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lecture_5

# lecture_5 - Looking at a Moving Clock Consider a flashing...

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Looking at a Moving Clock Consider a flashing clock (i.e. one that emits a flash of light every time it ticks). When at rest it ticks every t seconds. You are watching this flashing clock through a telescope as it moves away from you at a velocity v. According to you it ticks every seconds. What time elapses between your observations of successive ticks? Answer: you observe a tick once every t 1 - v 2 c 2 t 1 - v 2 c 2 + 1 c v t 1 - v 2 c 2 = tc + vt c 1 - v 2 c 2 = t (1 + v c ) 1 - v 2 c 2 = t 1 + v c 1 - v c seconds

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FLASHING  CLOCK Time between clock ticks (s) Time between OBSERVATIONS (s) Rest frame t t Moving away from observer Moving towards observer t 1 - β 2 1 + β 1 - β t t 1 - β 2 1 - β 1 + β t
Flashing Clock Time between clock ticks (s) Time between OBSERVATIONS (s) Rest frame t t Moving away from observer Moving towards observer t 1 - β 2 1 + β 1 - β t t 1 - β 2 1 - β 1 + β t Source in rest frame that emits pulses with a frequency f 0 = N pulses/s : Source Observed frequency ( f ) Rest frame f = f 0 Moving away from observer Moving towards observer f = 1 - β 1 + β f 0 f = 1 + β 1 - β f 0 This is known as the Relativistic Doppler Effect

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Manifestations of the Doppler Effect Red shift of distant galaxies (Edwin Hubble, Hubble’s law , Hubble telescope). Expanding Universe (Big-Bang) Astronomy: Venus rotates in the opposite direction of Earth. Radar Laser Cooling
A physicist brought to court for running a red light argues that the light looked green and thus must have been Doppler shifted. The judge changes the charge to speeding and fines the physicist a

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lecture_5 - Looking at a Moving Clock Consider a flashing...

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