Unformatted text preview: hagoras's theorem 2 2 t t c = d2 + v 2 2 1 2d t = (15) 2 /c2 c 1-v 3 d' v t1 (b) v t2 ct1 t1 Similarly, = = d + vt1 d c-v (16) d ct2 = d - vt2 t2 = v+c Using (16) and (17) we get tb = t1 + t2 = d (17) 1 1 2d 1 + = c-v c+v c 1 - v 2 /c2 (18) Suppose that the observer can "hear" the ticks but does not know the clock's orientation. Demand that the clock is not "pathological": ta = tb where a and b refer to the time between clicks when the clock is stationary, and moving respectively. Hence, (19) d = 1 - v 2 /c2 d 3 Carts on carts... Using the 1d velocity addition formula, vi+1 = vi + u ; c1 1 + vi u (20) Define i by vi = tanhi and by v = tanh. Then, tanh (i+1 ) = = tanh i + tanh 1 + tanh i tanh tanh (i + ) 4 (21) This implies i+1 = i + , v0 = 0 0 = 0. Thus n = n. Hence, vn = = = = tanh(n) tanh ntanh-1 (v) n...
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This note was uploaded on 04/26/2013 for the course PHYS 6561 taught by Professor Csaki, c during the Fall '09 term at Cornell.
- Fall '09
- CSAKI, C