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It appears that zitterbewegung, a frequency associated with the total energy of a particle or system, is widely considered to be an unphysical quantity (e.g., Kobakhidze et.al.), @Lubos Motl, McMillan). However, a few physicists including Hestenes, Recami et.al.,consider it to be a fundamental, physical quantity.

It appears that, for example, the photon emitted in transitions between two states in an atom has precisely the frequency of the "beat frequency" (difference frequency) between the zitterbewegung frequencies of the two states.

Why is zitterbewegung considered unphysical by most physicists, and has there been a solid refutation of Hestenes' position that zitterbewegung is physical?

Urb
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S. McGrew
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    well, "beat frequencies" are differences, they do not depend on the absolute quantity – lurscher May 18 '18 at 16:08
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    You appear to be misreading several of your sources and slapping an ill-defined "unphysical" label on selected statements in them. Zitterbewegung is needless in QFT, but topical and useful in Dirac's equivalent relativistic fermion QM and results in specific terms in the correct hamiltonian, so, then "physical". At least one source indicates it is merely obsolete, as you may bypass it in QFT, not "unphysical". – Cosmas Zachos May 18 '18 at 16:33
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    Some people claim that the Darwin term in fine structure of hydrogen is from the zitterbewegung. – Mauricio May 18 '18 at 16:37
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    @Mauricio. That's the point: "some people"="hole theory interpreters". It's a fine interpretation in that (holes in sea) picture. It is meaningless in QFT. Choose your language and use its tools. – Cosmas Zachos May 18 '18 at 16:47
  • @CosmasZachos, maybe I misread, but here are some quotes: "The "Zitterbewegung" is completely unphysical."(Lubos Motl), and "One such unphysical effect, zitterbewegung, is discussed in Section 4.4" (McMillan). – S. McGrew May 18 '18 at 16:55
  • Perhaps I gave too much weight to those two quotes. Can you provide a link to a good reference that discusses the physical meaning and significance of zitterbewegung? – S. McGrew May 18 '18 at 17:05
  • Any good book on relativistic quantum mechanics. "Advanced QM" by Sakurai, "Relativistic QM" by Bjorken & Drell, anything fussing the Darwin term of the Dirac hamiltonian. Zitterbewegung is physical in the contexts where it is meaningful: hole theory. – Cosmas Zachos May 18 '18 at 18:41
  • W Greiner's Relativistic wave equations Chapters 11 & 12 explain Hole theory, and apply the Darwin term to s-level energy shifts. ... pp 288-294. – Cosmas Zachos May 18 '18 at 22:38
  • The Capelle link to this answer produces the Darwin term neatly. – Cosmas Zachos May 19 '18 at 13:10
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    @LubosMotl, in https://physics.stackexchange.com/questions/19378 was adamant that zitterbewegung is unphysical. It seems that his main argument was that zbw is unobservable. This seems analogous to saying that imaginary numbers are unphysical. Or, it is a relatively old series of posts, so maybe he has changed his position. – S. McGrew May 19 '18 at 14:14
  • He might say the same thing about holes: he effectively means obsolete. But why are you focussing on theological "physicality" litmus tests? If you are reaching for quick-and-dirty 1-particle pictures, Zbwgng is a useful picture. Imaginary numbers is a good example. – Cosmas Zachos May 19 '18 at 15:58
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    To tell the truth, I'm intrigued by an impression that the Feynman path integral looks a lot like Huygens' principle applied to a wave whose frequency corresponds directly to the zbw frequency of the particle whose motion is being described-- the zbw frequency based on its total energy including its relativistic mass. I'm trying to look at the idea from multiple perspectives so I can understand it. – S. McGrew May 20 '18 at 03:27
  • Related: Modern understanding of zitterbewegung? – Chiral Anomaly Jul 27 '20 at 01:13

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I think the answer to your question might be that no one yet knows whether zitterbewegung is physical or not because no one really knows what the physical underpinnings of quantum physics are yet.

For a discussion of what zitterbewegung might mean physically, I would study walking droplets / hydrodynamic quantum analogs. Here a particle (droplet) always has an intrinsic oscillation, as it bounces along the bath propelled by the Faraday waves from its impacts.

Disclaimer: I am not familiar with zitterbewegung in other contexts than HQA, so I don't know exactly how the original idea of zitterbewegung relates to this phenomenon in HQA.

boojumAndSnark
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How are we supposed to decide if something is physical or not? Probably, something is physical if one can observe it. So can we observe zitterbewegung? I don't know. I know only one experiment where direct observation of zitterbewegung is claimed:

Catillon, P.; Cue, N.; Gaillard, M.; Genre, R.; Gouanère, M.; Kirsch, R.; Poizat, J.C.; Remillieux, J.; Roussel, L.; Spighel, M. A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling. Found. Phys. 2008, 38, 659.

Abstract The particle internal clock conjectured by de Broglie in 1924 was investigated in a channeling experiment using a beam of ∼80 MeV electrons aligned along the 110 direction of a 1 μm thick silicon crystal. Some of the electrons undergo a rosette motion, in which they interact with a single atomic row. When the electron energy is finely varied, the rate of electron transmission at 0° shows a 8% dip within 0.5% of the resonance energy, 80.874 MeV, for which the frequency of atomic collisions matches the electron’s internal clock frequency. A model is presented to show the compatibility of our data with the de Broglie hypothesis.

The article looks strange, as the experiment was performed decades before the publication of the article, as far as I can see. Last year, I spoke to a pretty well-known experimental physicist who was much interested in the above experiment. He said he had tried to find out more about the experiment, and those he talked to assured him that it was quite solid work. Nevertheless, there are still some doubts.

In my work (e.g., Entropy 2022, 24(2), 261), I considered a description of one-particle wave functions as plasma-like collections of a large number of particles and antiparticles. In this context the Zitterbewegung frequency plays a role of a “natural frequency”, rather than a frequency of some “internal clock”, so oscillations at this frequency do not have to exist in all situations, but can be driven, as in the case of the above experiment.

akhmeteli
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