Unified Field Theory and Occam's Razor: Simple Solutions to Deep Questions

Contents
Preface
About the Authors
Mathematical Preliminaries
0.1. Clifford Algebra Introduction
0.2. The Geometry of Clifford Algebra
0.2.1. Reflection and rotation of vectors
0.2.2. Clifford reversion
0.3. Exterior Algebra and Wedge Products
0.4. Tensors
0.5. Singlet State
0.6. Group Actions
0.7. Harmonic Functions
0.8. Notation for Quantum Mechanics
0.8.1. Definition of quantum states
0.8.2. Probability and quantum states
0.8.3. Spin
0.8.4. Indistinguishability
0.8.5. Spin entanglement into opposite chirality
0.9. Spinors
0.9.1. Introduction to spinors
0.9.2. An alternative construction of the eigenvector equation
0.9.3. Spacetime vectors under Cartan’s approach
0.9.4. Weyl’s approach to spinors
0.10. Angular Momentum Theory
References
Part 1: Foundations: Electromagnetism, General Relativity, and Quantum Mechanics
Chapter 1. Maxwell’s Equations and Occam’s Razor
1.1. Introduction
1.2. The Electromagnetic Field and the Wave Function
1.2.1. The electromagnetic four potential
1.2.2. Maxwell’s equations
1.3. Properties of the Electromagnetic Field
1.3.1. Derivation of Maxwell’s equations from Lagrangian density
1.3.2. Energy of the electromagnetic field
1.3.3. The scalar field and the Feynman concept of unworldliness
1.3.4. Electrostatic field and vector potential
1.3.5. Electric charge, antimatter, and time direction
1.3.6. Magnetic charges and currents
1.4. Conclusions
References
Chapter 2. Electromagnetic and Quantum Mechanical Waves
2.1. Introduction
2.2. Maxwell’s Equation Revisited
2.3. Two Different Time Representations
2.4. The Energy and Lagrangian of the F+ and F− Fields
2.5. What is the Quantum Mechanical Wavefunction?
2.6. Spacetime Solutions of Wave Equations
2.7. From Vacuum Fluctuations to Heisenberg Uncertainty
2.8. The Electromagnetic Frequency of a Massive Particle
2.9. A New “Rotation” Axis
2.10. The Longitudinal Electromagnetic Wave
Acknowledgments
References
Chapter 3. The Electron and Occam’s Razor
3.1. Introduction
3.2. Maxwell’s Equations in Cl3,1
3.3. Electron Zitterbewegung Model
3.3.1. Simple electron model
3.3.2. Spin and intrinsic angular momentum
3.3.3. Value of the vector potential, cyclotron resonance, and flux density field
3.3.4. Value of magnetic and electrostatic energy, magnetic flux quantization, and radius of the elementary charge
3.3.5. Electron kinematics
3.3.6. Electron and electromagnetic Lagrangian density
3.3.7. Zitterbewegung and a simple derivation of the relativistic mass
3.4. Electromagnetism, Mechanics, and Lorentz Force
3.5. Energy, Momentum, and Quanta Current
3.5.1. Zitterbewegung and Heisenberg’s uncertainty principle
3.6. Electromagnetic Composite at Compton Scale
3.7. Some Other Spinning Charge Models
3.8. Conclusions
References
Chapter 4. The Aharonov–Bohm Effect, Proca Fields, and Flux Quantization
4.1. Introduction
4.2. Energy, Mass, Frequency, and Information
4.3. Magnetic Flux, Phase Shift, Proca Field, and Charge Quantization
4.3.1. Aharonov–Bohm equations and Zitterbewegung model
4.3.2. Proca equation and Zitterbewegung electron model
4.3.3. An equivalence between the electromagnetic Proca and the Klein–Gordon equations
4.3.4. The electromagnetic Dirac equation
4.3.5. Proca equation, electric charge quantization, and Josephson constant
4.4. ESR, NMR, Spin, and “Intrinsic” Angular Momentum
4.5. Hypotheses on the Structure of Ultra-Dense Hydrogen
4.6. Ultra-Dense Hydrogen and Low-Energy Nuclear Reactions
4.7. Conclusions
Acknowledgments
References
Chapter 5. Wave–Particle Duality
5.1. Introduction
5.2. Metrics and the Dirac Equation
5.2.1. Dual equations
5.2.2. Clifford algebra properties
5.2.3. Hamilton–Jacobi functions and the Dirac equation
5.2.4. Exact differentials and metrics
5.2.5. Some examples
5.2.6. Wave–particle duality and the Zitterbewegung phenomenon
5.2.7. Summary of this section
5.3. Geometric Interpretation of e− Mass and de Broglie Wavelength
5.3.1. Electromagnetic analysis of electron mass and Zitterbewegung radius
5.3.2. Relativistic analysis of electron mass and Zitterbewegung radius
5.3.3. Electromagnetic analysis of electron momentum
5.3.4. Relativistic analysis of electron momentum
5.3.5. Quantum mechanical wavelength from de Broglie principle
5.4. Lorentz Transformations of Electromagnetic Waves
5.5. Conclusions
Appendix: Hamilton–Jacobi Functions and Exact Differentials
Appendix: Clifford Algebra and Directional Derivatives
Appendix: Clifford Algebra and Harmonic Functions
References
Chapter 6. Battle of Theories: Magnetic Moment and Lamb Shift Calculations
6.1. Introduction
6.2. The Electron’s Anomalous Magnetic Moment
6.3. A Possible Connection Between α, ΦM, and the Feigenbaum Constant
6.4. The Proton’s Anomalous Magnetic Moment
6.5. Electromagnetic Vacuum Fluctuations
6.6. Lamb Shift
6.7. Which Microscopic Vacuum Model is the Correct One?
6.8. The Magnetic Moment of a Bound-State Electron
6.9. Orbital Angular Momentum Entanglement
6.10. Conclusions
References
Chapter 7. Spinor Fields
7.1. Introduction
7.2. What is the Dirac Spinor Field?
7.3. Optical Spinor Representation of Electromagnetic Fields
7.4. One Particle — Two Fields
7.5. A Factorization of the Electron State
7.5.1. The Dirac–Hestenes and Dirac–Baylis factorization
7.5.2. A factorization with vectorial mass representation
7.6. An Electron Wave at Potential Steps
7.7. Rotor Representation of Zitterbewegung Motion
7.8. From Rotors to Spinors
7.9. Neutrino Waves and Isospin
7.10. Conclusions
Chapter 8. Electron Orbitals and Space–Time Curvature
8.1. Introduction
8.2. A Method of Solving the Dirac Equation
8.2.1. A mass gauge
8.3. Covariance
8.4. Wave Equations for Geodesic
8.5. Quantum Mechanics and Hilbert Spaces
8.6. Classical Mechanics
8.7. One-Dimensional Potential Well
8.8. The Hydrogen Atom
8.9. Light Emission and Absorption
8.9.1. Quantum mechanical state transition
8.9.2. Light detection
8.9.3. Ionization of atoms by low-frequency light
8.10. Conclusion
Appendix: The Schwarzschild Metric
References
Chapter 9. The Pauli Exclusion Principle
9.1. Introduction
9.2. Isotropic Spin Correlation
9.2.1. Rotational invariance in two dimensions
9.2.2. Rotational invariance in three dimensions
9.2.3. The physical origin of Pauli exclusion
9.3. Isotropic Coupling Principle
9.4. From Isotropic Coupling to Pauli Exclusion
9.5. From Pauli Exclusion to Fermi–Dirac Statistics
9.6. Experimental Proofs of Isotropic Electron Entanglement
9.7. Antisymmetric Versus Symmetric Spin Entanglement
9.8. Conclusions
References
Chapter 10. Electron Dynamics in Metals
10.1. Introduction
10.2. The Drude–Sommerfeld Model of Delocalized Electrons
10.3. Thomas–Fermi Screening
10.4. Orbitals Under Electron Screening Effect
10.5. Screening in Weakly Metallic Materials
10.6. Conclusions
References
Part 2: Experimental Validation and Practical Applications
Chapter 11. Superconductivity
11.1. The Bose–Einstein Condensation of Weakly Bound Electrons
11.2. The London Equation
11.3. Tc optimization
11.4. Rotating Superconductors
11.5. Magnetic Flux Quantization
11.6. Conclusions
Appendix: A Useful Vector Field Identity
Acknowledgments
References
Chapter 12. Compton-Scale Electron–Proton Composite
12.1. Introduction
12.2. The Theory of Close Proximity Electron–Nucleus Composite
12.2.1. Characterization of the electron state
12.2.2. Magnetic electron–proton and electron–electron interactions
12.3. Transition to Compton-Scale Composite State
12.3.1. Cooling deuterium plasma
12.3.2. Decelerating particles
12.4. Summary of Experimental Signatures
12.5. Conclusions
Acknowledgments
References
Chapter 13. Electron-Mediated Nuclear Fusion
13.1. Electron-Mediated Fusion Signatures
13.2. Degassing of Metal Deuterides
13.3. Electrochemically Driven Deuteron–Electron Recombination
13.4. Deuterium Diffusion Across Heterogeneous Nanolayers
13.5. Conclusions
References
Chapter 14. Nuclear Forces and Occam’s Razor
14.1. Introduction
14.2. What is the “Strong Nuclear Force”?
14.2.1. Maxwell’s equations and the binding energy
14.2.2. Further evidence from pions
14.2.3. More evidence from scattering experiments
14.2.4. A new proton model
14.3. What is the “Weak Nuclear Force”?
14.4. What Particles are Released During Nuclear Fission?
14.5. The Nuclear Electron Particle
14.5.1. A precise measurement of the nuclear electron mass
14.5.2. A further characterization of the nuclear electron
14.6. A New Landscape of Elementary Particles
14.7. Conclusions
Acknowledgments
References
Chapter 15. Transmutations by Evanescent Neutrinos
15.1. Introduction
15.2. Fission-like Transmutations
15.3. A Physical Model of Fission-Like Transmutations
15.4. Are We Observing Fission or Fusion?
15.5. Conclusions
Acknowledgments
References
Chapter 16. Do Magnetic Monopoles Exist?
16.1. Introduction
16.2. Observation of Helicoidal Particle Tracks
16.3. What are the Helicoidally Spiraling Particles?
16.4. The Muon’s Anomalous Magnetic Moment
Acknowledgments
References
Chapter 17. Simple Experiments
17.1. Introduction
17.2. Bulk Metal Fueled Energy Production
17.3. Thin Wire Fueled Energy Production
Acknowledgments
References
Index