100 years of gravity and accelerated frames : the deepest insights of Einstein and Yang-Mills

This collection of papers presents ideas and problems arising over the past 100 years regarding classical and quantum gravity, gauge theories of gravity, and spacetime transformations of accelerated frames. Both Einstein's theory of gravity and the Yang-Mills theory are gauge invariant. The invariance principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the physical world. In this spirit, this book attempts to survey the development of various formulations for gravitational and Yang-Mills fields and spacetime transformations of accelerated frames, and to reveal their associated problems and limitations.The aim is to present some of the leading ideas and problems discussed by physicists and mathematicians. We highlight three aspects: formulations of gravity as a Yang-Mills field, first discussed by Utiyama; problems of gravitational theory, discussed by Feynman, Dyson and others; spacetime properties and the physics of fields and particles in accelerated frames of reference.These unfulfilled aspects of Einstein and Yang-Mills' profound thoughts present a great challenge to physicists and mathematicians in the 21st century.

I. NewtonH. PoincareA. EinsteinA. Einstein and M. GrossmannA. EinsteinD. HilbertE. CartanP. Jordanvon M. FierzC. Brans and R. H. DickeC. N. Yang and R. L. MillsT. D. Lee and C. N. YangR. UtiyamaT. W. B. KibbleC. MollerT. Fulton and F. Rohrlich and L. WittenT. Y. Wu and Y. C. LeeJ. P. Hsu and L. HsuJ. P. Hsu and L. HsuD. T. Schmitt and T. KleinschmidtR. P. FeynmanB. S. DeWittB. S. DeWittL. D. Faddeev and V. N. PopovS. MendelstamE. S. Fradkin and I. V. TyutinF. J. DysonK. Hayashi and T. NakanoR. Utiyama and T. FukuyamaC. N. YangW. T. NiY. M. ChoJ. P. HsuP. A. M. DiracK. Hayashi and T. ShirafujiA. A. Logunov and M. A. MestvirishviliJ. P. HsuW. T. NiJ. H. Taylor, Jr.T. T. Wu and C. N. YangR. L. MillsC. N. YangL. O'Raifeartaigh and N. StraumannP.-M. HoS. WeinbergP. J. E. Peebles and B. RatraJ. P. Hsu and D. FineS. L. Marateck

Preface	p. ix
Acknowledgements	p. xiv
Remarks on the Development of the Gravitational and Yang-Mills Fields, and Accelerated Frames	p. xix
Chapter 1 The Dawn of Gravitation
A The Mathematical Principles of Natural Philosophy (Extract) Rules of Reasoning in Philosophy Phenomena, or Appearances	p. 2
B On the Dynamics of the Electron (Extract) Introduction, Hypotheses Concerning Gravitation	p. 13
C On the Relativity Principle and the Conclusions Drawn from It (Extract)	p. 33
Chapter 2 Einstein's Deepest Insight and Its Early Impacts
A Outline of a Generalized Theory of Relativity and of a Theory of Gravitation (Extract)	p. 48
B The Foundation of the General Theory of Relativity	p. 65
C The Foundation of Physics	p. 120
D On a Generalization of the Concept of Riemann Curvature and Spaces with Torsion	p. 132
Chapter 3 The Scalar-Tensor Theory of Gravity
A Formation of the Stars and Development of the Universe	p. 136
B On the Physical Interpretation of P. Jordan's Extended Theory of Gravitation (Extract)	p. 140
C Mach's Principle and a Relativistic Theory of Gravitation (Extract)	p. 142
Chapter 4 Yang-Mills' Deepest Insight and Its Relation to Gravity
A Conservation of Isotopic Spin and Isotopic Gauge Invariance	p. 150
B Conservation of Heavy Particles and Generalized Gauge Transformations	p. 155
C Invariant Theoretical Interpretation of Interaction	p. 157
D Lorentz Invariance and the Gravitational Field	p. 168
Chapter 5 Accelerated Frames: Generalizing the Lorentz Transformations
A On Homogeneous Gravitational Fields in the General Theory of Relativity and the Clock Paradox	p. 180
B Physical Consequences of a Co-ordinate Transformation to a Uniformly Accelerating Frame	p. 204
C The Clock Paradox in the Relativity Theory	p. 223
D Four-dimensional Symmetry of Taiji Relativity and Coordinate Transformations Based on a Weaker Postulate for the Speed of Light (Extract)	p. 240
E Generalized Lorentz Transformations for Linearly Accelerated Frames with Limiting Four-Dimensional Symmetry	p. 247
F Generalizing Lorentz Transformations for Accelerated Frames and Their Physical Implications	p. 258
Chapter 6 Quantum Gravity and 'Ghosts'
A Quantum Theory of Gravitation	p. 272
B Quantum Theory of Gravity. II The Manifestly Covariant Theory (Extract)	p. 298
C Quantum Theory of Gravity, III Applications of the Covariant Theory	p. 307
D Feynman Diagrams for the Yang-Mills Field	p. 325
E Feynman Rules for Electromagnetic and Yang-Mills Fields from the Gauge-Independent Field-Theoretic Formalism (Extract)	p. 327
F S Matrix for Yang-Mills and Gravitational Fields (Extract)	p. 339
G Missed Opportunities (Extract, with a brief comment of the author) Introduction, General Coordinate Invariance	p. 347
Chapter 7 Gauge Theories of Gravity
A Extended Translation Invariance and Associated Gauge Fields	p. 354
B Gravitational Field as a Generalized Gauge Field	p. 371
C Integral Formalism for Gauge Fields (with a brief comment)	p. 387
D Yang's Gravitational Field Equations	p. 391
E Einstein Lagrangian as the Translational Yang-Mills Lagrangian	p. 393
F De Sitter and Poincare Gauge-Invariant Fermion Lagrangians and Gravity	p. 398
Chapter 8 Alternate Approaches to Gravity: Roads Less Traveled By
A Fixation of Coordinates in the Hamiltonian Theory of Gravitation	p. 402
B New General Relativity (with Addendun)	p. 409
C Relativistic Theory of Gravitation	p. 442
D Yang-Mills Gravity: A Union of Einstein-Grossmann Metric with Yang-Mills Tensor Fields in Flat Spacetime with Translation Symmetry	p. 462
Chapter 9 Experimental Tests of Gravitational Theories
A Empirical Foundations of the Relativistic Gravity	p. 476
B Binary Pulsars and Relativistic Gravity	p. 494
Chapter 10 Other Perspectives
A Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields (Extract)	p. 504
B Gauge Fields	p. 512
C Magnetic Monopoles, Fiber Bundles, and Gauge Fields	p. 527
D Gauge Theory: Historical Origins and Some Modern Developments	p. 539
E String Theory as a Generalization of Gauge Symmetry	p. 562
F The Cosmological Constant Problem	p. 569
G The Cosmological Constant and Dark Energy (Extract)	p. 592
Appendices
A Marcel Grossmann (1878-1936)	p. 618
B Remembering Robert L. Mills	p. 622

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