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Unformatted text preview: /2 1+v tanh log 1-v 1 - [(1 - v)/(1 + v)] n 1 + [(1 - v)/(1 + v)]
n n (22) (b) As n , [(1 - v)/(1 + v)] 0 and vn 1, the speed of light. Properties of the tanh(x) function have not been used. 4 Jackson (a) The time for round trip is tround trip = 2L/v (b) The time taken for the tachyon to reach the observer is tout = L/v. The speed of the tachyon(s) sent by the moving observer in reply, as measured in the rest frame of the transmitter, is obtained by using the velocity naively, vback = Thus, tback = L Hence, ttotal = = = u-v 1 - uv c2 (u - v) 1 - uv/c2 (23) (24) tout + tback L (1 - uv/c2 ) +L v u-v 2u - v 1 + u2 /c2 L u(u - v) (25) (c) The required condition is t < 0, 2u - v(1 + u2 /c2 ) v < > 0 2u 1 + u2 /c2 (26) 5...
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- Fall '09
- CSAKI, C