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I know that the one-way speed of light cannot be measured due to clock synchronization. Knowing this, is it possible to place some kinds of maximum or minimum values on the one-way speed of light, and if so, what are they and why? From what I have seen the maximum could be instantaneous and the minimum could be $c/2$, but I saw no real math or reasons why these values were chosen.

Qmechanic
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Lonestar
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    Certain popular YouTube channels notwithstanding, one way speed of light is not a deep mystery of the universe that's hard to measure; it's one part an utterly meaningless concept that can't be measured because it has the logical quality of the flavor of the color six; and one part a value that need not be measured because it is defined into existence by an arbitrary choice of synchronization convention chosen for mathematical convenience. See the answers to multiple versions of this question on this site. – g s Apr 21 '22 at 22:19
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    @gs Off-topic, but imo certain YouTube channels should really have their own tags so one could theoretically filter them out. – noah Apr 21 '22 at 22:25
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    @noah We've (kind of) discussed that on meta: https://physics.meta.stackexchange.com/q/13917/123208 – PM 2Ring Apr 21 '22 at 23:49
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    The various one-way-speed-of-light / clock synchronisation conventions can be parameterised via Reichenbach's epsilon, with $0 \le \epsilon \le 1$, as explained here: https://physics.stackexchange.com/a/591436/123208 – PM 2Ring Apr 21 '22 at 23:56
  • we know the 2 way speed of light. the limitations you've stated (instant and c/2) are merely the extremal values which give this 2 way speed of light to be c – shai horowitz Apr 21 '22 at 22:14
  • This is more for an ongoing conversation with a creationist friend of mine. I took microwave engineering a long time ago, and knew there had to be a practical minimum. Thanks all! – Lonestar Apr 22 '22 at 13:35

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If we assume the one-way speed of light is different from the two-way speed of light, we must first pick a direction to analyse. We know that for any given direction in a vacuum, the two-way speed of light is $c$, which means for light to travel a distance $s$ away from us and back in that direction, it will take a time of $t=2s/c$.

You can see that if a round trip takes $t=2s/c$, then assuming the trips there and back take different amounts of time, the trip to travel a distance $s$ away from us cannot take longer than the total time to travel there and back, which is $t=2s/c$ as before. This is the slowest possible speed; if we rearrange the equation we get $$ c_{\mathrm{one-way,min}}=\frac{s}{t} = \frac{c}{2} $$

And if the light indeed took that long to reach the point at a distance $s$, all the available time $t=2s/c$ has already passed, so its trip back must be instantaneous. This is your upper limit (and also because we need causality; the light can't arrive back before it's been there).

noah
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