Question

Probiem 12.19 The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity: e tanh(u/c). (12.34)

Answer 1

(c) Given that - Velocity V = 4/5 C then Lorentz matrix -lambda = (r -r beta -beta r r) r = 1/squareroot 1 - v^2/c^2, beta = v/c = 4/5 r = 1/squareroot 1 - (4/5)^2 = 5/3 -r beta = -5/3 middot 4/5 = -4/3 lambda = (5/3 -4/3 -4/3 5/3) = (5/3 -4/3 -4/3 5/3) As we know that - r = 1/squareroot 1 - v^2/c^2 = cos h theta + r beta = v/c/squareroot 1 - v^2/c^2 = sin h theta cos h theta = 5/3, sin h theta = 4/3 \r\n tan h theta = sin h theta/cos h theta = 4/3/5/3 = 4/5 rapidity theta = tan h^-1 (4/5) = tan^-1 (v/c) given that particle moving in s system in x direction with velocity U_x = 3/5 c then velocity in s^bar frame of U_x^bar By Einstein velocity addition law - U_x^bar = U_x - v/1 - U_x v/c^2 = 3/5 c - 4/5 c/1 - 12/25 U_x^bar = -1/5 c/13/25