different: you even said something like the QED expressions for S-matrix should not be called second quantized) and it preceded SFED, so if you like, you can say that chronologically QED is prior to SFED. So it is psychologically understandable why I talked about Barut smuggling in the contents of second quantization from QED into SFED. If you are trying to say that this expression is out of place when we are talking about, say, Dirac’s equation with Dirac sea, well, I could agree that it does not sound good. But your expression “blatant bias” also looks misplaced. I would say I did not imply “physically and conceptually prior” – these are your words. You could say I implied “chronologically prior” – and only as far as QED and SFED are concerned.

Again, that doesn't mean it "smuggles" elements of 2nd quantization. You are again implicitly assuming that these physical contents are a natural property of 2nd quantization, and not a natural property of 1st quantization.

What I actually implied I described a few lines above. I don’t think there is any real depth here. In other words, I don’t think we essentially disagree on this issue. I agree that my “smuggles” does sound awkward in some situations.

No, wrong again. See above and below.

So we disagree on this point. On the other hand, it may well be that you're right, and I'm wrong.

Again, there is no physical reason to think that the "particles" in this KSP Fock space are the physically real particles that we manipulate in real EPRB experiments.

I’d say there is indeed such a physical reason: the Fock space is present in both post-KSTP and in QED, which (I mean QED) seems to describe correctly current EPRB experiments. On the other hand, I could agree with you that in the absence of a “final” theory it is difficult to compare “KSP-particles” with real particles.

Furthermore, based on your first comment above, I don't know if you have in mind bosons or fermions when you talk about the creation-annihilation operators or the word "particle". The situation is quite different for fermions and bosons. You should know that if you have studied QED and QM.

As I said, I have in mind both fermions and bosons.

Um, no, QED is not always relativistic. Indeed the description of "photons" are. But if you're talking about electrons, then they can certainly have a nonrelativistic wavefunction or path integral desciption that is quite independent of real or virtual photons.

I am not sure this is so clear-cut. As you know, the experimental low-energy values of the electron mass, charge, and so on correspond to renormalized values of the theoretical infinite mass and charge of “naked” particles. And they are renormalized, among other things, due to creation of virtual electron-positron pairs. Furthermore, the Dirac equation describes Zitterbewegung for low-energy electrons as well. Actually, the eigenvalues of projections of instantaneous velocity in the Dirac theory are +-c.

Furthermore, your speculation makes no sense because, again, the phenomenon of entanglement nonlocality for two electrons has absolutely no need for any element of relativitistic physics.

Yeah, sure:-) Especially if you use PP:-) My reading is that the influence of a measurement on one particle of a singlet propagates to the other particle of the singlet with the speed of light. PP, however, basically states that this influence propagates with infinite velocity. If genuine VBI are demonstrated, I’ll have to admit that I was dead wrong though.

The physical motivation you speculate makes absolutely no physical sense. So more like senseless ground than shaky ground at this point. I think it would help you enormously to clear your mind about the difference between fermions and bosons, and the physical description of entanglement nonlocality in nonrelativistic QED and QM before you present me with any further half-baked speculations about this.

I see your point of view.

 

[akhmeteli]

. If you actually do read everything as it is written (and I highly doubt it at this point), it would be immediately clear to you that we initially agreed to assume that VBI and nonlocality meant the same thing.

I don’t remember such an agreement. Could you remind me the exact words?

You call "I beg you, please" a request?

Of course, and a humble one at that.

Anyway, my point was that I went above and beyond, and you haven't even lifted a finger even after my repeated requests (which later turned into demands because of your deaf ear). Let me give you a bit of advice about how to lead a productive discussion - when someone requests you to read into something, and you beg them to read into something, it is ALWAYS a good idea to heed their request as well, especially if it is critical to understanding their point of view. It's clear to me now that you never had any interest in understanding my point of view, but instead in just spewing your random speculations. And please, don't bother to try and give me advice in return.

If to understand your point I am supposed to read dozens of articles on dBB and GRW, then no, I have no interest in understanding your point, sorry. I just don’t have time for that. I tried to explain to you that I don’t even understand how dBB and GRW are relevant: if they are experimentally equivalent to SQM, they have to contain the SQM’s contradictions, if they are not experimentally equivalent, then their experimental status is dubious, so why should I care? I did not hear your answer, so I clearly lacked motivation. Again, I just don’t understand how dBB and GRW are relevant to this discussion. I just don’t owe you enough to fulfill really burdensome requests, so your demands are just out of place. You have found time in your busy schedule to read about KSP – I do appreciate that. If you had not found time, I would certainly not have called you names.

I never said I was your boss and I never ordered you to do anything (that would require a threat, which I have never made).

That may be technically correct, as you often did not bother to threaten me and just resorted to personal insults. Furthermore, you admitted that your requests turned into demands. And I just don’t think we are in a position to demand anything from each other.

I merely expressed my opinion about your lack of knowledge and understanding, and my opinion about what you should do to address it. Of course, I don't care to have to always qualify everything I say by pointing out that they are my opinions (that should be obvious to you). If you feel easily threatened by that, then you have more serious personal issues to deal with.

And who you are? A shrink? Frankly, I just have no interest in your opinion of me personally. I resent your numerous arguments ad hominem.

Did you feel uncomfortable with that? If so, then I apologize. If you don't have a problem with that, then get over it. Personal information is mentioned by members of this forum quite frequently and without much objection.

I did, but I am satisfied with your reply.

First off, I am not asking you to "trust" me on my word. I am asking you to read, learn, and understand for yourself - but you obviously don't want to and never wanted to. Secondly, you clearly did not understand a damn thing about what I said in #68 and #70. My "modification" in #70 was actually just an elaboration of what I said in #68. And there was absolutely no contradiction made. Again, you are being disingenuous.

If you stand by what you said in #68, that means that in your opinion dBB implies both unitary evolution and PP, therefore, it contains a contradiction.

And, if you would like to know why I am being abrasive with you now, then think back to my first email to you where I explained my reasons for being abrasive in previous threads with certain other people. It seems, regrettably, that you are absolutely no different than those individuals in that regard.

I regret that I disappointed you (I am not sure the exact words in your e-mail are applicable to me though). But sometimes I also have problems with bending backwards.

I think you have wasted a lot of time and energy by your frequent lack of clear explanations, your unwillingness to have either intellectual or academic integrity in discussing these issues, and for your repeated misrepresentations of my views.

I regret that my explanations lacked clarity. We are discussing complex issues under time constraints.
If I misrepresented your views, that was not deliberate. As for your comments on my integrity, I reject them as baseless.

 

[Maaneli]

Actually, I was talking about both bosons and fermions (for example, I specifically mentioned fermions in post #96). I could agree that there are no photons in SFED (they were eliminated there), but why do you say that there are no photons in DM (Dirac-Maxwell)?

If you were talking about both bosons and fermions, then you haven't shown that you understand the different equations of motion for each. Also, you always talk about DM equations in an SFED form (which is the basis of your half-baked idea) and in that sense there are no photons. Also, you didn't specify whether or not you assume the vector potential A_mu is a second quantized field coupled to the Dirac equation (which is in fact an inconsistent theory) or a classical EM free-field. In the latter case, there definitely are no photons by the QED definition.

So it is psychologically understandable why I talked about Barut smuggling in the contents of second quantization from QED into SFED.

But this isn't about psychology. This is about physics.

If you are trying to say that this expression is out of place when we are talking about, say, Dirac’s equation with Dirac sea, well, I could agree that it does not sound good. But your expression “blatant bias” also looks misplaced. I would say I did not imply “physically and conceptually prior” – these are your words. You could say I implied “chronologically prior” – and only as far as QED and SFED are concerned.

OK, fair enough distinction.

What I actually implied I described a few lines above. I don’t think there is any real depth here. In other words, I don’t think we essentially disagree on this issue. I agree that my “smuggles” does sound awkward in some situations.

Glad you admit that.

So we disagree on this point. On the other hand, it may well be that you're right, and I'm wrong.

Yes I think you're wrong about the Pauli principle and 2nd quantization.

I’d say there is indeed such a physical reason: the Fock space is present in both post-KSTP and in QED, which (I mean QED) seems to describe correctly current EPRB experiments. On the other hand, I could agree with you that in the absence of a “final” theory it is difficult to compare “KSP-particles” with real particles.

This makes no sense. QED can describe only a two-particle Fock space (which is all that is necessary to get entanglement nonlocality), whereas you seem to be saying that the KSP equation is always about N-particles in Fock space. Then I don't see how the KSP equation could possibly describe something as basic as the singlet-state.

I am not sure this is so clear-cut. As you know, the experimental low-energy values of the electron mass, charge, and so on correspond to renormalized values of the theoretical infinite mass and charge of “naked” particles. And they are renormalized, among other things, due to creation of virtual electron-positron pairs. Furthermore, the Dirac equation describes Zitterbewegung for low-energy electrons as well. Actually, the eigenvalues of projections of instantaneous velocity in the Dirac theory are +-c.

Yes it is clear cut. In quantum mechanics (NOT QED), there is no renormalization, and yet the entanglement nonlocality of the singlet-state is perfectly well describe. Even in nonrelativistic QED, renormalization is not at all relevant to describing the singlet-state. That's just elementary quantum optics. Furthermore, your appeal to Zitterbewegung from the Dirac equation makes no sense. The nonrelativistic limit of the Dirac equation is the Pauli equation, and there is definitely NO Zittebewegung in the Pauli equation.

Yeah, sure:-) Especially if you use PP:-) My reading is that the influence of a measurement on one particle of a singlet propagates to the other particle of the singlet with the speed of light. PP, however, basically states that this influence propagates with infinite velocity. If genuine VBI are demonstrated, I’ll have to admit that I was dead wrong though.

As usual, you're missing the point. I am and have always been talking about the entanglement nonlocality in standard, deBB, and GRW QM and QED, not about your half-baked speculative alternative.

 

[Maaneli]

I don’t remember such an agreement. Could you remind me the exact words?

How the hell can you say this? Do you have no long-term memory of anything? Look at posts #99 and earlier, and you will see that I repeatedly equate entanglement nonlocality (entanglement of wavefunctions in configuration space) with VBI. And you can clearly seen that you never ever objected to this in all those posts. You never said until very recently that the instantaneous collapse of the wavefunction was what you meant by nonlocality in PP. And just so that you don't even try to BS your way out of this, let me quote myself from post #99:

"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."

That's the last time.

If to understand your point I am supposed to read dozens of articles on dBB and GRW, then no, I have no interest in understanding your point, sorry. I just don’t have time for that.

I didn't say read dozens of articles. There are very specific references (no more than 3) I supplied you with in earlier posts and Emails that you could read.

I tried to explain to you that I don’t even understand how dBB and GRW are relevant: if they are experimentally equivalent to SQM, they have to contain the SQM’s contradictions,

That could not be more wrong. For the millionth time, deBB and GRW are empirically equivalent to SQM, BUT THEY DO NOT SHARE THE SAME CONTRADICTIONS. You would quickly understand that if you just looked at one of the review articles on deBB or GRW theory.

if they are not experimentally equivalent, then their experimental status is dubious, so why should I care? I did not hear your answer, so I clearly lacked motivation.

I said plenty of times that they are empirically equivalent. For example (12 posts earlier),

"In fact I repeatedly said to consider a QMMT like deBB or GRW which are empirically equivalent to SQM, but are NOT based on ad hoc and imprecise postulates about "measurements". "

I guess you didn't read carefully as usual.

Again, I just don’t understand how dBB and GRW are relevant to this discussion. I just don’t owe you enough to fulfill really burdensome requests, so your demands are just out of place. You have found time in your busy schedule to read about KSP – I do appreciate that. If you had not found time, I would certainly not have called you names.

I have not called you names, I have curtly called you out on your obvious disingenuousness and laziness.

That may be technically correct, as you often did not bother to threaten me and just resorted to personal insults.

I think the "personal insults" are perfectly justified reactions in your case.

Furthermore, you admitted that your requests turned into demands. And I just don’t think we are in a position to demand anything from each other.

As usual, you missed the point.

And who you are? A shrink? Frankly, I just have no interest in your opinion of me personally. I resent your numerous arguments ad hominem.

You don't need to be a shrink to see your obvious insecurities. Furthermore, I just have no interest in your opinion of my numerous "arguments ad hominem". As I explained, they are perfectly justifiable reactions to your outright disingenuousness and laziness. If you don't agree, too bad for you.

If you stand by what you said in #68, that means that in your opinion dBB implies both unitary evolution and PP, therefore, it contains a contradiction.

Wow, how can you be so dishonest? I didn't say that deBB implies PP, I said it implies the APPEARANCE of PP. Again, you need to read a basic review article on deBB that I have supplied you with in earlier posts (or Emails) if you want to understand this point once and for all.

I regret that I disappointed you (I am not sure the exact words in your e-mail are applicable to me though). But sometimes I also have problems with bending backwards.

No, I think the words do perfectly fit you as well. Again, I have not asked you to bend backwards, but to have the respect to at least sincerely try to understand my point of view. But it is clear to me now that you never had any intention of this and are more interested in laziness.

I regret that my explanations lacked clarity. We are discussing complex issues under time constraints.

These issues aren't that complex really. Furthermore, it's always better to take your time to construct a thoughtful response than to write something half-assed.

If I misrepresented your views, that was not deliberate. As for your comments on my integrity, I reject them as baseless.

I hope not, but I'm still skeptical.

 

[akhmeteli]

How the hell can you say this? Do you have no long-term memory of anything?

Sorry to disappoint you again by admitting that I don’t learn your posts by heart.

Look at posts #99 and earlier, and you will see that I repeatedly equate entanglement nonlocality (entanglement of wavefunctions in configuration space) with VBI.

I asked you to remind me the exact words confirming “that we initially agreed to assume that VBI and nonlocality meant the same thing” (and this is not the same as equating “entanglement nonlocality (entanglement of wavefunctions in configuration space) with VBI”, which, by the way seems absurd, because it basically includes in the definition the very phrase I object to: “PP is not a source of VBI”). I found nothing of the kind in your post #99. I also insist that the quote from post #99 that you give below contains nothing of the kind. Absolutely nothing. I am not going to look through the “earlier” 98 posts with a magnifying glass looking for confirmation of your words. Until you give me the exact words, I assume that there has been no such agreement.

And you can clearly seen that you never ever objected to this in all those posts. You never said until very recently that the instantaneous collapse of the wavefunction was what you meant by nonlocality in PP.

I clearly explained what I meant by nonlocality in PP much earlier, in my post #81: “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.”

And just so that you don't even try to BS your way out of this, let me quote myself from post #99:
"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."

Again, there is absolutely nothing in this quote confirming “that we initially agreed to assume that VBI and nonlocality meant the same thing”. Absolutely nothing. The word “nonlocality” itself is just missing, pure and simple. Some agreement indeed.
And I tried to explain to you several times that your reasoning in the quote brazenly defies logics (see, in particular, what you called a “horrible analogy”). I also dispute your phrase about dBB from the quote.

I didn't say read dozens of articles. There are very specific references (no more than 3) I supplied you with in earlier posts and Emails that you could read.

I am not going to read those references for the purpose of this discussion until I know what exactly I am expected to find there, sorry. I believe you failed to explain how dBB and GRW are relevant to this discussion, and I tried to explain to you several times why I believe so.

That could not be more wrong. For the millionth time, deBB and GRW are empirically equivalent to SQM, BUT THEY DO NOT SHARE THE SAME CONTRADICTIONS. You would quickly understand that if you just looked at one of the review articles on deBB or GRW theory.

OK, I have just re-read reviews by Passon (http://arxiv.org/PS_cache/quant-ph/pdf/0611/0611032v1.pdf (Physics and Philosophy 3 (2006) ), http://arxiv.org/PS_cache/quant-ph/pdf/0412/0412119v2.pdf ) and, as I expected, “I did not quickly understand that”. Actually, neither quickly, nor slowly. Please tell me one thing. In your opinion, is the projection postulate an approximation from the point of view of dBB or are its experimental implications supposed to be rigorously confirmed according to dBB?

I said plenty of times that they are empirically equivalent. For example (12 posts earlier),

"In fact I repeatedly said to consider a QMMT like deBB or GRW which are empirically equivalent to SQM, but are NOT based on ad hoc and imprecise postulates about "measurements". "

And I told you repeatedly something that can be rephrased as follows: if in such theories experimental predictions of both unitary evolution and of the projection postulate of SQM are expected to be rigorously confirmed, those theories include the contradiction between UE and PP, if such predictions are not expected to be rigorously confirmed, then those theories are not empirically equivalent to SQM.

I have not called you names, I have curtly called you out on your obvious disingenuousness and laziness.

Yeah, sure, and you did not accuse me baselessly of dishonesty and what not. As for laziness, I don’t work for you, and you are not in a position to accuse me of it.
Frankly, I am fed up. I warn you in no uncertain term: just one more personal attack, and I’ll leave this discussion all to yourself. If you don’t want a civil discussion, I don’t want any discussion with you.

I think the "personal insults" are perfectly justified reactions in your case.

See above.

You don't need to be a shrink to see your obvious insecurities. Furthermore, I just have no interest in your opinion of my numerous "arguments ad hominem". As I explained, they are perfectly justifiable reactions to your outright disingenuousness and laziness. If you don't agree, too bad for you.

See above.

Wow, how can you be so dishonest? I didn't say that deBB implies PP, I said it implies the APPEARANCE of PP. Again, you need to read a basic review article on deBB that I have supplied you with in earlier posts (or Emails) if you want to understand this point once and for all.

See above.

No, I think the words do perfectly fit you as well. Again, I have not asked you to bend backwards, but to have the respect to at least sincerely try to understand my point of view. But it is clear to me now that you never had any intention of this and are more interested in laziness.

See above.

 

[Maaneli]

Again, there is absolutely nothing in this quote confirming “that we initially agreed to assume that VBI and nonlocality meant the same thing”. Absolutely nothing. The word “nonlocality” itself is just missing, pure and simple. Some agreement indeed. And I tried to explain to you several times that your reasoning in the quote brazenly defies logics (see, in particular, what you called a “horrible analogy”). I also dispute your phrase about dBB from the quote.

First off, it doesn't defy logic at all, and you would know that if you understood QM. Secondly, VBI obviously means the same as entanglement nonlocality. Seriously, what the hell do you think VBI means?

I am not going to read those references for the purpose of this discussion until I know what exactly I am expected to find there, sorry. I believe you failed to explain how dBB and GRW are relevant to this discussion, and I tried to explain to you several times why I believe so.

As I said before, you have too look at the description of the theory of measurement interactions in deBB. Then you will learn why unitary evolution is preserved in deBB even during measurement interactions. And that the PP turns out to be an "effective colapse".

OK, I have just re-read reviews by Passon (http://arxiv.org/PS_cache/quant-ph/pdf/0611/0611032v1.pdf (Physics and Philosophy 3 (2006) ), http://arxiv.org/PS_cache/quant-ph/pdf/0412/0412119v2.pdf ) and, as I expected, “I did not quickly understand that”. Actually, neither quickly, nor slowly. Please tell me one thing. In your opinion, is the projection postulate an approximation from the point of view of dBB or are its experimental implications supposed to be rigorously confirmed according to dBB?

I don't know what you mean by "approximation", but what I mean by approximation is the "effective collapse" described exactly in the Passon paper.

And I told you repeatedly something that can be rephrased as follows: if in such theories experimental predictions of both unitary evolution and of the projection postulate of SQM are expected to be rigorously confirmed, those theories include the contradiction between UE and PP, if such predictions are not expected to be rigorously confirmed, then those theories are not empirically equivalent to SQM.

No. See the paper again.

Yeah, sure, and you did not accuse me baselessly of dishonesty and what not.

Yes, that's not an insult, that's what I really think.

As for laziness, I don’t work for you, and you are not in a position to accuse me of it.

I am in every position to call it as I see it.

Frankly, I am fed up. I warn you in no uncertain term: just one more personal attack, and I’ll leave this discussion all to yourself. If you don’t want a civil discussion, I don’t want any discussion with you.

Frankly, I am glad you are fed up. At least this has shaken you out of your previous behaviors. Oh and I could really care less at this point if you decided to leave. If you don't want to get serious about a discussion like this, then have fun with the rest of your life.

 

[akhmeteli]

Yes, that's not an insult, that's what I really think.

I warn you in no uncertain term: just one more personal attack, and I’ll leave this discussion all to yourself.

Have a nice day.

 

[Maaneli]

Have a nice day.

Yep, I knew you would find the slightest reason to ignore my latest arguments or look at those references. Don't be surprised from now on if you have lost all respect and integrity in the eyes of myself and other people on physics forum.