The Theory of Everything: Quantum and Relativity is Everywhere – A Fermat Universe By Norbert Schwarzer
Contents
1 Brief Introduction 1
The Stamler Approach: A Brief Historical Overview of the
Original Idea 1
2 Theory 7
The Generalized Metric Dirac Operator 7
Scalar Product in Laplace–Beltrami Form 10
Example: Schwarzschild Metric 15
odinger Covariant Schrodinger
Equation 16
Example: The Classical Dirac Equation in the Minkowski
| Example: Eigenvalue Solutions for Simple Fields | 29 |
Further Considerations 18
Space-Time and Its Extension to Arbitrary Coordinates 20
The Connection to the Einstein Field Equations 24
Summing Up the Recipe: The Forward Derivation 25
Summing Up the Recipe: The Backward Derivation 26
Example: The Higgs Field 27
3 The 1D Quantum Oscillator in the Metric Picture 31
The Classical Harmonic Quantum Oscillator within the Metric
Picture or the Theory of Everything 32
Gaussian-Like Metric Approach 41
Cos-Like Metric Approach 44
Question of Quantizing the Solution 45
The Level Underneath 50
Conclusions to the “Einstein Oscillator” 52
4 The Quantized Schwarzschild Metric 55
The Quantization of Time in the Vicinity of a Schwarzschild Object 57
The Level Underneath (see also [16] or Section “The 1D Quantum
Investigations in Connection with the Speed of Light within the
The Quantization of Mass for a Schwarzschild Object 58
Oscillator in the Metric Picture”) 59
Level Underneath 60
Discussion with Respect to rs(nr)/t(nt) = clevel2 62
Discussion with Respect to rend(nr, nt)/t(nr, nt) = clevel2 63
How to Evaluate the Speed of Light of the Level Underneath? 64
Conclusions to Quantized Schwarzschild 65
5 Matter–Antimatter Asymmetry 67
Application to Dirac–Schwarzschild Particles at Rest 67
6 Generalization of “The Recipe”: From � to the Planck Tensor 69
Generalization to Non-diagonal Metrics 69
Simple square root with shear component with (X ) = X 2 with
Extension/Generalization to Arbitrary Functional Approaches for
Extension/Generalization to Arbitrary Derivative Approaches: The
Generalization of the “Clever Zero” 73
The Generalized “Vectorial Dirac Root” 73
Examples for Other “Vectorial Dirac Roots” 77
Simple square root with shear component with (X ) = X 2 77
virtual parameters E i of various orders of “virtuality” 77
Simple cubic root (X ) = X 3 78
Simple cubic root (X ) = X 3 with virtual parameter c 79
Simple quartic root (X ) = X 4 79
Simple quartic root (X ) = X 4 with virtual parameter c 80
K( fn) 81
The Planck functional 81
Generalized Gradient of fn 82
Extension/Generalization to Higher-Order Planck Tensors 83
Backward Example: The Higgs Field Revisited (Extended
Forward Example: The Harmonic Oscillator and Eigenvalue
Solutions for Simple Fields with K( fm) = F ( fm)∗ fm = p∗ fm
Summing Up the Generalized Recipe: The Forward Derivation 84
Summing Up the Generalized Recipe: The Backward Derivation 85
Consideration from [15]) 86
m
Revisited (Extended Consideration from [10]) 94
Conclusions to “Generalization of the Recipe” 97
7 About Fermat’s Last Theorem 99
Introduction 99
Motivation 100
Why is That? 100
Fermat’s Own Proof? 101
8 Dirac Quantization of the Kerr Metric 103
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The Generalized Metric Dirac Operator for a Kerr Object “at Rest” 103
Further Results and Trials 106
The Spatial Appearance of the Leptons 109
Conclusions to the Quantized Schwarzschild and Kerr Objects 111
9 The Photon 115
The Photon Metric 115
Connections with Maxwell 119
The Other Way to Fulfill the Maxwell Equations with Plane Waves 121
Illustrations 122
Spatial Extension of the Solution and the Localized Photon 123
Localizing the Photon Forces It to Evolve Spin 128
Option A: Leading to Magnetic Charges 130
Option B: Leading to Magnetic Displacement Current Density 131
Option C: Finding the Correct Metric, a Yet Unsolved Problem 132
Suspicion about Connections to Compactified Coordinates 137
The Alternative Interpretation Using Real and Imaginary Part 140
Further Illustrations and a Few Words about the Absence of
Magnetic Monopoles in Our Observable Universe 143
The Total Spatial Displacement for the Photon 146
Conclusions to the Photon 148
10 How the Quantum Theory Already Resides in the Einstein–Hilbert
Action 149
Theory: The Discarded Term 149
Connection with the Technique of the “Intelligent Zero” of a Line
Theory: The Conjecture δRαβ = Matter & Energy and the
Most Symmetric and Isotropic Virtual Matter Solutions in 2D,
Four Most Simple Solutions for the Whole Thing in 4D: The Matter
The One-Dimensional Case 157
The Harmonic Quantum Oscillator in 1D in the Metric Picture 159
The Three-Dimensional Case 164
Element 170
Extended-Einstein Field Equations 172
3D, and 4D 173
and Antimatter Asymmetry and Why Time is Different 174
The Two-Dimensional Case 176
Intermediate Result: The n-Dimensional Case 176
Antimatter and Spin 177
An Adapted Schwarzschild Solution 178
Eigenequations Derived from δRαβ for Shear-Free Metrics 181
In Four Dimensions 182
In Three Dimensions 184
In Two Dimensions 185
Summing Up This Section 187
Separation Approaches 187
The 2D Case 187
The 3D Case 188
The 4D Case 189
Summing the Last Section Up 189
Example: Symmetry of Revolution 192
References 195
Index 199
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