Relativistic Addition and Group Theory
نویسنده
چکیده
For three particles P,Q,R travelling on a straight line, let vPQ be the (relative) velocity of P as measured by Q, and define vQR, vPR similarly. According to classical mechanics, the velocity v of a particle moving on a line can be any real number, and relative velocities add by the simple formula vPR = vPQ + vQR. On the other hand, the special theory of relativity says velocities are restricted to a bounded range, −c < v < c, where c is the speed of light (whose value of course depends on the choice of units, and it is convenient to choose them so c = 1, but we won’t do that.) The relativistic addition formula for velocities is:
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