Quantum Mechanics of a Single Particle in One-Dimensional Space I

T. Banks

Dariusz Stanisław Sobolewski

The article, based on the structure of elementary particles in the form of spatial vortices revealed in the Theory of Space, the four-dimensional structure of space, and the essence of electromagnetic interactions, formulates Hamilton and Hamiltonian-Jacobi functions describing the free motion of an elementary particle and the system of elementary particles in a hydrogen atom, approximating elementary particles with a single spatial vortex. It is shown that the complex nutation and precession of a spatial vortex identified with an elementary particle can be identified with matter waves described by transverse de Broglie plane waves of classical quantum mechanics on the boundary hypersurface βϰβ, which also determines the limit of applicability of classical quantum mechanics, which reduces the complex trajectory of spatial vortices to the analysis of deformations on one of the boundary hypersurfaces.

Peter Bongaarts

Peter Bongaarts

Romulus Breban

We attempt a unification between the Quantum and the Statistical Mechanics of a single spinless particle. We consider a five dimensional (5D) space-time with no matter. We postulate that all physical information on single particle propagation is given by statistics on null paths in this space-time. If the 5D metric doesn't depend on the fifth space-like coordinate, then the propagation problem can be reduced to 4D by foliation along the fifth coordinate and we obtain Quantum Mechanics. If the 5D metric doesn't depend on time, we can foliate along the time coordinate and obtain a formulation of Statistical Mechanics. Quantum Mechanics and Statistical Mechanics prove to be particular cases of a 5D Optics. If the 5D metric is independent on both time and the fifth coordinate, then Quantum Mechanics and Statistical Mechanics are pictures of the same 5D reality.

Robert Gilmore