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Louis De Broglie has postulated in 1924 that with electron's mass there comes some $\approx 10^{21}$Hz inner oscillation: $E=mc^2=h f=\hbar \omega$.

We would get such oscillation e.g. if using $E=mc^2$ energy in stationary solution of Schrödinger's equation: $\psi=\psi_0 e^{iEt/\hbar}$.

Somehow similar (?) oscillations come out of solution of Dirac equation - called Zitterbewegung ("trembling motion").

Regarding their experimental status, I have found 2008 Foundation of Physics paper: A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling. Thanks to using ~80MeV electrons, time dilation leads to ~0.4nm distance between "ticks" of such clock, which agrees with lattice constant of silicon crystal they shoot at. While tuning the angle, they observe narrow absorption maximum when distances agree - intuitively, the electron's clock finds resonance with periodic structure of the crystal. Here is Hestenes paper about this experiment.

There are a few more papers claiming experimental observation of Zitterbewegung (e.g. [1], [2], [3]), but they are for physical simulation of Dirac equation - not exactly of electron.

Can we say that electron has some intrinsic ~$10^{21}$Hz oscillations, or maybe there is still some problem/doubts regarding such claim? Does it also concern other particles? Molecules? Larger objects? It seems problematic as its frequency is proportional to mass.

How such oscillation is realized? Do e.g. breathers (oscillating solitons) bring a proper intuition? Can such oscillations be imagined as the source of coupled "pilot" waves in dBB interpretation?

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Yes, there are experimental and theoretical works proving that the electron is a spherical standing wave without dispersion. Relevant references can be found in the recommended literature for the article. http://vixra.org/abs/1710.0239

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  • $\begingroup$ Any peer reviewed articles? $\endgroup$ – lalala Feb 16 '18 at 18:23
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    $\begingroup$ science.sciencemag.org/content/early/2013/01/09/science.1230767 $\endgroup$ – Mareta Arakelyan Feb 17 '18 at 6:51
  • $\begingroup$ The Science article does not seem to support the statement of your answer. It does not seem to have anything to do with the Compton frequency of the electron, it is about the Compton frequency of the Cs atom. However, the Cs atom contains a lot of protons and neutrons, and if we assume that each proton and neutron has some intrinsic frequency, then the Cs atom, being a composite particle, does not have such intrinsic frequency. $\endgroup$ – akhmeteli Feb 17 '18 at 10:48
  • $\begingroup$ But this article exposes the hypothesis of de Broglie $\hbar\omega =mc^{2}$. For an electron there are many such experimental studies and articles. $\endgroup$ – Mareta Arakelyan Feb 17 '18 at 11:40
  • $\begingroup$ I explained why this article does not really support the idea of intrinsic frequency for Cs atom. As for electrons, you should quote a peer- reviewed article supporting your answer. A vixra article? Really? $\endgroup$ – akhmeteli Feb 17 '18 at 13:58

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