The special theory of relativity : Einstein's world in new axiomatics
著者
書誌事項
The special theory of relativity : Einstein's world in new axiomatics
Springer, c2019
- タイトル別名
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Die spezielle Relativitätstheorie : Einsteins Welt in einer neuen Axiomatik
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注記
Extension to General relativity theory and translation: Volker Müller
Includes bibliographical references (p. 527-530) and index
内容説明・目次
内容説明
This book discusses in detail the special theory of relativity without including all the instruments of theoretical physics, enabling readers who are not budding theoretical physicists to develop competence in the field. An arbitrary but fixed inertial system is chosen, where the known velocity of light is measured. With respect to this system a moving clock loses time and a moving length contracts. The book then presents a definition of simultaneity for the other inertial frames without using the velocity of light. To do so it employs the known reciprocity principle, which in this context serves to provide a definition of simultaneity in the other inertial frames. As a consequence, the Lorentz transformation is deduced and the universal constancy of light is established. With the help of a lattice model of the special theory of relativity the book provides a deeper understanding of the relativistic effects. Further, it discusses the key STR experiments and formulates and solves 54 problems in detail.
目次
I Space Time Motion 1 Measuring-Rods and Clocks 2 Inertial Systems 3 Coordinates and Velocities 3.1 One Inertial System 3.1.1 Space Coordinates 3.1.2 The Problem of Time Measurement 3.1.3 The Relative Velocity 3.2 Two Inertial Systems3.2.1 Coordinate Transformations3.2.2 Composition of Velocities 4 Special Coordinate Transformations4.1 Definition of Simultaneity 4.2 The Linear Transformation Formulae4.3 Composition of Velocities 5 Moving Measuring-Rods and Clocks 5.1 Moving and Stationary Measuring-Rods 5.2 Moving and Stationary Clocks
II The Principle of Relativity 6 Einstein's Principle of Relativity Portrait Albert Einstein 7 Elementary Relativity 8 A Metrical Principle of Relativity
III Elementary Structure of Classical Spacetime 9 The Physical Postulates of Classical Spacetime 10 Elementary Relativity - The Galilean Transformation
IV Elementary Structure of Relativistic Spacetime 11 The Moving Rod is Shortened - The Michelson Experiment Portrait Albert Abraham Michelson Portrait Hendrik Antoon Lorentz 12 The Moving Clock Goes Behind -Einstein's Experimentum Crucis of Special Relativity 12.1 The Light Cock Portrait Emmy Noether 12.2 The General Law of Time Dilatation 13 The Physical Postulates of Relativistic Spacetime 14 Elementary Relativity - The Lorentz Transformation 15 Einstein's Composition Law for Arbitrary Directed Velocities 16 Test Experiments of Special Relativity17 The Linear Approximation of Special Relativity 18 Overview of the Axiomatic Structure of Special Relativity
V Entire Theory on One Page
VI Newtonian Mechanics 19 The Newtonian Axioms Portrait Isaac Newton 20 Classical Mechanics 21 The Tolman Thought Experiment - The Relativistic Mechanics 21.1 The Relativistic Mass Formula 21.2 The Basic Relativistic Equations of Mechanics
VII Einstein's Idea of Energy-Mass Equivalence 22 The Inertia of Energy 23 Einstein's Idea of Energy-Mass Equivalence
VIII Relativistic Phenomena and Paradoxes 24 Fresnel's Drag Coefficient 25 A Paradox to the Drag Coefficient 26 Thomas Precession 27 The Measuring-Rod Paradox 28 Doppler Effect28.1 Classical Theory of Doppler Effect 28.1.1 Longitudinal Observation28.1.2 Transversal Observation 28.2 Exact Theory of Doppler Effect 28.2.1 Longitudinal Observation28.2.2 Transversal Observation 29 Aberration 29.1 Aberration in the Particle Picture 29.2 Aberration in the Wave Picture 30 A Paradox for the Aberration of Waves 31 The Twin Paradox 32 The Measuring-Rod Paradox and the Twin Paradox using Non-Conventional Simultaneity 32.1 The Measuring-Rod Paradox 32.2 The Twin Paradox
IX Mathematical Formalism of Special Relativity33 The Lorentz Group33.1 The Special Lorentz- Transformation 33.2 The General Lorentz- Transformation 33.3 The General Proper Lorentz- Transformation 33.4 General Theory of Thomas- Precession 33.5 Geometry in Minkowski- Space 33.6 Einstein's Principle of Relativity in Minkowski-Space34 The Covariant Formulation of Relativistic Mechanics 34.1 The Motion of a Particle in Minkowski-Space 34.1.1 Proper-Time of Particle Motion 34.1 The Motion of a Particle in Minkowski-Space 34.2 Dynamics of Particles in Minkowski-Space 35 Electrodynamics - Covariant Formulation 35.1 Maxwell-Theory 35.1.1 Charges and Currents - Continuity Equation35.1.2 Lorentz-Force 35.1.3 Magnetic Flux and Law of Induction35.1.4 Electrical Displacement and Magnetic Excitation 35.1.5 Maxwell's Equations - Electromagnetic Waves Portrait James Clerk Maxwell 35.2 The Covariant Formulation of Electrodynamics 35.2.1 The Four-dimensional Variables of Electrodynamics 35.2.2 Four-dimensional Electrodynamics in Vacuum. 35.2.3 Four-dimensional Electrodynamics of Moving MediaPortrait Hermann Minkowski35.3 Electrodynamics in Absolut Units 35.3.1 Electrodynamics in a medium35.3.2 Electrodynamics in a - Four-dimensional Formulation 35.3.3 The Energy-Momentum- Tensor of the Maxwell-Field
X The Representations of the Lorentz-Group Weyl-Equation and Dirac-Equation36 Remembering to Group-Theory37 The Tensorial Representations of Lorentz-GroupRelativistic Mechanics and Electrodynamics 38 The Spinorial Representations of Lorentz-GroupWeyl-Equation and Dirac-Equation38.1 The group C2 38.2 The relation between C2 to Lorentz-Group A2 38.3 Spinor Calculus39 The Covariant Formulation of the Principle of RelativityWeyl-Equation and Dirac-Equation 39.1 Weyl-Equation 39.2 Dirac-Equation 40 The Physical Background of Dirac-Equation 40.1 Remembering Quantum Mechanics Portrait David Hilbert Portrait Werner Karl Heisenberg 40.1.1 Angular Momentum. Portrait Erwin Schroedinger 40.2 Transition to Dirac-Equation 41 Other Representations of Dirac-Equation 42 Dirac-Equation, Schroedinger-Equation and Pauli-Equation
XI Electrodynamics in Exterior Calculus 43 The Wedge Product 44 Di_erential Forms 45 Maxwell-Equations
XIIA Lattice Modell of Relativistic Space -Time46 The Lattice Model 47 A Clock Paradox
XIII Einstein's General Theory of Relativity48 Gravitation according to Newton and EinsteinPortrait Georg Friedrich Bernhard Riemann
XIV Appendix 49 Problems and Solutions 50 Mathematical Tools 50.1 Remembering to Tensor Calculus50.2 Integral TheoremsPortrait Carl Friedrich Gauss 50.3 The _-Function
References Index
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