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Practical Relativity


Practical Relativity

From First Principles to the Theory of Gravity
1. Aufl.

von: Richard N. Henriksen

47,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 16.09.2010
ISBN/EAN: 9780470972038
Sprache: englisch
Anzahl Seiten: 280

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Beschreibungen

The book is intended to serve as lecture material for courses on relativity at undergraduate level. Although there has been much written on special relativity the present book will emphasize the real applications of relativity. In addition, it will be physically designed with the use of box summaries so as to allow easy access of practical results. The book will be composed of eight chapters. Chapter 1 will give an introduction to special relativity that is the world without gravity. Implications will be presented with emphasis on time dilation and the Doppler shift as practical considerations. In Chapter 2, the four-vector representation of events will be introduced. The bulk of this chapter will deal with flat space dynamics. This will require the generalization of Newton's first and second laws. Some important astronomical applications will be discussed in Chapter 3 and in Chapter 4 some engineering applications of special relativity such as atomic clocks will be presented. Chapter 5 will be dedicated to the thorny question of gravity. The physical motivation of the theory must be examined and the geometrical interpretation presented. Chapter 6 will present astronomical applications of relativistic gravity. These include the usual solar system tests; light bending, time delay, gravitational red-shift, precession of Keplerian orbits. Chapter 7 will be dedicated to relativistic cosmology. Many of the standard cosmological concepts will be introduced, being mathematically simple but conceptually subtle. The concluding chapter will be largely dedicated to the global positioning system as an engineering problem that requires both inertial and gravitational relativity. The large interferometers designed as gravitational wave telescopes will be discussed here.
<p>Preface ix</p> <p>Acknowledgements xi</p> <p>Introduction xiii</p> <p><b>Part I: The World Without Gravity 1</b></p> <p><b>1. Non-Relativity for Relativists 3</b></p> <p>1.1 Vectors and Reference Frames 3</p> <p>1.1.1 Reference Frames 4</p> <p>1.1.2 Inertial Reference Frames 25</p> <p><b>2. Invariance of Physical Law Under Change of Inertial Frame of Reference 45</b></p> <p>2.1 Prologue 45</p> <p>2.2 The Theory of Light or Electromagnetic Waves 48</p> <p>2.2.1 Wave Propagation Speed 48</p> <p>2.3 Measurement Theory and the Lorentz Transformations 62</p> <p><b>3. Implications: Using and Understanding the Lorentz Transformations 79</b></p> <p>3.1 Prologue 79</p> <p>3.2 Kinematic Applications 80</p> <p>3.2.1 Time 80</p> <p>3.2.2 Time and Rotation 91</p> <p>3.2.3 Time and the Lorentz Transformation 93</p> <p>3.2.4 Space 94</p> <p>3.2.5 Space and Time 99</p> <p>3.3 Kinematic Acceleration 101</p> <p>3.3.1 Thomas Precession 104</p> <p>3.4 Geometrical Optics 108</p> <p>3.4.1 Pictures of Moving Objects 111</p> <p>3.4.2 Light Echoes 118</p> <p><b>4. The Measure of Space-Time 123</b></p> <p>4.1 Prologue 123</p> <p>4.2 Metric Space-Time 124</p> <p>4.2.1 Two Metric Derivations of the Lorentz Transformation 133</p> <p>4.3 Four-Vector Dynamics 136</p> <p>4.3.1 Lagrangian Dynamics Without Fundamental Forces 140</p> <p>4.3.2 Collisions Between Free Particles 152</p> <p><b>5. Electromagnetic Theory in Space-Time 161</b></p> <p>5.1 Prologue 161</p> <p>5.1.1 Electromagnetic Four-Potential 162</p> <p>5.2 Lagrangian Dynamics of an Electromagnetic Charge 165</p> <p>5.2.1 Field Transformations Between Inertial Frames 179</p> <p>5.3 Electromagnetism for Arbitrary Inertial Observers 182</p> <p>5.3.1 Curvilinear Electromagnetic Theory 192</p> <p><b>Part II: Relativity With the Gravitational Field 203</b></p> <p><b>6. Gravitational Structure of Space-Time 205</b></p> <p>6.1 Prologue 205</p> <p>6.2 The Weak Gravitational Field 209</p> <p>6.3 Constant or Stationary Gravitational Field 215</p> <p>6.4 Strong Gravitational Field 222</p> <p>6.4.1 The Schwarzschild Metric 222</p> <p>6.4.2 Orbital Precession and Light Bending in a Schwarzschild Geometry 229</p> <p>6.4.3 Kerr Metric Outside a Rotating Mass 240</p> <p>6.4.4 Relativistic Continua 244</p> <p>6.4.5 The Curvature of Space-Time 247</p> <p>Index 257</p>
"What makes his textbook for a graduate or undergraduate course practical, says Henriksen (Queen's U., Kingston, Canada), is that it starts at the very beginning and goes nearly to the end; that in so far as he can balance between tedium and necessity, he covers each step along the way; and that he uses familiar concepts of vectors, tensors, and reference systems rather than fancy new ones that students might have to learn along the way." (Booknews, 1 February 2011)
<b>Professor Richard Henriksen</b> is a full professor of astrophysics at Queen's University, Kingston (Canada). He was awarded his PhD at Manchester (UK) and he has been a senior visitor at Stanford (USA), a Humbolt Fellow in Germany and Engineur/chercheur at CEA Saclay in France. Professor Henriksen has published over 125 research papers of various kinds, many of which employ relativistic concepts. Together with Geoff Bicknell, he published in the astrophysical journal one of the first papers in which the formation of primordial black holes was calculated correctly. He has extensive experience lecturing, having lectured at all graduate and undergraduate levels in physics of most types. He has in addition presented many professional colloquia and has won the Queen’s University research excellence award. His areas of research range widely over the field of astronomy and astrophysics.
<i>Practical Relativity</i> is an advanced textbook that aims to emphasize the real applications of relativity and places the topic in the context of experimental science.  The ‘practical’ aspect of the book rests primarily on the author’s method of starting at the beginning of the topic and proceeding to advanced material, while including all the stages that lead to important results. This book encompasses an approach that remains as close as possible to familiar concepts of vectors, tensors and reference systems in the hope of capitalizing on received wisdom. <p>Presented in six chapters, each chapter takes a logical step on the way to relativistic electromagnetism and gravity.</p> <p>Chapter topics are:</p> <ul type="disc"> <li>Non-relativity for Relativists</li> <li>Invariance of Physical Law Under Change of Inertial Frame of Reference</li> <li>Implications: Using and Understanding the Lorentz Transformations</li> <li>Electromagnetic Theory in Space-time</li> <li>Gravitational Structure of Space-time</li> <li>The Measure of Space-time</li> </ul> <p>Problems and examples are included throughout the book and a solutions manual is available at www.wiley.com/go/henriksen.</p> <p>This book may be used as lecture material for a course on special relativity and gravitation at an undergraduate and graduate level, and will appeal to students studying for both physics and astronomy. In addition, it will be a useful source book for physicists, astronomers and engineers.</p>

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