Why measure the speed of light in one direction?

[James Hasty]

TL;DR

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.

 

[Sagittarius A-Star]

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?

You could write Maxwell's equations in the following primed coordinates (given any inertial coordinate system x,y,z,t).
$$x' = x \ \ \ \ \ y' = y \ \ \ \ \ z' = z \ \ \ \ \ t' = t + \frac{kx}{c}$$Source:
https://www.mathpages.com/home/kmath229/kmath229.htm

Then the one-way (cordinate-)speed of light will be anisotropic in $\pm x'$ direction.

 

[James Hasty]

My viewpoint is that for all inertial observers with Minkowski coordinates, Maxwell's equations posit the speed of light to be isotropic. But YES, I agree with your comments. Thank you.

 

[Sagittarius A-Star]

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.

That's not completely correct. Before Einstein, when the physically relevant coordinate transformation was thought to be the GT, Maxwell's theory was thought to be strictly true in only one inertial frame - that of still ether.

Source: Chapter "6.1 Transformation of the Field Vectors" in W. Rindler "Essential Relativity".
https://www.amazon.com/-/de/dp/3540100903?tag=pfamazon01-20

According to SR, Maxwell's equations are strictly true in each inertial frame.

 

[Sagittarius A-Star]

My viewpoint is that for all inertial observers with Minkowski coordinates, Maxwell's equations posit the speed of light to be isotropic.

This must be true, because the definition of such coordinates is based on the Einstein clock synchronization, that means on the definition, that the one-way speed of light is the same in opposite directions.

 

[Herman Trivilino]

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.

Not without experimental verification.

So why bother trying to measure the speed of light in one direction?

Because it wouldn't provide that verification.