Modern Special Relativity - Johann Rafelski

Modern Special Relativity

A Student's Guide with Discussions and Examples

This book presents Special Relativity in a language accessible to students while avoiding the burdens of geometry, tensor calculus, space-time symmetries, and the introduction of four vectors. The search for clarity in the fundamental questions about Relativity, the discussion of historical developments before and after 1905, the strong connection to current research topics, many solved examples and problems, and illustrations of the material in colloquial discussions are the most significant and original assets of this book. Les mer
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This book presents Special Relativity in a language accessible to students while avoiding the burdens of geometry, tensor calculus, space-time symmetries, and the introduction of four vectors. The search for clarity in the fundamental questions about Relativity, the discussion of historical developments before and after 1905, the strong connection to current research topics, many solved examples and problems, and illustrations of the material in colloquial discussions are the most significant and original assets of this book. Importantly for first-time students, Special Relativity is presented such that nothing needs to be called paradoxical or apparent; everything is explained.



The content of this volume develops and builds on the book Relativity Matters (Springer, 2017). However, this presentation of Special Relativity does not require 4-vector tools. The relevant material has been extended and reformulated, with additional examples and clarifications.



This introduction of Special Relativity offers conceptual insights reaching well beyond the usual method of teaching relativity. It considers relevant developments after the discovery of General Relativity (which itself is not presented), and advances the reader into contemporary research fields. This presentation of Special Relativity is connected to present day research topics in particle, nuclear, and high intensity pulsed laser physics and is complemented by the current cosmological perspective. The conceptual reach of Special Relativity today extends significantly further compared even to a few decades ago.



As the book progresses, the qualitative and historical introduction turns into a textbook-style presentation with many detailed results derived in an explicit manner. The reader reaching the end of this text needs knowledge of classical mechanics, a good command of elementary algebra, basic knowledge of calculus, and introductory know-how of electromagnetism.
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Forlag: Springer Nature Switzerland AG
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Språk: Engelsk
Sider: 458
ISBN: 9783030543518
Format: 24 x 16 cm
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I Space-Time, Light and the aether 1
1 What is (Special) Relativity? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1 Principle of Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Time, a 4th coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Path toward Lorentz coordinate transformations . . . . . . . . . . . . . . 101.4 Highlights: How did relativity happen? . . . . . . . . . . . . . . . . . . . 13
2 Light and the aether . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1 Measuring space and time: SI unit system . . . . . . . . . . . . . . . . . . 152.2 Speed of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Essay: aether and Special Relativity . . . . . . . . . . . . . . . . . . . . . 25
3 Material Bodies in SR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1 The Michelson-Morley Experiment . . . . . . . . . . . . . . . . . . . . . . 333.2 Body contraction and time dilation . . . . . . . . . . . . . . . . . . . . . . 363.3 Is the Lorentz-FitzGerald body contraction measurable? . . . . . . . . . . 383.4 Experiments require understanding of body contraction . . . . . . . . . . 403.5 Resolving misunderstandings of SR . . . . . . . . . . . . . . . . . . . . . . 42
II Time Dilation, and Lorentz-Fitzgerald Body Contraction 47

4 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.1 Proper time of a traveler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2 Relativistic light-clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.3 Talking about time (dilation) . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 The Lorentz-FitzGerald Body Contraction . . . . . . . . . . . . . . . . . . . . . . 615.1 Light-clock moving parallel to light path . . . . . . . . . . . . . . . . . . . 615.2 Body contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.3 Arbitrary orientation of the light clock . . . . . . . . . . . . . . . . . . . . 66
III The Lorentz Transformation 73
6 Relativistic Coordinate Transformation . . . . . . . . . . . . . . . . . . . . . . . 756.1 Derivation of the Lorentz coordinate transformation . . . . . . . . . . . . 756.2 Explicit form of the Lorentz transformation . . . . . . . . . . . . . . . . . 796.3 The nonrelativistic Galilean limit . . . . . . . . . . . . . . . . . . . . . . . 846.4 The inverse Lorentz coordinate transformation . . . . . . . . . . . . . . . 85
7 Some Consequences of Lorentz Transformation . . . . . . . . . . . . . . . . . . . 887.1 Invariance of proper time . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.2 Relativistic addition of velocities . . . . . . . . . . . . . . . . . . . . . . . 927.3 Two Lorentz coordinate transformations in sequence . . . . . . . . . . . . 997.4 Rapidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
IV Measurement 111
8 Time Measurement and Lorentz Transformation . . . . . . . . . . . . . . . . . . 1138.1 Graphic representation of Lorentz Transformation . . . . . . . . . . . . . 1138.2 Time dilation and simultaneity . . . . . . . . . . . . . . . . . . . . . . . . 114
9 Methods of Measuring Spatial Separation . . . . . . . . . . . . . . . . . . . . . . 1199.1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.2 Determination of spatial separation . . . . . . . . . . . . . . . . . . . . . . 1209.3 Light illumination emitted in the rest-frame of the observer . . . . . . . . 1239.4 Train in the tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
10 The Bell Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13010.1 Rockets connected by a thread . . . . . . . . . . . . . . . . . . . . . . . . 13010.2 The thread breaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13210.3 Lorentz-FitzGerald body contraction measured . . . . . . . . . . . . . . . 133
V Space, Time, Doppler Shift 139
11 The Light-Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14111.1 The future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14111.2 The past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
12 Space-time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14912.1 Timelike and spacelike event separation . . . . . . . . . . . . . . . . . . . 14912.2 Time dilation revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15312.3 Essay: Quantum entanglement and causality . . . . . . . . . . . . . . . . 156
13 SR-Doppler Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16213.1 Introducing the nonrelativistic Doppler shift . . . . . . . . . . . . . . . . . 16213.2 Misunderstanding of the relativistic Doppler eect . . . . . . . . . . . . . 16413.3 SR-Aberration of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16713.4 SR-Doppler shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
VI Mass, Energy, Momentum 177
14 Mass and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17914.1 Energy of a body at rest . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17914.2 Relativistic energy of a moving body . . . . . . . . . . . . . . . . . . . . . 18214.3 Mass of a body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
15 Particle Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18615.1 Relation between energy and momentum . . . . . . . . . . . . . . . . . . 18615.2 Particle rapidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
16 Generalized Mass-Energy Equivalence . . . . . . . . . . . . . . . . . . . . . . . . 20116.1 Where does energy come from? . . . . . . . . . . . . . . . . . . . . . . . . 20116.2 Mass equivalence for kinetic energy in a gas . . . . . . . . . . . . . . . . . 20216.3 Potential energy mass equivalence . . . . . . . . . . . . . . . . . . . . . . 20316.4 Atomic mass defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20516.5 Rotational energy mass equivalence . . . . . . . . . . . . . . . . . . . . . 20616.6 Chemical energy mass defect . . . . . . . . . . . . . . . . . . . . . . . . . 20716.7 Nuclear mass defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20816.8 Origin of energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
VII Collisions, Decays 213
17 Preferred Frame of Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21517.1 The center of momentum frame (CM-Frame) . . . . . . . . . . . . . . . . 21517.2 The Lorentz transformation to the CM-frame . . . . . . . . . . . . . . . . 21717.3 Particle decay in the CM-frame . . . . . 228 . . . . . . . . . . . . . . . . . . . 22017.4 Decay energy balance in CM-frame . . . . . . . . . . . . . . . . . . . . . . 22217.5 Decay of a body in flight . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
18 Particle Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22818.1 Elastic two body reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 22818.2 Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23018.3 Elastic bounce from a moving wall . . . . . . . . . . . . . . . . . . . . . . 23318.4 Inelastic two-body reaction threshold . . . . . . . . . . . . . . . . . . . . . 23718.5 Energy available in a two body collision . . . . . . . . . . . . . . . . . . . 24118.6 Inelastic collision and particle production . . . . . . . . . . . . . . . . . . 247
VIII SR-Tests & Open Questions 251
19 Tests of Special Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25319.1 Overview: Testing SR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25319.2 The Michelson-Morley experiment today . . . . . . . . . . . . . . . . . . . 25419.3 How constant is the speed of light? . . . . . . . . . . . . . . . . . . . . . . 25519.4 Tests of SR material body properties . . . . . . . . . . . . . . . . . . . . . 25619.5 Doppler effect and tests of the Lorentz coordinate transformation . . . . . 25819.6 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
20 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26420.1 Accelerated motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26420.2 Can there be acceleration in SR? . . . . . . . . . . . . . . . . . . . . . . . 26520.3 Evidence for the existence of acceleration . . . . . . . . . . . . . . . . . . 26620.4 Small and large acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 26820.5 Achieving strong acceleration . . . . . . . . . . . . . . . . . . . . . . . . . 269
IX Lorentz Force and Particle Motion 275
21 Acceleration and Lorentz Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27721.1 Newton's second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27721.2 Motion in magnetic and electric elds . . . . . . . . . . . . . . . . . . . . 28021.3 Variational principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28721.4 Electron Coulomb orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
22 Electrons Riding a Plane Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29822.1 Fields and potentials for a plane wave . . . . . . . . . . . . . . . . . . . . 29822.2 Role of conservation laws . . . . . . . . . . . . . . . . . . . . . . . . . . . 30222.3 Surng the plane wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
X Space Travel 311
23 Spaceship Travel in the Milky Way . . . . . . . . . . . . . . . . . . . . . . . . . . 31323.1 Space travel with constant acceleration . . . . . . . . . . . . . . . . . . . 31323.2 The eect of time dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 31523.3 How far can we travel? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31523.4 Variable acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
24 Relativistic Rocket equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32224.1 Nonrelativistic rocket equation . . . . . . . . . . . . . . . . . . . . . . . . 32224.2 Relativistic rocket equation . . . . . . . . . . . . . . . . . . . . . . . . . . 32324.3 Energy of relativistic rocket . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Johann Rafelski is a theoretical physicist working at The University of Arizona in Tucson, USA. Born in Krakow, Poland in 1950, he received his Ph.D. with Walter Greiner at Johann Wolfgang Goethe University, Frankfurt, Germany in 1973. In 1977 Rafelski arrived at CERN-Geneva, where with Rolf Hagedorn he developed the search for quark-gluon plasma in relativistic heavy ion collision as a novel research domain. He invented and developed the strangeness quark flavor as the signature of quark-gluon plasma, advancing the discovery of this new phase of primordial matter. Professor Rafelski teaches Relativity, Quantum, Particle and Nuclear Physics; in addition to CERN and Arizona, he also has held professional appointments at the University of Pennsylvania in Philadelphia, Argonne National Laboratory in Chicago, the University of Frankfurt, the University of Cape Town, the University of Paris-Jussieu, and the Ecole Polytechnique. He has been a DFG Excellence Initiative Professor at Ludwig-Maximillian University Munich. In collaboration with researchers from the Ecole Polytechnique in Paris and ELI-Beamlines in Prague he is using ultra-intense lasers in nuclear and fundamental physics.



Prof. Rafelski is the editor of the open-access book: Melting Hadrons, Boiling Quarks - From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN - With a Tribute to Rolf Hagedorn (Springer, 2016) and he has authored the book: Relativity Matters - From Einstein's EMC2 to Laser Particle Acceleration and Quark-Gluon Plasma (Springer, 2017).