Description
SPRINGER Modern Special Relativity A Students Guide With Discussions And Examples (Pb 2022) by RAFELSKI J.
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. I Space-Time, Light and the aether 11 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? . . . . . . . . . . . . . . . . . . . 132 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 . . . . . . . . . . . . . . . . . . . . . 253 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 . . . . . . . . . . . . . . . . . . . . . . 42II Time Dilation, and Lorentz-Fitzgerald Body Contraction 474 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.1 Proper time of a traveler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2 Relativistic light-clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.3 Talking about time (dilation) . . . . . . . . . . . . . . . . . . . . . . . . . 565 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 . . . . . . . . . . . . . . . . . . . . 66III The Lorentz Transformation 736 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 . . . . . . . . . . . . . . . 857 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102IV Measurement 1118 Time Measurement and Lorentz Transformation . . . . . . . . . . . . . . . . . . 1138.1 Graphic representation of Lorentz Transformation . . . . . . . . . . . . . 1138.2 Time dilation and simultaneity . . . . . . . . . . . . . . . . . . . . . . . . 1149 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12610 The Bell Rockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13010.1 Rockets connected by a thread . . . . . . . . . . . . . . . . . . . . . . . . 13010.2 The thread breaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13210.3 Lorentz-FitzGerald body contraction measured . . . . . . . . . . . . . . . 133V Space, Time, Doppler Shift 13911 The Light-Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14111.1 The future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14111.2 The past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14412 Space-time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14912.1 Timelike and spacelike event separation . . . . . . . . . . . . . . . . . . . 14912.2 Time dilation revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15312.3 Essay: Quantum entanglement and causality . . . . . . . . . . . . . . . . 15613 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173VI Mass, Energy, Momentum 17714 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18315 Particle Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18615.1 Relation between energy and momentum . . . . . . . . . . . . . . . . . . 18615.2 Particle rapidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19316 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210VII Collisions, Decays 21317 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . 22318 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 . . . . . . . . . . . . . . . . . . 247VIII SR-Tests & Open Questions 25119 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26020 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 . . . . . . . . . . . . . . . . . . . . . . . . . 269IX Lorentz Force and Particle Motion 27521 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29122 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305X Space Travel 31123 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31924 Relativistic Rocket equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32224.1 Nonrelativistic rocket equation . . . . . . . . . . . . . . . . . . . . . . . . 32224.2 Relativistic rocket equation . . . . . . . . . . . . . . . . . . . . . . . . . . 32324.3 Energy of relativistic rocket . . . . . . . . . . . . . . . . . . . . . . . . . . 325show more