An implicit restriction in the Dirac quantization

TL;DR

This paper explores how changing the perspective of spacetime variables in the Dirac equation affects the mathematical description of a neutrino, revealing an implicit restriction when combining different viewpoints.

Contribution

It introduces a novel approach of applying mixed metric tensors to analyze the Dirac equation under perspective shifts, uncovering an internal change in neutrino description.

Findings

Neutrino description is altered when switching between space and time perspectives.

A Lorentz invariant mixed metric tensor equation can be formulated.

The internal properties of neutrinos depend on the chosen spacetime perspective.

Abstract

A restriction was found in the mathematics of the Dirac equation for a free neutrino type of particle. The basic assumption here is the equivalence of the four variables of spacetime. A perspective is defined as a metric tensor format. We asked what happens when we add a perspective where a time variable, $\sim ct$ unit [meter], becomes a space variable, unit [meter], and vice versa. A Lorentz invariant mixed metric tensor equation can be set up in an attempt to describe the neutrino in the cross-hairs of two different perspectives. Despite the equivalence of variables, and despite the fact that no single perspective is likely to be preferred, we find that the neutrino is "internally" changed in the cross-hairs of two different perspectives. Of course, if the two perspectives do not go together this conclusion collapses.