The Special Theory Of Relativity - Günther Helmut; Müller Volker | Libro Springer 10/2019 - HOEPLI.it


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günther helmut; müller volker - the special theory of relativity

The Special Theory of Relativity Einstein’s World in New Axiomatics

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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 10/2019
Edizione: 1st ed. 2019





Sommario


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 





Trama

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.







Autore

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.







Altre Informazioni

ISBN:

9789811377822

Condizione: Nuovo
Dimensioni: 235 x 155 mm Ø 992 gr
Formato: Copertina rigida
Illustration Notes:143 Illustrations, black and white
Pagine Arabe: 542
Pagine Romane: xii






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