MP09SpecialRelativity3

# - CHAPTER 2 Special Theory of Relativity 3 2.1 The Need for Aether 2.2 The Michelson-Morley Experiment 2.3 Einsteins Postulates 2.4 The Lorentz

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2.1 The Need for Aether 2.2 The Michelson-Morley Experiment 2.3 Einstein’s Postulates 2.4 The Lorentz Transformation 2.5 Time Dilation and Length Contraction 2.6 Addition of Velocities 2.7 Experimental Verification 2.8 Twin Paradox 2.9 Space-time 2.10 Doppler Effect 2.11 Relativistic Momentum 2.12 Relativistic Energy 2.13 Computations in Modern Physics 2.14 Electromagnetism and Relativity CHAPTER 2 Special Theory of Relativity 3 Albert Einstein (1879-1955) If you are out to describe the truth, leave elegance to the tailor. The most incomprehen- sible thing about the world is that it is at all comprehensible. - Albert Einstein

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2.10: The Doppler Effect A similar change in sound frequency occurs when the source is fixed and the receiver is moving. But the formula depends on whether the source or receiver is moving. The Doppler effect in sound violates the principle of relativity because there is in fact a special frame for sound waves. Sound waves depend on media such as air, water, or a steel plate in order to propagate. Of course, light does not! Christian Andreas Doppler (1803-1853) The Doppler effect for sound yields an increased sound frequency as a source such as a train (with whistle blowing) approaches a receiver and a decreased frequency as the source recedes.
Waves from a source at rest Viewers at rest everywhere see the waves with their appropriate frequency and wavelength.

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Recall th e D o p p l er Effect A receding source yields a red-shifted wave, and an approaching source yields a blue-shifted wave. A source passing by emits blue- then red- shifted waves.
The Relativistic Doppler Effect So what happens when we throw in Relativity? Consider a source of light (for example, a star) in system K receding from a receiver (an astronomer) in system K with a relative velocity v . Suppose that (in the observer frame) the source emits N waves during the time interval T ( T 0 in the source frame). In the observer frame: Because the speed of light is always c and the source is moving with velocity v , the total distance between the front and rear of the wave transmitted during the time interval T is: Length of wave train = cT + v T cT v T

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The Relativistic Doppler Effect Because there are N waves, the wavelength is given by: And the resulting frequency is: v cT T N v c cN cT T  In the source frame: and 0 / TT Thus: 00 NT 22 0 [ ( / )] 1 1 v / v 1 v/ cT c cT T c c  0 1 v / 1 v / c c Use a + sign for v/ c when the source and receiver are receding from each other and a – sign when they’re approaching. 0 (1 v / )(1 v / ) (1 v / )(1 v / ) cc   So: Source frame is proper time.
Using the Doppler shift to sense rotation The Doppler shift has a zillion uses.

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v K v K 2.11: Relativistic Momentum Because physicists believe that the conservation of momentum is fundamental, we begin by considering collisions without external forces: Frank is at rest in K and throws a ball of mass m in the - y -direction. Mary (in the moving system) similarly throws a ball in system K that’s moving in the x direction with velocity v with respect to system K.
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## This note was uploaded on 05/14/2010 for the course EAD 234 taught by Professor Ncl during the Spring '10 term at École Normale Supérieure.

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- CHAPTER 2 Special Theory of Relativity 3 2.1 The Need for Aether 2.2 The Michelson-Morley Experiment 2.3 Einsteins Postulates 2.4 The Lorentz

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