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Imagine this, a spherical planet with a spherical moon which spherically orbits the planet every 24 hours. On this planet is a rail system with a camera attached which points perpendicular to the planet, straight at the moons centre of mass, at all times. The moon, like ours, has a rotational orbit that means one side is always facing the planet. Following so far?

There's a person on the moon with a light emitter that they activate every hour. The camera (which is always pointing at the spot where the person is) has a clock attached to it and it records every time it sees the light being emitted.

If the time between the cameras logs changes then since the moon is constantly rotating at the same distance, the speed of light is different depending on direction. If the logs show the same result then no matter where the moon is in its orbit, the light takes the same amount of time to cover the constant distance between the moon and its planet proving that light travels the same speed in all directions.

I'm sure there's something I've missed but I'm wondering if this is possible proof?

As for time dilation, if the speed of the camera and moon is constant throughout the experiment then any potential influences would appear across all the results and not affect the proof.

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Theoretically an interesting experiment that in practice would be nearly impossible to implement in that the rail system would need to be on a perfectly spherical planet (or else engineered so that the rail system is perfectly spherical). Also, the idea of a moon in a perfectly spherical orbit around the planet is not something that typically occurs in nature. Also, this planet/moon system would need to be free of any other gravitational influences. That is, they could not be part of a larger solar system with a central star (sun) and other planets that would influence both the motion of the planet and the moon.

There is also a subtle difference between saying that the moon to planet distance is always a constant and a statement that the distance the light pulse traveled from its source to detection is always the same. The emission of the light pulse is an event (defined by three spatial dimensions and a temporal dimension). This is a fixed event, whereas the planet and moon may be drifting through space. This means the distance from source to detector is not guaranteed to be the same as the moon to planet distance.

So, an interesting thought experiment under ideal conditions, but there would be little interest in pursing this. In practice - it is physically not achievable and the Michelson-Morley experiment has already provided the proof to the constancy of the speed of light regardless of direction.

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  • $\begingroup$ Isnt discussing the feasibility of the experiment missing the point of it? I thought it is a thought experiment aiming to prove that it is "theoretically" possible to figure out if light is having different speeds in different directions. As opposed to the well known fact that it is theoretically impossible to do that. I think The feasibility of the actual implementation is irrelevant . The point is to figure out, why this setup would be "theoretically" impossible. $\endgroup$
    – silverrahul
    Commented Aug 19, 2021 at 7:02
  • $\begingroup$ I see your point that its impossible in reality since perfect spheres don't exist in nature, would it be possible to more feasibly replicate this with a pole (the longer the better) in space slowly spinning with the aforementioned camera at one end and light emitter at the other. The clocks wouldn't need to be synced this way and they don't even need to know the same time, they just need to count evenly. Then the same theory applies that if there's no change in the time between logs then it's all even and if there is then its not all even and there does indeed exist a light aether. $\endgroup$
    – Evorage
    Commented Aug 19, 2021 at 7:43
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It seems that what you are trying to do is replicate the Michelson–Morley experiment with much greater sophistication and accuracy. It really wouldn't be necessary to use a rail on the earth and a light on the moon. Satellites could very easily replicate what you are thinking, with just a bit of math thrown in to adjust for altitude, time dilation, etc. Quoting from wikipedia: "The experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The result was negative, in that Michelson and Morley found no significant difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles. This result is generally considered to be the first strong evidence against the then-prevalent aether theory, as well as initiating a line of research that eventually led to special relativity, which rules out a stationary aether."

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