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Special Relativity Special Relativity A Wikibook http://en.wikibooks.org/wiki/Special_relativity Second edition (2.1) Part 1: Introductory text Cover photo: The XX-34 BADGER explosion on April 18, 1953, as part of Operation Upshot-Knothole, at the Nevada Test Site. The photo is from the Department of Energy, Nevada Site Office's Photo Library - Atmospheric, specifically XX34.JPG. Alternative source: http://www.nv.doe.gov/library/photos/photodetails.aspx?ID=1048 Table of Contents Contributors.......................................................................................................................4 Introduction........................................................................................................................5 Historical Development............................................................................................5 Intended Audience....................................................................................................9 What's so special?.....................................................................................................9 Common Pitfalls in Relativity..................................................................................9 A Word about Wiki................................................................................................10 The principle of relativity................................................................................................11 Special relativity.....................................................................................................12 Frames of reference, events and transformations...................................................13 The postulates of special relativity..............................................................................15 Einstein's Relativity - the electrodynamic approach..............................................16 Inertial reference frames.............................................................................................19 The modern approach to special relativity.......................................................................22 Spacetime...............................................................................................................29 The lightcone..........................................................................................................30 The Lorentz transformation equations...................................................................31 A spacetime representation of the Lorentz Transformation...................................32 More about the relativity of simultaneity........................................................................33 The Andromeda paradox........................................................................................34 The nature of length contraction............................................................................36 More about time dilation........................................................................................37 The twin paradox....................................................................................................39 Jim and Bill's view of the journey..........................................................................43 The Pole-barn paradox...........................................................................................46 Evidence for length contraction, the field of an infinite straight current...............48 De Broglie waves...................................................................................................50 Bell's spaceship paradox.........................................................................................51 The transverse Doppler effect................................................................................53 Relativistic transformation of angles......................................................................53 Addition of velocities.............................................................................................54 Relativistic Dynamics......................................................................................................57 Momentum..................................................................................................................57 Force............................................................................................................................61 Energy.........................................................................................................................62 Derivation of relativistic energy using relativistic momentum..............................62 Derivation of relativistic energy using the concept of relativistic mass.................64 Nuclear Energy...........................................................................................................66 Light propagation and the aether.....................................................................................68 The aether drag hypothesis.........................................................................................68 The Michelson-Morley experiment............................................................................73 The experiments.....................................................................................................74 Fallout.....................................................................................................................77 Mathematical analysis of the Michelson Morley Experiment....................................79 Coherence length....................................................................................................82 Lorentz-Fitzgerald Contraction Hypothesis...........................................................82 Appendix 1.......................................................................................................................84 Mathematics of the Lorentz Transformation Equations.........................................84 Einstein's original approach...................................................................................87 1 License.............................................................................................................................90 GNU Free Documentation License.............................................................................90 0. PREAMBLE...........................................................................................................90 1. APPLICABILITY AND DEFINITIONS...............................................................90 2. VERBATIM COPYING.........................................................................................91 3. COPYING IN QUANTITY....................................................................................91 4. MODIFICATIONS.................................................................................................91 5. COMBINING DOCUMENTS................................................................................92 6. COLLECTIONS OF DOCUMENTS.....................................................................92 7. AGGREGATION WITH INDEPENDENT WORKS............................................92 8. TRANSLATION.....................................................................................................92 9. TERMINATION.....................................................................................................93 10. FUTURE REVISIONS OF THIS LICENSE........................................................93 Contributors RobinH, Moriconne, Tikai, Mwhizz, EvanR, Mglg, Read-write-services and many others. 2 Introduction The Special Theory of Relativity was the result of developments in physics at the end of the nineteenth century and the beginning of the twentieth century. It changed our understanding of older physical theories such as Newtonian Physics and led to early Quantum Theory and General Relativity. Special Relativity does not just apply to fast moving objects, it affects the everyday world directly through "relativistic" effects such as magnetism and the relativistic inertia that underlies kinetic energy and hence the whole of dynamics. Special Relativity is now one of the foundation blocks of physics. It is in no sense a provisional theory and is largely compatible with quantum theory; it not only led to the idea of matter waves but is the origin of quantum 'spin' and underlies the existence of the antiparticles. Special Relativity is a theory of exceptional elegance, Einstein crafted the theory from simple postulates about the constancy of physical laws and of the speed of light and his work has been refined further so that the laws of physics themselves and even the constancy of the speed of light are now understood in terms of the most basic symmetries in a four dimensional universe. Further Reading Feynman Lectures on Physics. Symmetry in Physical Laws. (World Student) Vol 1. Ch 52. Gross, D.J. The role of symmetry in fundamental physics. PNAS December 10, 1996 vol. 93 no. 25 14256-14259 http://www.pnas.org/content/93/25/14256.full Historical Development In the nineteenth century it was widely believed that light was propagated in a medium called the "aether". In 1865 James Clerk Maxwell produced a theory of electromagnetic waves that seemed to be based on this aether concept. According to his theory the velocity of electromagnetic waves such as light would depend on two constant factors, the permittivity and permeability constants, which were properties of the aether. Anyone who was stationary within the aether would measure the speed
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