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I just watched this Veritasium video, explaining the difficulty of measuring the one-way speed of light. The presenter explains that a round-trip will always average out to $c$ even if the speed in one direction isn't always the same as the speed in a different direction. He used the example of an astronaut on Mars synching his clock with Earth, and how different aberrations would still always make it end up looking like it was consistently $c$.

But the example of Mars got me thinking. Mars has two interesting properties: it's far enough away from Earth that there's a very noticeable time delay, and it's in a different orbit around the sun than we are, so its direction relative to us is constantly changing. So here's an experimental proposal that doesn't require any synchronization: Put a radio beacon on Mars that pulses in a regular, well-defined rhythm, then observe it from Earth for a Martian year or three.

No clock synchronization is necessary; just observe the rhythm. If the speed of light is not constant in all directions, this will create a Doppler effect in the pulses that can't be explained simply by the movement of the two planets. If no such Doppler distortion is detected, we can safely conclude that the speed of light is invariant in different directions. (Or at least in all the directions along the essentially 2-dimensional orbital plane of Sol.)

Is there anything that would cause this experiment to not produce correct results, if it were tried?

Qmechanic
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Mason Wheeler
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Is there anything that would cause this experiment to not produce correct results, if it were tried?

Reichenbach proved almost a century ago that there is simply no possible way to measure the one-way speed of light, regardless of your experimental design. The one way speed of light is simply a convention, the flip side of your synchronization convention. Like any convention, it can take any admissible value without changing any of the physics.

There is no way to measure a convention, you just choose it. It is not a matter of of making a clever experiment.

In your case, you forgot that if the speed of light is anisotropic then time dilation is also anisotropic. The two effects exactly cancel. So regardless of the one way speed of light the Doppler shift measurements will be the same.

Dale
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    I'm not sure I get you. Won't faraway stars look different if the speed was different in two directions? In the case of infinite speed you would see the stars as they are right now 9simultaneity). In the other direction as they were some time ago. a problem would arise if the universe was closed, in which case both directions (opposite) are the same. – Deschele Schilder Jun 01 '21 at 02:13
  • @DescheleSchilder But how would you know if you are seeing an "instantaneous" star or not? – BioPhysicist Jun 01 '21 at 02:34
  • @BioPhysicist You can't. But you could infer a difference in lightspeed by seeing different things. Assuming the universe is homogeneous. – Deschele Schilder Jun 01 '21 at 02:44
  • @DescheleSchilder That doesn't make sense. What "different things" would you see? – BioPhysicist Jun 01 '21 at 02:54
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    @BioPhysicist Young stars and old stars. – Deschele Schilder Jun 01 '21 at 02:59
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    @Deschele Schilder said “Won't faraway stars look different if the speed was different in two directions?” No, the laws of physics are covariant, so changing your synchronization convention cannot change any observable, but it does change the one way speed of light. What you see will not change regardless of your synchronization convention therefore it will not change regardless of the one way speed of light. – Dale Jun 01 '21 at 03:13
  • @DescheleSchilder That still doesn't make sense. The age of the star has nothing to do with the time it takes for you see it. If you see a "young star" you still won't know how long it look the light to reach you, and the same is true for the older star. You could have older instantaneously viewed stars and younger delayed view stars, but you could also have younger instantaneously viewed stars and older delayed view stars. – BioPhysicist Jun 01 '21 at 03:48
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    I always wonder why people are obsessed with this in the first place. Seriously, why do they care? What physical problem are they trying to solve? Or what "deficiency" in the current theories are they trying to fix? Or is this just a last desperate hope that "Einstein was wrong after all"? – m4r35n357 Jun 01 '21 at 08:59