Essential Relativity: Special, General, and CosmologicalThis 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. |
Contents
1 | |
2 | |
3 | |
4 | |
6 | |
7 | |
8 | |
The Relativity Principle | 11 |
SPACETIME AND FOURVECTORS | 78 |
44 | 84 |
12 | 87 |
Wave Motion | 91 |
51 | 99 |
The Center of Momentum Frame | 105 |
57 | 111 |
60 | 117 |
Arguments for the Relativity Principle | 12 |
Maxwellian Relativity | 13 |
Origins of General Relativity | 14 |
Machs Principle 16 Consequences of Machs Principle | 15 |
Cosmology | 18 |
Inertial and Gravitational Mass | 20 |
The Equivalence Principle | 22 |
The SemiStrong Equivalence Principle | 25 |
Consequences of the Equivalence Principle | 26 |
2 | 29 |
The Relativity of Simultaneity | 35 |
4 | 40 |
6 | 41 |
Length Contraction | 50 |
Velocity Transformation | 59 |
BASIC IDEAS OF GENERAL RELATIVITY | 65 |
EINSTEINIAN OPTICS | 68 |
Static Fields Geodesics and Hamiltons Principle | 71 |
9 | 74 |
15 | 131 |
16 | 132 |
18 | 136 |
20 | 152 |
FORMAL DEVELOPMENT OF GENERAL RELATIVITY | 155 |
The Vacuum Field Equations of General Relativity | 166 |
76 | 173 |
The Schwarzschild Radius | 184 |
25 | 188 |
80 | 195 |
CHAPTER 9 | 211 |
83 | 221 |
84 | 227 |
86 | 237 |
Cosmic Dynamics According to PseudoNewtonian Theory | 248 |
The Friedmann Models | 257 |
Machs Principle Reexamined | 271 |
313 | |
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Common terms and phrases
acceleration analog angle arbitrary axes axis CM frame collision components cone conservation constant coordinate system corresponding curvature defined density diagram dilation distance Doppler effect dr² dx² dy² Einstein's energy equivalent ether Euclidean example field equations Figure finite force formula four-acceleration four-force four-momentum four-tensors four-vector four-velocity galaxies Galilean Galilean transformation geodesic geometry given gravitational field Hence implies inertial frames inertial observer invariant isotropy length contraction light signal Lorentz factor Lorentz transformations Lorentz-invariant LT's Mach's principle Maxwell's mechanics metric Minkowski Minkowski space momentum motion moving Newtonian null orbit P₁ photon physical plane postulate principle radial radius rela relativistic rest frame rest mass result rotation scalar Schwarzschild Schwarzschild radius Section space spacetime spatial special relativity speed of light sphere standard clock surface symmetry synchronized tensor three-vector timelike tion universe vanish vector velocity worldlines zero μν