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Tables of Contents for On Einstein's Path
Chapter/Section Title
Page #
Page Count
Preface
v
14
Contributors
xix
 
1 Jordan, Pauli, Politics, Brecht...and a Variable Gravitational Constant
1
14
Engelbert L. Schucking
2 Thomson Scattering in an Expanding Universe
15
8
James L. Anderson
2.1 Introduction
15
1
2.2 EIH Surface Integrals
16
1
2.3 Approximation Procedures
17
2
2.4 Thomson Scattering
19
4
3 Geometrical Formulation of Quantum Mechanics
23
44
Abhay Ashtekar
Troy A. Schilling
3.1 Introduction
23
5
3.2 Geometric Formulation of Quantum Mechanics
28
16
3.2.1 The Hilbert Space as a Kahler Space
28
4
3.2.2 The Quantum Phase Space
32
3
3.2.3 Riemannian Geometry and Measurement Theory
35
7
3.2.4 The Postulates of Quantum Mechanics
42
2
3.3 A Unified Framework for Generalizations of Quantum Mechanics
44
9
3.3.1 Generalized Dynamics
45
4
3.3.2 Characterization of the Standard Quantum Kinematics
49
4
3.4 Semiclassical Considerations
53
8
3.4.1 Kinematics
53
4
3.4.2 Dynamics: Oscillators
57
1
3.4.3 Dynamics: WKB Approximation
58
3
3.5 Discussion
61
6
4 General Covariance is Bose-Einstein Statistics
67
14
James Baugh
David Ritz Finkelstein
Heinrich Saller
Zhong Tang
4.1 Quantum Relativity
67
1
4.2 General Covariance and Bosonic Statistics
68
1
4.3 The Two-Point Paradox
69
1
4.4 The Quantum Causal Relation
70
1
4.5 Quantum is Simpler
71
1
4.6 Limits to Spacetime
72
1
4.7 The Elephantine Chronon
73
1
4.8 Topological Nature of Gauge
73
2
4.9 Paradox Lost
75
4
4.10 Summation
79
2
5 The Split and Propagation of Light Rays in Relativity
81
14
Stanislaw L. Bazanski
5.1 Introduction
81
1
5.2 Traditional Approach
81
4
5.3 Modified Approach
85
2
5.4 Sagnac-Like Effects
87
2
5.5 Examples
89
6
6 How to Define a Unique Vacuum in Cosmology
95
12
Lluis Bel
6.1 Klein-Gordon Equation
95
1
6.2 Quantization of a Scalar Field
96
1
6.3 Robertson-Walker Models
97
1
6.4 Modes
97
1
6.5 Reduction of the Evolution Equation
98
1
6.6 Approximations to the Regular Solutions
99
2
6.7 Critical Points at t = Infinity
101
1
6.8 Special Cases
102
1
6.9 Positive and Negative Energy Modes
102
2
6.10 Concluding Remarks
104
3
7 EIH Theory and Noether's Theorem
107
6
Peter G. Bergmann
7.1 Introduction
107
1
7.2 Invariance Group and Noether's Theorem
108
1
7.3 An Example
108
2
7.4 The Generalized EIH Theory
110
1
7.5 Concluding Remarks
111
2
8 The Static Cylinder in General Relativity
113
8
W.B. Bonnor
8.1 Introduction
113
2
8.2 The HD Solution
115
1
8.3 Matching to LC Spacetime
115
2
8.4 Physical Interpretation
117
1
8.5 The Whittaker Mass per Unit Length
117
2
8.6 Conclusion
119
2
9 Gravity and the Tenacious Scalar Field
121
18
Carl H. Brans
9.1 Scalar Gravity?
121
5
9.2 Kaluza-Klein Theories
126
2
9.3 Dirac's Numbers
128
1
9.4 Scalar-Tensor Theories
129
5
9.5 Dilatons
134
2
9.6 Inflatons
136
1
9.7 Conclusion
137
2
10 The Cavendish Experiment in General Relativity
139
8
Dieter Brill
10.1 Introduction
139
1
10.2 Planar Symmetry
140
1
10.3 Exact, Static Solutions
141
3
10.4 Test Particle Motion
144
1
10.5 Conclusion
145
2
11 Wave Maps in General Relativity
147
24
Yvonne Choquet-Bruhat
11.1 Introduction
147
1
11.2 Definitions
148
1
11.3 Wave Maps--the Cauchy Problem
149
4
11.4 Harmonic Gauges in General Relativity
153
2
11.4.1 Existence of a Solution of the Vacuum Einstein Equations
154
1
11.4.2 Uniqueness Theorem
154
1
11.5 Global Problem--the First Energy Estimate
155
3
11.6 Second Energy Inequality
158
5
11.7 Wave Map from the Outside of a Black Hole
163
8
12 General Relativity and Experiment
171
18
Thibault Damour
12.1 Introduction
171
1
12.2 Experimental Tests of the Coupling Between Matter and Gravity
172
2
12.3 Tests of the Dynamics of the Gravitational Field in the Weak-Field Regime
174
2
12.4 Tests of the Dynamics of the Gravitational Field in the Strong-Field Regime
176
4
12.5 Cosmological Tests
180
1
12.6 Was Einstein 100% Right?
181
8
13 Some Developments in Newtonian Cosmology
189
14
Jurgen Ehlers
13.1 Introduction: The Curious History of Newtonian Cosmology
189
1
13.2 Two Formulations of Newtonian Cosmology and its Relationship to Relativistic Cosmology
190
5
13.2.1 The Heckmann-Schucking Formulation
190
2
13.2.2 The Cartan-Friedrichs Formulation
192
1
13.2.3 Electrodynamics and Optics in Newtonian Cosmology
193
1
13.2.4 Relations Between Relativistic and Newtonian Cosmological Models
194
1
13.3 Observer-Homogenous, Bianchi-Type Models
195
1
13.4 Averaging in Cosmology
196
3
13.5 Lagrangian Perturbation Theory
199
4
14 Deviation of Geodesics in FLRW Spacetime Geometries
203
24
George F.R. Ellis
Henk van Elst
14.1 Introduction
203
2
14.1.1 The Cosmological Context
205
1
14.2 The Riemann Curvature Tensor
205
2
14.3 The Geodesics
207
3
14.3.1 Timelike
209
1
14.3.2 Spacelike
209
1
14.3.3 Null
210
1
14.4 The Geodesic Deviation Equation
210
13
14.4.1 The Deviation Vectors
210
2
14.4.2 Geodesic Deviation for a Fundamental Observer
212
5
14.4.3 Past Directed Null Vector Fields
217
3
14.4.4 Generic Geodesic Vector Fields
220
3
14.5 Conclusion
223
4
15 Poincare Pseudosymmetries in Asymptotically Flat Spacetimes
227
14
Simonetta Frittelli
Ezra T. Newman
15.1 Introduction
227
2
15.2 Minkowski Space
229
3
15.3 Asymptotically Flat Spacetimes
232
4
15.4 Discussion
236
5
16 Taub Numbers and Asymptotic Invariants
241
10
Edward N. Glass
16.1 Introduction
241
2
16.2 Taub Numbers and Superpotential
243
2
16.3 Null Infinity
245
1
16.4 Kerr-Schild Solutions
246
1
16.5 Bondi-Sachs Solutions
247
2
16.6 Summary
249
2
17 Second-Class Constraints
251
6
Joshua N. Goldberg
17.1 Introduction
251
1
17.2 The Mechanical System
252
2
17.3 The Self-Dual Maxwell Field
254
1
17.4 Conclusion
255
2
18 On the Structure of the Energy-Momentum and the Spin Currents in Dirac's Electron Theory
257
18
Friedrich W. Hehl
Alfredo Macias
Eckehard W. Mielke
Yuri N. Obukhov
18.1 Introduction
257
2
18.2 Dirac-Yang-Mills Theory
259
2
18.3 Gordon Decomposition of Energy-Momentum and Spin Currents
261
3
18.4 Relocalization of Energy-Momentum and Spin
264
2
18.5 Trivial Lagrangians and Relocalization
266
2
18.6 Belinfante Symmetrization of the Energy-Momentum Current
268
2
18.7 Properties of the Gravitational Moments and Nonrelativistic Limit
270
1
18.8 Discussion
271
4
19 The Physical Reality of the Quantum Wave Function
275
8
Arthur Komar
19.1 Introduction
275
2
19.2 The Thought Experiment
277
3
19.3 Schrodinger's Cats
280
3
20 The Ultimate Extension of the Bianchi Classification for Rotating Dust Models
283
16
Andrzej Krasinski
20.1 Introduction and Summary
283
1
20.2 The Classification of Differential Forms of First Order and the Darboux Theorem
284
1
20.3 Geodesically Moving Fluids
285
3
20.4 The Killing Vector Fields Compatible with Rotation
288
1
20.5 The Case of Two Generators Spanned on u(Alpha) and w(Alpha)
289
4
20.6 The Case of One Generator Spanned on u(Alpha) and w(Alpha)
293
3
20.7 The Case of All Three Generators Being Linearly Independent of u(Alpha) and w(Alpha)
296
1
20.8 Conclusion
297
2
21 On the Classification of the Real Four-Dimensional Lie Algebras
299
20
M.A.H. MacCallum
21.1 Introduction
300
2
21.2 An Enumeration of the 4-Dimensional Algebras
302
5
21.3 Comparison with Other Enumerations
307
3
21.4 Extensions, Applications and Other Work
310
9
22 Spinning Universes in Newtonian Cosmology
319
10
Jayant V. Narlikar
22.1 Introduction
319
1
22.2 Homogeneous and Anisotropic Cosmologies
320
4
22.2.1 The Potential Function Approach
321
1
22.2.2 The Gravitational Force Approach
322
2
22.3 The Work of Davidson and Evans
324
3
22.4 Concluding Remarks
327
2
23 Relativistic Gravitational Fields with Close Newtonian Analogs
329
10
Pawel Nurowski
Engelbert Schucking
Andrzej Trautman
23.1 Introduction
329
1
23.2 Notation
330
1
23.3 The Metric, the Curvature, and the Ricci Tensors
330
1
23.4 The Comoving Coordinate System
331
1
23.5 Flat Space-Times
331
1
23.6 Nontrivial Solutions
332
4
23.6.1 Equations for a Perfect Fluid
332
1
23.6.2 Spherically Symmetric Spaces
332
1
23.6.3 The Kasner Solution
333
1
23.6.4 Perfect Fluid Generalizations of the Kasner Solution
334
2
23.7 Congruences of Null Geodesics
336
3
24 Working with Engelbert
339
14
Istvan Ozsvath
24.1 Introduction
339
1
24.2 Exact Solutions
339
3
24.2.1 Remarks by Kurt Godel
339
1
24.2.2 The Schucking Equations
340
1
24.2.3 The Schucking Solution
341
1
24.2.4 The Finite Rotating Universe
341
1
24.2.5 The Anti-Mach Metric
342
1
24.3 More on Exact Solutions
342
3
24.3.1 All Homogeneous Vacuum Solutions with A term
342
1
24.3.2 All Type N Vacuum Solutions with A term Vanishing Shear and Expansion
343
1
24.3.3 Finite Rotating Universe Revisited
343
2
24.4 Embedding Problems
345
4
24.4.1 Embedding of Dantes into S(4)
346
1
24.4.2 A Special Case for Lambda = 0
346
1
24.4.3 Embedding of Dantes into S(5)
347
1
24.4.4 Embedding of Dantes into S(8)
347
1
24.4.5 Embedding the General Dantes into S(8)
348
1
24.5 The SU(3) Group
349
1
24.6 In Closing
350
3
25 Some Remarks on Twistor Theory
353
14
Roger Penrose
25.1 Historical Comments
353
5
25.2 Twistors and the Einstein Equations
358
9
26 Critique of the Wheeler-DeWitt Equation
367
14
Asher Peres
26.1 Introduction
367
2
26.2 A Simple Example of Constrained Dynamics
369
2
26.3 Definition of a Dynamical Time
371
2
26.4 Quantization of a Minisuperspace
373
8
27 A New Version of the Heavenly Equation
381
26
Jerzy F. Plebanski
Maciej Przanowski
27.1 Introduction
381
1
27.2 An Expanding Congruence of Null Strings
382
11
27.3 Hermitian and Kahlerian Structures on H Space in Euclidean Relativity
393
5
27.4 The Heavenly Equation
398
9
28 A Plain Man's Guide to Bivectors, Biquaternions, and the Algebra and Geometry of Lorentz Transformations
407
28
Wolfgang Rindler
Ivor Robinson
28.1 Introduction
407
1
28.2 Basic Algebra of Real Bivectors and Complex Scalars
408
3
28.3 Basic Geometry of Bivectors
411
5
28.4 Biquaternions and the Bivector Transformations They Generate
416
3
28.5 Lorentz Matrices
419
4
28.6 The Geometry of Lorentz Transformations
423
5
28.7 t-Real Biquaternions, t-Rotations, and t-Boosts
428
3
28.8 The Thomas Precession
431
4
29 Leon Lichtenstein's Work on Rotating Fluids
435
8
Bernd Schmidt
29.1 Introduction
435
1
29.2 Rigidly Rotating Fluids in Newtonian Theory
435
4
29.3 Rigidly Rotating Fluids in Einstein's Theory of Gravity
439
1
29.4 Speculations
440
3
30 Decaying Neutrinos and the Flattening of the Galactic Halo
443
6
Dennis W. Sciama
30.1 Introduction
443
1
30.2 The Neutrino Density Near the Sun
444
2
30.3 Tan(23) and the H(Alpha) Data
446
1
30.4 Tan(23) and the Extragalactic Background at 1500 (Degree)A
446
1
30.5 Conclusions
447
2
31 The Kasner Condition and Inhomogeneous Perfect Fluid Cosmologies
449
16
Jim E.F. Skea
31.1 Introduction
449
3
31.2 Mathematical Background
452
2
31.3 The Basic Quantities
454
2
31.4 The Cosmological Models
456
3
31.5 Application to Space-Times Admitting a G(1)
459
2
31.6 Aspects of Invariant Classification
461
1
31.7 Discussion
462
3
32 Gravitational Screening
465
10
E.A. Spiegel
32.1 Gravitational Stopping Power
465
1
32.2 A Drag Crisis
466
3
32.3 Saved by Self-Gravity
469
4
32.4 The Message Is The Medium
473
2
33 On the Interpretation of the Einstein-Cartan Formalism
475
12
John Stachel
33.1 Introduction
475
1
33.2 The Analogy: Electromagnetism
476
2
33.3 The Analogy: Gravitation
478
3
33.4 Discussion
481
6
34 On Complex Structures in Physics
487
16
Andrzej Trautman
34.1 Introduction
487
1
34.2 Definitions and Notation
488
2
34.3 A Complex Structure Defined by Differentiation
490
1
34.4 Complex Structures Associated with Pseudo-Euclidean Vector Spaces
491
2
34.5 Charge Conjugation
493
2
34.6 CR Structures Associated with Integrable Optical Geometries
495
8
35 The Engelbert Experience: Pathways from the Past
503
12
C. V. Vishveshwara
36 Curriculum Vita
515
 
Engelbert Schucking