Discovery of Quantum Hidden Variable

TL;DR

This paper proposes a hidden variable in quantum mechanics derived from an undefined component of the 4-vector Coulomb force, leading to a new wave equation from relativistic principles.

Contribution

It introduces the concept of Z-space and identifies a hidden variable as an undefined component of the 4-vector Coulomb force, connecting classical forces to quantum wave equations.

Findings

Derived Maxwell's equations from Coulomb's force and orthogonality.

Identified a missing component as a hidden variable in quantum mechanics.

Formulated a new quantum wave equation from relativistic Newton's law.

Abstract

The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual statement: the Coulomb's force (or gravitational force) acts along the line joining a couple of particles (in usual 3D space), so the direction of 4-vector Coulomb's force is carefully investigated, it is found that Maxwell's equations can be derived from classical Coulomb's force and the orthogonality. The second clue, a 4-vector force has 4 components, because of the orthogonality of 4-vector force and 4-vector velocity, the number of independent components of the 4-vector force reduces to 3, however we prove that 4-vector Coulomb's force can merely provide 2 independent components, this situation means that there is an undefined component accompanying the 4-vector Coulomb's force, hinting that this missing undefined component is a hidden variable. The third clue, the best way to study the hidden variable is to establish a new concept: Z-space, in which the undefined component of 4-vector Coulomb's force can be clearly defined as the hidden variable for the quantum mechanics. At the last, the undefined component is regarded as a fluctuating source that contributes to Lorentz force, so that the quantum wave equation can be derived out in the ensemble space of particle motion from the relativistic Newton's second law.