The Planck length and the constancy of the speed of light in five dimensional space parametrized with two time coordinates

TL;DR

This paper proposes a five-dimensional spacetime model with two time coordinates, deriving a minimal length scale as the Planck length and explaining the constancy of the speed of light.

Contribution

It introduces a novel five-dimensional framework with two time dimensions to explain the invariance of light speed and the origin of the Planck length.

Findings

Identification of a minimal length scale as the Planck length

Derivation of a space-time dependent speed of light

Demonstration of the constancy of light speed in observable universe

Abstract

In relativity and quantum field theory, the vacuum speed of light is assumed to be constant; the range of validity of general relativity is determined by the Planck length. However, there has been no convincing theory explaining the constancy of the light speed. In this paper, we assume a five dimensional spacetime with three spatial dimensions and two local time coordinates giving us a hint about the constancy of the speed of light. By decomposing the five dimensional spacetime vector into four-dimensional vectors for each time dimension and by minimizing the resulting action, for a certain class of additional time dimensions, we observe the existence of a minimal length scale, which we identify as the Planck scale. We derive an expression for the speed of light as a function of space and time and observe the constancy of the vacuum speed of light in the observable universe.