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

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
Waves from a source at rest Viewers at rest everywhere see the waves with their appropriate frequency and wavelength.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 6
Using the Doppler shift to sense rotation The Doppler shift has a zillion uses.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 31

- 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

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online