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This question is inspired by a recent video by Veritasium Why no one has measured the speed of light linked below.

To summarize the video, Derek points out that it is impossible to measure the one-way speed of light, and shows examples of what the consequences of a preferential direction for the speed of light might be.

While the examples given of the measurement problem and consequences all appear valid on local scales, they seem to me to fall apart when you look at the scale of the observable universe. Wouldn't we be able to observe the effects of a preferential direction to the speed of light at cosmological scales? Take the extreme case: the speed of light in one direction is 1/2c and infinite in the opposite direction. If this was true, we should be able to observe the entire universe in the direction where light is approaching us at infinite speed, and see no redshift due to the expansion of the universe (because the photons would reach us instantaneously, there would be no time for the expansion of the universe to stretch them out). Even in less extreme cases, we should still see "more" universe and less redshift in one direction than its opposite.

Since we don't (to my knowledge) observe any difference in the "quantity" of universe (for lack of a better term, feel free to edit if there is a better term for this) in any direction, or any difference in the amount of redshift in any direction, then if there exists a preferential direction to the speed of light, it must be small enough that its effects lie within the error bars for our ability to measure the universe on cosmic scales.

Is my reasoning correct here, or is there some effect I did not take into account that would adjust things so we wouldn't see any difference? (or perhaps my understanding of cosmology is entirely flawed?)

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    $\begingroup$ We also have several fresh questions about this on the Physics stack, eg physics.stackexchange.com/q/590790/123208 $\endgroup$ – PM 2Ring Nov 1 '20 at 0:06
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    $\begingroup$ I just read that question and its answers, and while it is related, I don't think it is a duplicate question, and its answers do not address the specifics of my question. $\endgroup$ – asgallant Nov 1 '20 at 2:13
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    $\begingroup$ Don't worry, we can't close questions as duplicates of questions on other Stack Exchange sites. ;) OTOH, we do often close questions here if they are pure physics with little relevance to astronomy. However, this question has been historically important in astronomy, going back to the determination of the speed of light by Ole Rømer in 1676, using the eclipse data of the Jovian moon Io. So I feel that this question is appropriate on this site. $\endgroup$ – PM 2Ring Nov 1 '20 at 8:58
  • $\begingroup$ I suppose I ought to add that link to the material by John D. Norton on this issue: pitt.edu/~jdnorton/teaching/HPS_0410/chapters/… Hans Reichenbach discusses it extensively in The Philosophy of Space and Time. $\endgroup$ – PM 2Ring Nov 1 '20 at 9:17
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Prior to Einstein's 1905 paper, the Lorentz transformation had already been worked out by Lorentz and others. Only their interpretation of it was lacking. They still clung to the idea that there was a Newtonian absolute time, and the times in the Lorentz transform were only apparent times. Einstein was the first to realize that there doesn't need to be a Newtonian time; the Lorentz transform stands perfectly well on its own.

The guy in this video is thinking the same way as Einstein's predecessors; he's an aetherist, though he doesn't realize it. He's stuck to the idea that there's a real time with respect to which the true speed of light is defined, but various "effects" prevent any experiment from actually determining what it is. This is most obvious starting from 11:32, where he says he wants to show how differently the universe works if light is anisotropic, but then shows that it works exactly the same in every experimentally measurable way.

The reality is that only what is operationally measurable matters. What we mean when we say that the speed of light is constant is that there exist coordinates with respect to which it's constant. In a Newtonian corpuscular world, no such coordinates would exist, so the fact that they do exist in the real world is physically meaningful. It's not necessary to use these isotropic coordinates, but it's frequently convenient. That's the only reason we use them. To put it another way, the Einstein synchronization convention really is a convention; it isn't an assumption.

There also exist coordinates with respect to which the speed of light isn't constant. This is not physically meaningful, because no theory could ever avoid them; you can always do a formal substitution of variables, as long as it's invertible and you're consistent about it. The result of any experiment in these coordinates is always the transformation of the result of the experiment in inertial coordinates, because they both describe the same reality.

If $(x,t)$ are standard inertial coordinates, then with respect to coordinates $(x,t')$ where $t'=t-x$, the speed of light $|dx/dt'|$ ranges from $c/2$ to $\infty$ depending on direction. Why don't we see this as an anisotropy in the sky? Because the universe in different directions has aged by different amounts, and their ages differ by just the right amount to compensate for the different light travel times. This is similar to the way that length contraction, the relativity of simultaneity, and so forth always conspire to make things consistent in different inertial frames.

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