Quantum Mechanics and Gravity

By: Mendel Sachs

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Hardcover | 1 January 2004

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208 Pages

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22.86 x 15.88 x 1.27

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Theoretical physics is presently at a very exciting time in the history of scientific discovery. For we are at a precipice facing two conflicting 20th century revolutionary movements in physics, each purporting to be basic truths of nature - the quantum theory and the theory of relativity. In the 20th century the mathematical expression of the quantum theory yielded correct predictions of a great deal of the data on the behavior of the molecular, atomic, nuelear and elementary partiele domains of matter. In the same period, the theory of relativity suc- cessfully described new features of material systems. In special rela- tivity, the relativistic Doppler effects (transverse and longitudinal) of electromagnetic radiation, and the mechanics of matter that moves at speeds elose to the speed of light, revealing, for example, the en- 2 ergy mass relation, E = mc , revolutionized our thinking. In its form of general relativity, it has yielded a formalism that successfully pre- dicted features of the phenomenon of gravity, also predicted by the elassical Newtonian theory, but in addition, features not predicted by the elassical theory, thereby superceding Newton's theory of universal gravitation. The problem we are now faced with, in these early decades of the 21st century, is that in their precise mathematical forms and their conceptual bases, the theory of relativity and the quantum theory are both logically and mathematically incompatible.

Industry Reviews

From the reviews:

"This book differs from the many other books on the same topics in three essential points: 1st, it concentrates on the historical development of the question of the unification of quantum theory and gravity, 2nd, it uses the quaternion approach to describe the metric and other geometric objects, and 3rd, it is a quite personal book. ... a very readable monograph, containing also philosophical issues, considerations about electromagnetism, and unified field theory." (Hans-Juergen Schmidt, Zentralblatt MATH, Vol. 1052, 2005)

"The basic attempt of this book is to initiate a study of a single, coherent theory of matter applicable to all domains, from elementary particle physics to cosmology. ... This very interesting and clearly written book is even readable by a final year's student in physics. The presentation is very well got-up. ... I highly recommend this excellent work to every theoretical physicist interested in general relativity and unified field theories." (Fernand Dhoore, Physicalia, Vol. 57 (3), 2005)

"Sachs' book is a fascinating exposition of how an approximation in general relativity brings out quantum mechanical features. Perhaps Einstein would have been greatly interested. ... I think it should be read by anyone who is interested in quantum mechanics and gravity." (J. Hartley, Contemporary Physics, Vol. 45 (6), 2004)

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Non-Fiction Science Physics Relativity Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Mathematics Applied Physics Astrophysics Nuclear Physics Astronomy, Space & Time Cosmology & The Universe Geophysics

Classical Mathematics Gravity

Introduction	p. 1
History and Philosophy of the Quantum Theory	p. 2
Blackbody Radiation	p. 2
Photoelectric Effect	p. 3
Compton Effect	p. 4
Atomic Spectra and the Bohr Atom	p. 4
The Seminal Experiment: Electron Diffraction	p. 6
Interpretations of Quantum Mechanics	p. 9
History and Philosophy of Theories of Gravity Leading to the Theory of General Relativity	p. 11
Newton's Third Law of Motion	p. 15
Predictions of Einstein's Theory of General Relativity	p. 18
A Quantum Theory of Gravity	p. 21
The Theory of General Relativity: Einstein's Formulation	p. 25
The Spacetime Language	p. 26
On Invariance of the Speed of Light	p. 27
The Riemannian Metric	p. 28
Expression of Einstein's Field Equations	p. 30
Einstein's Equations from the Variational Principle	p. 31
The Vacuum Equation	p. 34
The Geodesic Equation	p. 36
The Schwarzschild Solution and the Newtonian Limit	p. 39
A Unified Field Theory	p. 43
Einstein's Field Theory in Quaternion Form	p. 44
Spin Affine Connection	p. 47
The Quaternion Variables in a Riemannian Spacetime	p. 48
Derivation of the Quaternion Metrical Field Equations from the Principle of Least Action	p. 50
A Symmetric Tensor-Antisymmetric Tensor Representation of General Relativity	p. 53
Einstein's Field Equation from the Symmetric Tensor Part	p. 54
The Maxwell Field Equations from the Antisymmetric Part	p. 55
The Geodesic Equation in Quaternion Form	p. 58
Summary	p. 61
Quantum Mechanics from a Theory of Inertial Mass in Relativity	p. 63
Introduction	p. 64
Discovery of Quantum Mechanics	p. 67
Inertial Mass from General Relativity	p. 71
The Matter Field Equations in General Relativity	p. 73
Gauge Covariance	p. 73
The Elementary Interaction	p. 75
Proof of the Attractive Gravitational Force in the Newtonian Limit and the Oscillating Universe Cosmology	p. 76
From the Mach Principle to the Generalized Mach Principle	p. 77
Electromagnetism	p. 79
Introduction	p. 80
Interpretation of Maxwell's Equations in the Holistic Field Theory	p. 83
The Elementary Interaction Formulation	p. 84
A Spinor Formulation of Electromagnetic Theory in Special Relativity	p. 85
Invariants and Conservation Equations in the Spinor Formalism	p. 86
Lagrangian for the Spinor Formulation of Electromagnetism	p. 88
Faraday's Approach and the Mach Principle	p. 90
Spinor Formulation of Electromagnetism in General Relativity	p. 90
Extension of the Spinor Conservation Laws of Electromagnetism in General Relativity	p. 91
The Electromagnetic Interaction Functional in the Matter Field Equations	p. 94
Delayed Action at a Distance	p. 95
The Pauli Principle and Pair Creation/Annihilation	p. 97
Introduction	p. 98
The Individual Particle Model	p. 100
The Free Field Limit	p. 100
Conservation of Interaction	p. 101
The Pauli Exclusion Principle	p. 103
Sufficiency of the Three Conditions for Proof of the Pauli Principle	p. 108
Fermi-Dirac Statistics from the Nonrelativistic Approximation for ¿	p. 110
Bound Particle-Antiparticle Pairs. Ground State	p. 111
Energy and Momentum of the Bound Pair in its Ground State	p. 113
Dynamical Properties of the Pair in its Ground State	p. 114
Pair Creation, the Physical Vacuum, and Blackbody Radiation	p. 117
Atomic and Elementary Particle Physics	p. 121
Introduction	p. 122
Hydrogen	p. 124
Linearization of the Hydrogen Field Equation	p. 124
The Lamb Splitting	p. 127
The Neutron	p. 130
Binding Energy of the Neutron: A Phenomenological Determination	p. 131
The Neutron Lifetime	p. 132
The Neutron Magnetic Moment	p. 134
Mass Doublets: The Electron-Muon	p. 135
Infinite Lepton Spectrum	p. 136
The Pion	p. 138
Ratio of Neutral and Charged Pion Masses	p. 139
Ratio of Neutral and Charged Pion Lifetimes	p. 140
CP Violation in Neutral Kaon Decay	p. 141
Charge Quantization in General Relativity	p. 143
Astrophysics and Cosmology in General Relativity	p. 147
Introduction	p. 148
Principle of Equivalence	p. 150
The Quaternion Geodesic for a Stationary Orbit	p. 152
Planetary Motion	p. 153
The Schwarzschild Problem	p. 155
The Radial Solution and Perihelion Precession	p. 158
The Hubble Law and Cosmology	p. 159
The Oscillating Universe Cosmology	p. 160
Dynamics of the Expansion and Contraction of the Universe	p. 161
Spiral Structure of the Universe	p. 163
Black Holes and Pulsars	p. 166
Possible Model of a Pulsar	p. 168
Damped Oscillatory Motion and Pulsars	p. 170
Separation of Matter and Antimatter in the Early Universe	p. 171
Bibliography	p. 175
Index	p. 189
Table of Contents provided by Publisher. All Rights Reserved.

Quantum Mechanics and Gravity

At a Glance

Hardcover

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