The Theory of Everything: Quantum and Relativity is everywhere – A Fermat Universe

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
About Motivation and Luck
1: Brief Introduction
	The Stamler Approach: A Brief Historical Overview of the Original Idea
2: Theory
	The Generalized Metric Dirac Operator
	Scalar Product in Laplace–Beltrami Form
	Example: Schwarzschild Metric
	Transition to the Metric Schrödinger or Covariant Schrödinger Equation
	Further Considerations
	Example: The Classical Dirac Equation in the Minkowski Space-Time and Its Extension to Arbitrary Coordinates
	The Connection to the Einstein Field Equations
	Summing Up the Recipe: The Forward Derivation
	Summing Up the Recipe: The Backward Derivation
	Example: The Higgs Field
	Example: Eigenvalue Solutions for Simple Fields with K( fm) = F(fm)* fm = p*m fm
3: The 1D Quantum Oscillator in the Metric Picture
	The Classical Harmonic Quantum Oscillator within the Metric Picture or the Theory of Everything
	Gaussian-Like Metric Approach
	Cos-Like Metric Approach
	Question of Quantizing the Solution
	The Level Underneath
	Conclusions to the “Einstein Oscillator”
4: The Quantized Schwarzschild Metric
	The Quantization of Time in the Vicinity of a Schwarzschild Object
	The Quantization of Mass for a Schwarzschild Object
	The Level Underneath (see also [16] or Section “The 1D Quantum Oscillator in the Metric Picture”)
	Investigations in Connection with the Speed of Light within the Level Underneath
	Discussion with Respect to rs(nr)/t(nt) = clevel2
	Discussion with Respect to rend(nr, nt)/t(nr, nt) = clevel2
	How to Evaluate the Speed of Light of the Level Underneath?
	Conclusions to Quantized Schwarzschild
5: Matter–Antimatter Asymmetry
	Application to Dirac–Schwarzschild Particles at Rest
6: Generalization of “The Recipe”: From ħ to the Planck Tensor
	Generalization to Non-diagonal Metrics
	Generalization of the “Clever Zero”
	The Generalized “Vectorial Dirac Root”
	Examples for Other “Vectorial Dirac Roots”
		Simple Square Root with Shear Component with (X) = X2
		Simple Square Root with Shear Component with (X) = X2 with Virtual Parameters Ei of Various Orders of “Virtuality”
		Simple Cubic Root Ξ (X) = X3
		Simple Cubic Root Ξ (X) = X3 with Virtual Parameter c
		Simple Quartic Root Ξ (X) = X4
		Simple Quartic Root Ξ (X) = X4 with Virtual Parameter c
	Extension/Generalization to Arbitrary Functional Approaches for K(fn)
		The Planck functional
	Extension/Generalization to Arbitrary Derivative Approaches: The Generalized Gradient of fn
	Extension/Generalization to Higher-Order Planck Tensors
	Summing Up the Generalized Recipe: The Forward Derivation
	Summing Up the Generalized Recipe: The Backward Derivation
	Backward Example: The Higgs Field Revisited (Extended Consideration from [15])
	Forward Example: The Harmonic Oscillator and Eigenvalue Solutions for Simple Fields with K(fm) = F(fm)* fm = p*m fm Revisited (Extended Consideration from [10])
	Conclusions to “Generalization of the Recipe”
7: About Fermat’s Last Theorem
	Introduction
	Motivation
		Why is That?
	Fermat’s Own Proof?
8: Dirac Quantization of the Kerr Metric
	The Generalized Metric Dirac Operator for a Kerr Object “at Rest”
	Further Results and Trials
	The Spatial Appearance of the Leptons
	Conclusions to the Quantized Schwarzschild and Kerr Objects
9: The Photon
	The Photon Metric
	Connections with Maxwell
	The Other Way to Fulfill the Maxwell Equations with Plane Waves
	Illustrations
	Spatial Extension of the Solution and the Localized Photon
	Localizing the Photon Forces It to Evolve Spin
	Option A: Leading to Magnetic Charges
	Option B: Leading to Magnetic Displacement Current Density
	Option C: Finding the Correct Metric, a Yet Unsolved Problem
	Suspicion about Connections to Compactified Coordinates
	The Alternative Interpretation Using Real and Imaginary Part
	Further Illustrations and a Few Words about the Absence of Magnetic Monopoles in Our Observable Universe
	The Total Spatial Displacement for the Photon
	Conclusions to the Photon
10: How the Quantum Theory Already Resides in the Einstein–Hilbert Action
	Theory: The Discarded Term
	The One-Dimensional Case
	The Harmonic Quantum Oscillator in 1D in the Metric Picture
	The Three-Dimensional Case
	Connection with the Technique of the “Intelligent Zero” of a Line Element
	Theory: The Conjecture δRαß = Matter & Energy and the Extended-Einstein Field Equations
	Most Symmetric and Isotropic Virtual Matter Solutions in 2D, 3D, and 4D
	Four Most Simple Solutions for the Whole Thing in 4D: The Matter and Antimatter Asymmetry and Why Time is Different
	The Two-Dimensional Case
	Intermediate Result: The n-Dimensional Case
	Antimatter and Spin
	An Adapted Schwarzschild Solution
	Eigenequations Derived from δRαß for Shear-Free Metrics
		In Four Dimensions
		In Three Dimensions
		In Two Dimensions
		Summing Up This Section
	Separation Approaches
		The 2D Case
		The 3D Case
		The 4D Case
		Summing the Last Section Up
	Example: Symmetry of Revolution
References
Index