Can we determine the one way speed of light by combined measurements?

[Ibix]

are you measuring the one way speed of light then?

No, I'd say it's a two way measure. You can run the light either way round it, which might be misleading you, but you could do the same with a triangular trip (still a two way measure) in flat spacetime. All the flexibility here is in how you define space, which is usually glossed over in SR because you can always choose a flat plane.

 

[HansH]

No, I'd say it's a two way measure. You can run the light either way round it, which might be misleading you, but you could do the same with a triangular trip (still a two way measure) in flat spacetime. All the flexibility here is in how you define space, which is usually glossed over in SR because you can always choose a flat plane.

I would assume the difference between the 2 is that with the triangular trip in flat space you change the direction of the light 3 times therefore using more directions in space. But in the other case you do not change the direction of the light by some mechanical means. so if you say it is the same, then I am again lost.

 

[HansH]

As an aside, “direction” is a slippery concept in spacetime - you may be giving it more weight that it deserves.

talking about one way speed of light it first requires to understand what 'direction' actually means. so at that point I am already lost. I would assume direction means what a light beam does always keeping the same direction (in vacuum) following a geodesic. so I think this reqires an explanation 1 level deeper about what direction actually is.

 

[HansH]

Hopefully this graphic helps.

actually I do not understand what you plot there. do you send lightbeams in a different direction? but how does that fit into the circular ring of light at 1.5 times the Schwarzschild radius? or do you do something else?

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[Dale]

but how does that fit into the circular ring of light at 1.5 times the Schwarzschild radius?

$\theta$ is the angular position around the ring. It is a spacetime diagram around the ring. The two plots show the same loop of light under two different synchronization conventions. Both are compatible with the same observation but they disagree about the one way speed of light.

 

[Nugatory]

talking about one way speed of light it first requires to understand what 'direction' actually means.

We’re doing a one-way measurement of the speed of light if we’re looking at the time it takes for light to travel along a path from the starting point to a different endpoint.
We’re doing a two-way measurement if we’re looking at the time it takes for light to travel a path that takes the light on a round trip back to the starting point.

Stated this way, we don’t need to understand what ‘direction’ actually means.

 

[Ibix]

I would assume the difference between the 2 is that with the triangular trip in flat space you change the direction of the light 3 times therefore using more directions in space. But in the other case you do not change the direction of the light by some mechanical means. so if you say it is the same, then I am again lost.

I would say that if this is confusing you, don't worry about it. By introducing curved spacetime you are adding a lot of complications that aren't really relevant to your original problem.

Fundamentally, the problem with the one way speed of light in flat spacetime boils down to the fact that you cannot synchronise clocks that are not in the same place without assuming a speed of light. If you have a method that only uses one clock then it's a two-way measure, however you construct the details. The same is true in curved spacetime, except there are added complications around what you mean by distance that mean that you won't necessarily find your speed of light to be constant over a long path (google Shapiro delay - one interpretation is in terms of a variable speed of light) although all local two way measurements along the path will show it to be $c$.

Ultimately, this kind of thing is why physicists don't care about the one way speed of light. It's just a consequence of the relativity of simultaneity, and understanding that is a help in curved spacetime. The only lesson to take from the one-way speed of light is that Newtonian physics isn't the same as relativity.

talking about one way speed of light it first requires to understand what 'direction' actually means

The problem is that "direction in spacetime" is well-defined but "direction in space" (and hence "velocity through space") depends on your definition of "space". You (whether you know it or not) want One True Division of spacetime into space and time, as there is in Newtonian physics. That is why one-way speeds are measurable in Newtonian physics. But relativity does not work that way - dividing spacetime into space and time can be done in many ways and one way speeds (of everything, not just light) depend on that choice.