The Special Theory of Relativity: Einstein's World in New Axiomatics

ISBN-13: 9789811377853 / Angielski / Miękka / 2020 / 542 str.

Helmut Günther;Volker Müller

Opis

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.

Spis treści

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 Systems

3.2.1 Coordinate Transformations

3.2.2 Composition of Velocities 

4 Special Coordinate Transformations

4.1 Definition of Simultaneity 

4.2 The Linear Transformation Formulae

4.3 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 Relativity

17 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 Effect

28.1 Classical Theory of Doppler Effect 

28.1.1 Longitudinal Observation

28.1.2 Transversal Observation 

28.2 Exact Theory of Doppler Effect 

28.2.1 Longitudinal Observation

28.2.2 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 Relativity

33 The Lorentz Group

33.1 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-Space

34 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 Equation

35.1.2 Lorentz-Force 

35.1.3 Magnetic Flux and Law of Induction

35.1.4 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 Media

Portrait Hermann Minkowski

35.3 Electrodynamics in Absolut Units 

35.3.1 Electrodynamics in a medium

35.3.2 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-Equation

36 Remembering to Group-Theory

37 The Tensorial Representations of Lorentz-Group

Relativistic Mechanics and Electrodynamics 

38 The Spinorial Representations of Lorentz-Group

Weyl-Equation and Dirac-Equation

38.1 The group C2 

38.2 The relation between C2 to Lorentz-Group A2 

38.3 Spinor Calculus

39 The Covariant Formulation of the Principle of Relativity

Weyl-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 -Time

46 The Lattice Model 

47 A Clock Paradox 

XIII Einstein's General Theory of Relativity

48 Gravitation according to Newton and Einstein

Portrait Georg Friedrich Bernhard Riemann

XIV Appendix 

49 Problems and Solutions 

50 Mathematical Tools 

50.1 Remembering to Tensor Calculus

50.2 Integral Theorems

Portrait Carl Friedrich Gauss 

50.3 The _-Function 

References 

Index 

O autorze

Helmut Günther was professor at the Bielefeld University of Applied Sciences for Mathematics and Physics until 2005 and currently teaches relativity theory at the Humboldt University in Berlin.

Blurb

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 48 problems in detail.