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Quantum Population Dynamics: A Broad View from an Exploration beyond the Standard Model |
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PP: 31-50 |
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Author(s) |
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Jean-Pierre Blanchet,
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Abstract |
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| To explore quantum and classical connection from a new perspective, a Quantum Population Dynamics (QPoD) model
based on the logistic relation common to several sciences is investigated from a very broad perspective to explore the numerous
links to current physics. From postulates of causality and finiteness a classical quantum entity, a quanta of spacetime, is defined with
unitary extension and intensity. Applying the logistic equation to a quantum population of non-local two-state oscillators results in a
quantum-classical equation linking wave and particle dynamics with an explicit account of decoherence. Varying over 124 orders of
magnitude, the coupling constant acts like a delta Dirac function between regimes. The quantum regime is conform to Schršodinger
and Dirac equations according to respective Hamiltonian while the classical mode suppresses the quantum wave function and follows
the Hamilton-Jacobi equation. Besides the quantum wave solutions, in the classical range, the general equation admits Fermi-Dirac
and Bose-Einstein solutions, relating to thermodynamics. Inertial mass is found in terms of the quantum entropy gradient. The most
compact quantum cluster forming a crystal produces a unique flat space filling lattice cells of one simple tetrahedron and one composite
truncated tetrahedron corresponding respectively to a fermionic cell and a bosonic cell. From this lattice geometry alone, the mass
ratios of all fermions are expressed uniquely in terms of vertices and faces, matching charges properties of three generations and three
families. Except for a minor degeneracy correction, the solution is shown to follow the logistic dynamics. The resulting mass equation
is a function of dimensionless natural numbers. Many properties of the Standard Model are recovered from geometry at the Planck
scale, respecting naturalness, uniqueness and minimality. QPoD may help addressing questions about the nature of spacetime and the
physical microstructure of particles. The model predicts a single spinless matter particle of a 4th generation as a WIMP particle close
to Higgs mass. |
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