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I am having a hard time grasping the idea that one-way speed of light is immeasurable. I have watched several videos (including the Veritasium one), read the Wikipedia article, and read some questions on Stack Exchange and no one seems to proposed this exact setup that seems the most obvious way to do it to me. Can someone please point out what I'm missing here?

If I am equidistant from the source light as from the mirror light, then I KNOW how far away each light is, correct? Therefore, there seems to be two possibilities:

  • The light takes the SAME time to travel both equidistant directions

OR

  • The light takes DIFFERENT times to travel each equidistant direction

To test this first question, I can simply change the orientation of the source, mirror, and detector (the distances remaining the same between them each time) and run the experiment multiple times. If the time between the detector receiving photons from both light sources is THE SAME for every orientation in a complete sphere then I can conclude:

  • The light travels the same speed when traveling the same distance regardless of direction (This only indicates light travels the same speed TOWARDS me, but it may be a different speed AWAY from me.)

OR

  • The distortion between the two distances is coupled somehow (i.e. one shortens exactly as the other lengthens) If THIS was true, then changing the angles between the vectors (i.e. changing the height of the isosceles triangle) should produce different results because it is changing two directions but not the direction between source and mirror.

If the latter case is true then we have proven light travels different speeds in different directions and that opens a whole can of worms. (Probably not the case.)

However, if the first case is true then we have a way to measure the one-way speed of light because we can now simply subtract both travel times from the light traveling from the source as from the mirror and get a one-way speed of light between the source and mirror. (It doesn't matter that the towards and away times might still be different.)

Basic equation:

[(time observer sees reflection from mirror) - (travel time from mirror to observer)] - [(time observer sees source) - (travel time from source to observer ] = (travel time from source to mirror)

(t_om - t_mo) - (t_os - t_so) = t_om - t_os = t_sm

When  t_so = t_mo

s = source,     m = mirror,     o = observer/detector

Once you have the travel time from the source to the mirror, simply measure the distance from the source to the mirror and you have your one-way speed!

What am I missing?

(See diagram of setup below.)

One-way light speed setup

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  • $\begingroup$ Not sure, thus making it a comment not an answer. SO and MO have components (considering them to be vectors) along the direction of SM. These components have opposite sign and thus possibly different velocities and you are back at the initial problem. $\endgroup$
    – Hartmut Braun
    Jun 16, 2021 at 8:51
  • $\begingroup$ If you travel from Paris to London then the local time on arrival is only a little more than the local time where you set out. If you travel in the other direction then there is a bigger time difference. It is no use measuring speeds to detect this effect. It is merely a result of the convention of setting clocks in different countries. The "one way speed of light" idea is the same; it has been mis-named. $\endgroup$
    – Andrew Steane
    Jun 16, 2021 at 9:10

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The problem here is simply "time observer sees light". What time do they record? The time on their watch? Those can't be guaranteed to be synchronized due to relativity.

The extent to which you can synchronize clocks this is possible, a few methods are outlined here: https://en.wikipedia.org/wiki/One-way_speed_of_light#The_one-way_speed

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  • $\begingroup$ Yes, the observer would simply use whatever time measuring device they have to record the time the light from the source reaches them and the mirror reaches them. If the source is a pulse, the observer could simply use a light sensor which records the timestamp. $\endgroup$
    – JDUdall
    Jun 16, 2021 at 17:15
  • $\begingroup$ Why do you say we need to "synchronize" any other clock? We are doing a "one-way" measurement so we are using just the observers clock. We measure the arrival time between two pulses of light from the source and the mirror (which are coupled together by reflection). The distance to each light source is the same, so the travel time can be ignored (if c is same in both directions), OR the arrival time delta would change with different orientations if c travels at different speeds in different directions. Correct? $\endgroup$
    – JDUdall
    Jun 16, 2021 at 17:21
  • $\begingroup$ I don't understand how the travel from Paris to London is relevant here. None of the inertial frames are moving relative to each other. $\endgroup$
    – JDUdall
    Jun 16, 2021 at 17:23
  • $\begingroup$ @JDUdall how do you intend to measure "time from source to mirror" and "time from source to observer" without 3 clocks? With 1 clock all you can measure is time of arrival of each photon. $\endgroup$
    – Señor O
    Jun 16, 2021 at 18:32
  • $\begingroup$ @ Señor O, please see the equation: (t_om - t_mo) - (t_os - t_so) = t_om - t_os = t_sm Because we know the length of so and mo, and so = mo, we know that if c is constant the travel time for both would be equal and can therefore be negated. Therefore, the delta t between observing the signal and observing the mirror will equal the travel time from the signal to the mirror. We can test if c is constant in all directions by re-orienting the setup and conducting the experiment over and over again. We can also change the length of SM and re-run experiment to detect any change in travel time. $\endgroup$
    – JDUdall
    Jun 16, 2021 at 19:23

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