Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Jarek Duda on 19/03/2020 08:22:25
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Time crystals (https://en.wikipedia.org/wiki/Time_crystal) first described by Frank Wilczek in 2012 have got a lot of attention, recent popular review: https://physicsworld.com/a/time-crystals-enter-the-real-world-of-condensed-matter/
If I properly understand, they would like a lowest energy state spontaneously self-organizing into a periodic process - and propose sophisticated e.g. solid state experiments, or ping-pong of Bose-Einstein condensate, which don't really seem to satisfy this defining requirement (?)
But Louis De Broglie has already postulated in 1924 that with electron's mass there comes some ≈10^21 Hz intrinsic oscillation (https://en.wikipedia.org/wiki/Matter_wave_clock): E = mc^2 = hf = hbar ω, obtained if using E=mc^2 rest mass energy in stationary solution of Schrödinger's equation: ψ=ψ0 exp(iEt / hbar).
Similar oscillations come out of solution of Dirac equation - called Zitterbewegung (https://en.wikipedia.org/wiki/Zitterbewegung)("trembling motion"). Here is one of its experimental confirmation papers - by observing increased absorption when ticks of such clock agree with spatial lattice of silicon crystal target: https://link.springer.com/article/10.1007/s10701-008-9225-1
Electron can be created together with positron from just 2 x 511keV energy of EM field - after which it (the field?) should self-organize into these ≈10^21 Hz intrinsic oscillations.
So can we call electron an example of time crystal?
What other examples of lowest energy state self-organizing into periodic process are there?
ps. Beside self-organization of the lowest energy state into periodic motion (I don't see they got? in contrast to electron), they alternatively want "period doubling": that system oscillating with T period, self-organizes into 2T period process - breaking discrete time symmetry (invariance to shift by T).
So these popular Couders' walkers recreating many quantum phenomena in classical systems (slides with links (https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf)) also have period-doubling (can they be classified as time crystals?) - here is such plot from this paper (https://dualwalkers.com/PDF/2006,%20particle-wave%20JFM.pdf), horizontal axis is time, lower periodic process is for liquid surface - externally enforced by some shaker, upper periodic process shows droplet trajectory - self organizing into twice larger period than enforced:
(https://i.imgur.com/BSRh1to.png)
But generally it seems very valuable to find analogies between spatial and temporal phenomena like crystals here.
Great tool for that is Ising model: Boltzmann ensemble among spatial sequences, what mathematically is very similar to Feynman path (temporal) ensemble of QM - using this mathematical similarity, for Ising model we get Born rule, Bell violation (https://physics.stackexchange.com/questions/524856/violation-of-bell-like-inequalities-with-spatial-boltzmann-path-ensemble-ising), or analogues of quantum computers.
What other phenomena can be translated between spatial and temporal dimensions?