General Galilean Transformations and Boosts

We now exploit the relativity (in the sense of Galilei) of Newton s laws for the determination of the most general Galilean transformations. Newtonian physics crucially relies on the concept of absolute time the time difference df between two events is the same in all inertial frames. The time shown by a clock is in particular independent of the state of motion of the clock. As a consequence the most general relation between the time f in IS and the time f in IS is given by 

As a direct consequence of Eq. (2.15) we find the general Galilean formula for the transformation of velocities. 

The discussion in this book will mostly be restricted to very special Galilean transformations for which the relative velocity v in x-direction between IS and 

It is accompanied by the simple Galilean formula for the addition of velocities, Jt = X — V, which is a special case of Eq. (2.16) for vanishing rotation of the two inertial frames. 

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