Another approach to the Lorentz Transformations. Relativists often use a quantit

Question

Another approach to the Lorentz Transformations. Relativists often use a quantity called rapidity to describe the frame transformations. It is related to the speed factor ? by ? = f(R), where f is a hyperbolic function. The reason for using rapidity is that it is additive across reference frames. That is to say, if a particle has rapidity R in the unprimed frame, rapidity R? in the primed frame, and Rv is the rapidity of the primed frame to the unprimed frame, then

R = R? + Rv. Using this fact, the velocity addition formula, and the addition formulas for hyperbolic functions, determine the function f(R).

Explanation / Answer

f = f(0) sqrt(1-?^2)

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