No drama quantum electrodynamics? (was: Local realism ruled out?)

[DrChinese]

But rejecting locality? This is, of course, horrible. My home is my castle, I do not want to have nonlocal influences into my home. Realism or not, that doesn't matter that much.

Don't come to my home either! I live in Texas, and here we have "castle" laws for intruders. Especially if they are not locals.

 

[Nugatory]

The above seems quite arbitrary: who decides what is plausible and what is not? I just cannot agree with such logic: "C'mon, there are loopholes in every experiment, so you're just nit-picking." As of today, all Bell experiments have had significant deficiencies, so they cannot be accepted as evidence of violations of the true Bell inequalities. The issue is too important to accept far-reaching, extraordinary conclusions without proper proof.

I'm not suggesting that you're nitpicking (your word, not mine); I'm suggesting that you are displaying a basic misunderstanding of the differences between scientific proof based on experimental methods and mathematical proof based on logical methods. (A fair case could be made that we shouldn't use the word "proof" for the former, and again, it's your word not mine).

Experimental methods never prove the truth of a proposition; instead they disprove competing propositions. Therefore the observation that an experiment contains loopholes isn't especially compelling in itself; we also need a plausible (and ideally, testable) conjecture as to how the loopholes allow for some alternative proposition to hold instead.

 

[akhmeteli]

I'm not suggesting that you're nitpicking (your word, not mine); I'm suggesting that you are displaying a basic misunderstanding of the differences between scientific proof based on experimental methods and mathematical proof based on logical methods. (A fair case could be made that we shouldn't use the word "proof" for the former, and again, it's your word not mine).

Experimental methods never prove the truth of a proposition; instead they disprove competing propositions. Therefore the observation that an experiment contains loopholes isn't especially compelling in itself; we also need a plausible (and ideally, testable) conjecture as to how the loopholes allow for some alternative proposition to hold instead.

OK, so the existing experimental data is good enough for you, but not good enough for me. You believe I misunderstand something, I respectfully disagree.

 

[akhmeteli]

Arbitrary? Then how does anyone know anything? You are entitled to your own opinion about Bell, the Big Bang, and evolution - as is anyone. But the scientific community decided shortly after Aspect's groundbreaking work to accept the results. Modern discussion of "loopholes" is more for completeness than anything. Note that experiments are currently underway which similarly test General Relativity, nearly 100 years after its advent. This was Nugatory's point.

This issue cannot be decided by popular vote. Whatever scientific community believes, it agrees that there has been no loophole-free experimental evidence of violations. Belief is one thing, experimental evidence is quite a different thing. Again, Zeilinger ea believe that "The realization of an experiment that is free of all three assumptions - a so-called loophole-free Bell test - remains an important outstanding goal for the physics community". Apparently, you disagree. That does not necessarily mean that you're right and he's wrong, or vice versa.

In case you were asleep, Wineland received the Nobel prize partially for his work in the area. He was part of a team that closed the detection "loophole" over a decade ago. Apparently, even ions can be made to violate local realistic inequalities:

Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away. Einstein, Podolsky and Rosen used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments 1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome ‘loopholes’ that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's ‘signal’ is 2.25 ± 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called ‘detection’ loophole.

Of course, perhaps this experiment has deficiencies that you are privileged to be able to provide a theoretical description of. (Such as: what kind of force or signal is occurring between Alice and Bob's measurement devices to yield the Bell inequality violation. After all, discovery of that currently unknown mechanism would be quite an astonishing breakthrough. And following that, you can explain why such mechanism is elsewhere not apparent.)

Let me just repeat that this work does not contradict the following statement: there has been no loophole-free experimental evidence of violations, sorry. As for "theoretical description"... I often say: we all do what we can, not what we want. I believe that I presented some meaningful and relevant mathematical results in my articles. I wish I could do more, but something is better than nothing. A few years ago these results were unknown.

 

[akhmeteli]

I should hope that the mathematical and physical definitions for fields are not wholly unrelated! I was under the impression that there are certain basic physical notions that are ultimately based upon mathematics. When I said that a mathematical field only has physical significance when there are "somethings" at the given locations, then I hope I made the proper transition to the currently accepted notion of the physical field.

No, sorry. Physical fields typically are not mathematical fields (as defined in your post 36 in this thread): for example, as far as I know, division cannot be reasonably defined for vector or spinor fields.

We know that an EM field is just a mathematical field (ie, a set of points that constitute the dimensions of space and time) that at each point consists of an energy potential for electrically charged particles like electrons. Failing the existence of any of these particles, then the entire concept of the field is meaningless. This is the same as trying to talk about gravity fields without any massive objects to be affected by them. In other words, it is only because there are objects whose behaviours are affected (eg, through acceleration) that the concept of the field in physics attains any significance.

Again, the objects do not have to be point-like.

 

[Charles Wilson]

A theory with maximum speed of information transfer c is named "local". But what about a theory with maximum speed of information transfer of 2c? Or, say, of 10000 c? All the difference is, clearly, only another maximal speed of information transfer.

If it makes sense to distinguish local theories from nonlocal theories, then the difference between the two is clearly not the maximal speed of information transfer.

Ilja, I think you are close to something important.

1. "All the difference is, clearly, only another maximal speed of information transfer."

A theory with a speed limit greater than c must still be mapped onto the "Reality of Speed Limit c". It may be mapped into R(c) in which case, some >R(c) members may not be found in R(c). A good Scientific Theory would in R(c) have to have evidence of something beyond c and R(c).

If I find in my travels, at regular intervals, pieces of paper that have 1, then 2, then 3 and so on, 4, 5, 6, 7, 8, 9, 10, printed on them, I may also find other pieces of paper such that where I go from 1 to 2, the other paper goes "1, 2" then "3, 4" and so on. Maybe I find pieces of paper that read, "1, 4", then "7, 10" and so on.

I may deduce that there is a "Numbers on Paper Reality" where the orders may occur in a different, maybe faster order. Maybe this faster order leaves numbers out when it gets to my R(c).

Now, suppose that I find papers that start at 10 and descend to 1. Or maybe a piece of paper that simply lists the numbers 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. What to make of that?

2. "If it makes sense to distinguish local theories from nonlocal theories, then the difference between the two is clearly not the maximal speed of information transfer."

You are correct. There is, however a mistake made by some. Information Transfer occurs in R(c). "Then, that's all there is, right?"

No. The Information Transfer Protocol may be in some >R(c). There might be a type of Symmetry Break that starts with a "Handshake": "I am a Point "A" with energy X looking for a point "B" with energy - X. I desire to exchange values ". A suitable Point B responds and the values are exchanged. Or maybe it's reversed. Maybe Point B starts first. Maybe the Exchange appears instantaneous to any point residing in R(c).

At the Symmetry Break, the Information Exchange Protocol begins as before, but now information transfer is defined to be only at speed no greater than c. Information appears as a positive P filling a Hole - P. The negative location is only a possibility in a time through space. The arrival of Particle P at Point O is now only a probability. It is important to see that this is not re-establishing a type of Determinism. The screen that receives Einstein's electron ONLY offers possibilities for the electron's arrival (See: Einstein @ Solvay Conference, 1927). Since it only offered an exchange of two opposing values at the exchange, only one electron appears. The energy contract completed, another possibility arises. See Whitehead. See Stapp.

The Hole should appear to be from the future but it maps into the present as a time reversed sequence: "The electron went through both slits but when we check, it only went through one slit and the interference pattern disappeared". "Some puzzles remain. The device should detect both quasi-particles or quasiholes. Push a particle and it moves away. Push a hole and it approaches. Yet the device only detects pushes. (paraphrased from He3 Superfluids, SciAm, June 1990). This is a record in a Positive Universe, R(c). Sometimes we use "Intentional Language": "It's as if the photon knew which path to take".

Entanglement, for example, gives us evidence that there is a >R(c). Our math is almost miraculous in its development in parallel with our empirical discoveries.

Our language is ingenious in picturing possibilities (Wittgenstein) but in use serves many other functions (Later Wittgenstein).
I need to know and use more math to make sure I'm well grounded.
And maybe Zoloft.

CW

 

[Charles Wilson]

AS I went to bed after my long Post, it occurred to me that there was a loophole in my argument concerning "Multiple c's".

Ilja Stated:

"All the difference is, clearly, only another maximal speed of information transfer."
AND
"If it makes sense to distinguish local theories from nonlocal theories, then the difference between the two is clearly not the maximal speed of information transfer."

I agreed with this line of thought. What kept me awake for a half hour longer was something I had settled on some time ago:

http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

Clearly, or maybe not so clearly, if this is a sturdy case of "Information Theory", then there must be a "> c" component and it must be ≥ 2c if "Every electron in the Universe has the same attributes". So the problem is at least a compound one. There must be a "> R(c)" Universe and there must be a Wave Component in it. There may be some aspect of this that both Controls this and does not map to "R (c)" but Nyquist-Shannon is pretty much settled.

What is the missing piece? After some thought and some interestingly playful half dreams, the assumption came into my consciousness:

In R(c), information transfers in a time-reversable sequence of X => - X and - X => X at the speed of light. (There is another hidden assumption that there is ONLY a transfer in a single exchange of +/- values. So far, this is still a toy universe example. See Whitehead, "Nexus".) In the > R(c) Universe, the "Handshake" to exchange between points appears to occur "simultaneously".

There is a Logic Problem here and its not just a violation of Special Relativity Sensibilities. To go all Feynman here, consider 2 particles approaching and interacting in an exchange. As you go up the Time axis, the particles approach, approach and approach until "Suddenly a Miracle occurs!", as the old cartoon went. To use what I called "Intentional Language" above, "How did the particles know to exchange at that moment?"

This is a question about the signaling mechanism. Point "A" signals to a field that it can exchange some value and receives a signal that Point "B" can exchange an appropriate opposite value. This symmetric exchange is complex, as in "complicated". "A" must find "B" and receive from "B" AND "B" must find "A" and receive from "A". As a picture, it is not "From a center A of a Circle, construct a radius to a point on the circle and label this point B." It is "There are 2 circles of equal radius in the same plane that intersect with the center of one circle being on the circle of the other and (necessarily) vice versa."

This cannot occur at the speed of light, it must be at some speed > c, indeed, by Nyquist-Shannon, it must be > 2c. 'N if this is a Symmetry Break problem, the "Agreement to Exchange" is made in this > R(c) Universe but the value exchange is made at c.

This gives both an understanding of c but also anchors the "faster than light" statements into a Mathematizable form, without appeal to a Metaphysic. Einstein is satisfied, QM is satisfied. What's not to like?

One thing not to like is the amount of sleep I'm NOT getting. See, the Contra-Positive Problem appears here and...

CW

 

[harrylin]

As the only thread I've ever started before (https://www.physicsforums.com/showthread.php?t=369328 ) attracted a lot of interest, became one of the most viewed threads in the forum, and was closed :-), I'd like to make a short update here.

I have published a new article on the topic: "No drama quantum electrodynamics?", European Physical Journal C, (2013) 73:2371 (http://link.springer.com/content/pdf/10.1140/epjc/s10052-013-2371-4.pdf - open access).

Abstract:

This article builds on recent work (Akhmeteli in Int. J. Quantum Inf. 9(Supp01):17, 2011; J. Math. Phys. 52:082303, 2011), providing a theory that is based on spinor electrodynamics, is described by a system of partial differential equations in 3+1 dimensions, but reproduces unitary evolution of a quantum field theory in the Fock space. To this end, after introduction of a complex four-potential of electromagnetic field, which generates the same electromagnetic fields as the initial real four-potential, the spinor field is algebraically eliminated from the equations of spinor electrodynamics. It is proven that the resulting equations for electromagnetic field describe independent evolution of the latter and can be embedded into a quantum field theory using a generalized Carleman linearization procedure. The theory provides a simple and at least reasonably realistic model, valuable for interpretation of quantum theory. The issues related to the Bell theorem are discussed.

That looks very interesting, as the experimental results to date suggest to me that perhaps no experiment can be done that proves or disproves "quantum non-locality" - a bit like the original formulation of the PoR. Thanks!

 

[harrylin]

[..] if you adopt both unitary evolution and the projection postulate, you just cannot get a local realistic theory. You have to ditch one of the assumptions. Santos opined that we should ditch the theory of quantum measurements. And this is exactly what I do: I reject the theory of quantum measurements, at least as a precise theory. Then I successfully reproduce unitary evolution of a quantum field theory in a local realistic theory [..]
first, the projection postulate contradicts unitary evolution anyway, second, there is no experimental evidence of violations of the genuine Bell inequalities. [..]

OK that clarifies it a little to me. However, I remain puzzled (surely not in the least because spinors and Fock space go over my head!):

[..] This rule is a rule of the theory of quantum measurements (which, strictly speaking, contradicts unitary evolution), as it does not take into account unitary evolution of the total system including the photons and the instrument. Let me note that, strictly speaking, no measurement result is ever final (at least not in a limited volume with impenetrable walls) due to recurrence theorem, so how can your rule be precise? Let me also note that statements of the theory of quantum measurements are derived from unitary evolution in Allahverdyan’s article I quoted earlier, but as approximations, not as precise results. It turns out that there are even some subtle deviations from the Born rule! The derivation of their article was not reproduced for photons yet, but the contradiction between unitary evolution and the theory of quantum measurements exists for photons as well.

What does that mean in practice, concerning expected predictions with your model? Similarly, following DevilsAvocado simplification that "classic says 1+1=2 and QM says 1+1=3"(sic), where will the predictions of your model fit in, for a typical "non-ideal" Bell experiment? You seem to suggest in your latest paper that you expect results that are close to that of standard QM.

[..] People typically say that violations are demonstrated with loopholes closed separately and tend to make a conclusion that therefore violations will demonstrated when all loopholes are closed. However, if there is just one loophole, local realism does not imply the inequalities, so demonstrated violations cannot eliminate local realism. I believe there is full analogy with my example: if just one assumption is not fulfilled, e.g., the triangle is on a sphere, rather than on a plane, the theorem on the sum of the angles being equal to 180 degrees does not hold (as its assumptions are not satisfied simultaneously), so apparent violations of the theorem do not compromise the validity of the theorem. [..]

Let me clarify in this context my comparison with the PoR.
The null result of MMX to verify wave theory would have been interpreted to prove ballistic light theory if such had not been at odds with earlier results from other types of experiments. Then a "loophole" was found: length contraction. And later as a follow-up, the null result of KTX could again be interpreted to prove ballistic light theory, as length contraction is insufficient to compensate the expected effect. However, another "loophole" had already been found: time dilation. Is that a conspiracy of Nature to save the relativity principle? Only if one considers the conservation laws a "conspiracy".

PS: I would appreciate it if you could elaborate on the following statement:

[..] if you use the "EPR definition" of local realism, then classical electrodynamics is not local realistic. The models of my articles are similar to classical electrodynamics and are not "EPR realistic" either - the statement "there are definite values for spin components at all times" is not correct for them, but they are no less realistic than classical electrodynamics. [..]

How is classical electrodynamics not local realistic in that sense?

 

[Ilja]

then there must be a "> c" component and it must be ≥ 2c if "Every electron in the Universe has the same attributes". So the problem is at least a compound one. There must be a "> R(c)" Universe and there must be a Wave Component in it.

AFAIR Gisin has tried to find some observational limits and obtained something like a 10⁴c lower bound. For exact QT we need ∞, but this does not matter if QT is only an approximation.

There is a Logic Problem here and its not just a violation of Special Relativity Sensibilities.

Sorry but I do not see any logic problem here.

The particles are flying away. Whatever particle is measured first (in absolute time, of course) sends a message to the other one which result has been measured. If this information is transferred with high enough speed, so that it reaches the other particle before the second measurement, everything is fine and Bell's inequality can be violated.

Einstein is satisfied, QM is satisfied. What's not to like?

I have not understood your description. But with the straightforward scenario I have give Einstein is not satisfied (because Einstein causality claims <c and is violated) and QM is not satisfied too (because QM requires ∞ as the maximal speed).

 

[Bryan Sanctuar]

Bell's view of breakdown of local causality

Where have you seen this stated about Bell's position on non-locality? As far as I have read, he felt Bohmian type theories were good candidates.

You can read this point of view in a paper by T. Norsen Local causality and completeness: Bell vs. Jarrett

http://arxiv.org/pdf/0808.2178.pdf

 

[akhmeteli]

That looks very interesting, as the experimental results to date suggest to me that perhaps no experiment can be done that proves or disproves "quantum non-locality" - a bit like the original formulation of the PoR. Thanks!

Thank you for your interest.

 

[akhmeteli]

OK that clarifies it a little to me. However, I remain puzzled (surely not in the least because spinors and Fock space go over my head!):

You don't need to now anything about spinors to understand the model based on scalar electrodynamics. The model based on spinor electrodynamics is more realistic, but more complex. However, the logic is pretty much the same for both models. The Fock space... Well, you do need to know something about the Fock space to understand some aspects of my work. However, you need to know something about it to understand quantum field theory anyway.

What does that mean in practice, concerning expected predictions with your model? Similarly, following DevilsAvocado simplification that "classic says 1+1=2 and QM says 1+1=3"(sic), where will the predictions of your model fit in, for a typical "non-ideal" Bell experiment? You seem to suggest in your latest paper that you expect results that are close to that of standard QM.

Well, you see, the model of my work is based on spinor electrodynamics. This is a complex nonlinear theory, so it is not easy to derive specific predictions for specific experimental setups. However, this model is reasonably realistic, as it includes spinor electrodynamics, which is a decent theory, so it is indeed reasonable to expect that predictions of this model will be reasonably close to those of quantum electrodynamics. For this reason one can hope that the model's predictions would be close to the experimental results of typical "non-ideal" Bell experiments. This possibility is not eliminated by the Bell theorem, although the model of my work is local realistic, as those experiments are not loophole-free. Let me also add that the model of my work may require some modification to provide predictions that are closer to those of quantum electrodynamics.

Maybe the above is overcomplicated, so let me rephrase it "in DevilsAvocado's terms": QM says 1+1=3 only if you start with the two mutually contradictory assumptions of QM, and that is not a good way to start anything anyway.

Let me clarify in this context my comparison with the PoR.
The null result of MMX to verify wave theory would have been interpreted to prove ballistic light theory if such had not been at odds with earlier results from other types of experiments. Then a "loophole" was found: length contraction. And later as a follow-up, the null result of KTX could again be interpreted to prove ballistic light theory, as length contraction is insufficient to compensate the expected effect. However, another "loophole" had already been found: time dilation. Is that a conspiracy of Nature to save the relativity principle? Only if one considers the conservation laws a "conspiracy".

Something like that (although I had difficulties with your abbreviations: I guess MMX is Michelson-Morley experiment, PoR is Principle of relativity, and KTX is Kennedy-Thorndike experiment).

PS: I would appreciate it if you could elaborate on the following statement:

if you use the "EPR definition" of local realism, then classical electrodynamics is not local realistic. The models of my articles are similar to classical electrodynamics and are not "EPR realistic" either - the statement "there are definite values for spin components at all times" is not correct for them, but they are no less realistic than classical electrodynamics.

How is classical electrodynamics not local realistic in that sense?

I thought I explained that, but let me try to rephrase that. As far as I understand, under EPR definition, realism assumes that observables have definite values irrespective of any measurement, however, classical electrodynamics does not seem realistic in this sense, as electromagnetic field is typically distributed, so it does not have, say, definite coordinates, independent of any measurement, but, depending on your instrument, you can observe the field in some point, which will depend on the instrument, so classical electrodynamics is "contextual" in this respect.

 

[DrChinese]

You can read this point of view in a paper by T. Norsen Local causality and completeness: Bell vs. Jarrett

http://arxiv.org/pdf/0808.2178.pdf

This paper states the exact opposite of your statement. Bell felt non-local theories to be viable. In case you weren't aware, Norsen is a Bohmian.

 

[harrylin]

[..] Well, you see, the model of my work is based on spinor electrodynamics. This is a complex nonlinear theory, so it is not easy to derive specific predictions for specific experimental setups. However, this model is reasonably realistic, as it includes spinor electrodynamics, which is a decent theory, so it is indeed reasonable to expect that predictions of this model will be reasonably close to those of quantum electrodynamics. For this reason one can hope that the model's predictions would be close to the experimental results of typical "non-ideal" Bell experiments. This possibility is not eliminated by the Bell theorem, although the model of my work is local realistic, as those experiments are not loophole-free. Let me also add that the model of my work may require some modification to provide predictions that are closer to those of quantum electrodynamics. [..]

OK

[..] I had difficulties with your abbreviations: I guess MMX is Michelson-Morley experiment, PoR is Principle of relativity, and KTX is Kennedy-Thorndike experiment).

Yes indeed - sorry for that!

I thought I explained that, but let me try to rephrase that. As far as I understand, under EPR definition, realism assumes that observables have definite values irrespective of any measurement, however, classical electrodynamics does not seem realistic in this sense, as electromagnetic field is typically distributed, so it does not have, say, definite coordinates, independent of any measurement, but, depending on your instrument, you can observe the field in some point, which will depend on the instrument, so classical electrodynamics is "contextual" in this respect.

OK, meanwhile it's also getting clearer to me from other papers - apparently, Bell's interpretation of EPR is that "realism" means that all properties are pre-existing and fixed, independent from measurement. Indeed, EM fields do not adhere to such a concept.

 

[Ilja]

As far as I understand, under EPR definition, realism assumes that observables have definite values irrespective of any measurement,

Completely wrong.

It follows from EPR realism and from locality (more accurate, from Einstein causality) and from the 100% correlation predicted from quantum theory that those special observables which have such 100% correlations between nonlocal observations have to have definite values before measurements.

however, classical electrodynamics does not seem realistic in this sense, as electromagnetic field is typically distributed, so it does not have, say, definite coordinates, independent of any measurement

Also completely wrong. Of course, there is no such observable as "the coordinate of the EM field", thus, there is also no such value of the classical EM field.

But, independent of what defines the classical EM field - or the vector fields E_i(x,t), H_i(x,t), or the corresponding potentials A_μ(x,t), these fields at a given moment t define every observable of classical EM theory which can be measured at a given point x.

 

[akhmeteli]

Completely wrong.

It follows from EPR realism and from locality (more accurate, from Einstein causality) and from the 100% correlation predicted from quantum theory that those special observables which have such 100% correlations between nonlocal observations have to have definite values before measurements.


Also completely wrong. Of course, there is no such observable as "the coordinate of the EM field", thus, there is also no such value of the classical EM field.

But, independent of what defines the classical EM field - or the vector fields E_i(x,t), H_i(x,t), or the corresponding potentials A_μ(x,t), these fields at a given moment t define every observable of classical EM theory which can be measured at a given point x.

Thank you. I will try to reply in a couple of days.

 

[akhmeteli]

As far as I understand, under EPR definition, realism assumes that observables have definite values irrespective of any measurement

Completely wrong.

It follows from EPR realism and from locality (more accurate, from Einstein causality) and from the 100% correlation predicted from quantum theory that those special observables which have such 100% correlations between nonlocal observations have to have definite values before measurements.

I stand corrected. And sorry about "a couple of days" turning into a year:-(

What I should have said is the models of my article do not predict definite values before measurement for the conditions of the EPR (or EPR-B) experiment. For example, when we measure a spin projection for one particle of the singlet in the EPR-B, then, according to standard quantum theory, the spin projection of the other particle of the singlet becomes determinate with 100% probability immediately, no matter what separation between the particles of the singlet. This is not true for the models of my articles. However, this also contradicts unitary evolution of quantum theory, as unitary evolution cannot turn a pure state into a mixture.

classical electrodynamics does not seem realistic in this sense, as electromagnetic field is typically distributed, so it does not have, say, definite coordinates, independent of any measurement, but, depending on your instrument, you can observe the field in some point, which will depend on the instrument, so classical electrodynamics is "contextual" in this respect.

Also completely wrong. Of course, there is no such observable as "the coordinate of the EM field", thus, there is also no such value of the classical EM field.

But, independent of what defines the classical EM field - or the vector fields E_i(x,t), H_i(x,t), or the corresponding potentials A_μ(x,t), these fields at a given moment t define every observable of classical EM theory which can be measured at a given point x.

Again, I stand corrected, and this mistake is a direct consequence of the first one - the wrong idea of what is EPR reality.

So what should I have said instead? The models of my articles describe independent evolution of electromagnetic field. On the other hand, they describe electrons (interacting with the electromagnetic field) in the same time, as, say, the Klein-Gordon equation or Dirac equation is satisfied within the models, however typical observables of quantum theory, such as electron coordinates or spin projections, are typically not defined precisely before measurement (so the uncertainty principle is not violated). Whatever is the electron wave function in quantum theory, is a complex function of electromagnetic potential in the models of my articles.