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Two-Time Relativistic Bohmian Model of Quantum Mechanics

Giuseppe Raguní

TL;DR

This work proposes two-time relativistic Bohmian Mechanics by introducing an independent time parameter $\tau$ to restore determinism in quantum phenomena. The main approach defines a two-time formalism with separate $t$-motion and $\tau$-motion, governed by a quantum potential $V_Q$ derived from the amplitude $R$ of the wavefunction $\psi(\vec{r},t,\tau)$ and a two-time action $S=S_t+S_\tau$. Key contributions include deriving $\tau$-oscillations for free particles and atomic orbitals, predicting an anisotropic and relativistically modified uncertainty principle, and suggesting possible astrophysical consequences and a new perspective on time in QM. The work offers testable predictions, discusses potential implications for spin and dark matter, and acknowledges gaps such as deriving full spin-relativistic wave equations and experimental verification.

Abstract

Two-Time relativistic Bohmian Model (TTBM) is a theory in which the apparently paradoxical aspects of Quantum Mechanics are the effect of the existence of an extra unobservable time dimension. The hypothesis that matter is capable of motion with respect to an additional independent time (thus resulting instantaneous with respect to usual time) is capable of restoring determinism, explaining the Zitterbewegung without evoking antimatter. The model also predicts a relativistic correction of the uncertainty principle. Here the model is first summarized (definition, salient properties and empiricism) and after applied to a generic spherical atomic orbit, obtaining electron oscillations in the new time dimension, tau, which demonstrate the static nature of the orbitals. Something very similar happens in the case of a particle in a box, where tau-oscillations cause the particle to spread out at steady states. Some astrophysical and about spin speculations follow. Finally, it is discussed how the model fits into the fundamental problem of the definition of time in Quantum Mechanics. Keywords: Quantum Mechanics Foundations; de Broglie-Bohm Theory; Zitterbewegung; Uncertainty principle verification; Extra dimensions, Atomic orbitals, Spin, Definition of time in Quantum Mechanics.

Two-Time Relativistic Bohmian Model of Quantum Mechanics

TL;DR

This work proposes two-time relativistic Bohmian Mechanics by introducing an independent time parameter to restore determinism in quantum phenomena. The main approach defines a two-time formalism with separate -motion and -motion, governed by a quantum potential derived from the amplitude of the wavefunction and a two-time action . Key contributions include deriving -oscillations for free particles and atomic orbitals, predicting an anisotropic and relativistically modified uncertainty principle, and suggesting possible astrophysical consequences and a new perspective on time in QM. The work offers testable predictions, discusses potential implications for spin and dark matter, and acknowledges gaps such as deriving full spin-relativistic wave equations and experimental verification.

Abstract

Two-Time relativistic Bohmian Model (TTBM) is a theory in which the apparently paradoxical aspects of Quantum Mechanics are the effect of the existence of an extra unobservable time dimension. The hypothesis that matter is capable of motion with respect to an additional independent time (thus resulting instantaneous with respect to usual time) is capable of restoring determinism, explaining the Zitterbewegung without evoking antimatter. The model also predicts a relativistic correction of the uncertainty principle. Here the model is first summarized (definition, salient properties and empiricism) and after applied to a generic spherical atomic orbit, obtaining electron oscillations in the new time dimension, tau, which demonstrate the static nature of the orbitals. Something very similar happens in the case of a particle in a box, where tau-oscillations cause the particle to spread out at steady states. Some astrophysical and about spin speculations follow. Finally, it is discussed how the model fits into the fundamental problem of the definition of time in Quantum Mechanics. Keywords: Quantum Mechanics Foundations; de Broglie-Bohm Theory; Zitterbewegung; Uncertainty principle verification; Extra dimensions, Atomic orbitals, Spin, Definition of time in Quantum Mechanics.
Paper Structure (12 sections, 41 equations, 2 figures)

This paper contains 12 sections, 41 equations, 2 figures.

Table of Contents

  1. Introduction
  2. TTBM definition and properties
  3. Some fundamental properties
  4. Free particle
  5. TTBM empiricism
  6. Atomic orbitals
  7. Tangential $\tau$-oscillation
  8. Radial $\tau$-oscillation
  9. Particle in box. Possible astrophysical consequence
  10. Considerations on spin
  11. TTBM and the problem of Time in Quantum Mechanics
  12. Final remarks

Figures (2)

  • Figure 1: Phenomenology of particle motion in a vacuum: self-interactions, interference (by wall slits), and observational collapses. The wavefunctions depicted are representative of packets.
  • Figure 2: The atomic static orbitals (shaded area) arise as a result of tangential and radial $\tau$-oscillations combined with the classical orbital motion.