SR-2011-supplementery-notes

SR-2011-supplementer - School Of Mathematics Statistics and Operations Research Te Kura M¯ atai Tatauranga Rangahau P¯unaha MATH 321/322/323

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Unformatted text preview: School Of Mathematics, Statistics, and Operations Research Te Kura M¯ atai Tatauranga, Rangahau P¯unaha MATH 321/322/323 Applied Math (Special Relativity) T1 and T2 2011 Math 322: Applied Mathematics Supplementary Notes — Special Relativity module — Matt Visser School of Mathematics, Statistics, and Operations Research, Victoria University of Wellington, New Zealand. E-mail: [email protected] URL: http://www.mcs.vuw.ac.nz/˜visser Version of 23 February 2011; L A T E X-ed February 23, 2011 Warning: These notes are provided as a supplement to the textbook. This is a reading course, so the textbook, these notes, and various web resources should be your primary source of information. There are still a few rough edges: If you find errors, typos, and/or obscurities, please let me know. Contents 1 Einstein’s special relativity 6 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 SR is a Superb theory — “Never to be Discarded” . . . . . . . . . . . . . 7 1.3 Textual analysis: A warning . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Filtering out the nonsense . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.1 The two faces of physical theory . . . . . . . . . . . . . . . . . . . . 9 1.4.2 Rules based on mathematical consistency . . . . . . . . . . . . . . . 10 1.4.3 The Rough Guide to crackpot filtering . . . . . . . . . . . . . . . . 12 1.5 Last Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Notes on notation 15 3 Notes on the “light clock” 17 4 Notes on the Lorentz transformation 20 4.1 Step 0: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.2 Step 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3 Step 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 Step 3: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.5 Step 4: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.6 Step 5: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.7 Summary: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5 Notes on the combination of velocities 27 5.1 Derivation: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.2 Step 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Step 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.4 Comments: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.5 Non-collinear velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6 Notes on the twin pseudo-paradox 34 6.1 Analysis using the invariant interval: . . . . . . . . . . . . . . . . . . . . . 34 6.1.1 Step 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.1.2 Step 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2 Math 321/322/323: Special Relativity...
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This note was uploaded on 07/14/2011 for the course MATH 322 taught by Professor Matt during the Spring '11 term at Victoria Wellington.

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SR-2011-supplementer - School Of Mathematics Statistics and Operations Research Te Kura M¯ atai Tatauranga Rangahau P¯unaha MATH 321/322/323

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