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.
Highlights
Since Maxwell’s theory of classical electrodynamics [1], it has been known that all electromagnetic waves travel with 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
1 we show that the existence of the Planck length p ~ Ωk and the subsequent limit Ωk → ∞ implies the constancy of the speed of light for the observable universe
Summary
Since Maxwell’s theory of classical electrodynamics [1], it has been known that all electromagnetic waves travel with the speed of light. In 1864 and 1881, experiments performed by Michelson and Morley [2] [3] gave a hint that electromagnetic waves travel fast in all inertial systems. This result was confirmed by many more experiments [4] [5] [6] [7] [8] proofing the constancy of the speed of light within the validity of the laboratory setups. When Albert Einstein derived special relativity [9], he postulated that the speed of light be constant, and he used this assumption as a key ingredient for special relativity. He derived that the speed of light is the upper
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