[ben_w]

I've heard it claimed that we can only measure the round-trip speed of light, not the one-way speed of light, because the maths says that reality would look identical if it was 0.5c in the x+ direction and ∞ in the x- direction.

I find this hard to stomach, but I'm going to trust it also applies to e.g. magnetism being Lorenz transformed electric fields, because relativity violates "common sense" all over the place and reality doesn't care about my stomach.

https://www.youtube.com/watch?app=desktop&v=pTn6Ewhb27k&them...

[AnimalMuppet]

I also have heard that, multiple times. I don't buy it. I think there are at least two experiments that could show the difference.

First, you could time the travel of light from one place to another. To do that, you need synchronized clocks. The easy way to do that is to start with clocks synchronized at a central point, then very slowly move them from the central point to the endpoints. Why very slowly? Because you have to worry about time dilation with the clocks. For small v, the difference in the rate of time is approximately v^2/2c^2 (to first order). The amount of time you have to maintain it is t = d/v. The corresponding difference in clock time still approaches zero as v approaches zero, so in principle, the clocks can be arbitrarily close to each other in time if you just move them slowly enough.

But what if c has different values in opposite directions? Well, then time dilates different amounts for the clocks going in opposite directions, but the amount of time dilation for each clock still approaches zero if the velocity is low enough.

Second: If you have a cyclotron or synchrotron, with charged particles moving in a circle in a magnetic field, and those charged particles are moving a significant fraction of the speed of light, if the speed of light is not uniform, their motion should deviate from a circle. Why? Because the force on them due to the magnetic field should be the same, but the acceleration should be different depending on what fraction of the speed of light they're moving. (Due to increased mass, if you think of it that way. If you don't, well, the equation doesn't change.)

I think that some experiments would fail to show a non-uniform speed of light, but I think experiments could be devised that would show it.

[Dylan16807]

Unfortunately, if the one-way speed of light is anisotropic, the correct time dilation factor becomes 1/(γ(1−κv/c)), with the anisotropy parameter κ between -1 and +1.[17] This introduces a new linear term, meaning time dilation can no longer be ignored at small velocities, and slow clock-transport will fail to detect this anisotropy. Thus it is equivalent to Einstein synchronization.

https://en.wikipedia.org/wiki/One-way_speed_of_light

A lot of scientists have thought about this. Step one is checking their work.

[AnimalMuppet]

Ah, I see.

I see nothing there that would invalidate my synchrotron argument, though.

[Dylan16807]

If you apply the more detailed equation I bet it says the mass doesn't change, so there is no change around the circle to measure.

I'm sure someone has thought of an experiment that simple. If you can't find anything close enough you can ask on one of the stack exchanges.

[AnimalMuppet]

Well, the equation says that, unlike in newtonian physics, there's a gamma times the mass in the force equation. You can think of that as "the mass changing from the rest mass", or you can think of the mass as being constant and the gamma just being an additional factor, but either way, the gamma is still there.

Before I looked at stack exchange, I thought of another, much simpler experiment. Generate plane wave radio waves of a frequency such that the nominal wavelength would be meters or tens of meters. (By "nominal wavelength", I mean the wavelength l=c/f, the wavelength as if the speed of light were the same both directions.) Run those plane waves into a reflector a couple of nominal wavelengths away. Measure the RF energy at various points along the path to the reflector. Does it look like a standing wave of the expected wavelength, or not?

I actually saw that idea on the discussion I found on stack exchange. The only reply I saw was "well, the relationship between wavelength and frequency might not hold if the speed of light is asymmetrical", which seemed very weak to me. What, we have waves propagating with velocity v, but wavelength l =/= v/f? How can you do that without destroying the continuity of the wave? How much of physics is that going to destroy? And, how many "well, maybe..." items are you willing to stack up to make it impossible to detect your first "well, maybe"?

I didn't leave a question on stack exchange. The discussion was nine years old.