chap11 - The Special Theory of Relativity Albert...

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Unformatted text preview: The Special Theory of Relativity Albert Einstein (1879 - 1955) November 9, 2001 Contents 1 Einstein’s Two Postulates 1 1.1 Galilean Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The difficulty with Galilean Invariance . . . . . . . . . . . . . . . . . 4 2 Simultaneity, Separation, Causality, and the Light Cone 6 2.1 Simultaneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Separation and Causality . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The Light Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 The invariance of Separation . . . . . . . . . . . . . . . . . . . . . . . 10 3 Proper time 11 3.1 Proper Time of an Oscillating Clock . . . . . . . . . . . . . . . . . . 13 4 Lorentz Transformations 14 4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.3 Elapsed Proper Time Revisited . . . . . . . . . . . . . . . . . . . . . 17 4.4 Proper Length and Length Contraction . . . . . . . . . . . . . . . . . 18 1 5 Transformation of Velocities 20 5.1 Aberration of Starlight . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6 Doppler Shift 23 6.1 Stellar Red Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 7 Four-tensors and all that 27 7.1 The Metric Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 7.2 Differential Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 8 Representation of the Lorentz transformation 35 9 Covariance of Electrodynamics 40 9.1 Transformations of Source and Fields . . . . . . . . . . . . . . . . . . 40 9.1.1 ρ and J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 9.1.2 Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 9.1.3 Fields, Field-Strength Tensor . . . . . . . . . . . . . . . . . . 43 9.2 Invariance of Maxwell Equations . . . . . . . . . . . . . . . . . . . . . 45 10 Transformation of the electromagnetic field 46 10.1 Fields Due to a Point Charge . . . . . . . . . . . . . . . . . . . . . . 48 In this chapter we depart temporarily from the study of electromagnetism to ex- plore Einstein’s special theory of relativity. One reason for doing so is that Maxwell’s field equations are inconsistent with the tenets of “classical” or “Galilean” relativity. After developing the special theory, we will apply it to both particle kinematics and electromagnetism and will find that Maxwell’s equations are completely consistent with the requirements of the special theory....
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This note was uploaded on 01/08/2012 for the course PHYSICS 707 taught by Professor Electrodynamics during the Fall '11 term at LSU.

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chap11 - The Special Theory of Relativity Albert...

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