What is used to define an inertial frame in special relativity? Do I need to take one of the postulates as defining an inertial frame? What is bothering me is that I used to use Newton\'s first law to define inertial frames (a freely moving object will have a constant velocity). This can not be the definition in SR because I could use the galilean transformations and Newton\'s first law would still hold (yet these are not inertial frames according to SR). So how do you define an inertial frame in SR?
An inertial frame in SR is the same as in Newtonian mechanics: the frame of reference of an observer who is experiencing no external force (dp/dt=0). AM
Specifying a freely moving observer only specifies one point (an origin if you will), but not an entire coordinate system. So unfortunately, that does not answer the question. As I explained above, there are an infinite number of coordinate systems in which Newton\'s first law is true, yet the coordinate system is not an inertial one. You merely picked one of these freely moving points. If Newton\'s first law is not sufficient to define an inertial frame, definitely picking just one point will not be. The more I think about it, I believe the answer is: an inertial frame in SR is defined by the Minkowski metric. Which in essence means the second postulate of SR is used to define an inertial frame. Is this correct? Or are there other ways of looking at it?