I One-Way Speed of Light: Is it Possible?

[PeterDonis]

we're debating whether or not, when measuring the round-trip speed, the light travels a different speed in on the going leg direction of the journey than it does on the return leg direction of the journey

No, we're not. For a round-trip speed measurement, you do not have to assume anything about the one-way speed of light.

We are not "debating" anything here. We are continuing to tell you that for a one-way measurement, doing it the way you are describing (the way Roemer did it), you do have to assume something about the one-way speed of light--that it is isotropic.

 

[PeterDonis]

Doesn't the fact that Roemer got repeatable results over dozens of tests that including dozens of different directional parameters argue against your claim that his experiment includes an assumption..."

Not at all. It just shows that he used the same assumption every time.

 

[PeterDonis]

Thread closed for moderation.

 

[Dale]

After discussion among the mentors, we will leave this thread closed. In closing, I wanted to briefly summarize a small part of the existing literature on this topic for @Eclipse Chaser

Using Anderson's convention, the metric in 1+1D flat spacetime is $$ds^2=-c^2 \ dt^2 + dx^2 - 2c\kappa \ dx dt - \kappa^2 \ dx^2$$ Here, $\kappa$ is a factor that describes the assumed asymmetry in the one-way speed of light. The speed of light in the $+x$ direction is $c/(1-\kappa)$ and the speed of light in the $-x$ direction is $c/(1+\kappa)$. Isotropic one-way speed is $\kappa=0$.

This gives a time dilation factor of $$\lambda = \left( 1- \frac{v^2}{c^2} +2 \kappa \frac{v}{c} + \kappa \frac{v^2}{c^2} \right)^{-1/2}$$ a series expansion to second order for small $v$ gives $$\lambda \approx 1 - \kappa \frac{v}{c} + \left( \frac{1}{2} + \kappa^2 \right)\frac{v^2}{c^2} $$ Notice that relativistic time dilation is a first order effect for $\kappa \ne 0$. Meaning that the assumption that

Earth's orbital speed is about 67,000 MPH = 0.0001C, hardly sufficient for relativistic effects to slow down a timer.

already implicitly assumes $\kappa=0$.

A measurement that would attempt to measure the one way speed of light cannot assume $\kappa$. The measurement itself must be sensitive to $\kappa$. No such measurement exists, for reasons described in detail in Anderson's paper above.

Romer did not know anything about time dilation, so he unknowingly assumed that there was no time dilation and thereby assumed $\kappa=0$. So his measurements were a measurement of $c$, not $c/(1\pm \kappa)$.