QED Lagrangian lead to self-interaction?

[akhmeteli]

I think there is good reason to expect that Barut's theory does violate the Bell inequalities. The self-field is defined in terms of the probability current j_mu, which is a current in configuration space. Therefore, for two electrons in an atom entangled in configuration space at the level of their probability currents, let's say, then their radiated source fields will also be entangled in terms of their polarizations and wavevectors.

I am not sure j_mu is a current in configuration space in the Barut's theory (which I'll call SFED hereafter - self-field electrodynamics) - just look how Barut defines the current for two particles (in the quote in one of my posts related to the Pauli principle) - the wavefunctions for the two particles, \psi_1 and \psi_2, are in 3D, and the current depends locally on them. nightlight, for example, does not believe there are any VBI in SFED, as far as I understand.

Furthermore, entanglement is not enough for VBI, as far as I understand, you need the projection postulate as well, or something like it, to obtain VBI.

I understand that POV, and am sympathetic to it. But there's nothing that logically implies physical laws <=> beauty.

Certainly, but I don't believe my wording ("I just tend to think that fundamental theories are typically simple and beautiful") was categorical.

 

[per.sundqvist]

Hi,


I believe your choices for A and V must be co-dependent. Barut always uses the Lorentz gauge for his choices of A and V, which means both depend on retarded time. I believe initially you wrote your V in the Coulomb gauge.

Hi, thanks, yes the Lorentz gauge makes sense! I had a look in Jackson so now its clear, so my equation in the original poster should have been:
$$\left(\frac{\hat{p}^2}{2m}+q\Phi_{ext}- \frac{q^2}{4\pi\epsilon} \int\frac{\mid\psi(\vec{r}^{\prime},t-\frac{\mid \vec{r}-\vec{r}^{\prime}\mid}{c})\mid^2} {\mid\vec{r}-\vec{r}^{\prime}\mid}d^3r^{\prime}\right)\psi= -i\hbar\frac{\partial\psi}{\partial t}$$

This makes sense, since self-interaction is restricted to a very short time. So now there is no problem, and you would not need second quantization (unless you like it)?

 

[Maaneli]

I am not sure j_mu is a current in configuration space in the Barut's theory (which I'll call SFED hereafter - self-field electrodynamics) - just look how Barut defines the current for two particles (in the quote in one of my posts related to the Pauli principle) - the wavefunctions for the two particles, \psi_1 and \psi_2, are in 3D, and the current depends locally on them. nightlight, for example, does not believe there are any VBI in SFED, as far as I understand.

Furthermore, entanglement is not enough for VBI, as far as I understand, you need the projection postulate as well, or something like it, to obtain VBI.



Certainly, but I don't believe my wording ("I just tend to think that fundamental theories are typically simple and beautiful") was categorical.

Sorry, I should have read your words more carefully. But another consideration is how do you judge what theory is more "beautiful" than another? Certainly there is no objective criterion, as you can see by the fact that we disagree about which is more "beautiful" a theory QED or SFED. And of course neither of us is more "correct". I agree however that simplicity is a more objective property of a theory, and there I would also suggest the Barut theory is superior (at least in form).

Actually, I have communicated with Jonathan Dowling (Barut's former graduate student who worked on SFED) in the past about some of these issues, and he did say to me that Asim and he hoped entanglement could be accounted for by SFED. However, while it is true that in the 2-particle examples that Barut uses the currents are in 3D, this is because he never considers an entanglement case to my knowledge. The wavefunctions in the cases you mention are factorizable, meaning that

psi(x1, x2) = psi(x1)$$\otimes$$psi(x2),

and so his currents will be given by

j(x1) + j(x2) = rho(x1)*v1 + rho(x2)*v2,

where

rho(x1) = |psi(x1)|^2 and rho(x2) = |psi(x2)|^2.

If he were to consider the basic singlet state for two electrons, and include the self-fields, then it seems obvious to me that not only would the wavefunctions not be factorizable, but neither would the currents. In other words, he would only have

rho(x1, x2) = |psi(x1, x2)|^2

and

j_n(x1, x2) = rho(x1, x2)*v_n = rho(x1, x2)*(v1 + v2).

So the probability currents would necessarily be in configuration space. This also means that the self-fields would not be distinctly separable as being sourced by two separate electrons.

As for the projection postulate, no you don't necessarily need it to get VBI. In the pilot wave theory, or stochastic mechanics, you can easily account for VBI due to the branching of wavefunctions after a measurement interaction, from the initial superposition state, and the observed point particle goes into only one of those branches. No postulates are needed. This is why I want to combine SFED with pilot wave theory and stochastic mechanics. It is the easiest and most rigorous way to account for measurement interactions, which Barut didn't really focus on with his theory. Of course, if you want a wavefunction collapse mechanism, you can certainly obtain it in a mathematically rigorous way, also without postulates, using the GRW stochastic collapse mechanism. By the way, all these mechanisms can be made relativistically covariant, so that is no problem either. And I see no fundamental obstacle to combining these measurement theories with SFED.

 

[Maaneli]

Hi, thanks, yes the Lorentz gauge makes sense! I had a look in Jackson so now its clear, so my equation in the original poster should have been:
$$\left(\frac{\hat{p}^2}{2m}+q\Phi_{ext}- \frac{q^2}{4\pi\epsilon} \int\frac{\mid\psi(\vec{r}^{\prime},t-\frac{\mid \vec{r}-\vec{r}^{\prime}\mid}{c})\mid^2} {\mid\vec{r}-\vec{r}^{\prime}\mid}d^3r^{\prime}\right)\psi= -i\hbar\frac{\partial\psi}{\partial t}$$

This makes sense, since self-interaction is restricted to a very short time. So now there is no problem, and you would not need second quantization (unless you like it)?

Hi Per,

Yes, you got it right. Now there is no problem. And you don't need second quantization for anything other than practical convenience in dealing with relativistic N-body systems, as Barut also mentions in his papers.

 

[Maaneli]

Hi, thanks, yes the Lorentz gauge makes sense! I had a look in Jackson so now its clear, so my equation in the original poster should have been:
$$\left(\frac{\hat{p}^2}{2m}+q\Phi_{ext}- \frac{q^2}{4\pi\epsilon} \int\frac{\mid\psi(\vec{r}^{\prime},t-\frac{\mid \vec{r}-\vec{r}^{\prime}\mid}{c})\mid^2} {\mid\vec{r}-\vec{r}^{\prime}\mid}d^3r^{\prime}\right)\psi= -i\hbar\frac{\partial\psi}{\partial t}$$

This makes sense, since self-interaction is restricted to a very short time. So now there is no problem, and you would not need second quantization (unless you like it)?

And you know how to include the vector potential in this equation?

 

[per.sundqvist]

And you know how to include the vector potential in this equation?

Thanks Maaneli,

Oh yes, I only included the dominating part because of simplicity. I read part of Baruts paper also, interesting. In the non-relativistic limit it should be:

$$\frac{\hat{p}^2}{2m}\rightarrow \frac{\vec{(\sigma\cdot (\hat{p}+q\vec{A}))^2}}{2m}$$

and A is similar given by the free Green function using the quantum current density as a source. I know its a dirty trick to replace E with -ihd/dt in Diracs equation to get the time-dependent Schrödinger, but I believe that the correction is very small any way.

 

[Maaneli]

Thanks Maaneli,

Oh yes, I only included the dominating part because of simplicity. I read part of Baruts paper also, interesting. In the non-relativistic limit it should be:

$$\frac{\hat{p}^2}{2m}\rightarrow \frac{\vec{(\sigma\cdot (\hat{p}+q\vec{A}))^2}}{2m}$$

and A is similar given by the free Green function using the quantum current density as a source. I know its a dirty trick to replace E with -ihd/dt in Diracs equation to get the time-dependent Schrödinger, but I believe that the correction is very small any way.

OK. Yes, the corrections are small, and of course we aren't trying to do anything too precise here.

So what do you think of these results? I like to imagine how much easier QED might have been if it had started from this route.

 

[Maaneli]

Hi Per,

Yes, you got it right. Now there is no problem. And you don't need second quantization for anything other than practical convenience in dealing with relativistic N-body systems, as Barut also mentions in his papers.

Hey, woops I made a big error. This isn't quite right from the Barut POV. In particular, it is problematic to find a normalization based on rho = |psi(x, t - r/c)|^2. In Barut SFED you would have to replace the Green's function you're using with the Feynman propagator in order to satisfy the Lorentz gauge. The wavefunction does not depend on retarded time in that case. Then the self-interaction is self-consistent.

For more details on this, see this paper:

http://phys.lsu.edu/~jdowling/publications/Barut89b.pdf

 

[Maaneli]

Hi, I have been busy with other things for a while. This is an interesting discussion you have here, but I don't think I have got any real answers how to deal with the "unphysical" self-interaction yet, only disputes over which formalism is the best...

Well I know that a localized state, like the 1s state (the "blob"), which you get from the equation I presented in the original post, could be Fourier expanded into waves, but it does not imply its not physical. The non-physical nature must be a consequense of that the particle cannot feel its own electric field.

For the magnetic vector potential, this problem is solved, since its a time-dependent wave equation. you integrate over $$\vec{j}(\vec{r}-ct\hat{n})$$, like:

$$\vec{A}(\vec{r},t)=\frac{1}{\mu}\int\frac{\vec{j}(\vec{r}-ct\hat{n})} {\mid\vec{r}-\vec{r}^{\prime}\mid}d^3r^{\prime}$$

I might missed some details here, because I don't have my books at hand right now. The result is however that the field is moving away from its source (by speed of light) and can not really interact with its source particle at the "same place". But for the scalar field $$A^0=\Phi/c$$, you obtain Poisson equation from the QED-Lagrangian, i.e., there is no second time-derivative in Poissons equation. This means that the field is instantanious, and therefore the unphysical self-interaction could take place. Maby there must be some special case with the scalar field? Because you get anyway an electric field in photon creation since $$\vec{E}=-\nabla\Phi-\partial\vec{A}/\partial t$$. Should you write $$\sqrt{i}qA^0$$ in the Lagrangian or should you postulate $$\Phi(\vec{r}-ct)$$ in some way?

One other thing I should have added. Even if you use the Green's function, 1/|r - r'|, I think you can still use the Coulomb gauge here just as well as the Lorentz gauge and get the same empirical predictions. Recall that the gauge you choose does not affect the empirical predictions. In that sense, the instantaneous nonlocal interaction is not "unphysical".

 

[akhmeteli]

Sorry, I should have read your words more carefully. But another consideration is how do you judge what theory is more "beautiful" than another? Certainly there is no objective criterion, as you can see by the fact that we disagree about which is more "beautiful" a theory QED or SFED. And of course neither of us is more "correct". I agree however that simplicity is a more objective property of a theory, and there I would also suggest the Barut theory is superior (at least in form).

Again, I just described my "expectations" and "feelings" in reply to your "what do you think" question. I readily admit that I don't have much to support them.

Actually, I have communicated with Jonathan Dowling (Barut's former graduate student who worked on SFED) in the past about some of these issues, and he did say to me that Asim and he hoped entanglement could be accounted for by SFED. However, while it is true that in the 2-particle examples that Barut uses the currents are in 3D, this is because he never considers an entanglement case to my knowledge. The wavefunctions in the cases you mention are factorizable, meaning that

psi(x1, x2) = psi(x1)$$\otimes$$psi(x2),

and so his currents will be given by

j(x1) + j(x2) = rho(x1)*v1 + rho(x2)*v2,

where

rho(x1) = |psi(x1)|^2 and rho(x2) = |psi(x2)|^2.

If he were to consider the basic singlet state for two electrons, and include the self-fields, then it seems obvious to me that not only would the wavefunctions not be factorizable, but neither would the currents. In other words, he would only have

rho(x1, x2) = |psi(x1, x2)|^2

and

j_n(x1, x2) = rho(x1, x2)*v_n = rho(x1, x2)*(v1 + v2).

So the probability currents would necessarily be in configuration space. This also means that the self-fields would not be distinctly separable as being sourced by two separate electrons.

It does not seem obvious to me that the wavefunctions would not be factorizable. Furthermore, in the current form of SFED they are factorizable, to the best of my knowledge. If and when Dowling or somebody else proposes a new version of the theory, this issue may be discussed again.

As for the projection postulate, no you don't necessarily need it to get VBI. In the pilot wave theory, or stochastic mechanics, you can easily account for VBI due to the branching of wavefunctions after a measurement interaction, from the initial superposition state, and the observed point particle goes into only one of those branches. No postulates are needed. This is why I want to combine SFED with pilot wave theory and stochastic mechanics. It is the easiest and most rigorous way to account for measurement interactions, which Barut didn't really focus on with his theory. Of course, if you want a wavefunction collapse mechanism, you can certainly obtain it in a mathematically rigorous way, also without postulates, using the GRW stochastic collapse mechanism. By the way, all these mechanisms can be made relativistically covariant, so that is no problem either. And I see no fundamental obstacle to combining these measurement theories with SFED.

I just wanted to say that one needs the projection postulate or something like that to prove that there can be VBI in the standard quantum theory.

I'd say you have an ambitious program. It is not quite clear though why you need SFED at all, if you are going to make it nonlocal and stochastic anyway:-)

 

[per.sundqvist]

Hey, woops I made a big error. This isn't quite right from the Barut POV. In particular, it is problematic to find a normalization based on rho = |psi(x, t - r/c)|^2. In Barut SFED you would have to replace the Green's function you're using with the Feynman propagator in order to satisfy the Lorentz gauge. The wave function does not depend on retarded time in that case. Then the self-interaction is self-consistent.

For more details on this, see this paper:

http://phys.lsu.edu/~jdowling/publications/Barut89b.pdf

Ok I read it briefly, and what I understood was that you include heavyside functions also in the propagator. Is that right?

Now I was actually going to try to solve this numerically for some simple system using 3D FEM-numerics. So I want to solve Maxwell's equations and Schrödinger coupled (self-consistently) in time. But do I have to change Maxwell's equ to get the Feynman propagator? Normalizing time-Schrödinger is not a problem numerically these days. My little project is to make a movie showing how the EM-wave is created and the wave function is changed. But it all relies on that the equations are ok.

 

[Maaneli]

Again, I just described my "expectations" and "feelings" in reply to your "what do you think" question. I readily admit that I don't have much to support them.



It does not seem obvious to me that the wavefunctions would not be factorizable. Furthermore, in the current form of SFED they are factorizable, to the best of my knowledge. If and when Dowling or somebody else proposes a new version of the theory, this issue may be discussed again.



I just wanted to say that one needs the projection postulate or something like that to prove that there can be VBI in the standard quantum theory.

I'd say you have an ambitious program. It is not quite clear though why you need SFED at all, if you are going to make it nonlocal and stochastic anyway:-)

<< Furthermore, in the current form of SFED they are factorizable, to the best of my knowledge. >>

But that's my point, I don't think they are factorizable even in the current form of SFED. It's just that Barut never bothered to analyze the singlet state according to Dowling.

<< If and when Dowling or somebody else proposes a new version of the theory, this issue may be discussed again. >>

I think we can discuss it now.

<< I just wanted to say that one needs the projection postulate or something like that to prove that there can be VBI in the standard quantum theory.>>

That's true.

<< I'd say you have an ambitious program. It is not quite clear though why you need SFED at all, if you are going to make it nonlocal and stochastic anyway:-) >>

I don't think it's that ambitious in the sense that it is not that hard to combine SFED with pilot wave theory or stochastic mechanics. I have unpublished notes in which I have already done this. Of course, I already think the SFED wavefunction is generally nonlocal, until I see an argument otherwise. BTW, the reasons why I want to combine SFED with pilot wave theory and stochastic mechanics is first just because SFED as it is needs a measurement theory that solves the measurement problem, and second because I do not believe the wavefunction is a fundamental field (in either an ontological or nomological sense). A stochastic mechanical theory allows one to derive the wavefunction as a phenomenological approximation (much like the transition probability solution to a diffusion equation) to a more fundamental, causally symmetric, stochastic particle dynamics that, I believe, can show that nonlocality is only an approximation. Currently, it is believed that a stochastic mechanical derivation of the wavefuncton in QM is unsuccessful because of Timothy Wallstrom's criticism that such derivations cannot satisfy the Bohr-Sommerfeld quantization condition for the gradient of the phase of a wavefunction around a closed loop. However, I believe a stochastic mechanical derivation of the SFED wavefunction solves that problem simply because its phase doesn't have to satisfy the Bohr-Sommerfeld quantization condition.

And of course I do desire a pilot wave or stochastic theory of electrodynamics that is nonperturbative and finite; and combining SFED with pilot wave theory and stochastic mechanics is the only way to do that thus far.

Hope that helps clarify my view.

 

[Maaneli]

Ok I read it briefly, and what I understood was that you include heavyside functions also in the propagator. Is that right?

Now I was actually going to try to solve this numerically for some simple system using 3D FEM-numerics. So I want to solve Maxwell's equations and Schrödinger coupled (self-consistently) in time. But do I have to change Maxwell's equ to get the Feynman propagator? Normalizing time-Schrödinger is not a problem numerically these days. My little project is to make a movie showing how the EM-wave is created and the wave function is changed. But it all relies on that the equations are ok.

<< Ok I read it briefly, and what I understood was that you include heavyside functions also in the propagator. Is that right? >>

Unfortunately I can't look at the paper again right now, but that sounds OK. That paper should have defined everything you need.

<< Normalizing time-Schrödinger is not a problem numerically these days. >>

I meant two things. First, if I recall correctly, for some reason there is no way to interpret

rho = |psi(x, t - r/c)|^2

as a probability measure on configuration space, as Squires, Duerr, Goldstein, and Berndl have shown. Besides that, if the wavefunction did depend on retarded time, then it would be a locally propagating signal, just like a classical EM wave, and then this theory could never be nonlocal or violate the Bell inequalities, which means it would be empirically inadequate.

Although, such a physically incorrect theory could still be mathematically well-defined enough for you to do your simulations.

 

[akhmeteli]

But that's my point, I don't think they are factorizable even in the current form of SFED. It's just that Barut never bothered to analyze the singlet state according to Dowling.

What I'm saying is based on the quote from Barut on the current for two identical particles.

I think we can discuss it now.

So what version are we supposed to discuss?

BTW, the reasons why I want to combine SFED with pilot wave theory and stochastic mechanics is first just because SFED as it is needs a measurement theory that solves the measurement problem, and second because I do not believe the wavefunction is a fundamental field (in either an ontological or nomological sense). A stochastic mechanical theory allows one to derive the wavefunction as a phenomenological approximation (much like the transition probability solution to a diffusion equation) to a more fundamental, causally symmetric, stochastic particle dynamics that, I believe, can show that nonlocality is only an approximation. Currently, it is believed that a stochastic mechanical derivation of the wavefuncton in QM is unsuccessful because of Timothy Wallstrom's criticism that such derivations cannot satisfy the Bohr-Sommerfeld quantization condition for the gradient of the phase of a wavefunction around a closed loop. However, I believe a stochastic mechanical derivation of the SFED wavefunction solves that problem simply because its phase doesn't have to satisfy the Bohr-Sommerfeld quantization condition.

And of course I do desire a pilot wave or stochastic theory of electrodynamics that is nonperturbative and finite; and combining SFED with pilot wave theory and stochastic mechanics is the only way to do that thus far.

Hope that helps clarify my view.

Yes, it does. Although it is difficult for me to judge how promising is the direction you chose.

 

[Maaneli]

What I'm saying is based on the quote from Barut on the current for two identical particles.

But I don't recall he was explicitly talking about two entangled particles. One can still write down the two-body theory without entanglement even in standard QM. Can you refer me to the exact paper again?

So what version are we supposed to discuss?

As I had discussed, we should consider the singlet state for spinor wavefunctions. Then put in the self-fields. I see no reason why putting in the self-fields will make the singlet state wavefunctions factorziable, since the self-fields are already defined in terms of the same entangled probability currents of the singlet state in QM without the self-fields.

Yes, it does. Although it is difficult for me to judge how promising is the direction you chose.

Understandable that it's difficult to judge the fruitfulness of my approach. I would have to go into much more detail which I don't know if we can do here.

 

[akhmeteli]

But I don't recall he was explicitly talking about two entangled particles. One can still write down the two-body theory without entanglement even in standard QM. Can you refer me to the exact paper again?

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

As I had discussed, we should consider the singlet state for spinor wavefunctions. Then put in the self-fields. I see no reason why putting in the self-fields will make the singlet state wavefunctions factorziable, since the self-fields are already defined in terms of the same entangled probability currents of the singlet state in QM without the self-fields.?

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

 

[Maaneli]

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



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

Hi,

OK, thanks again for the book reference.

I am aware of the obvious difference between the Barut theory and standard QM. I am aware of the Barut ansatz and that the linear superposition principle is not a method of solution to the Barut Schroedinger equation. About entanglement in Barut theory, I will quote you Dowling's comments to me:

<< For entanglement our argument was that there are no such thing as entangled photons. One looks at correlations between detector events after eliminating the field, and the hope would be -- I don't think this was ever worked out -- that the correlations would violate a Bell inequality, for example, so long as the E&M source was in an entangled state to start with. Again it is not clear if the Barut theory is more economical here or easier to compute with. Jon >>

 

[Maaneli]

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



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

Hi,

OK, thanks again for the book reference.

I am aware of the obvious difference between the Barut theory and standard QM. I am aware of the Barut ansatz and that the linear superposition principle is not a method of solution to the Barut Schroedinger equation. About entanglement in Barut theory, I will quote you Dowling's comments to me:

<< For entanglement our argument was that there are no such thing as entangled photons. One looks at correlations between detector events after eliminating the field, and the hope would be -- I don't think this was ever worked out -- that the correlations would violate a Bell inequality, for example, so long as the E&M source was in an entangled state to start with. Again it is not clear if the Barut theory is more economical here or easier to compute with. Jon >>

 

[akhmeteli]

I am aware of the obvious difference between the Barut theory and standard QM. I am aware of the Barut ansatz and that the linear superposition principle is not a method of solution to the Barut Schroedinger equation. About entanglement in Barut theory, I will quote you Dowling's comments to me:

<< For entanglement our argument was that there are no such thing as entangled photons. One looks at correlations between detector events after eliminating the field, and the hope would be -- I don't think this was ever worked out -- that the correlations would violate a Bell inequality, for example, so long as the E&M source was in an entangled state to start with. Again it is not clear if the Barut theory is more economical here or easier to compute with. Jon >>

I see. But why do you or Dowling need VBI in SFED, in the first place, unless you want a theory emulating not just the existing experimental results, but all predictions of the standard quantum theory?

 

[Maaneli]

I see. But why do you or Dowling need VBI in SFED, in the first place, unless you want a theory emulating not just the existing experimental results, but all predictions of the standard quantum theory?

Why do we need VBI in SFED? Simply because we are basing this on the assumption that QM is fundamentally right about nonlocality and VBI. And if SFED, which still shares much of the same mathematics, did not predict this at all, it would be empirically inadequate. This obviously wouldn't be any contradiction to the other virtues of SFED however.

Of course, you might argue that SFED might suggest some theoretical explanation for why detector efficiencies never get high enough (greater than ~80%) for a VBI to occur; but that could only be the case for "photon" entanglement, where detection efficiencies are already very low (10-30%). For electrons, we know that detection efficiencies are ~100%. You might argue that, well entanglement experiments have never been done with electrons or other massive particles (like kaons), which also satisfy the locality condition. That's also true, and for all we know maybe once the locality condition is imposed in experiments with massive particles, we will see a breakdown of standard QM nonlocality.

But currently I don't see SFED making predictions of the second scenario, and if it cannot be used to do so, then it is not unreasonable to consider how SFED might also describe true entanglement nonlocality.

 

[Maaneli]

Why do we need VBI in SFED? Simply because we are basing this on the assumption that QM is fundamentally right about nonlocality and VBI. And if SFED, which still shares much of the same mathematics, did not predict this at all, it would be empirically inadequate. This obviously wouldn't be any contradiction to the other virtues of SFED however.

Of course, you might argue that SFED might suggest some theoretical explanation for why detector efficiencies never get high enough (greater than ~80%) for a VBI to occur; but that could only be the case for "photon" entanglement, where detection efficiencies are already very low (10-30%). For electrons, we know that detection efficiencies are ~100%. You might argue that, well entanglement experiments have never been done with electrons or other massive particles (like kaons), which also satisfy the locality condition. That's also true, and for all we know maybe once the locality condition is imposed in experiments with massive particles, we will see a breakdown of standard QM nonlocality.

But currently I don't see SFED making predictions of the second scenario, and if it cannot be used to do so, then it is not unreasonable to consider how SFED might also describe true entanglement nonlocality.

<< This obviously wouldn't be any contradiction to the other virtues of SFED however. >>

I mean that if Barut did predict VBI's, this wouldn't at all contradict the fact that it is a nonperturbative and finite theory.

 

[akhmeteli]

Why do we need VBI in SFED? Simply because we are basing this on the assumption that QM is fundamentally right about nonlocality and VBI. And if SFED, which still shares much of the same mathematics, did not predict this at all, it would be empirically inadequate. This obviously wouldn't be any contradiction to the other virtues of SFED however.

Of course, you might argue that SFED might suggest some theoretical explanation for why detector efficiencies never get high enough (greater than ~80%) for a VBI to occur; but that could only be the case for "photon" entanglement, where detection efficiencies are already very low (10-30%). For electrons, we know that detection efficiencies are ~100%. You might argue that, well entanglement experiments have never been done with electrons or other massive particles (like kaons), which also satisfy the locality condition. That's also true, and for all we know maybe once the locality condition is imposed in experiments with massive particles, we will see a breakdown of standard QM nonlocality.

But currently I don't see SFED making predictions of the second scenario, and if it cannot be used to do so, then it is not unreasonable to consider how SFED might also describe true entanglement nonlocality.

I was not trying to say that something is unreasonable. It is my understanding, however, that there are no VBI in the current form of SFED. Does your phrase "currently I don't see SFED making predictions of the second scenario" imply that you disagree? As for empirical inadequacy, judging by your post, you are aware that, strictly speaking, genuine VBI have never been demonstrated experimentally.

Anyway, your words "Why do we need VBI in SFED? Simply because we are basing this on the assumption that QM is fundamentally right about nonlocality and VBI" do answer the question of my previous post.

 

[Maaneli]

I was not trying to say that something is unreasonable. It is my understanding, however, that there are no VBI in the current form of SFED. Does your phrase "currently I don't see SFED making predictions of the second scenario" imply that you disagree? As for empirical inadequacy, judging by your post, you are aware that, strictly speaking, genuine VBI have never been demonstrated experimentally.

Anyway, your words "Why do we need VBI in SFED? Simply because we are basing this on the assumption that QM is fundamentally right about nonlocality and VBI" do answer the question of my previous post.

I am curious, do you happen to know who Nightlight really is or if he ever worked with Barut?

I found some of his old posts on google.

 

[akhmeteli]

I am curious, do you happen to know who Nightlight really is or if he ever worked with Barut?

I don't have any information beyond what he posted.

 

[Maaneli]

I don't have any information beyond what he posted.

OK thanks anyway.

Also, I just wanted to let you know that I have studied and done some work in the past on the issues of detection loopholes, and LCHV (locally causal hidden variable) models like Marshall-Santos stochastic optics (which Nightlight also references when talking about the impossibility of VBI). In fact, in my undergraduate sophomore year, I attempted to do an experiment (along with the backing of my research adivsor Prof. Harold Metcalf) proposed by Trevor Marshall to test his claim that semiclassical electrodynamics with a classical ZPF predicts the existence of SPUC (spontaneous parametric up conversion) from a BBO crystal, while QO doesn't predict it. We even applied for a grant to the FQXi foundation but were rejected. Trevor Marshall and Emilio Santos had even agreed to be consultants on the experiment. Unfortunately, it turned out that an experimental QO team in Italy, led by Marco Genovese and Gilbert Brida, had done the experiment and they reported to me negative results to a very high and convincing degree of accuracy. Also, they have done experimental tests of some different predictions of Marshall-Santos stochastic optics. Their experiments also found negative results to a high degree of accuracy. Those negative results don't necessarily disprove SO, but they certainly do put serious constraints on it as a phenomenological semiclassical model of quantum optical phenomena. I have also had debates with Zapper on these issues:

https://www.physicsforums.com/showthread.php?t=128410

My general opinion is that, yes, to date no VBI has ever been demostrated, nor has any GHZ inequality violation ever been demonstrated due to low detector efficiencies for light. And as I said, it is not clear to me if there will ever be a violation of any kind because I doubt that PMT's can ever have a 80% efficiency for detecting "photons", especially given that the efficiency now (after 30 years) is no better than 30% even in the best case scenario, and that the fundamentally metastable nature of electrons in these detectors makes shot noise and dark noise impossible to fully eliminate. But of course there is still no rigorous proof of this.

As for VBI tests with massive particles like electrons or kaons, I also agree that, despite the perfect detector efficiencies, VBI has not been demonstrated at all yet because the locality condition has not been met in these experiments. Also, to my knowledge, no experimental tests of GHZ involving electrons or other massive particles has ever been done either. If anyone tries the latter, they will still have to deal with satisfying the locality condition.

Now given all this, and the fact that the only counterexample LCHV models that actually reproduce all the predictions of current OPTICAL experiments are the phenomenological Marshall-Santos stochastic optics and the Fine-Maudlin prism models (neither of which reproduce any of the other quantum optical predictions (like squeezed states) of course), I am not willing to expect that no genuine violation of the Bell or GHZ inequalities will ever be obtained, simply because it is still quite possible (even if technically challenging) for experimentalists to do GHZ experiments with massive particles and to implement the locality condition in those tests. It is also still possible for them to do an experimental test of Bell's inequality with electrons that also implements the locality condition. And all these experiments would definitely refute the LCHV models of Marshall, Santos, Fine, and Maudlin. So until those experiments are done, and until there is yet another LCHV phenomenological model or (even better) physical theory that can account for these currently undone experiments as well as all the other quantum predictions, I think the situation is still somewhat in favor of standard QM.

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

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

Hope this helps a little more to explain where I'm coming from.

I'll address my views about how all this relates to SFED and Nightlight's posts at a later date.

Peace,
Maaneli

 

[akhmeteli]

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

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

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

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

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

 

[Maaneli]

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



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

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

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


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

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

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

 

[Maaneli]

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



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

Andy,

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

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

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

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

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

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

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

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

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

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

~Maaneli

 

[Maaneli]

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

Sorry I meant separable but weakly interacting electrons.

 

[akhmeteli]

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

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

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

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

 

[Maaneli]

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

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


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

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

 

[akhmeteli]

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

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

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

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

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

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

 

[Maaneli]

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

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

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

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

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

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

 

[akhmeteli]

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

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

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

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

 

[Maaneli]

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

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

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

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

There are three statements which are mutually inconsistent:

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

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

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

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

Hope this helps.