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In a YouTube video, popphysicist "Veritasium" points out that the speed of light has never directly been measured, that is that it is experimentally impossible for two viewers at different points, A, B in space to synchronously start, and to stop, their stopwatches from the time that light is sent from point A to B. Rather, experimental confirmations of the speed of light have relied on mirroring light from point B so that the time measured is from A to B to A.

He goes on to posit a wild idea that time dilates and rarefracts going each way, so that $c$ is not constant depending on if the light is coming toward you versus away from you. I am not sure if any experimental evidence warrants this kind of conjecture. But couldn't this be easily dismissed by setting up a 3-way experiment with 2 mirrors and a single observer? He discusses a series of convoluted experiments to measure the one-way speed of light, such as the intermediary synchronizer.

I feel like I'm missing an obvious experiment. Referring to the A-B-A experiment of Hippolyte Fizeau in 1849, introduce a third point C not on the A-B path but no farther from A than C is. Direct mirrors from B to C, and then from C to A. Measure the travel time of light emitted from A to B to C to A. We should be able to calculate the total distance traveled, but the distance from- and to-observer remains conserved. Is it not the case that, if the one-way speed of light were not constant, then the A-B-C-A time would be somewhat less than the supposed speed of light multiplied by the path-length because the distance to and from the observer remains conserved?

EDIT: this question references the same video as this one but my question is different because it deals with the feasibility of experiments and knowledge of extant experiments on the topic to date. I am not asking whether the speed of light can be instantaneous. I am asking if a three observer experiment is conceptually different than a two observer experiment, and if this can prove or disprove the hypothesis about unequal lightspeeds.

Dale
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AdamO
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It is not possible to measure the one-way speed of light. In fact, with a suitable understanding of geometry, you can show that it doesn't matter if the speed of light is anisotropic (different in different directions): it is always physically identical to an isotropic lightspeed.

One such issue with measuring one-way lightspeed: the arrival of the photon at the detector, if it is not with you, will be spacelike-separated from you. You can never be able to tell if the photon has reached the detector or not, and thus how long it took to reach the detector, and thus how fast light is moving, if the detection event is not local to you. If you could, that would constitute being able to send the information about the detection along a spacelike curve, which would be equivalent in nature to time traveling, which is not possible.

Or, more simply put: for you to be able to have accurate information about how long the light beam took to hit the detector, wherever it is, you have to either

  1. be standing right next to the detector so that the interval between the detector's going-off and your recording of that information is zero; or

  2. be able to instantly know what's going on wherever the detector is, even if it's at a distance from you, which is FTL communication.

If you do the former, you have just set up a two-way speed of light experiment and failed to measure the one-way speed of light. If you do the latter (which you otherwise must; simply beaming the results to you from the detector won't work, because who's to say how fast that information will travel?), then you are violating causality.

Thus, on the reasonable assumption that causality is not violated, you cannot know the one-way speed of light.

Fortunately, it turns out not to be physically-meaningful anyways, so it hardly matters what it actually is. We just call it isotropic because that's what it looks like, and that's what it probably is. General relativity predicts an isotropic speed of light and is very simple and otherwise accurate; making it more complicated to try and predict something that literally can't be predicted is pointless.

controlgroup
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