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by: Natalie Wolchover/ Simons Foundation: In February 2012, the Nobel Prize-winning physicist Frank Wilczek decided to go public with a strange and, he worried, somewhat embarrassing idea. Impossible as it seemed, Wilczek had developed an apparent proof of “time crystals” — physical structures that move in a repeating pattern, like minute hands rounding clocks, without expending energy or ever winding down. Unlike clocks or any other known objects, time crystals derive their movement not from stored energy but from a break in the symmetry of time, enabling a special form of perpetual motion.
I’m missing what is really new here – continuous periodic motion is implied by basic quantum mechanics. The simplest interpretation of the quantum numbers of an electron in a hydrogen atom is that the electron really does orbit the proton. De Broglie’s matter waves were conceived as circular motions of a point particle, with the frequency found by noticing that energy is equivalent to both mass and frequency, the former scaled by c-squared and the latter by Planck’s constant. Schrodinger worked out the implications for the Dirac (electron) equation, calling the phenomenon “zitterbewegung”, meaning “trembling motion”. It is of very high frequency – 1.6E21 Hz = 1.6 zettaherz, or billion trillion cycles per second, double that of the De Broglie wave of an electron.
As Oersted Medal winner David Hestenes worked out (using his marvelously clear applied, real-valued Clifford algebras, or “Geometric Algebra”, a lingua franca for mathematical physics) zitterbewegung at its simplest is a helical, light-speed motion of a point charge around its average path.* Further he found that the orientation of the helix is the electron spin, the curvature of the helix is the electron mass, the angle of the particle around the helix is the electron phase, and the helical motion creates a static magnetic dipole and a rotating electric dipole. This is far more comprehensible than the usual explanations (insofar as there are any usual explanations!). His interpretation was borne out by the discovery an absorption of 81.1MeV electrons in silicon crystals, due to the spatial zitter frequency and its electric dipole lining up at that speed with the spatial period of the crystal lattice. Before Hestenes’ explanation, the experimental results were so unexpected as to be implausible to most of the reviewers at the journal Physical Review Letters.
So the eternal and intrinsic helical motion of electrons in any state, including the ground state, is an established fact. How does that differ from the proposed time crystals?
*[It seems to me that this actually makes time simpler - if both light and electrons are constrained to move at c, then time for either sort of particle, rather than being some mysterious quantity with a square opposite in sign to the other dimensions ( x^2 + y^2 +z^2 - (ct)^2 = 1 - (v/c)^2) ) becomes instead simply a distance, the hypotenuse in x^2 + y^2 +z^2 = ct^2. Also it should be noted that electrons can move in more complicated ways than single simple helices, and superpositions are possible. ] See Hestenes essay Electron time, mass and zitter [www.fqxi.org] at FQXi for more information.