Time Isotropy, Lorentz Transformation and Inertial Frames

TL;DR

This paper demonstrates that time isotropy, or time-reversal symmetry, is a necessary explicit assumption for deriving Lorentz transformations, and it restores symmetry between space and time in special relativity.

Contribution

It reveals that time isotropy is independent of other relativity postulates and must be explicitly assumed to derive Lorentz transformations.

Findings

Lorentz transformations require explicit time isotropy assumption.

Time isotropy restores space-time symmetry in relativity.

Inclusion of time isotropy refines the definition of inertial frames.

Abstract

Homogeneity of space and time, spatial isotropy, principle of relativity and the existence of a finite speed limit (or its variants) are commonly believed to be the only axioms required for developing the special theory of relativity (Lorentz transformations). In this paper it is shown, however, that Lorentz transformation cannot actually be derived without the explicit assumption of time isotropy (time-reversal symmetry) which is logically independent of the other postulates of relativity. Postulating time isotropy also restores the symmetry between space and time in the postulates of relativity. Inertial frames are defined in influential texts as frames having space-time homogeneity and spatial isotropy only. Inclusion of time isotropy in that definition is also suggested.