Quantum Mechanics from General Relativity: An Approximation for a Theory of Inertia

ISBN-13: 9789027722478 / Angielski / Twarda / 1986 / 227 str.

Mendel Sachs; M. Sachs

Opis

This monograph is a sequel to my earlier work, General Relativity and Matter 1], which will be referred to henceforth as GRM. The monograph, GRM, focuses on the full set of implications of General Relativity Theory, as a fundamental theory of matter in all domains, from elementary particle physics to cosmology. It is shown there to exhibit an explicit unification of the gravitational and electromagnetic fields of force with the inertial manifestations of matter, expressing the latter explicitly in terms of a covariant field theory within the structure of this general theory. This monograph will focus, primarily, on the special relativistic limit of the part of this general field theory of matter that deals with inertia, in the domain where quantum mechanics has been evoked in contemporary physics as a funda mental explanation for the behavior of elementary matter. Many of the results presented in this book are based on earlier published works in the journals, which will be listed in the Bibliography. These results will be presented here in an expanded form, with more discussion on the motivation and explanation for the theoretical development of the subject than space would allow in normal journal articles, and they will be presented in one place where there would then be a more unified and coherent explication of the subject.

Spis treści

1 / Fundamental Outlook.- 2 / On the Comparison of the Quantum and Relativity Theories.- 2.1 Competing Concepts.- 2.2 Is the Quantum Jump Compatible with the Theory of Relativity?.- 2.3 Is the Theory of Relativity Complete as a Theory of Matter?.- 2.4 The Einstein—Podolsky—Rosen Paradox.- 2.4.1. Bohr’s Reply to Einstein, Podolsky and Rosen.- 2.5 The Hidden Variable Approach.- 2.6 Bell’s Inequalities and General Relativity.- 2.6.1. The State Vector and Bell’s Inequalities.- 3 / Basis of a Matter Field Theory of Inertia — a Generalization of Quantum Mechanics.- 3.1. The General Mathematical Structure and Philosophical Implications.- 3.1.1. The Symmetry Group from Axiom 1 and Funda mental Field Variables.- 3.1.2. The Generalized Mach Principle.- 3.2. The Conservation of Interaction.- 3.3. Determinism.- 4 / A Covariant Field Theory of Inertia.- 4.1. On the Origin of Inertial Mass.- 4.2. The Spinor Formalism in Special Relativity.- 4.3. The Spinor Variables in General Relativity.- 4.4. The Spinor Matter Field Equations in General Relativity.- 4.4.1. Gauge Invariance.- 4.4.2. Electromagnetic Coupling.- 4.5. Matter and Antimatter.- 4.5.1. Proof of Force Symmetry of Matter and Antimatter.- 4.6. On the Quantization of Electrical Charge from General Relativity.- 4.7. Conclusions.- 5 / The Electromagnetic Interaction.- 5.1. On the Meaning of the Electromagnetic Field Equations.- 5.2. Generalization of the Elementary Interaction Formalism.- 5.3. A Spinor Formulation of Electromagnetism.- 5.3.1. Invariants and Conservation Equations.- 5.4. The Interaction Lagrangian.- 5.4.1. The Electromagnetic Four-Potential.- 6 / Quantum Mechanics from the Matter Field Equations and Derivation of the Pauli Exclusion Principle.- 6.1. Approximations to Quantum Mechanics.- 6.1.1. The Free Field Limit.- 6.1.2. Coupling to an External Potential.- 6.2. The Pauli Exclusion Principle — a Derivation.- 6.2.1. Sufficiency of the Three Conditions for Proof of the Pauli Principle.- 6.2.2. Fermi—Dirac Statistics from the Nonrelativistic Approximation for ?.- 6.3. The Hartree Approximation for the Matter Field Equations.- 6.3.1. Another Approximation for the Many-Electron Atom.- 6.4 Scattering Cross Section.- 7 / The Particle—Antiparticle Pair without Annihilation Creation.- 7.1. The Field Equations for the Particle—Antiparticle Pair.- 7.2. An Exact Bound State Solution for the Particle—Antiparticle Pair.- 7.3. The Energy and Momentum of the Bound Particle—Anti particle in its Ground State.- 7.4. The Free Particle Limit and Pair Creation.- 7.5. The Continuity of Energy Values.- 7.5.1. Rejection of the Photon Model in ‘Pair Annihilation’.- 7.6. Dynamical Properties of the Pair in the Ground State.- 7.7. The Compton Effect.- 7.8. Blackbody Radiation — a Derivation of Plank’s Law.- 7.9. The Anomalous Magnetic Moment of the Electron.- 8 / The Electron—Proton System.- 8.1. Linearization of the Hydrogen Field Equations.- 8.2. The Lamb Splitting.- 8.3. Deuterium and He+.- 8.4. The Lifetimes of Atomic Excited States.- 8.5. Atomic Helium.- 8.6. Electron—Proton Scattering in a Vacuum.- 8.7. Electron—Proton Scattering in a Background of Pairs.- 8.7.1. The Screening Effect of the Background Pairs on the e—p Interaction.- 8.7.2. The Generalized Electromagnetic Interaction.- 8.7.3. Concluding Remarks.- 8.8. Summary.- 9 / Elementary Particle Physics.- 9.1. The Neutron.- 9.1.1. Polarization of the Pair Participation in the Neutron State.- 9.1.2. The Binding Energy of the Neutron.- 9.1.3. The Magnetic Moment of the Neutron.- 9.2. The Pion.- 9.2.1. The Mass Ratio of Neutral to Charged Pions.- 9.2.2. The Ratio of Neutral to Charged Pion Lifetimes.- 9.3. On the Possible Origin of CP-Violation in Neutral Kaon Decay.- 9.3.1. Neutral Kaon Decay.- 9.3.2. The Irreducible Spinor Matter Field Equations and CP-Violation.- 9.3.3. The Generalized Electromagnetic Interaction.- 9.3.4. CP-Violation in Kaon Decay.- 9.3.5. Estimates of the Magnitude of CP-Violation in K0L Decay.- 9.4. On Time Reversal Noninvariance in Nuclear Forces — a Magnetic Resonance Experimental Test.- 9.4.1. A Possible Source of T-Violation in Nuclear Forces.- 9.5. Proton—Antiproton Collisions and the W±-Particle from General Relativity.- 9.6. Concluding Remarks.- Epilogue.- Appendix A / Computation of the Lamb Splitting 207.