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Physics International

Quantum Uncertainty and the Fifth Dimension

Paul S. Wesson

Published Feb 1, 2015• 1 citation
Publisher

Abstract

If the world has an extra dimension, the motion of a particle in spacetime may be slightly modified, producing a correlation between the momentum and position similar to that familiar from the uncertainty relation in quantum mechanics.
DOI
10.3844/pisp.2015.78.81

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Uncertainty principles for the average fluctuations of momentum and position per particle in an ensemble are derived. For bosons, these results are similar to the usual uncertainty principle, with slight corrections for the correlated motion of the particles. For fermions, a large correction for the Pauli exclusion principle is necessary, which causes 〈p2〉〈r2〉〈{p}^{2}〉〈{\mathcal{r}}^{2}〉〈p2〉〈r2〉 to be proportional to the two-thirds power of the number of particles in the ensemble.
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described by the wave function is subatomic particle moving randomly. Therefore, the characteristics of quantum mechanics have a dual nature, one of them is the deterministic nature carried on from classical physics, and the other is the probabilistic nature coined by particle's random motion. Based on this model, almost all of open questions in quantum mechanics can be explained consistently, which include the particle-wave duality, the principle of quantum superposition, the interference pattern of double-slit experiments, and the boundary between the classical world and the quantum world. The current quantum mechanics is a mixture of matrix mechanics and wave mechanics, which are sharply conflicting in principle. Matrix mechanics treats quantum particles as classical particles with fixed relation between the particle's position and its momentum. The matrix mechanics, in fact, belongs to the old quantum theory. Both Born's non-commutative relation and Heisenberg uncertainty relation originate from matrix mechanics. However, in wave mechanics, there is no any fixed relation between the particle's position and its momentum, and the particle's position and its momentum belong to immeasurable physical quantities. Therefore, there is no need for non-commutative relation and uncertainty relation in wave mechanics.
It has recently been argued that quantization can be established within classical theory as a consequence of lost information. In this view, classical mechanics is regarded as a union of quantum mechanics and what are called 'hidden variables'. Hidden variable theories were first considered some years ago and abandoned because they did not produce new physics. They have now been revived however, because they appear to provide a logically sound means of relating classical and quantum theories. It is argued here that the Heisenberg uncertainty relations constitute a necessary condition for gauge invariance in the 5-dimensional Kaluza-Klein theory, where the fifth dimension of 5-spacetime is hidden as a 5-dimensional theory of general relativity is projected onto 4-spacetime.