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From my (basic) understanding the biggest problem of measuring the speed of light is clock synchronization. But I question why this is necessary. To be more specific, what if, instead of measuring absolute time, you measure relative time and use that to determine the relative speed.

More concretely, have 2 vacuum tubes 1km long with an emitter on one side and a detector on the other. One tube will have light and the other could be anything, but for the example, I'll propose sound. Now, we emit from both emitters at the same time and the receivers measure the difference in time between receiving the signal from the light and the signal from the sound. Knowing the distance, the speed of sound, and the relative time difference should be enough to compute the speed of light. Right?

To be more mathematical:

c = speed of light in 1 direction
vo = the known speed of the thing traveling in the other tube
dt = the difference in time measured between the tubes at the end
d = distance of the tube
to = the time taken for the thing to travel in the other tube
tl = the time taken for light to travel down its tube

It should then follow that:

to = d/vo
tl = to - dt
c = tl / d

If there is some issue with sound, we could use a metallic ball which rolls at a known (or calculable) speed as well, right? If for some reason that doesnt work, couldnt we slow down light to a known speed and race that?

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  • $\begingroup$ How do you synchronize the clocks in the first place? $\endgroup$ Oct 8 at 0:58
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    $\begingroup$ You never need to synchronize, thats the point. The start just emits both at the same time and the end uses a single clock to measure the difference in time between the two receivers. $\endgroup$
    – chacham15
    Oct 8 at 0:59
  • $\begingroup$ How will the clock at the end know the start time? $\endgroup$ Oct 8 at 1:15
  • $\begingroup$ @BioPhysicist I've added a mathematical explanation, does that clear the question up? $\endgroup$
    – chacham15
    Oct 8 at 1:28
  • $\begingroup$ Why the downvotes? I thought it was a good question... $\endgroup$
    – chacham15
    Oct 8 at 1:30
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Determining the one way speed of sound runs into similar problems to the one way speed of light -- you still need to define a synchronization convention. And really, that's not a problem: there's a perfectly good synchronization convention (the Einstein one, equivalent to slow clock transport) that you can use.

The main thing is that the one way speed of light (really, the invariant speed of causality, $c$) is a matter of definition, precisely because it depends on how you synchronize clocks. You can define it to be almost anything you want, as long as it gives the answer $c$ for the round trip value. But there's no reason to define it to be anything other than the same in every direction, and that is how working physicists do so.

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The reason why this setup doesn't work has little to do with clocks and a lot to do with anything to do with the one-way speed of light being a nonsense question. No disrespect to the OP - it's not a dumb question, just a meaningless one.

Define $c$, not as the arbitrary speed at which something called a photon happens to travel, but as the speed of causal influence. A beam of light is an oscillating magnetic field that induces an oscillating electric field that induces an oscillating magnetic field and so on. $c$ is the speed at which that induction transpires, so we would infer that a quantum of light - the propagation front at which the electric field and magnetic field are turning into each other - should travel at $c$.

All causal influence propagates at $c$. If we model the universe as consisting of particles that emit force fields, when the particle moves, for that movement to causally influence something else, the change in its force field's shape needs to reach another particle. The propagation front of the change in the force field travels at $c$, the speed of causal influence.

Macroscopic processes are the gestalts of countless fundamental particle interactions, and macroscopic objects are just macroscopic processes that keep more or less the same character over the time period of a human attention span.

So, if you make c faster in one direction, everything you can measure is proportionately faster in that direction... including the sequence of fundamental interactions that makes up a meter stick or whatever else you want to use to measure distance. The end result is that a universe in which $c$ varies is indistinguishable from a universe in which $c$ is a constant.

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Your proposed experiment faces practical difficulties and a theoretical one.

Practically, light will travel 1km in a few microseconds. This means that whatever effect you use to trigger the timer at the other end- for example, your rolling metal ball- would have to have a speed that could be reliably measured with sufficient precision that the uncertainty in its travel time was significantly less than a few micro seconds. I doubt that a rolling ball would satisfy the necessary requirements. As for sound- it doesn't travel in a vacuum tube. You would also have to measure the length of the tube with great precision.

The theoretical difficulty you would face is that you could not be sure that the speed of your trigger effect was independent of direction. Suppose you decided to trigger the timer by accelerating an electron to a calculable speed and sending it down a 1km long vacuum tube. The acceleration would be brought about by electromagnetic effects, which themselves propagate at the speed of light, so how could you be sure that the electron was definitely accelerated to the right speed (unless, of course, you timed its speed, but that leads you back to the clock synchronisation problem)? You also could not be sure that the length of the vacuum tube- which is determined by electromagnetic interactions between its constituent atoms- did not vary minutely depending upon its orientation owing to the difference in the speed of light from one direction to another.

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