There’s a postulate in special relativity as following: Physics laws are identical in all inertial reference frames.
I’m a math student, recently when I reviewed special relativity before learning general relativity, I ran into this question which I cast aside long time ago. Here’s my question: what does the physics law mean in the statement? For example, relativity is a physics law as well, would it fail in a non-inertial reference frame as the statement suggests? There’s another example, Newton’s Law $F=ma$, it can be applied in both inertial and non-inertial frame in elementary physics. What’s wrong? What exactly does the statement suggest? Is there any precise mathematical description?