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Unformatted text preview: of the astronaut as measured by Earth can increase arbitrarily due to time dilation. 2a Since E = mc 2 / ± 1v 2 c 2 ² 1 / 2 , if E is to remain ﬁnite as m → 0, then v must approach c . Thus, a massless particle must travel at the speed of light. E  p  = c 2  u   u  = c E = pc 2b K ≡ EE K = ( γ1) mc 2 γ = ³ 1u 2 c 2 ´1 / 2 γ ≈ 1 + 1 2 u 2 c 2 + ··· K ≈ ³ 1 + 1 2 u 2 c 21 ´ mc 2 K = 1 2 mu 2 2c 1 dx = γ ( dxvdt ) dt = γ ± dtv c 2 dx ² u x ≡ dx dt u x ≡ dx dt u x = u xv 1u x v c 2 if v ± c this reduces to u x = u xv 3 Use conservation of energy. The energy of the initial particle is Mc 2 . The energy of each of the 2 photons is pc From conservation of momentum, the photons must be traveling in opposite directions. Mc 2 = 2 pc p = 1 2 Mc 2...
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 Spring '10
 SINHA
 Special Relativity, inertial reference frames, 2 photons, dx ux dt, ux dt ux, ux dt dx

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