According to the first postulate of Special Relativity, all the laws of physics are symmetrical in all inertial frames. So that also means that Maxwell's equations are true in any such frame (experimentally verified). Now we can easily uncouple the four first-order differential equations in free...
So my next question is, can we assume that Newton's Third Law is still valid for interacting objects in any frame to test whether it is actually an inertial frame or not, that is, the first two laws of Newton hold or not?
Is Newton's third law valid in non-inertial frames? For example, in a rotating frame of reference, can Newton's third law still be applied? Or does the non-inertial character of the frame violate it?