Fractal universe and the speed of light: Revision of the universal constants

TL;DR

This paper proposes a fractal universe model where time's self-similarity leads to a decreasing speed of light over cosmic time, revising universal constants and explaining redshift without universe expansion.

Contribution

It introduces a fractal universe framework linking time, space, and mass, and revises universal constants to be of order one at cosmological scales.

Findings

Speed of light decreases inversely with time.

Universal constants are of order one at large scales.

Redshift explained by decreasing light speed, not expansion.

Abstract

We apply the property of selfsimilarity that corresponds to the concept of a fractal universe, to the dimension of time. It follows that any interval of time, given by any tick of any clock, is proportional to the age of the universe. The fractality of time gives the fractality of space and mass. First consequence is that the speed of light decreases inversely proportional to time, same as the Hubble parameter. We then revise the universal constants and, at the cosmological scale, they are all of order one, as Dirac proposed. We find three different scales, each one separated by a factor of about 5x10^60: the universe, the Planck scale and what we call the sub Planck scale. Integration of the Einstein cosmological equations, for this fractal universe, gives the solution of a non-expanding universe with the present value of the observed numerical parameters. The red shift measured from the distant galaxies is interpreted here as due to the decreasing speed of light in a fractal universe.