Lecture1-2

O spacelike if 0 o cmelike if 0 o invariant under

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Unformatted text preview: posiCve. u༇  Now transform to a system moving with a velocity –v along the x direcCon, so that the signs of the velociCes will add u༇  Get perpendicular velocity component transformaCon too. 35 Example: Parallel Velocity AddiCon u༇  A starship moving at a velocity of 0.9c directly toward the earth ﬁres a missile which is moving at 0.5c (in the starship frame of reference) directly toward the earth. What is the velocity of the missile in the earth’s frame? =(0.9+0.5)c/(1+(0.5)(0.9))) =1.4c/1.45=0.966c 36 RelaCvisCc Doppler Eﬀect Part A, Time DilaCon of Emission u༇ The beginning of a wave cycle is emioed at x=y=t=0. u༇ The end of the cycle is emioed from x=y=0 but one period τ of the wave later. u༇ Transform to a frame moving in the x direcCon. 37 RelaCvisCc Doppler Eﬀect Part B, Transverse Doppler Eﬀect u༇  If the observer is some large distance away in the y direcCon and near x=0, we have the transverse Doppler eﬀect. u༇  The travel Cme of the beginning and end of the wave are essenCally the same, so o  τ’=γτ o  f’=f/γ 38 RelaCvisCc Doppler Eﬀect Part C, Parallel Doppler Eﬀect u༇  u༇  u༇  u༇  If the source is moving directly toward or directly away from the observer, we have the parallel Doppler eﬀect. The transit Cme for the light coming from the beginning and the end of the wave is diﬀerent due to the diﬀerence in emission locaCon in the K’ frame. We compute for the source moving away from the observer. In the K’ system, the source is at negaCve x when the end of the wave is emioed. for source moving away call that negaCve relaCve velocity 39 General Doppler Formulas u༇ Call relaCve velocity posiCve if source and observer are moving away each other (red shi^). o  β negaCve for moCon toward (blue shi^) u༇ Transverse Doppler eﬀect doesn’t depend on sign of β. 40 QuesCon: Michelson Morley u༇  Which of the following statements is false? A) MM compares the speed of light in perpendicular directions. B) MM should have detected the ether had it existed. C) MM used the interference of light waves. D) MM clearly proved the theory of Special Relativity. E) None of the above. 41 Example: Velocity of a Galaxy from Red- shi^ u༇ Hot stars in a distant galaxy emit a conCnuous spectrum of light. u༇ We see narrow absor...
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This note was uploaded on 02/24/2014 for the course PHYS 2D taught by Professor Hirsch during the Winter '08 term at UCSD.

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