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I just came across this problem that I didn't even know existed, how to measure the speed of light in the universe in a specific, given direction with respect to the universe or "in one way/direction only". Found it from here: https://www.youtube.com/watch?v=pTn6Ewhb27k

Anyway, to briefly state the problem, hypothetically apparently $c$ could be different in different directions with respect to say... whatever, any point really. And it could vary by as much as up to 1/2 the current accepted standard for $c$ in a given direction, as long as it goes infinitely fast in the exact opposite direction, as all attempts to measure it average each other out to $c$. Seems daft I know, surely there must be a way to tie some other fundamental constant(s) into knowing it exactly without regard to preferential direction. But it still seems to be an unsolved measurement problem as according to the above there's no known way of measuring it exactly.

Well after giving it a think last night I do believe I've come up with a way. It's dead simple and while it doesn't measure the speed of light "one way" it could be used to determine if the speed of light differed/had a preferred direction.

It only involves a pair of clocks, a beam splitter, and some mirrors. Generate a light pulse and start a clock from point A, send it off into a square pattern with mirrors, however just before returning the light back to A on the last turn use a beam splitter instead of a mirror to send the light to clock B. A will measure the light pulse returning at the speed of C no matter what, but B will return a different time if C has a preferential direction. Now here's the subtle bit, you can flip the entire device 180 degrees and if the preferential direction remains the same, you get a precise measurement of the preferential speed in the exact same way, and directly relative and predictable in comparison to the measurement of clock B pointing in the opposite way. All arguments about moving the clocks to cause time dilation or etc. are nullified, the measurements are only relative to each other and can only possibly be changed by you pointing the apparatus in a different direction.

To make it clearer here's a diagram showing the most extreme possible case, C being 1/2c in one direction and infinite in another:

Measuring preferential C direction

And that's it, spin the thing on a table and run the experiment. Do it in space to see if that makes a difference. Maybe there's something wrong with my setup, could easily be. Point it out if so by all means. And I don't personally doubt anything would come of it even if the setup is valid and given a go. Ok maybe there'd be some nagging uncertainty if it was fantastically sensitive due to some niggling quantum gravity effects, if it could be made sensitive enough for that somehow. But otherwise I'd be surprised at results other than "$c = c$ in all directions".

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    $\begingroup$ You still have two clocks in your system and you have not given any mention to how you plan to synchronize them. If the speed of light was different in different directions as per your example, and you synchronized the two clocks while they were next to each other, then the very act of bringing the two clocks apart and over to their positions in the setup would make it so that "synchronous time" for the two different clocks would take into account the difference in light speed making it again an unmeasurable quantity. $\endgroup$ – Vinzent Nov 2 '20 at 9:48
  • $\begingroup$ The fact that we cannot measure if light travels faster in one direction than in another is much more fundamental. Imagine that you live on a grid, you can only be on any one of the squares in the grid, now if the length of one of the dimensions of the grid was changed, how would you measure it?. Or imagine that you are a picture, and now you are asked to measure the resolution (x*y) of the screen that you are being displayed on.. $\endgroup$ – Vinzent Nov 2 '20 at 9:56
  • $\begingroup$ You can sync the clocks just fine after moving the apparatus. Any effect of different C directional speed will still affect it, but only proportionally to the speed and not as much as the total difference itself, so you can still measure it. The question is also not if the universe somehow "contracts" or "expands" without you noticing somehow, the problem specifically states, and includes, the possibility of exactly cancelling opposite directions, which this solves, among other things. $\endgroup$ – Sora Thompson Nov 3 '20 at 4:21
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How do you synchronize these clocks?

You can't just not synchronize them. Otherwise the yellow one will receive its light pulse at time 546456873242 and the green one will receive its light pulse at time 4673462131 and you don't get any useful information (subtracting these numbers only tells you the clocks aren't synchronized).

Here's how you might synchronize two clocks: you make one of them send out a pulse when it's time 100, and when the other one receives the pulse, it sets its time to 100, and then you adjust the second one by adding the speed-of-light delay. (so if they're 2 light-seconds apart then you make the second clock say 102 when it gets the pulse)

Consider the top diagram for example. Here's how you sync the clocks: The yellow one sends out a pulse at time 100, and it travels down and right to the green one, with a total delay of 1, but you think the delay is 2. The green one receives the pulse and sets the time to 102 when the yellow one says 101.

Now you wait until the yellow clock says 200 and run the experiment. The light takes 3 time to get to the green clock and 4 time to get to the yellow clock, so the yellow one notes 204 and the green one also notes 204. The clocks tell you that they received the pulse at the same time (204). You do not discover the speed-of-light difference.

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