Nonlocal Graphene Relativistic Doppler quantum pumping Yuan Qi subwavelength tubulin consciousness

In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental ... The Dirac spinor for the positive-frequency solution
Graphene on two dimensional (2D) noncommutative (NC) plane in the presence of a constant background magnetic field has been studied.
Tuning quantum nonlocal effects in graphene plasmonics
Quasi-Relativistic Doppler Effect and Non-Reciprocal Plasmons in Graphene
Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene
pure spin currents via non local injection and spin pumping

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This duality is less apparent in the DIRAC equation, and one has to look for the
representation of de BROGLIE's phase wave to find out where the speed of the particle is. The
counterpart of this difficulty is found in the relativistic power of this equation which allows the
proper time of the particle to emerge in complete coherence with de BROGLIE's phase harmony
theorem. This contributes, in the eyes of the author, to make it truly the fundamental equation
of quantum physics.

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This solution is attributed to the antiparticle. It appears that all the energy components vibrate in phase with the solution attributed to the particle, except the mass energy which vibrates in phase opposition.

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We begin this chapter by highlighting a progressive wave, as solution to Dirac's
equation, on a particular example. By analyzing the properties of the obtained wave, we will
show that it has all the characteristics of a de BROGLIE wave. ...the solutions are expressed to a multiplicative
constant close, without changing the notation for the components of the bispinor. (ψ0, ψ1, ψ2, ψ3). This simplification of writing does not seem to interfere with the understanding of the ideas that are developed. We also know that, in a more complete theory, a constant of normalization is necessary to give each term of the bispinor the dimension of the square root of a volumic density of energy....In view of the previous chapter, we formulate the hypothesis that this wave, which is an exact solution of the DIRAC equation, is a phase wave, in the sense that de BROGLIE defined it in his thesis.

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the "Hempel Effect" is called (2, 3, infinity) by Alain Connes, Fields Medal math professor
Talk by Alain Connes in Global Noncommutative Geometry Seminar (Americas)
on September 3, 2021.

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We will show that the travelling wave that appears in the solutions to the DIRAC
equation is a phase wave of de BROGLIE. Therefore, the link with the "physical" velocity of
the particle will become clearer, since this velocity is equal to the group velocity associated
with the phase wave. From this observation, it becomes possible to analyze the internal changes that occur
when a particle at rest receives energy from another particle. The classical experimental
This wave is of a surprising nature: it has the property of propagating a quantity at a
speed greater than that of light. It will be identified by de BROGLIE as a phase wave that does
not carry energy, but in fact represents a phase shift.
. It falls to de BROGLIE to have succeeded in removing this ambiguity by establishing a theorem which he calls the "phase
harmony theorem". This theorem was obtained without any calculation. It represents, in the
eyes of the author, a model of physical reasoning...
This is the phase harmony theorem established by Louis de BROGLIE. The phase of
the wave (ω0t0) seen by an observer of the frame (R0) is identical to the phase of a progressive wave (ωt - kzz) seen by an observer of the frame (R).