[Physics] Time dilation derivation of special relativity


In almost all of the derivations using the postulates of special relativity (SR), we use experiments involving light signals. For example, we make a clock using a light signal or measure lengths using light signals, etc. The reason for doing this is never stated. Why do we do this?

Aren't there any other thought experiments that could help us achieve the expressions for time dilation and length contractions without using light signals?

Is it even possible to derive expressions for the Lorentz transformation without using experiments involving light signals in some form?

Please don't start off with space-time metric. I want to know if such a thing can be done using the two postulates given by Einstein.

Best Answer

Einstein's two postulates of special relativity are:

1) The laws of physics are the same in all inertial frames of reference

2) Light propagating through empty space always appears to go at the same velocity, $c$.

The expressions we're trying to derive from these postulates, eg. the Lorentz transformations, or time dilation all have that constant $c$ in them, so we're going to have to somehow use postulate 2 (where else could that number come from?). But all that postulate 2 tells us is about beams of light travelling through empty space, so we're necessarily going to have to think about that to derive the rest of special relativity.

Alternative derivations do exist, but usually using Maxwell's equations or some other electrodynamics (see Wikipedia on this).

It is possible to derive the Lorentz transformations using just the first postulate, but you have a constant (which is $c$) that needs to be empirically verified. However, this requires additional assumptions.

Ultimately I think the reason that SR is usually derived by thinking about light clocks and rulers is that is it the simplest way, and the easiest to understand since it all just follows from those two simple and fairly intuitive ideas.

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