A Constructive Derivation of the One-Way speed of Light

Iyer, Chandru and Prabhu, G. M. (2008) A Constructive Derivation of the One-Way speed of Light. Technical Report 08-08, Computer Science, Iowa State University.

Abstract

Under a universal synchronization of clocks, the two-way speed of light being a constant is explained by the Lorentz length contraction and time dilation. We revisit the derivation of length contraction and time dilation based on the following two premises: (1) There exists a frame of reference where the speed of light is c in each and every direction, and (2) the two-way speed of light is c in every frame of reference. Continuing from there, we derive a formula for the speed of light in a moving frame in any arbitrary direction, assuming that the rest frame is isotropic and the Lorentz length contraction and time dilation apply to a moving frame. This formula maintains the Michelson-Morley experimental result that the average round-trip speed of light will be constant in an arbitrary round-trip path. Even though the speed of propagation of light in the moving frame was derived constructively through some complex considerations, the formulae in terms of the proper angle in the rest frame as well as in terms of the proper angle in the moving frame turned out to be simple. The well known resynchronization formula immediately restores equivalence of the frames.