https://arxiv.org/pdf/2207.00346.pdf
noncommutative = NC
Alex E Bernardini and O Bertolami
https://arxiv.org/pdf/1303.0685.pdf
A time crystal keeps moving and repeats itself periodically in time in the absence of external encouragement,” said Autti. This is possible because the time crystal is in its lowest energy state. The basic rules of quantum mechanics prevent the motion from becoming completely still, and so the time crystal remains “stuck” in its never-ending cycle.
“This means they are perpetual motion machines, and therefore impossible,” remarked Autti.
“In quantum physics, a perpetual motion machine is fine as long as we keep our eyes closed, and it must only start slowing down if we observe the motion,” Autti said, referring to the fact that the exotic quantum mechanical states required for time crystals cannot keep operating once they interact with their environment (for example, if we observe them).
Quite literally - as in meditation with the eyes closed!!
In that condensate, all the spins of the electrons in the helium-3 linked up and worked together, generating waves of magnetic energy, the magnons. These waves sloshed back and forth forever, making them a time crystal.
yes but a Bose-Einstein condensate is not nonlocality since it's still a separation of molecules - this crucial point is made by Professor Tejinder P. Singh.
Propagating, pure-field solutions may have any energy, but the energy transferred must
be proportional to the frequency. These are identified with the physical photon. Solutions with a rest-mass term allow any incoming propagating field to merge into re-circulating vortex-like solutions. The minimum energy
configuration “rectifies” the oscillating electric field of light into a uni-directional, radial (inward or outward directed) configuration. The resulting apparent external charge may be readily estimated and is found to be of the order of the elementary charge. The spin may, likewise, be calculated, and is found to be half integral,
exhibiting a double-covering internal symmetry. Charge is then not a fundamental quantity in the theory - but is a result of the way field folds from a rest-massless bosonic to a rest-massive fermionic configuration.
p-vot may be conveniently thought of as a square-root rest mass field.
The incoming photons are shown on a different scale to the electron and positron vortices. The
vortices are double-covering single wavelength loops with radius is a factor of 4π smaller than the photon wavelength.
The electron(above) encloses a pool of positive p-vot, the positron (below) a pool of negative p-vot.
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