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As a kind of empirical debunking of some of the things that Crothers says in the video referenced, I would offer the following link, https://www.physlink.com/Education/AskExperts/ae433.cfm, with the key paragraph there stating that:
“In October 1971, Hafele and Keating flew cesium-beam atomic clocks, initially synchronized with the atomic clock at the US Naval Observatory in Washington, D.C., around the world both eastward and westward. After each flight, they compared the time on the clocks in the aircraft to the time on the clock at the Observatory. Their experimental data agreed within error to the predicted effects of time dilation. Of course, the effects were quite small since the planes were flying nowhere near the speed of light. ”

Now. bearing in mind that the above described verification of Einstein’s Special Relativity no doubt takes into account Einstein’s concept of synchronized systems of time keeping, plus* also* being no doubt based on Lorentz transformation as a basic principle, try to make sense then , of Crowther’s statements! The claim that he is making (both on a visual slide about 36 minutes into the video, as well as spoken by Crowther) is to say that “Einstein’s Clock Synchronization is Inconsistent With the Lorentz Transformation” – ?

As an ‘aside’ here, I note that I’ve read interesting things before, about alternative ways to look at or reassess Special Relativity. It is a matter of history, for instance, that Lorentz himself challenged what is usually called “Lorentz Invariance”, suggesting in discussions with Einstein that there might be a privileged “luminiferous ether-like special motion framework after all! In a similar spirit, later on, in 1959, the American physicist Tangherlini did his doctoral thesis on an advanced refinement of Lorentz’s “privileged framework” idea. In Tangherlini’s way of doing things, the whole concept of time dilation is handled somewhat differently compared to Einstein’s original treatment. Apparently, some people see practical benefits from this, such as making experimental results like the times recorded by atomic clocks on airplanes more intuitive to understand.

Now having mentioned that there might be a “clock tracking” benefit to such an “alternative” to Einstein, I had better cut right to the chase by also mentioning the well known fact that in particle accelerators particles travelling near the speed of light tend to “live longer” than a stationary particle (owing to the effect of relativistic time dilation). The advantage of Dr. Tangherlini’s approach to accounting for timings, is that if one wants, one can easily take the Earth as such to be a “privileged” system (at least approximately for some short period of time), while at the same time, we could look at an accelerated particle as “truly moving”. One then gets to regard time as being really “stretched out” or dilated for the moving particle in the accelerator. It is then intuitive to say that the particle would live longer or not decay so quickly, as being a truly fast moving object *under those particular assumptions*. In contrast, it is actually more difficult, in strictly “Einstein” terms, to visualize why the particle lives longer, since in Einstein’s original thesis, time is never really regarded as “stretched”. In “original” Einstein theory, everything has to be accounted for as being due to the particle going through different clock synchronizations as it whips around a circle (i.e., it is just conceptually more difficult, if you really want to do things the original “authentic Einstein” way). So it seems there *is* something to be said for certain alternative ways of developing relativity theory, and maybe this is what Crowther was reaching for in his video?

In any case, there is quite a difference between looking at clock synchronizations a *different way*, versus taking the Crowther approach of saying that “Clock Synchronization is Inconsistent” in Einstein’s theories! I am reminded of the time that someone told me that rocket motors obviously couldn’t work, since a rocket motor could obviously never throw enough stuff backward to make a huge spacecraft accelerate forward! In Crowther’s view, it seems that you can never really synchronize anyone’s clocks, since well, you just *can’t*, that’s why! I mean, back in 1971, someone really should have told Hafele and Keating that they were wasting their time trying to synchronize their atomic clocks? After all, Crowther’s view of Einstein’s work says that synchronizing is impossible?