It is predicted but was never experimentally confirmed because technical limitations but also physical observation limitation of HUP (Heisenberg Uncertainty Principle) that an electron at rest has an intrinsically caused jittery motion similar as an analogy, to the Brownian vibration motion observed on atoms. Although the Brownian motion of atoms we must differentiate here, in a fluid for example, is not caused intrinsically inside the atom, but rather due to extrinsic causes like different atoms bumping on each other all the time.
Nevertheless, the Zitterbewengung (German term for jittery vibrational motion) of the electron is predicted to be twice the electron's Compton frequency fc :
fc ~ 127 EHz (i.e. one ExaHertz [EHz] unit is 1018 Hz)
Thus,
fZ = 2fc~254 EHz
which is an enormous high frequency vibration.
However, if the cause of the electron's Zitterbewengung at rest, is to be attributed to the unknown possible intrinsic mechanics of the electron then this also possible mean, and also predicted by de Broglie theory about every subatomic particle, that a kind of intrinsic harmonic energy oscillation exists for the electron that is the classical cause for the electron Zitterbewengung.
My question here is and discussion topic, what do you think is the physical reason (please do not use just equations to explain or abstract effective terminology) this frequency to be twice the Compton frequency?
I found this question always to be a big mystery which however if answered could be the key for deciphering the electron.
Emmanouil
p.s. In my "Intrinsic Mechanics" for example model of the electron, the electron undergoes in superposition two overlapping different harmonic energy oscillations at a 90º angle. One latitudinal and one longitudinal harmonic oscillation of its energy string :
see animation, https://www.horntorus.com/particle-model/e_spin-up.html
This combinatoric motion is of two harmonic oscillations is in my theory and model, is the reason why the zitter vibration of the electron is twice its Compton frequency.
Relater paper of my model:
Article A ½ spin fiber model for the electron
Why do I the zitterbewegung frequency is twice the Compton frequency? Because the electron is a self-trapped 511keV photon in a 720° spin ½ double loop. I first saw this described in Williamson & van der Mark's 1997 paper "Is the electron a photon with toroidal topology?" It's here on Researchgate. I don't think they got everything quite right, and sadly they are no longer with us. But I do think it's largely correct.
I think your paper is largely correct too. However when it comes to mass, take a look at [1508.06478] Light is Heavy. If you trap a photon in a mirror box, you increase the mass of the box, because as per Einstein's E=mc² paper, the mass of a body is a measure of its energy-content. That's because to get the box moving, you have to push against the photon momentum impacting the near side of the box. There are other issues too. In your paper you referred repeatedly to the word vortex. I think you are correct to do so, because the motion of electrons and say positrons is vorticial: counter rotating vortices attract, and co-rotating vortices repel. However things like this present some issues for certain other concepts. Perhaps we could discuss these offline. See the attached popular science article written by me for some useful references.
Brownian motion is due to thermal fluctuations, Zitterbewegung is due to quantum fluctuations. So, while historically, it's been discussed in relation to electrons, it's a property of any quantum object.
That the frequency of the Zitterbewegung is proportional to the Compton frequency is just dimensional analysis, the physics, indeed, is in the dimensionless prefactor.
The reason the prefactor is equal to 2 may be understood as due to the fact that the relativistic electron-which displays Zitterbewegung, while the non-relativistic limit of the electron does not-has two spin states, that contribute coherently. It's worth doing the calculation, however, there are too many vague claims about it.
The question
“Predicted Zitterbewengung of electron thought similar to Brownian vibration motion of atoms”
- relates to a really fundamental physical problem – “what is Z”itterbewengung”? ”
- which – as any other really fundamental problem - really can be, and in this case is, scientifically rationally solved only in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read one of two main papers
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics
- where the scientifically rational model of “particle” is given. In the model particles are some cyclic disturbances - cyclic algorithms that tick with frequencies ω - in the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE],
- which [lattice] is placed in the Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct). FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP, correspondingly the always constantly running algorithms-particles move constantly in the utmost universal, “kinematical” 4D space with metrics (at least) (cτ,X,Y,Z) with the speed of light, c, c= lP/tP,
So a particle’s “Zitterbewegung” is just the particle’s algorithm ticking. When a having rest mass particle is at rest in the 3DXYZ space, it moves only in thecτ-dimension with the speed of light and its algorithm ticks with maximal frequency, when the particle moves also in the 3D space, the algorithm’s FLE sequence is diluted by [in certain sense, but that isn’t essential here] “blank” FLE steps ; so the algorithm ticks slower in Lorentz factor, unstable particles live longer,
- and Zitterbewengung can be experimentally observed. What seems was really made, see for example https://arxiv.org/pdf/1409.0888.pdf
More see the links above, to read https://www.researchgate.net/publication/387933457_A_response_to_question_What_is_the_The_Information_as_Absolute_conception it is useful as well.
Cheers
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