I Why measure the speed of light in one direction?

[James Hasty]

TL;DR Summary

It may be shown from the Maxwell Equations for electromagnetism that the speed of light is a constant regardless of the motion of the observer. So why bother trying to measure the speed of light in one direction?

It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) .
This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.

 

[Ibix]

You can construct Maxwell's equations in non-orthogonal coordinates if you like. Then you'll get a non-isotropic speed. As always, this has no effect on any physical measurement.

 

[Dale]

In general, you like to try to validate your theories against experiment. However, in this case the one way speed of light is a convention that you choose and not a fact of nature that you measure.