Essential Relativity: Special, General, and Cosmological

Front Cover
Springer, Apr 17, 2013 - Science - 319 pages
0 Reviews
This book is an attempt to bring the full range of relativity theory within reach of advanced undergraduates, while containing enough new material and simplifications of old arguments so as not to bore the expert teacher. Roughly equal coverage is given tospecial relativity, general relativity, and cosmology. With many judicious omissions it can be taught in one semester, but it would better serve as the basis of a year's work. It is my hope, anyway, that its level and style of presentation may appeal also to wider c1asses of readers unrestricted by credit considerations. General relativity, the modern theory of gravitation in which free particles move along "straightest possible" lines in curved spacetime, and cosmology, with its dynamics for the whole possibly curved uni verse, not only seem necessary for a scientist's balanced view of the world, but offer some of the greatest intellectual thrills of modern physics. Nevertheless, considered luxuries, they are usu ally squeezed out of the graduate curriculum by the pressure of specialization. Special relativity escapes this tag with a ven geance, and tends to be taught as a pure service discipline, with too little emphasis on its startling ideas. What better time, there fore, to enjoy these subjects for their own sake than as an und- v vi PREFACE graduate? In spite of its forbidding mathematical reputation, even general relativity is accessible at that stage.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

EINSTEINIAN KINEMATICS 22 Basic Features of Special Relativity
29
On the Nature of Physical Laws
32
An Archetypal Relativistic Argument
33
The Relativity of Simultaneity
35
The Coordinate Lattice
37
The Lorentz Transformation
39
Properties of the Lorentz Transformation
41
Alternative Form of the Lorentz Transformation
45
Photons The Compton Effect
115
The Matter Tensor of Dust 17
117
RELATIVITY AND ELECTRODYNAMICS 61 Transformation of the Field Vectors
120
Magnetic Deflection of Charged Particles
124
The Field of a Uniformly Moving Charge
125
The Field of an Infinite Straight Current
127
BASIC IDEAS OF GENERAL RELATIVITY 65 Curved Surfaces
130
Curved Spaces of Higher Dimensions
134

Graphical Representation of the Lorentz Transformation
46
WorldPicture and WorldMap
48
Length Contraction
49
Length Contraction Paradoxes
51
Time Dilation
53
The Twin Paradox
56
Velocity Transformation
59
Proper Acceleration
62
Special Relativity Without the Second Postulate
64
EINSTEINIAN OPTICS 39 The Drag Effect
68
The Doppler Effect
69
Aberration and the Visual Appearance of Moving Objects
72
SPACETIME AND FOURVECTORS 42 Spacetime
78
ThreeVectors
81
FourVectors
84
FourTensors
88
The Null Cone
89
Wave Motion
91
RELATIVISTIC PARTICLE MECHANICS 48 Domain of Sufficient Validity of Newtons Laws
95
Why Gravity Does not Fit into Special Relativity
96
Shortcut to Relativistic Mechanics
97
Formal Approach to Relativistic Mechanics
99
A Note on Galilean FourVectors
102
Equivalence of Mass and Energy
103
The Center of Momentum Frame
105
Relativistic Billiards
107
p E Diagrams and Threshold Energies
108
ThreeForce and FourForce 1 11
111
De Broglie Waves 13
113
Riemannian Spaces
136
A Plan for General Relativity
141
The Gravitational Doppler Effect
145
The Spacetime Around a Spherical Mass
147
Static Fields Geodesics and Hamiltons Principle
151
FORMAL DEVELOPMENT OF GENERAL RELATIVITY 72 Tensors in General Relativity
155
The Vacuum Field Equations of General Relativity
162
The Schwarzschild Solution
166
Rays and Orbits in Schwarzschild Space
174
A GeneralRelativistic Proof of E mc
181
The Schwarzschild Radius
184
The Laws of Physics in Curved Spacetime
195
The Field Equations in the Presence of Matter
199
Modified Schwarzschild Space
207
COSMOLOGY 81 The Basic Facts
213
Apparent Difficulties of PreRelativistic Cosmology
221
The Cosmological Principle
225
Milnes Model
227
The RobertsonWalker Metric
232
Rubber Models Red Shifts and Horizons
237
Comparison with Observation
242
Cosmic Dynamics According to PseudoNewtonian Theory
248
Cosmic Dynamics According to General Relativity
251
The Friedmann Models
257
Once Again Comparison with Observation
265
Machs Principle Reexamined
271
EXERCISES
275
INDEX
313
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information