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.
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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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