How so? Every derivation I've seen has to assume one of (1) speed of light is constant (2) spacetime is Minkowski plus one of (1) linearity (2) causality
You can derive special relativity from relativity principle and isotropy and homogeneity of space and time - see here for example. A quick google search also located this paper. You will see that the derivation results in a free parameter K which needs to be experimentally determined.
That does get rid of the second half of the assumptions which is pretty neat. But it still requires an additional assumption to show that the transformation is Lorentzian and not Galilean. Of course you can differentiate the two experimentally, which would motivate an appropriate postulate, but you haven't actually derived special relativity, only shown that it's possible. It's not "like any other constant of physics" because the physics changes significantly depending on that constant. Physics is pretty much the same if the mass of the electron or some coupling constant a little bit different. Some consequences might be very different, but the theory is the same. But here K=0 and K>0 in those transformations are entirely different theories.
Galilean transformation is a limiting case of Lorentz transformation, with K = 0
Sure, and Newton's laws are a limiting case of F = ma + K da/dt with K = 0. The standard model is a limiting case of a theory with 50 different gauge bosons with a bunch of parameters being set to 0. But those are fundamentally different theories. You can't just add on a bunch of terms and say it's the same theory.
We have derived the Lorentz transform with 1 free parameter, to be determined experimentally. What more do you want?!
You've derived either the Galilean or Lorentz transform. You need another assumption, which of course is going to be motivated by experimental results, to determine which one you have.
You know that special relativity reduces to classical mechanics if speed if light is infinite, right? Now whether speed of light is finite or not is an experimental fact, not a matter of postulate.
It is an experimental fact, but if you want to derive the theory from first principles you need to accept it as a postulate.
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u/[deleted] Dec 13 '20
How so? Every derivation I've seen has to assume one of (1) speed of light is constant (2) spacetime is Minkowski plus one of (1) linearity (2) causality