A while back I posted some links to anti-relativity sites and gg suggested that it would be fun to debunk the claims. Sometimes that’s fun, but often — and especially after doing it a number of times — I find that it’s tedious. An error is present, and one has to find it in a morass of often awkwardly defined and unnecessarily complicated scenarios (hey, let’s use three trains, and multiple clocks which will be juggled by a clown on each train!) set up by the author. Sometimes with some horrific ASCII “art,” to boot, though some do have fancy animated gifs.
The reason one knows that an error is present in these thought experiments is because a contradiction has been found. One might think that this is a dogmatic BESS (Because Einstein Said So) argument, but it isn’t — the issue here is that the ultimate authority, and the only authority one is allowed to quote, is absent from the problem: nature. These are thought experiments, and it all boils down to doing coordinate transformations and calculations. Special relativity consists of Lorentz transformations, which are derived from the hypothesis that the speed of light is invariant; all inertial reference frames will measure the same value. This has the admittedly strange consequence (especially to the uninitiated) of time and length not being absolute quantities, which runs counter to most peoples’ everyday experience. We think in Galilean terms which serves us reasonably well in everyday experience, and the differences presented by Lorentz transformations are not apparent to us under these conditions.
But the Lorentz transformations are valid — one can use these to jump between reference frames ’till the cows (spherical or not) come home, and everything will be consistent as long as you apply the transform properly and do the math correctly. You can do this with any self-consistent set of rules. The reason we focus on this particular one is that it describes how nature behaves, and a comparison with nature, i.e. an actual experiment, is the only way to falsify the hypothesis that these transforms describe nature. A thought experiment that finds a contradiction has only shown that the transforms have not been properly applied — the author has made a math error, or made a bad assumption (e.g. absolute simultaneity, or used an accelerating frame of reference or that a non-Lorentz transformation holds somewhere)
If you’re learning about relativity, or want to brush up on it, such an exercise might be very useful. You know the needle is there, and you just have to go through the haystack and find it. But don’t be fooled into thinking that the three-train scenario with the clowns juggling clocks actually can falsify relativity until you actually do the experiment.