Inertial Frames and Newtonian Mechanics

The theory of special relativity deals with the description of physical phenomena in frames that move at constant velocity relative to each other. The classroom is one such frame, the car passing at constant speed outside the classroom is another. The trajectory of a ball being thrown up vertically in the car will look quite different whether we describe it relative to the interior of the car or relative to the interior of the classroom. In particular we will be concerned with inertial frames. We define an inertial frame as a frame where spatial relations are Euclidean and where there is a universal time such that free particles move with constant velocities. 

In classical Newtonian mechanics, relations between the spatial parameters and time in two inertial frames S and S are expressed in terms of the Galilean transformations. Assume that S is moving with constant speed v in the direction of the positive x axis of S. If the coordinate axes of S are parallel to those of S, the Galilean coordinate transformations are 

We will not follow the historical development, but proceed straight to the resolution of these difficulties. The solution was provided by Albert Einstein in 1905, and may be cast in the form of the two postulates of special relativity  

Postulate 1. The laws of physics are identical in all inertial frames. 

Postulate 2. In empty space light signals propagate in straight lines with speed c 

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