Relativity and Cosmology


Fractional Calculus, Irreversible Time, and Hubble's Law

Authors: Yuli Vladimirsky

In this essay we suggest that description of processes in classical physics based on differential calculus of integer order is an approximation. We propose use of fractional calculus with orders very close to integers to replace classical equations. We define time axiomatically in terms of set theory: time is partially ordered, can be continuous or discrete, homogeneous, and, generally, nonuniform. Use of fractional calculus predicts irreversible time, temporal indefinitism, and evolution of the Universe, as described by the Hubble's Law of expansion. Dimensionless Hubble and Cosmological constants are numerically equated to first and second fractional derivatives deviations from corresponding integers. The deviations are extremely small and their ratio corresponds to the Universe expansion deceleration parameter.

Comments: 13 Pages.

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Submission history

[v1] 2019-12-15 20:18:03
[v2] 2019-12-29 09:20:54

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