The Riddle of Gravitation

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Courier Dover Publications, 1992 - Science - 233 pages
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In this thought-provoking book, written for the layman, a noted physicist offers a fresh, nonmathematical introduction to the conceptual foundations of both Newton's and Einstein's theories of gravitation. Since Einstein's general relativity theory, which deals with gravitation, requires some acquaintance with the ideas of the special theory of relativity (not in itself concerned with gravitation), the first part of the book is devoted primarily to the special theory. This section ranges from Newtonian physics through Einstein's discovery of the relativity of time and space, to the fusion of time and space into a four-dimensional whole by Hermann Minkowski.
Part Two is concerned with the general theory of relativity proper. General relativity is based on the hypothesis that, under the influence of gravity, space and time are curved, rather than flat, and that all aspects of gravity can be understood in terms of geometry. Part Three is devoted to recent developments, including the search for gravitational waves, the quantum theory of gravitation, particle motion, and other topics. Five appendixes contain mathematical derivations for the reader who desires a more technical treatment of the subject.
For this new edition, Professor Bergmann has also added updated material on gravitational radiation detectors, current problems in cosmology, the significance of singularities of the gravitational field, and more. The result is a fascinating excursion into the rarefied world of theoretical physics, yet one that is well within the grasp of the nonphysicist. Indeed, any intelligent layman, curious about relativity theory and its relation to current astronomical knowledge, will welcome this eloquent and cogent presentation of the subject.
  

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Contents

Two Inertial Frames according to Einstein
32
Components of a Vector in Two Lorentz Frames 80
43
The EnergyMomentum Vector in Minkowski SpaceTime
44
Great Circles
50
Relativity and Gravitation
57
Ambiguity of Distance
59
Gravitational Lens Action
67
The Principle of General Covariance
70
RECENT DEVELOPMENTS
129
Gravitational Collapse
131
Gravitational Radiation
136
A Gravitational Wave
137
Polarization of a Gravitational Wave Produced by a Double Star
138
The Search for Gravitational Waves
141
Michelson Interferometer I 44
143
I9 Cosmology
146

Curvature of the Earths Gravitational Field
77
Gravitation in the SpaceTime Continuum
79
Lines of Force
83
Schwarzschilds Solution
87
Curvature of Schwarzschilds Field
88
The Escape Velocity as a Function of Distance from a large Point Mass Newtonian Mechanics
89
Schwarzschild Radius versus Actual Radius of Density Taken as Constant and Equal to That of Water
90
Density versus Mass if the Schwarzschild Radius Is to Equal the Actual Radius
91
Elliptic Orbit with Perihelion Advance
92
Circles and Their Radii on a Sphere
94
Velocity of a Freefalling Particle
95
Freefall Velocity in Terms of Proper Time
96
Inside the Schwarzschild Radius
97
Redshift Dependence on Distance
98
Curves of Constant Acceleration
100
Curves of Constant Acceleration as Straight Lines
101
Geometry near the Schwarzschild Radius
102
Event Horizons
106
Two Accelerated Observers
107
Two Observers One Accelerated the Other Inertial I08 61 Past Light Cones of an Inertial Observer I 09
109
Newton
113
Pages from Principia
120
Linearly Expanding Universe
148
Expanding Universe with Constant Hubble Coefficient I48 68 Oscillating Universe I 49
150
Astronomical Observations Lead Billions of Years Back into the History of the Universe
151
Current Observational Programs
156
Particle Motion
163
Quantum Theory of Gravitation
167
What Is an Observable?
171
SpaceTime Today and Tomorrow
174
APPENDIXES
179
The EqualAreas law of Kepler
181
Two Coordinate Systems That Coincide for Part of the Time I64 72 EqualAreas law I82 73 Unaccelerated Motion
182
Detail of Fig 72
183
Derivation of the InverseSquare Law of Force
185
Acceleration on a Circular Trajectory I86 76 Two Events on a Line Perpendicular to the Relative Motion
186
The Lorentz Transformation
187
The SCl1waI7_Cl1lld Radius I93 V Gravitational Radiation
197
Glossary
203
Suggestions for Further Reading
223
A Small Segment of M 82 Further Enlarged
225
Index
227
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