Q:

Are Lorentz transformations a fundamental law?

I've seen derivations of Lorentz transformation but are they really derivations or are we just teasing out the formula using some special cases and then assuming it to be valid for all the cases.
Is this really a derivation as in the mathematical sense or are Lorentz transformations a law in themselves apart from conservation of the spacetime metric.
By Lorentz transformation, I mean the relation between space and time 'intervals' for two inertial observers.

A:

This is dangerously close to being a matter of opinion, but for what it's worth I would regard the Lorentz transformations as a special case rather than anything fundamental.
The fundamental principle in special relativity is the invariance of the proper time, which is presumably what you mean by conservation of the spacetime metric. The Lorentz transformations give you the coordinate transformations for the special case of relative motion at constant velocity. However in any system where the velocity is changing the Lorentz transformations don't apply.
In the past this has lead to the common claim that special relativity doesn't apply to accelerating systems. This is of course nonsense as the invariance of the proper time can be used to describe motion in a circle or accelerated motion in a straight line, or indeed any arbitrarily accelerated motion.
My point is that the Lorentz transformations describe only a subset of the motions that can be described using special relativity, and therefore they can't be a fundamental law.

