MP08SpecialRelativity2

MP08SpecialRelativity2 - CHAPTER 2 Special Theory of...

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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 2 Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. Albert Einstein Albert Einstein (1879-1955)
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Gedanken (Thought) experiments It was impossible to achieve the kinds of speeds necessary to test his ideas (especially while working in the patent office…), so Einstein used Gedanken experiments or Thought experiments . Young Einstein
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22 v 1 v / xt x c 2 v/ 1 v / t x c t c yy zz The complete Lorentz Transformation If v << c , i.e., β ≈ 0 and ≈ 1, yielding the familiar Galilean transformation. Space and time are now linked, and the frame velocity cannot exceed c . v 1 v / x c 2 1 v / t x c t c Length contraction Simultaneity problems Time dilation
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Simultaneity Timing events occurring in different places can be tricky. Depending on how they’re measured, different events will be perceived in different orders by different observers. Due to the finite speed of light, the order in which these two events will be seen will depend on the observer’s position . The time intervals will be: Fred: 2 L/c ; Frank: 0 ; Fil: +2 L/c But this obvious position-related simultaneity problem disappears if Fred and Fil have synchronized watches . Frank Fil Fred 0 L -L
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Synchronized clocks in a frame It’s possible to synchronize clocks throughout space in each frame. This will prevent the position-dependent simultaneity problem in the previous slide. But there will still be simultaneity problems due to velocity .
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Simultaneity So all stationary observers in the explosions’ frame measure these events as simultaneous. What about moving ones? 0 L -L Compute the interval as seen by Mary using the Lorentz time transformation. 22 [ v / ] [v(2 ) / ] t t x c L c Mary experiences the explosion in front of her before the one behind her. And note that t is independent of Mary’s position! K Mary (v/ )(2 / ) 0! c L c
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2.5: Time Dilation and Length Contraction Time Dilation : Clocks in K run slowly with respect to stationary clocks in K. Length Contraction : Lengths in K contract with respect to the same lengths in stationary K. More very interesting consequences of the Lorentz Transformation:
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We must think about how we measure space and time. In order to measure an object’s length in space , we must measure its leftmost and rightmost points at the same time if it’s not at rest . If it’s not at rest, we must ask someone else to stop by and be there to help out.
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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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MP08SpecialRelativity2 - CHAPTER 2 Special Theory of...

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