[From an April 2013 comment on an article about "time crystals" at (billionaire mathematician James Harris Simons') Simons Foundation: Perpetual Motion Test Could Amend Theory of Time]
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 at FQXi for more information.
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