lecture02 - Relativistic Kinematics Lecture II General...

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Relativistic Kinematics Lecture II General Relativity (PHY 6938), Fall 2007 Copyright © 2007 by Christopher Beetle
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future-directed¡time-like past-directed¡time-like future-directed light-like space-like past-directed light-like Structure of Minkowski Space • There are five kinds of vectors in Minkowski spacetime: • space-like • time-like • and light-like. • Time-like and light-like vectors can be either • future-directed • or past-directed. x 2 > 0 x 2 < 0 x 2 = 0 t x > 0 t x < 0 x 2 := - c 2 t 2 x + | x | 2
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future-directed¡time-like past-directed¡time-like future-directed light-like space-like past-directed light-like Structure of Minkowski Space • There are five kinds of vectors in Minkowski spacetime: • space-like • time-like • and light-like. • Time-like and light-like vectors can be either • future-directed • or past-directed. x 2 > 0 x 2 < 0 x 2 = 0 t x > 0 t x < 0 x 2 := - c 2 t 2 x + | x | 2 t = γ ( t - v · x/c 2 ) | v · x | | v | | x | < vc | t x | < c 2 | t x |
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future-directed¡time-like past-directed¡time-like future-directed light-like space-like past-directed light-like Structure of Minkowski Space • There are five kinds of vectors in Minkowski spacetime: • space-like • time-like • and light-like. • Time-like and light-like vectors can be either • future-directed • or past-directed. x 2 > 0 x 2 < 0 x 2 = 0 t x > 0 t x < 0 x 2 := - c 2 t 2 x + | x | 2 t = γ ( t - v · x/c 2 ) | v · x | | v | | x | < vc | t x | < c 2 | t x | Causal
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Kinematical Effects
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Length Contraction An inertial observer O carries a ruler of length L 0 at speed v past an inertial observer O . How long does O measure it to be? A B C D t t x x
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x 1 = L 0 = γ ( x 1 - vt ) Length Contraction An inertial observer O carries a ruler of length L 0 at speed v past an inertial observer O .
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