Two-Time Relativistic Bohmian Model of Quantum Mechanics

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 virtual 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.

💡 Research Summary

The paper introduces the Two‑Time Relativistic Bohmian Model (TTBM), a speculative extension of de Bohm’s pilot‑wave theory that adds a second, hidden temporal parameter τ in addition to the ordinary time t. The central hypothesis is that particles possess an intrinsic motion along τ that is instantaneous with respect to t. This extra time dimension is claimed to generate quantum indeterminacy, explain the Zitterbewegung of electrons without invoking virtual antiparticles, and produce a relativistic correction to the Heisenberg uncertainty relations that could be tested in high‑energy accelerators.

Mathematically the author starts from a wavefunction ψ(r,t,τ)=R(r,t,τ) exp