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I have read the following (here) by Stephen J. Crothers:

Einstein’s Special Theory of Relativity requires systems of clock-synchronised stationary observers and the Lorentz Transformation. Without both, the Theory of Relativity fails. A system of clock-synchronised stationary observers is proven inconsistent with the Lorentz Transformation, because it is Galilean. The Special Theory of Relativity insists that Galilean systems must transform not by the Galilean Transformation, but by the non-Galilean Lorentz Transformation. The Theory of Relativity is therefore invalid due to an intrinsic logical contradiction.

I'm not so are that I can follow this reasoning. Why is it said that "A system of clock-synchronized stationary observers is proven inconsistent with the Lorentz transformation"?

I thought the words were written by W. Engelhardt (retired). I saw this article, from his hand. Upon further googling his name I stumbled upon the words above. Of which I logically thought that it was written by Engelhardt. Does Engelhard hold the same attitude towards SR or does his article, called "Instantaneous Interaction between Charged Particles" (referring to instantaneous quasi-static fields in classical electrodynamics), respect SR? In other words, is the article mainstream? Engelhardt seems a respected (and retired) professor who worked at the Max-Planck-Institut für Plasmaphysik in Germany.

Or does this just show that classical electrodynamics is incompatible with Special Relativity?

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    $\begingroup$ physics.stackexchange.com/q/80465 $\endgroup$
    – jng224
    Commented May 15, 2021 at 11:42
  • $\begingroup$ @Jonas Ah, the same guy. I thought that what I cited above was written by W. Engelhardt. I found what was written above after further googling his name. Initially, I stumbled upon this (by Engelhardt): arxiv.org/pdf/physics/0511172.pdf Is this (though highly mathematical) written with a same attitude towards SR? $\endgroup$
    – Deschele Schilder
    Commented May 15, 2021 at 12:02

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Any claim that Special Relativity is logically inconsistent may safely be ignored. Relativity has been studied for over a century by tens of thousands of physicists and mathematicians. Some of those mathematicians include Kurt Goedel (possibly the greatest logician of all time!), David Hilbert, and Emmy Noether; the physicists include people like Richard Feynmann and Stephen Hawking. How likely is it that some random individual on the internet has found a glaring logical inconsistency overlooked by all of these people? (Answer: they haven't.)

This is not to say that special relativity must be absolutely true, just that it is logically consistent. Its actual truth or falsity may only be established by experiment. So far experiments support it extremely well.

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