Special Algebra for Special Relativity: Second Edition: Proposed Theory of Non-Finite Numbers

Table of Contents 5 Preface 8 Synopsis - Finite Precision for Numbers 9 Chapter 1 - Numbers 19 1.2 Geometric-Vectors 20 1.3 Quaternions 22 1.4 Translation Back to Geometry 37 1.5 Singular-Label-Numbers 38 1.6 Exercises (Numbers) 39 Chapter 2 - Particles 51 2.2 Inertial Reference Frames 54 2.3 The Unspecified-Speed-Parameter 56 2.4 Compound-Label-Numbers and Components 57 2.5 Adding Hyperbolic Angles 60 2.6 Energy, Time Dilation, Length Contraction 64 2.7 Space-Like and Time-Like Invariants 66 2.8 Electric Current Density 70 2.9 Motion Faster than Light 73 2.10 Anti-Matter 82 2.11 Distributed Material Theory 90 2.12 Exercises (Particles) 101 Chapter 3 - Fields 107 3.2 All-Number Notation 112 3.3 Gauges and Super-Potentials 123 3.4 Lorentz Transformation 126 3.5 Biot-Savart Law 134 3.6 Electric Energy-Momentum of an Electron 137 3.7 Maxwell's Wave Equation 144 3.8 Forces Using Geometric-Vector Notation 150 3.9 Force Density Invariant 151 3.10 Area and Volume Differential Operators 161 3.11 Exercises (Fields) 169 Chapter 4 - Waves 177 4.2 Development of the Dirac Equation 180 4.3 Solutions to the Dirac Equation 184 4.4 Particle Properties 187 4.5 Two Alternative Arrangements 191 4.6 Lorentz Transformation of a Dirac Spinor 193 4.7 Exercises (Waves) 199 Chapter 5 - Proposed Theory 205 5.2 Cantor's Theory of Infinite Sets 214 5.3 Algebra Field for Local-Real Numbers 222 5.4 Lorentz Transformation with Non-Finite Numbers 227 5.5 Dirac Equation Development 247 5.6 Force Density Using the Complex-Conjugate 255 5.7 Spin of a Photon 263 5.8 Exercises (Proposed Theory) 266 Appendix A - Octonions and Sedonions 275 Appendix B - Spooky Action at a Distance 295 Appendix C - Discovering an Abstraction 307 The Storybook 313 Glossary 314 Index 325 Back Cover 328