Chern Simons Spin density as hidden variable.

[Hans de Vries]

The electromagnetic Chern Simons spin density

is only know since the nineteen seventies from advanced Quantum Field Theory
on the chiral anomalies. It is the correct form of the electromagnetic spin-
density of the vacuum. It can be expressed as a 4-vector as follows:

$$\mbox{Chern Simons Spin Density:}\qquad \vec{\cal S}\ =\ \textsf{D} \times \vec{A}\ \ +\ \ \textsf{H}\ \Phi\ ,\qquad {\cal S}^o \ =\ \frac{1}{c}(\textsf{D}\cdot\vec{A})\ \quad$$

Which are just the familiar electromagnetic potentials and fields.
It's still virtually unknown to the wider audience, hidden as it is in the
more advanced QFT texts in a less accessible form. Especially interesting
are the electromagnetic spin density fields of the electron and the photon.

For instance:

Linear polarized photons, originating from spin 1 transitions, don't carry net
spin, however, they still contain the information of the original spin sign within
the canceling, non zero, components of the EM spin density from electric and
magnetic vacuum polarization. Linear photons therefor come in two types
which might be physically distinguishable in entanglement experiments.

$$\begin{array}{|l|c|c|c|c|} \hline &&&& \\ \mbox{polarization} &\ \ \mbox{orbit spin}\ \ &\ \mbox{EM spin}\ \vec{S}\ &\ \textsf{ D} \times \vec{A}\ & \ \ \ \textsf{ H}\ \Phi\ \ \\ &&&& \\ \hline &&&& \\ \mbox{Linear} & +\hbar & 0 & +\hbar & -\hbar \\ \mbox{Linear} & -\hbar & 0 & -\hbar & +\hbar \\ \mbox{Circular} & +\hbar & +\hbar & +\hbar & \ \ 0 \\ \mbox{Circular} & -\hbar & -\hbar & -\hbar & \ \ 0 \\ &&&& \\ \hline \end{array}$$

The current experimental status suggests that we have to either, give up
locality and/or reality, or show that Malus law can be violated in polarizing
beam splitters. The two types of linear polarized photons might open the
door to the latter possibility.

The derivations (which I had to do myself since somehow one can't find
these anywhere) and many details can be found in my paper, here:

http://chip-architect.com/physics/ChernSimonsSpinDensity.pdf" Regards, Hans

 

[strangerep]

[...] the electromagnetic spin-density of the vacuum.

In your paper, you say that

The term $\epsilon_0 E\times A$ is [...] discussed in Mandel & Wolf [sect 10.6]
as the angular momentum density of the vacuum.

I could not find that exact wording in M&W. At the start of their section 10.6 they talk
about angular momentum of the (classical) electromagnetic field in vacuum. And later,
around eqn(10.6-10) they talk about the term $\epsilon_0 E\times A$ as the intrinsic
(spin) angular momentum of the EM field. But I couldn't find where they talk about
angular momentum of the (quantum) vacuum.

Could you please give me a more precise reference?

TIA.

 

[Phred101.2]

Isn't this model being used in superconducting nanodevice research by somebody?

 

[Hans de Vries]

In your paper, you say that

I could not find that exact wording in M&W. At the start of their section 10.6 they talk
about angular momentum of the (classical) electromagnetic field in vacuum. And later,
around eqn(10.6-10) they talk about the term $\epsilon_0 E\times A$ as the intrinsic
(spin) angular momentum of the EM field. But I couldn't find where they talk about
angular momentum of the (quantum) vacuum.

Could you please give me a more precise reference?

TIA.

Hi, strangerep

In 10.6.3 they discuss the (integrated) term Js in terms of annihilation and
creation operators. Js is defined in 10.6.12


Mandel & Wolf start in section 10.6.2 with the (orbital) angular momentum
density and at some stage $\epsilon_0(E\times A)$, which is a spin-angular momentum
density, occurs in the 3rd and last term.

At that stage however the second term "hides" a term $-\epsilon_0 (E\times A)$ with
opposite sign. This second term is subsequently ignored as a surface term
after integration. Thus, $\epsilon_0(E\times A)$ is not part of the orbital angular momentum
density but it contributes to the total integrated angular momentum if the
surface term can be ignored.

So it's a little bit tricky but the end conclusion about $\epsilon_0(E\times A)$ is right.
It's however not the full contravariant 4-vector which is the Chern Simons
current. For circular polarized photons viewed form the source's restframe
it's OK since $\frac{1}{\mu_o}B\Phi$ vanishes in this case.


Regards, Hans

 

[Phred101.2]

Chern–Simons theory and BCS superconductivity

Manuel Asorey, Fernando Falceto and Germán Sierra
Departamento de Física Teórica, Univ. Zaragoza, Spain
Instituto de Matemáticas y Física Fundamental, CSIC, Spain
Received 30 October 2001; accepted 30 November 2001. Available online 11 December 2001.

Abstract

We study the relationship between the holomorphic unitary connection of Chern–Simons theory with temporal Wilson lines and the Richardson's exact solution of the reduced BCS Hamiltonian. We derive the integrals of motion of the BCS model, their eigenvalues and eigenvectors as a limiting case of the Chern–Simons theory.

--sciencedirect.com

"They're" able to build nanodevices that manipulate a BCS, I can recall reading somewhere...
It's just amazing what you can do with google:

The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems
Authors: Dror Orgad
Categories: physics.mes-hall Mesoscopic Systems and Quantum Hall Effect
Comments: 15 pages

Abstract: Wen's chiral Tomonaga-Luttinger model for the edge of an m-layer quantum Hall system of total filling factor nu=m/(pm +- 1) with even p, is derived as a random-phase approximation of the Chern-Simons theory for these states. The theory allows for a description of edges both in and out of equilibrium, including their collective excitation spectrum and the tunneling exponent into the edge. While the tunneling exponent is insensitive to the details of a nu=m/(pm + 1) edge, it tends to decrease when a nu=m/(pm - 1) edge is taken out of equilibrium. The applicability of the theory to fractional quantum Hall states in a single layer is discussed.

Version 1: Sun, 30 Jul 2006 09:50:04 GMT
http://front.math.ucdavis.edu/0607.0796"

 

[strangerep]

I still don't understand...

In 10.6.3 they discuss the (integrated) term Js in terms of annihilation and
creation operators. Js is defined in 10.6.12.

Mandel & Wolf start in section 10.6.2 with the (orbital) angular momentum
density and at some stage $\epsilon_0(E\times A)$, which is a
spin-angular momentum density, occurs in the 3rd and last term.

At that stage however the second term "hides" a term $-\epsilon_0 (E\times A)$
with opposite sign.

Do you mean M&W's eqn(10.6-8)? The 2nd term therein is

$$- \epsilon_0 \oint \underline{E} [(\underline{r} - \underline{r_0})\times \underline{A}] \bullet d\underline{s}$$

I don't see how a "$-\epsilon_0(E\times A)$" is "hidden" in that term.

This second term is subsequently ignored as a surface term
after integration. Thus, $\epsilon_0(E\times A)$ is not part of the orbital angular momentum
density but it contributes to the total integrated angular momentum if the
surface term can be ignored.

So it's a little bit tricky but the end conclusion about $\epsilon_0(E\times A)$ is right.
It's however not the full contravariant 4-vector which is the Chern Simons
current. For circular polarized photons viewed form the source's restframe
it's OK since $\frac{1}{\mu_o}B\Phi$ vanishes in this case.

I'm not sure you understood my original problem. I was objecting to the
word "of" in your "angular momentum ... of the vacuum". (I have no problem with the
usual notion of $J_s$ as an intrinsic spin contribution to the total angular
momentum of a non-vacuum EM field. That's standard fare.)

Also note that $<0|J_s|0> \,= 0$, where $J_s$ is given by M&W's eqn(10.6.16), i.e.,

$$\underline{J}_s = i \sum_k \hbar \kappa (a^\dagger_{k2}a_{k1} - a^\dagger_{k1}a_{k2})$$

 

[Hans de Vries]

I'm not sure you understood my original problem. I was objecting to the
word "of" in your "angular momentum ... of the vacuum". (I have no problem with the
usual notion of $J_s$ as an intrinsic spin contribution to the total angular
momentum of a non-vacuum EM field. That's standard fare.)

Ah, OK I agree with you here. I guess the word vacuum slipped in via the frequent
use of the terms "vacuum polarization" and "vacuum fluctuations" So I used the
word vacuum as in "in absence of matter", the Chern Simons current is the spin
density of the electromagnetic field in absence of matter. If there is matter then
it is "co-conserved" according to the chiral analomy.

Do you mean M&W's eqn(10.6-8)? The 2nd term therein is

$$- \epsilon_0 \oint \underline{E} [(\underline{r} - \underline{r_0})\times \underline{A}] \bullet d\underline{s}$$

I don't see how a "$-\epsilon_0(E\times A)$" is "hidden" in that term.

It's in the term below via the chain rule and $\nabla_i(r_m-r_{0m})=\delta_{im}$

$$-\varepsilon_0\epsilon_{lmn}\nabla_i(r_m-r_{0m})E_iA_n$$


Regards, Hans

 

[RandallB]

the Chern Simons current is the spin density of the electromagnetic field in absence of matter. If there is matter then it is "co-conserved" ...

“Chern Simons current is the spin density of the electromagnetic field in absence of matter”
Oddly this does make clearer your view of “Chern Simons Spin Density” or CSSD as I’ll call it here. I’m interested in your objective or opinion in how you define this Chern Simons approach.

As I understand what you’re saying the CSSD should obey conservations laws “if there is matter”. I’ll extend that just a bit by saying CSSD should maintain conservation if it affects and reacts to matter even if there is no matter in CSSD.

Do you consider the goal of this CSSD approach to satisfy the local & realistic expectations of Einstein even if CSSD is at odds with typical Local Realists?
That is; CSSD is it LR or Non-Local in your opinion?

LR meaning CSSD holds out the hope of defining a version of Local Realism that (although not deterministic) would be determinate enough in the local treatment of variables to deny the completeness of Non-Local Theories like QM & BM etc.

 

[Hans de Vries]

“Chern Simons current is the spin density of the electromagnetic field in absence of matter”
Oddly this does make clearer your view of “Chern Simons Spin Density” or CSSD as I’ll call it here. I’m interested in your objective or opinion in how you define this Chern Simons approach.

As I understand what you’re saying the CSSD should obey conservations laws “if there is matter”. I’ll extend that just a bit by saying CSSD should maintain conservation if it affects and reacts to matter even if there is no matter in CSSD.

Do you consider the goal of this CSSD approach to satisfy the local & realistic expectations of Einstein even if CSSD is at odds with typical Local Realists?
That is; CSSD is it LR or Non-Local in your opinion?

LR meaning CSSD holds out the hope of defining a version of Local Realism that (although not deterministic) would be determinate enough in the local treatment of variables to deny the completeness of Non-Local Theories like QM & BM etc.

The Chern Simons current, the electromagnetic spin density, comes from
Quantum Field Theory and is therefor local. It mixes with the spin density
(the axial current) of the Dirac electron as well as with a mass related term.

These three terms are conserved locally and globally together. Historically
it is a descendant of the discovery of the chiral anomaly by Adler, Jackiw and
Bell, (The John Bell from the EPR experiments) This was around 1969. This
discovery followed from theoretical work on the electromagnetic decay of
the pion and had in fact nothing to do with John Bell's inequalities.

There's for instance this recollection from Bell's partner Jackiw presented
at Bell's memorial in 2000 Vienna here:
http://arxiv.org/PS_cache/hep-th/pdf/0011/0011274v1.pdfRegards, Hans

 

[RandallB]

http://arxiv.org/PS_cache/hep-th/pdf/0011/0011274v1.pdf

Thanks Hans
Great reference it helped put in perspective their (Bell, Jackiw & Adler) views, such as “The symmetry breaking in question is a quantum phenomenon that violates the correspondence principle; it arises from the necessary infinities of quantum field theory.”

From the “necessary infinities of quantum field theory” I interpret that Bell would say QFT fails the “Classically Realistic” part of Einstein Local which requires both Local and Realistic.
Thus, CSSD or Chern Simons current - electromagnetic spin density, as a part of QFT; should not be thought of as an attempt to reach a “Local Realist” vision of reality.
But a “non-local” one that may only need the “unrealistic” part of “non-local”.
Therefore not in disagreement with the “non-local” conclusions of EPR-Bell.

 

[Hans de Vries]

Thanks Hans
Great reference it helped put in perspective their (Bell, Jackiw & Adler) views, such as “The symmetry breaking in question is a quantum phenomenon that violates the correspondence principle; it arises from the necessary infinities of quantum field theory.”

Form the “necessary infinities of quantum field theory” I interpret that Bell would say QFT fails the “Classically Realistic” part of Einstein Local which requires both Local and Realistic.
Thus, CSSD or Chern Simons current - electromagnetic spin density, as a part of QFT; should not be thought of as an attempt to reach a “Local Realist” vision of reality.
But a “non-local” one that may only need the “unrealistic” part of “non-local”.
Therefore not in disagreement with the “non-local” conclusions of EPR-Bell.

Randall, You puzzle me with what you are saying here and how you come to all
these conclusions...

Renormalization of infinities has nothing to do with locality or "realism"

The Chern Simons current propagation strictly respects locality but it was never
part of any EPR discussion as far as I know nor was it conceived as an attempt
to prove anything in that area.What I did in (my paper) was to calculate and visualize the spin density fields
for electrons and photon of arbitrary polarization and show that there are
two distinctly different types of linear polarized photons which might open the
door to a systematic violation of Malus law necessary to explain the correlations
with a hidden parameter model.

http://chip-architect.com/physics/ChernSimonsSpinDensity.pdf" Regards, Hans

 

[RandallB]

Randall, You puzzle me with what you are saying here and how you come to all these conclusions...

The Chern Simons ... was never part of any EPR discussion as far as I know ...

What I did in (my paper) was to calculate and visualize the spin density fields for electrons and photon of arbitrary polarization and show that there are two distinctly different types of linear polarized photons which might open the door to a systematic violation of Malus law necessary to explain the correlations with a hidden parameter model.

Since you didn’t directly answer my question I was trying to state what you seemed to imply in your answer.
So I’ll ask more directly:
Einstein always claimed Bohr’s QM was incomplete and when you use "hidden variable and EPR correlations” in your title I was trying to understand what you intended by it. Are you implying:
1) QFT with CSSD may be more complete that Bohr’s OQM could be.
And if so
2) do YOU consider such a “systematic violation of Malus law necessary to explain the correlations with a hidden parameter model” if successful as “Einstein local and realistic” or no.

That is all I was asking you make clear.

RB

 

[Hans de Vries]

Since you didn’t directly answer my question I was trying to state what you seemed to imply in your answer.
So I’ll ask more directly:
Einstein always claimed Bohr’s QM was incomplete and when you use "hidden variable and EPR correlations” in your title I was trying to understand what you intended by it. Are you implying:
1) QFT with CSSD may be more complete that Bohr’s OQM could be.
And if so
2) do YOU consider such a “systematic violation of Malus law necessary to explain the correlations with a hidden parameter model” if successful as “Einstein local and realistic” or no.

That is all I was asking you make clear.

RB

OK, sorry for not being clear.

To start with point 2.

Yes, It looks inevitable with all the experimental correlation results,
The models where the hidden parameter is an input for Malus law can't
explain the correlations seen.

Thus if you want to uphold locality then you need to find physics
which causes systematic violations of Malus law in polarizing beam
splitters.

For me this was for the reason to investigate in the Chern Simons spin
density of photons. First to show that this current indeed qualifies as
the electromagnetic spin density and then to show that there are
differences in linear polarized photons which might cause systematic
violations of Malus law.Regards, Hans

 

[RandallB]

Are you implying:
1) QFT with CSSD may be more complete that Bohr’s OQM could be.
And if so
2) do YOU consider such a “systematic violation of Malus law necessary to explain the correlations with a hidden parameter model” if successful as “Einstein local and realistic” or no.

That is all I was asking you make clear.

OK, sorry for not being clear.
To start with point 2.

Yes, It looks inevitable with all the experimental correlation results,
The models where the hidden parameter is an input for Malus law can't
explain the correlations seen.

Thus if you want to uphold locality then you need to find physics
which causes systematic violations of Malus law in polarizing beam
splitters.

Sorry, maybe we have a language or syntax problem in communicating;
I’m still not able to tell if you are saying “Yes or NO”.

In one line I see you say :
YES Chern Simons spin density (CSSD) as a identified physics of systematic violation of Malus law “looks inevitable” to be a successful ‘Einstein local and realistic’ solution for reality; based “all the experimental correlation results”. [If this is what you meant to say certainly on point 1 CSSD as a complete local solution would be more complete than orthodox QM by Bohr.]

However, you complete the line by saying:
“The models where the hidden parameter is an input for Malus law can't explain the correlations seen.”

Which I translate as NO
with CSSD being one of those models that “can't explain the correlations seen” Therefore CSSD cannot yet be viewed as a complete ‘Einstein local and realistic’ solution for reality.

So I still cannot tell if:
Y or N
1) Do you consider QFT (CSSD) capable of being more complete than ‘orthodox QM’.
And
Y or N
2) If the intent of your paper is to point towards a solution that MIGHT be so much better than ‘orthodox QM’ that with more work it could describe a hidden variable acceptable as a complete ‘Einstein local and realistic’ solution.

Just looking to clearly understand your opinion or intent, I do not expect you to prove the opinion here and now.

 

[Hans de Vries]

Sorry, maybe we have a language or syntax problem in communicating;
I’m still not able to tell if you are saying “Yes or NO”.

In one line I see you say :
YES Chern Simons spin density (CSSD) as a identified physics of systematic violation of Malus law “looks inevitable” to be a successful ‘Einstein local and realistic’ solution for reality; based “all the experimental correlation results”. [If this is what you meant to say certainly on point 1 CSSD as a complete local solution would be more complete than orthodox QM by Bohr.]

However, you complete the line by saying:
“The models where the hidden parameter is an input for Malus law can't explain the correlations seen.”

Which I translate as NO
with CSSD being one of those models that “can't explain the correlations seen” Therefore CSSD cannot yet be viewed as a complete ‘Einstein local and realistic’ solution for reality.

So I still cannot tell if:
Y or N
1) Do you consider QFT (CSSD) capable of being more complete than ‘orthodox QM’.
And
Y or N
2) If the intent of your paper is to point towards a solution that MIGHT be so much better than ‘orthodox QM’ that with more work it could describe a hidden variable acceptable as a complete ‘Einstein local and realistic’ solution.

Just looking to clearly understand your opinion or intent, I do not expect you to prove the opinion here and now.

Hi, Randall

The intent is to find an explanation of the correlations while upholding locality.

It is clear from the experimental data that such an explanation must explain
systematic violations of Malus law one way or the other. That is, Malus law
should be valid as an average over spins states, but it should be different
if the input photons are of only one of the two spin types given in the table
in post #1

The two types should be physically different, now, since the Chern Simons
current is co-conserved with the axial current of the Dirac electron $J_A$ one
could expect that it influences the so called vector current $J_V$ of the Dirac
electron as well, $J_V$ is the charge/current density of the electron.

A further requirement seems to be that the two spin components from ExA
and BV are propagated differently in two-axial birefringent dielectrics such
as the ones used in polarizing beam splitters. Regards, Hans

 

[monish]

I'm going to make a suggestion here that I hope someone can make sense of. I have always wondered what makes a two-photon emission different from a single-photon emission. When people talk about the EPR experiment, they sometimes invoke the decay of positronium as the source of entangled photons. I have trouble with this because I don't know how to visualize a detailed mechanism for the creation of light in this situation.

But isn't there a simpler case that gives us two entangled photons? I'm thinking of the 2s-1s decay of the hydrogen atom. In this case I can ALMOST visualize a mechanism for the generation of light. The reason I say "almost" is that there's a problem with this being one of the so-called "classically forbidden" transitions. The "allowed" transition (like the
2p-1s transition) is really quite easy to picture semi-classically, and the emission of light in this case is really no more mysterious than the transmission of a radio wave from a small dipole antenna.

My suggestion is to focus on the 2s-1s transition as a possible source of these new kinds of emissions, because you have a case where it might be simple enough to follow the time-evolution of the system in detail and actually understand what's going on. The interesting possibility would be if you could show that the light emitted from this system was really different from classical e-m radiation.

 

[RandallB]

I'm going to make a suggestion here ... a simpler case that gives us two entangled photons ... 2s-1s decay of the hydrogen ..

... really quite easy to picture semi-classically, really no more mysterious than the transmission of a radio wave ...

... it might be simple enough to follow the time-evolution of the system in detail and actually understand what's going on. The interesting possibility would be if you could show that the light emitted from this system was really different from classical e-m radiation.

You could eliminate the issue of interpreting how light emanates from atoms and use your complete photon description on the PDC creation of two photons from one photon. Although you don’t have the problems of dealing with atoms producing photons like 2s-1s decay, you still need an entirely complete classical description of a photon. Orthodox QM using a point particle and HUP description is as complete as it gets according to Bohr. Your effort would require a much more complete classical description than OQM claims is possible.

To do what you want requires you define a more complete description an individual photon than OQM allows. That is you need to displace and replace OQM first and that is not simple at all.

 

[monish]

Originally Posted by monish
I'm going to make a suggestion here ... a simpler case that gives us two entangled photons ... 2s-1s decay of the hydrogen ..

... really quite easy to picture semi-classically, really no more mysterious than the transmission of a radio wave ...

... it might be simple enough to follow the time-evolution of the system in detail and actually understand what's going on. The interesting possibility would be if you could show that the light emitted from this system was really different from classical e-m radiation.

You could eliminate the issue of interpreting how light emanates from atoms ... you need to displace and replace OQM first and that is not simple at all.

You've selectively edited my quote to say something different from what I originally said. I didn't say the 2s-1s decay was easy to picture classically, I said it was forbidden classically. It's the 2p-1s transition that looks like an ordinary (classical) dipole antenna.

 

[RandallB]

The intent is to find an explanation of the correlations while upholding locality.

But that still does not answer my question on what do you mean by “upholding locality” with QFT.

Especially when you use the term “Hidden Variable”.
Other non-local theories like BM and MWI sometimes claim a version of local. But not the same kind of “local” required to build a “Local & Realistic” HV as defined by Einstein needed to solve something like EPR-Bell. Thus in that context they are still “Non-Local” and no more complete than OQM. See thread: https://www.physicsforums.com/showthread.php?t=181904"


I and most recognize QFT as a non-local interpretation basically equivalent to OQM. Meaning the “local fields” as defined within the QFT interpretation is not the same as LOCAL required to build a classical HV as needed to satisfy the Einstein argument against the completeness of OQM.

So again is it your intent in describing CSSD as potentially a HV in QFT that the version of local used in the QFT interpretation, could be upgraded to the point where it might become a more complete description than OQM can be?
And thus show Bohr wrong about OQM being complete.
Essentially, this would mean a classically understandable photon description, more complete than OQM, something close to what monish is looking to use.

This is all I’m asking.
I’m just trying to find out if your use of the term HV is intended to define the possibility of a more complete solution in QFT, than OQM claims is possible.

For myself I view the spacelike separations of different parts of a single ‘local’ field defined by QFT marks it as a non-local theory in the Einstein “Local & Realistic” definition of “local” as it applied to things like EPR-Bell.
I’m willing to consider how CSSD might change that view of QFT.
Which is why I ask if your CSSD is intended to achieve that kind of changed view by QFT as superior to OQM view.

 

[Hans de Vries]

But isn't there a simpler case that gives us two entangled photons? I'm thinking of the 2s-1s decay of the hydrogen atom. In this case I can ALMOST visualize a mechanism for the generation of light. The reason I say "almost" is that there's a problem with this being one of the so-called "classically forbidden" transitions. The "allowed" transition (like the
2p-1s transition) is really quite easy to picture semi-classically, and the emission of light in this case is really no more mysterious than the transmission of a radio wave from a small dipole antenna.

The point is that the interference term in a superposition of the 1s and 2s state
does not produce a rotating charge density. You need a superposition of two
states with a different quantum number m for that.

Regards, Hans.

 

[monish]

The point is that the interference term in a superposition of the 1s and 2s state
does not produce a rotating charge density. You need a superposition of two
states with a different quantum number m for that.

Regards, Hans.

Right. You just get a pulsating balloon. Which doesn't radiate.

But if you give the two states opposite spins, then the superposition will have a magnetic moment that precesses. And this DOES radiate. It's not nearly as strong as the electric dipole you get from the s-p transition, but it radiates. And the decay time, calculated as a classical antenna, gives you approximately the right value for the life of the excited state.

And yet the picture isn't quite right, for one reason or another. For one thing, the frequency is wrong...I get emission at the frequency of 3/4 Rydberg, same as the sp transition, when we WANT to get half the frequency (because we want two photons...that's what we're supposed to get, right?). That's why I think it would be interesting to apply your ideas of Chern Simon spin density to this case. Because maybe you could fix things up and bring the semi-classical picture into agreement with quantum mechanics.

 

[Hans de Vries]

But that still does not answer my question on what do you mean by “upholding locality” with QFT.

Especially when you use the term “Hidden Variable”.
Other non-local theories like BM and MWI sometimes claim a version of local. But not the same kind of “local” required to build a “Local & Realistic” HV as defined by Einstein needed to solve something like EPR-Bell. Thus in that context they are still “Non-Local” and no more complete than OQM. See thread: https://www.physicsforums.com/showthread.php?t=181904"I and most recognize QFT as a non-local interpretation basically equivalent to OQM. Meaning the “local fields” as defined within the QFT interpretation is not the same as LOCAL required to build a classical HV as needed to satisfy the Einstein argument against the completeness of OQM.

So again is it your intent in describing CSSD as potentially a HV in QFT that the version of local used in the QFT interpretation, could be upgraded to the point where it might become a more complete description than OQM can be?
And thus show Bohr wrong about OQM being complete.
Essentially, this would mean a classically understandable photon description, more complete than OQM, something close to what monish is looking to use.

This is all I’m asking.
I’m just trying to find out if your use of the term HV is intended to define the possibility of a more complete solution in QFT, than OQM claims is possible.

For myself I view the spacelike separations of different parts of a single ‘local’ field defined by QFT marks it as a non-local theory in the Einstein “Local & Realistic” definition of “local” as it applied to things like EPR-Bell.
I’m willing to consider how CSSD might change that view of QFT.
Which is why I ask if your CSSD is intended to achieve that kind of changed view by QFT as superior to OQM view.

I would have to look more in what you exactly mean by these various kind of
non-local theories. I don't see any effective non-local behavior in QFT. The
standard books like those of Weinberg and Peskin and Schroeder teach likewise
that QFT is space-like commutative, that is, there can be no causal relationship
between space-like separated points.

In any way, the intent is to find an explanation of the correlations while upholding
locality and you can call that Einstein locality if you want to.Regards, Hans