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

  1. May 4, 2013 #1
    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).


    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.
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  3. May 4, 2013 #2


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    Since you claim this is about a quantum theory, can you show that this theory has no negative-norm states? With a complex gauge field, the gauge symmetry can only remove the real part of the longitudinal degrees of freedom. It doesn't seem that the quantum theory exists.

    Maybe a more basic question, but what happens if there is more than one matter field? What about chiral matter?
  4. May 4, 2013 #3
    Not sure I fully understand. There are actually two different theories related to spinor electrodynamics in my article. One of them, a "small" theory, is largely equivalent to spinor electrodynamics, so if something's wrong with this "small" theory, something's wrong with spinor electrodynamics as well. This "small" theory is embedded into a "large" quantum theory in the Fock space. I am not sure there are negative-norm states in the Fock space. Furthermore, if there were indeed negative-norm states in this "large" theory, I am not sure that would be my problem, as I am only interested in the "small" theory, and the only states of the "large" theory that have their match in the "small" theory are the functional coherent states, which have non-negative norm.

    Again, not sure I fully understand. It is my understanding that the longitudinal degrees of freedom are typically discussed in the context of the Lorenz gauge (in other gauges these degrees of freedom are typically not separated from the other degrees of freedom), and I don't use the Lorenz gauge. And again, the "small" theory, while uses complex potentials (note, by the way, that arbitrary complex potentials are not allowed in the "small" theory), is largely equivalent to spinor electrodynamics.

    I believe this problem is partly solved. Initially the results were obtained for scalar electrodynamics (in my IJQI article - http://akhmeteli.org/akh-prepr-ws-ijqi2.pdf ), where there is just one matter field with one component. The results for spinor electrodynamics offered in that older article were not very satisfactory, as generally you can make only one component of the Dirac spinor real with a gauge transform. However, I showed in my JMP article (http://akhmeteli.org/wp-content/uploads/2011/08/JMAPAQ528082303_1.pdf ) that, surprisingly, three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and it is obvious that the remaining component can be made real by a gauge transform. That opened the way for the results of the EPJC article. So I am not sure there is really more than one matter field in Nature. What we typically consider as different matter fields can be just different components of a representation of some group, so it is not obvious that the procedure of my articles cannot be implemented if the number of the components is greater than four. Remember that, while the number of different matter fields is much greater in the Standard Model than in quantum electrodynamics, the choice of gauge is also much richer in the former theory than in the latter one. So while I don't know if similar results can be obtained for the Standard Model or some GUT, it is not obvious that they cannot.
  5. May 5, 2013 #4


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    akhmeteli, can you then make the Noether current real and recover probabilistic interpretation(in QFT). I am not also clear if you are saying that your system solves (or clarifies it) the measurement problem or not.
  6. May 5, 2013 #5
    I do use the "generalized gauge transform", but I don't claim invariance under such transform, so I only have real Noether current.

    I recover unitary evolution of a quantum field theory. It is my understanding that, say, the Born rule is a great approximation, but still an approximation, if unitary evolution is precise. Such understanding is based on the results of Allahverdyan ea. (http://arxiv.org/abs/1107.2138, Phys. Rep. 525, 1 (2013)).

    I don't think my work solves the measurement problem. My position is that, strictly speaking, the measurement problem just cannot be solved, as unitary evolution and the theory of quantum measurements contradict each other. On the other hand, the theory of quantum measurements, at least, in some cases, can be derived from unitary evolution as some approximation (again, please see the work by Allahverdyan ea.) Therefore, I try to take care of unitary evolution and reject the theory of quantum measurements as a precise theory, hoping that the measurement problem will take care of itself :-) (at the level of approximations). Does this qualify as "clarification"? You decide.
  7. May 6, 2013 #6


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    You are being a bit generous here (and as well in your paper). The only discussion of Bell is to dismiss it as requiring "...mutually contradictory assumptions..." You may as well have left this line of reasoning out completely. Or more factually, simply state that your ideas contradict Bell completely.

    You also cite the lack of a loophole-free experimental test as evidence that local realism is not ruled out by Bell tests. I assume you are aware that the loopholes have been individually closed. It is a stretch, to say the least, to assert this is any kind of reason to believe test results are not representative. We could say the same thing about ANY physical test, including those regarding the speed of light or any other measurable constant - which certainly have not had "loophole-free" tests.
  8. May 6, 2013 #7


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    Objections from a layman:

    • Ref. [1]? Where is it? What is it? What does it prove?

    • Are you claiming that Zeilinger, in Ref. [2], is stating that all experiments performed by him will most probably not work once all loopholes are closed simultaneously?? Or is he saying the opposite?

    • “on the other hand, to prove that the inequalities can be violated in quantum theory, one needs to use the theory of quantum measurements, e.g., the projection postulate” – Says who? Proven by what??

    • Projection postulate? Please excuse a layman if I’m wrong; but QM theory doesn’t say anything about what happens at measurement (I think it’s titled “The Measurement Problem” by the way), and that’s the sole reason we have all this philosophical interpretation business going on. If this was perfectly clear from QM theory, interpretations would all be dead by now (except maybe one). Does anyone use von Neumann's projection postulate from the 1930s these days? Isn’t it completely overthrown??

    • From QM theory – entanglement is all you need. The rest; Polarizers & Malus' law (from 1809), and Bell's theorem, has nothing to do with QM theory. I hope you’re not saying that entanglement is dependent on von Neumann's projection postulate??

    ... Schrödinger & Bell are probably turning in their graves already ...
    Last edited by a moderator: May 7, 2013
  9. May 7, 2013 #8
    I agree that the discussion of the issues related to the Bell theorem is short. However, I refer the reader to a longer discussion in an earlier article in IJQI (http://akhmeteli.org/akh-prepr-ws-ijqi2.pdf ). I admit that I have little to add to that longer discussion. Furthermore, while "...mutually contradictory assumptions..." is called "only" in your book, it's "more than enough" in mine: according to formal logic, if you make two mutually contradictory assumptions, you can get any conclusion you want.

    As I said several times, until all assumptions of a theorem are fulfilled simultaneously, one cannot be sure that its conclusion holds. I asked you a few times: isn't your logic applicable to Euclidean geometry (https://www.physicsforums.com/showpost.php?p=2534347&postcount=34 )? Unless I missed something, you chose to ignore this question.

    Another thing. According to Zeilinger and his collaborators (http://arxiv.org/abs/1212.0533 ), "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", whereas for you everything is already crystal clear. I guess you would not fund such experiment as useless :-)

    I admit I am a bit confused: does this mean that we should "peacefully coexist" with lousy physics, as all physics is lousy anyway? Let me just repeat that extraordinary claims, such as ruling out local realism, require extraordinary proof. If some other experiments are deficient, I am sure someone will raise the issue of such deficiency, whereas I have to discuss weak points of Bell experiments to anticipate criticism of my work.
  10. May 7, 2013 #9


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    1. True enough, but you are kidding yourself if you think you can dismiss Bell with this comment, and then claim you address Bell. Seriously? This is the first thing anyone is going to look at in a paper of this type.

    2. There is no shortage of proof, just a shortage on your part to accept any of it. There isn't a hint that the QM cos^2(theta) rule for photons is incorrect. As experiments improve, the statistical deviation from the local realistic predictions (constrained of course by Bell) make that view MORE and MORE implausible. That is exactly the reverse of what would be expected by your position. And the comment that extraordinary claims require extraordinary proof is a meaningless application of Sagan's comments. Extraordinary is clearly in the eyes of the beholder.

    I am shocked by your claim that you are discussing Bell in your paper. A more accurate summary would be that you dismiss Bell by assumption; that way the reader knows what they must also do to go along with your mechanism.
  11. May 7, 2013 #10


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    General reminder: Please keep this discussion civil.
  12. May 7, 2013 #11


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    Although I do not agree with some of what you are saying, I was pleased to see the paper expressing your ideas. Certainly no easy effort on your part.

  13. May 7, 2013 #12
    It's pretty hard for me to understand the motivation behind this. In the heart of the argument, it seems, there lies a fundamental desire to "believe". In this case, the object of the belief happens to be the concept of local realism. In order to uphold this belief, I guess one must feel that, fundamentally, nature consists of nothing but material points. In order for this concept to be self consistent, matter must literally come in the form of mathematical points... that is, they must be zero dimensional.

    The first reservation is simply this: in a three-dimensional universe, all objects that consist of less than three full dimensions cannot be said to exist. They simply cannot take any part in our reality. I can't really go any deeper with this part of the argument. It's just what *I* believe.

    The next problem can be given a logical argument. Say there are two mathematical points approaching each other. At all times they are separated from each other by an infinite gap. (I say the gap is infinite, because in relation to an entity of zero measure, all other measures are infinite.) That is, except for one time... when they occupy the exact same location. There is no known form of mathematics that can handle this situation.

    The only idea that can fully address these problems is to think of reality as consisting fundamentally of "space like" objects. It turns out that the wavefunction works out quite well for this situation. While it is true that all current forms of "accepted" physics do not postulate any forms of multi-dimensional objects in classical spacetime, the reason for this has nothing to do with whether or not these kinds of objects are a "good idea." IMO, it has everything to do with the fact that we are still a fairly young species that still has a long ways to go... both theoretically and experimentally.

    I think there is no doubt that theorists will eventually start trying to somehow insert the wavefunction into the field of differential geometry. In fact, I am *always* doing this inside of my own head, and I am sometimes amazed by what I am able to visualize. But in terms of getting others to be interested in my, um, "visions"... I realize that I still have a very long ways to go. I know that I have to basically learn an entirely new language (diff. geom.), and I have to be able to speak it fluently.

    Perhaps the best thing about string theory/M theory is that it is the first attempt to rigorously apply higher dimensional thinking to our understanding of the universe. But I feel it is too much of a slave to the particle ontology in order to be much use as a truly unifying paradigm. No matter. I am sure that the mathematical advances being made in that arena will go quite far when it comes to developing the kinds of theories that interest me.

    So, it is important to understand that the point/location based approach of fundamental physical theory is on an inevitable march towards irrelevance... not simply because of the arguments that I outlined above. But rather because there is nowhere else we can go with it as a species. People are simply not inspired by it. Wavefunctions are beautiful. They are all about harmony. There's just no way to stop people from thinking that they are in integral part of our universe.
  14. May 8, 2013 #13
    I agree, the first question people ask looking at an article like that is "What about Bell?" But let me repeat that I include by reference the longer discussion of the issues related to Bell in my IJQI article. I just cannot repeat the same long discussion in every article on this topic. The most I can do is to offer a short summary.

    Let me also emphasize that the longer discussion does not just "dismiss Bell". The logic there is (or can be) actually somewhat different. I say that one needs both unitary evolution and the projection postulate (theory of quantum measurements) to prove that the Bell inequalities can be violated in standard quantum theory. That means that 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 (by the way, this per se provides a no-go theorem: you cannot derive the Bell theorem using just unitary evolution, without the theory of quantum measurements). So I explicitly state which assumption of the Bell theorem I reject to escape the conclusion of the Bell theorem. Then I state (or could state) that this rejection is not deadly for my theory (for example, in comparison with experimental data) for two reasons: first, the projection postulate contradicts unitary evolution anyway, second, there is no experimental evidence of violations of the genuine Bell inequalities. It looks like such logic seems at least tolerable to some referees and readers of my articles. You don’t like such logic? This is regrettable, but unfortunately I just cannot write an article that everybody would like. Maybe next time :-)

    There is no shortage of such hints, just a shortage on your part to accept any of it. 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.

    With all due respect, what statistical deviation from the local realistic predictions are you talking about? There have been no experimental evidence of violations of the genuine Bell inequalities so far, so there has been no evidence of “statistical deviation from the local realistic predictions”.
    His saying is famous enough, so I don’t think one can accuse me of plagiarism:-)
    OK, then, so we just disagree on what is and what is not extraordinary.

    I respectfully disagree. You may say that I offer just a summary of discussion in this article, but there is a solid discussion in the IJQI article, and it is referenced in the latest article.
  15. May 8, 2013 #14
    If you are talking about my article, then I don't know how this is relevant, as I mostly consider fields, not particles.
  16. May 8, 2013 #15
    Thank you very much for the kind words. It was indeed difficult to obtain the mathematical results, but as for publishing them... Well, it was not a walk in the park, but I expected greater resistance to articles on this topic.
  17. May 8, 2013 #16


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    1. Come on, the experiments have been run, published and been generally accepted. Need I post references?

    The fact is, you believe there are definite values for spin components at all times - realism - and those values are independent of measurement context. Such values cannot maintain - relative to each other - the cos^2 rule. Bell shows this.

    2. No plagarism, but technically the statement lacks merit. It is more of a guide, much like the dictum that you should accept the simpler explanation over the more complex one (Occam).
  18. May 9, 2013 #17
    It is my understanding that there has been no loophole-free experimental evidence of violations of the Bell inequalities. I don't believe you can post references to the contrary.

    I know that this is how realism is often defined in the context of quantum theory. Sometimes this "realism" is called "EPR realism". Actually, I don't believe in such "realism", and I stated that long ago (https://www.physicsforums.com/showpost.php?p=2534347&postcount=34 ): "As I tend to think Einstein was wrong about the uncertainty principle, I am not crying for that particular school." However, the notion of realism exists irrespective of quantum theory and means something different. Santos (http://arxiv.org/abs/quant-ph/0410193 , section II) illustrates this using the example of coin tossing: "head" state or "tail" state does not exist for a coin independently of the measurement procedure, even though the relevant measurement is classical. Another example: 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. Let me also add that the Bell theorem does not need to assume EPR realism (please see, e.g., Bell, Speakable and Unspeakable in Quantum Mechanics, Second Edition, Canbridge, Section 8, Locality in quantum mechanics:reply to critics)

    So you actually demand that I give experimentalists and you some slack and ignore the loopholes:-). Sorry, I just cannot do that:-). I owe nobody that much. The issue is too important to cut corners.
  19. May 9, 2013 #18


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    In the Nature issue just published today, there is the claim of a Bell experiment with entangled photons which closes all loop-holes:

    M. Giustina et al, Bell violation using entangled photons without the fair-sampling assumption, Nature 497, 227 (2013)

    Of course, sceptics, still adherent to socalled "local realistic models" could still argue that this is not an experiment that closes all loop-holes together but only the fair-sampling assumption. So today, there is not one single experiment that closes all loop-holes at the same time. But taken all experiments together you can say all loop-holes are closed.

    Anyway, I think even if all loop-holes are closed, there's still the possibility open that there might be a non-local realistic model of nature, but as long as none is found, we better stick to quantum theory.
  20. May 9, 2013 #19
    Bell used the term beables (properties of a system that are not observed). In EM theory, E and H are beables but not the scalar and vector potential because of gauge invariance. However the introduction of spinors to me hold the key to realism, and locality.

    Maybe some can help or comment: Bell's theorem is stated that LHV theories are ruled out. However Bell did not think the notion of non-locality to be reasonable. Rather the breakdown of local causality was an issue not with qm, but with Special Relativity. Is this an accurate view? (Bell wanted to do away with SR and find some aether frame which allows superluminal events).
  21. May 9, 2013 #20


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    In the Nature issue just published today, there is the claim of a Bell experiment with entangled photons which closes all loop-holes:

    M. Giustina et al, Bell violation using entangled photons without the fair-sampling assumption, Nature 497, 227 (2013)


    Here is the full version for post #18 above, in the archive:

    Last edited: May 9, 2013
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