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My understanding of what's said in the Veritasium video Why no one has measured the speed of light suggests that the one-way speed of light has not been measured and that it being isotropic has not been experimentally verified.

Wouldn't passing a pulsed beam through two identical but widely separated population inversions (e.g. lasers, masers) or for that matter beamsplitters allow a distant observer to immediately determine the one-way speed of the pulsed beam?

Granted each interception interacts with the beam and adds a phase delay, but that can be independently determined or simply subtracted by performing this using several separation distances.

screen shot from Veritasium's Why no one has measured the speed of light

Screenshot from the video further modified to illustrate two "cartoon lasers" pumped and ready to be stimulated by the beam passing through so that they can radiate towards us.

procedure: The beam under test is "in the page" and the observer is perpendicularly out of the page i.e. "towards us" at a much greater distance, approaching infinity. Observer has a stopwatch, times the difference between the two observed pulses of recombination radiation and divides the separation between the two devices by that time.

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Every experiment that we've ever performed is consistent with isotropic propagation of light, and yours would be too. To the extent that science can ever know anything, we do know that the propagation of light is isotropic, and your experiment would confirm it.

This is about the fifth question about the new Veritasium video that I've seen on this site today, so I finally watched it. It's pretty cranky. That the one-way speed of light has never been measured is in fact a common claim of aether-theory cranks, and the argument in the Veritasium video is the same that they use.

The argument amounts to the following: given inertial coordinates $(x,t)$ with respect to which the speed of light is constant ($|dx/dt| = c$), you can always define, say, $t'=t-x$, and with respect to those coordinates the speed of light $|dx/dt'|$ ranges from $c/2$ to $\infty$ depending on direction. That's the entire content of the video's claim that the light from Mars might "really" be traveling infinitely fast to Earth. It's purely a formal substitution of variables and there's no physical meaning to the different speeds.

The description of your experiment in nonisotropic coordinates depends on the particular coordinates that you choose. With respect to the $(x,t')$ coordinates above, the explanation is that the angle from the two lasers to the viewer is different, and so the speed of light along the two paths is different, and this together with the speed of the light between the lasers gives you exactly the same delay you'd get in the inertial coordinates. You could specify the experiment more precisely and go into more detail but it's really just a matter of substituting $t'+x$ for $t$.

The sensible way to look at it is the other way around: the fact that there exist any coordinate systems with respect to which the speed of light is constant is what we mean when we say the speed of light is constant. In principle we could live in a world in which there are no such coordinate systems (even locally), and in that world we wouldn't say that light speed is constant. Likewise, rotational symmetry means there exists a transformation of all of the fields that preserves the physics under rotation. It would make no sense to say that because there are also transformations that don't work, that we don't really know that the world is rotationally symmetric. That's what Veritasium is saying.

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  • $\begingroup$ The fact that the synchronisation of the lasers would be a synchronisation of the clocks is exactly the point; if the speed of light varies based on direction, then time dilation would obscure the difference in the clocks and make the one-way speed of light appear to be c when it actually isn’t. $\endgroup$
    – nick012000
    Nov 1, 2020 at 3:37
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    $\begingroup$ I was hoping that "a distant observer" implied the limit as it goes to infinity so that the angles would both be 90 degrees to the beam to be measured, but after reading this I'm thinking that my "towards us" proposed method cheats by sneaking in the inevitable transverse displacement. The two beams still have to meet at the same observer location. This doesn't do what I was hoping it would do. Thanks for the edit and +1! $\endgroup$
    – uhoh
    Nov 1, 2020 at 4:32
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    $\begingroup$ The weird thing about the Veritasium video is that while he is talking about Lorentz invariance he doesn't actually mention Lorentz invariance. It's clear that Derek feels he is on to something important, and he wants to make his mark. But he doesn't have the full picture. The proper way to present this subject is to start with Lorentz invariance, and then go through the ramifications of Lorentz invarience, including the implification that a Lorentz Aether theory with universal Lorentz invariance is observationally indistinguishable from SR . $\endgroup$
    – Cleonis
    Nov 1, 2020 at 5:11
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    $\begingroup$ @uhoh I concur. As you state: the two beams still have to meet at the same observer location. Hence not perfectly parallel, hence non-zero transversal displacement. You can represent that as a Pythagoras theorem triangle. The Minkowski metric fits the same pythagorean triplets as pythagoras' theorem. Thus - as a matter of principle - no experiment can be devised to have access to the one-way speed of light $\endgroup$
    – Cleonis
    Nov 1, 2020 at 5:23

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