The Math of Body, Soul, and the Universe

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Acknowledgment
About the Book
Technical Note
Personal Motivation
Some Fundamental Motivation
From the Fermi-Paradox to a “Fermi-Prophecy”
A Simple Calculation and a Terrible Result
A Postscript for a Current Occasion
Another Postscript
The Other Side of the Coin
The Other COVID Project for the Good Doctor Based on Honest Research and True Science
Seven Days
Preface
Day One
Day Two
Day Three
Day Four
Day Five
Day Six
Day Seven
Obituary
For You
The First Day: Let There Be Nothing
Chapter 1: Making Contact with Quantum Gravity
1.1: Brief Story about the Minimum Principle—Part I
1.2: No Stress Without Contact and No Contact Without Stress
1.3: World Formula and Psychology ... What Does Not Want to Enter Our Heads
The Second Day: Let There Be Photons
Chapter 2: Societons and Ecotons
2.1: Why Considering Socioeconomic Interaction via Photons?
2.1.1: Motivation
2.2: A Most Fundamental Starting Point and How to Proceed from There
2.3: An Equation for Everything
2.4: From Hilbert via Klein–Gordon to an Approximated Dirac Equation
2.4.1: Entanglement as Origin of Mass (and Potential) and Thus Possibly Also Any Kind of Inertia and Interaction (Including Interaction in Socioeconomic Space-Times)
2.5: A Little Bit Proof and Reassurance
2.5.1: Deriving the Electromagnetic Field
2.5.2: Toward a Dirac Equation in the Metric Picture and Its Connection to the Classical Quaternion Form
2.5.3: About a Small Extension and Generalization
2.5.4: Elastic Space-Times
2.6: Modeling Socioeconomic Space-Times
2.6.1: The Space-Time of Socioeconomy
2.6.2: Photons
2.7: Societons and Ecotons—The Photons of a Human Society
2.7.1: How to Prove the Existence of Societons and Ecotons and Measure the Strength of the Effect?
2.8: Appendix to “Societons and Ecotons”
2.8.1: Derivation of Electromagnetic Interaction (and Matter) via a Set of Creative Transformations
Chapter 3: Humanitons—The Intrinsic Photons of the Human Body Underst and Them and Cure Yourself
3.1: Why Should We Model the Intrinsic Communication of a Biological Entity Like Our Own Organism viaGeneralized Photons?
3.1.1: A Simple Motivation
3.2: Fundamental Top-Down Approach for Any System
3.3: The Human Body as a VERY Complex Communication System
3.4: From Hilbert’s World Formula
3.5: The Situation in 4 Dimensions
3.6: The Situation in n Dimensions
3.6.1: The 2-Dimensional Space
3.6.2: The 3-Dimensional Space
3.6.3: The 4-Dimensional Space
3.6.4: The 5-Dimensional Space
3.6.5: The 6-Dimensional Space
3.6.6: The 7-Dimensional Space
3.6.7: The 8-Dimensional Space
3.6.8: The 9-Dimensional Space
3.6.9: The 10-Dimensional Space
3.7: Periodic Space-Time Solutions
3.8: Cartesian Coordinates
3.8.1: A Somewhat More General Case
3.8.2: The Total Vacuum Case → Photonic Solutions
3.9: Higher Numbers of Dimensions
3.10: Conclusions about Our “Photonic Math” for the Description of the Human “Body System”
Chapter 4: Social Distancing
4.1: Motivation
4.2: Open Letter to Ray Dalio
4.3: The New Space-Time of Socio-Economy
4.4: The Fundamental Equation for Everything
4.5: From Hilbert via Klein–Gordon to Dirac
4.5.1: Entanglement as Origin of Mass (and Potential) and Thus Possible Also Any Kind of Inertia and Interaction (Including Interaction in Socioeconomic Space-Times)
4.6: Modeling Socioeconomic Space-Times
4.7: Interpretation
4.7.1: The Universal Wall Principle—Why Everything in Existence Needs Boundaries
4.7.2: The Generalization of the WALL Principle
4.7.3: Information and Progress Require Boundaries
4.8: Another Open Letter to the Poor Wombats of This World
4.9: Epilogue
4.10: Conclusions
4.11: Outlook
Chapter 5: Mastering Human Crises with Quantum Gravity-Based but Still Practicable Models
5.1: First Measure: SEEING and UNDERSTANDING the WHOLE
5.2: Motivation
5.3: How to Achieve the Necessary Complexity of Socioeconomic Space-Times?
5.3.1: Self-Similarity, Bi-harmonics, and Other Options
5.4: Simple Symmetries
5.5: Spherical Coordinates
5.6: Half Spin Hydrogen
5.7: Cylindrical Coordinates
5.8: Cartesian Coordinates
The Third Day: Let There Be Mass and Inertia
Chapter 6: Masses and the Infinity Options Principle
6.1: Abstract: Brief Description of Goals of This Section
6.2: Repetition: Fundamental Starting Point and How to Proceed from There
6.3: Repetition: Hilbert’s World Formula
6.4: The Infinity Options Principle
6.5: Considering the Vacuum State Leads to Broken Symmetry and Higgs Field
6.6: The Entanglement of Dimensions and the Production of Mass
6.7: Obtaining Quantized Masses in Situations of R* = 0
6.7.1: Several Time-Like Dimensions
6.7.2: Wave-Like Entanglement with Higher Dimensions
6.7.3: Periodic Coordinate Quantization
6.7.4: Quantum Well Quantization
6.8: The Schwarzschild Case and the Meaning of the Schwarzschild Radius
6.8.1: Brief Discussion of Singularity Problem
6.8.2: Back to the Case r >> rs
6.8.3: A Brief Reminder about Bekenstein Problem
6.8.4: Consequences with Respect to the Dimension of Time
6.8.4.1: How can a q-dimensional black hole object reside inside an only 4-dimensional space-time? Answer: Our supposedly 4-dimensional space-time is not 4- but n-dimensional!
6.8.5: The Observer and the Problem of the Transition to Newton’s Gravity Law
6.8.6: Back to Quantum-Mass-Schwarzschild Radius Discrepancy
6.9: More Metric Options and Subsequent Quantum Equations Plus Their Solutions
6.9.1: Five Dimensions
6.9.2: Six Dimensions
6.9.3: Eight Dimensions
6.10: A Few Words about n Dimensions and n−1 Spheres
6.11: Intermediate Sum-Up: Direct Extraction of Klein−Gordon and Schrödinger Equations from Metric Tensor
6.11.1: Repetition: Metric Klein−Gordon Equation without Mass or Potential
6.11.2: Metric Klein−Gordon Equation with Mass
6.11.3: Metric Klein−Gordon Equation with Mass and Potential
6.11.4: Derivation of the Schrödinger Equation
6.11.5: More General r-Dependent Potentials
6.12: Toward an Explanation for the 3-Generation Problem
6.12.1: Repetition: Dirac in the Metric Picture and Its Connection to the Classical Quaternion Form
6.12.1.1: Restriction to Laplace functions
6.12.2: Getting Rid of Quaternions
6.12.2.1: Treating classical Dirac approach with the new method
6.12.3: Repetition: Elastic Space-Times
6.12.4: Back to Main Section
6.12.5: Intermediate Section: Consequences of Infinite Options Principle
6.12.6: Back to the Sub-Section and the 3-Generation Problem of Elementary Particles
6.12.6.1: Applying metric Dirac or elastic approach
6.12.7: Incorporation of Our Bekenstein Information Solution with n-Dependent Schwarzschild Radius
6.12.7.1: Other inner solutions applyin grigid spheres and elastic shells
6.12.8: Summing It Up and Going for the Simplest Explanation of the Question: “Why Are There Three Masses for Charged Leptons, Neutrons, and Quarks?”
6.12.8.1: Brief repetition: Ricci scalar for a scaled metric
6.12.8.2: Intermediate remark
6.12.8.3: Finally, Klein−Gordon: Toward simplest explanation for the 3-generation problem
6.12.8.4: Finally, Dirac I: Toward simplest explanation for the 3-generation problem
6.12.8.5: Finally, Dirac II: Toward simplest explanation for the 3-generation problem
6.12.8.6: Finally, Klein−Gordon + Dirac: The simplest explanation for the 3-generation problem
6.12.8.7: How to avoid the octonions?
6.12.8.8: Interpretation and particle at rest
6.12.8.9: The further path forward
6.12.8.10: Moving on
6.13: Toward an Understanding of Fundamental Interactions and Their Origin
6.13.1: But What Could Be the Origin for such Interaction Dependencies and from Where Do the Differences in Their Strength Come?
6.14: Consequences of the Infinity Options Principle and the Disappearance of Quantum Theory with n→∞
6.14.1: Repetition
6.14.2: Repetition—Part I: Metric Klein−Gordon, Schrödinger, and Dirac Equations Potential
6.14.3: Repetition—Part II: Direct Extraction of the Dirac Equation from the Metric Tensor
6.14.4: Repetition—Part III: The Infinity Options Principle
6.14.5: Consequences
6.15: A Few Intermediate Conclusions
6.16: Appendix: A Few Words about Spin 1/2, 3/2, 5/2, and So On
6.16.1: A Few Illustrations
Chapter 7: The Three Generations of Elementary Particles
7.1: Abstract: From Quantum Gravity to the 3-Generation Problem
7.2: Extended (Quantum Gravity) Einstein Field Equations … of Third Order?
7.3: Centers of Gravity and Quantum Centers
7.3.1: Repetition: The Base-Vector Variation
7.3.2: Quantum Centers
7.3.2.1: A possible connection to the 3-generation problem?
7.3.3: Centers of Gravity or Metric Centers
7.3.4: Summing Up: Centers of Gravity and Quantum Centers → Thermodynamics
7.4: The Infinity Options Principle or What Happens in Infinitely Many Dimensions
7.5: Toward a Solution to the 3-Generation Problem
7.5.1: Pre-Variation Results: The Simplest Path
7.5.2: In Connection with Our Simplified Inner Equation (669)
7.5.2.1: A foam of surfaces as by-product
7.5.2.2: Back to arbitrary n
7.5.3: In Connection with the Infinity Options Principle
7.5.4: Back Again to the Simplified Inner Equation and n = 4
7.5.4.1: Generalization of the approach
7.5.4.2: Brief discussion of the fading Ricci curvature
7.6: Discussion with Respect to Fq
7.7: Conclusions about Our Attempts to Find an Explanation to the 3-Generation Problem
7.8: Appendix: Taking Care of Complex Curvatures R or R*
The Fourth Day: Let There Be Quantum Gravity
Chapter 8: Toward Quantum Einstein Field Equations
8.1: Abstract: About the Source
8.2: Extended (Quantum Gravity) Einstein Field Equations
8.2.1: Variation of the Laplace Operator
8.2.2: Back to the Total Variation of Our Scaled Metric Ricci Scalar
8.2.3: Variation of the Scaled Ricci Tensor Term
8.2.4: Back to the Total Variation of Our Scaled Metric Ricci Scalar
8.3: Metric of Constants as an Example
8.3.1: A Few Options to Think About
8.3.2: Separating the Metric from the Quantum Part: First Simple Trials
8.3.2.1: Elastic equations in n > 2 dimensions
8.3.3: Separating the Metric from the Quantum Part: A Bit More General
8.3.4: Brief Consideration of the Situation with Eigenvalue Solutions
8.4: Intermediate Sum-Up and Repetition of a Few Important Results
8.4.1: The Special Case of 2 Dimensions
8.4.2: The Linear Elastic Space-Time
8.4.2.1: Shear fields = spin fields
8.4.2.2: Quark-like 1/3 and 2/3 charges
8.4.2.3: Hydrostatic particle fields
8.4.2.4: Time-planes and time-layers
8.5: Brief Discussion Regarding Our Peculiar Results for the “Poisson’s Ratio”
8.6: Discussion with Respect to More General Scale Factors
8.6.1: About a Tensor Scaled Metric
8.6.2: About a More General Kernel within the Einstein−Hilbert Action
8.7: Discussion with Respect to Alternatives and Potentially Missing Features
8.7.1: Alternative Way for Deriving the Equations of Elasticity from the Metric Origin out of the Einstein−Hilbert Action
8.7.2: Where Is Thermodynamics?
8.7.3: Repetition: The Base-Vector Variation
8.7.4: The Variation with Respect to Ensemble Parameters
8.7.4.1: Ordinary derivative variation and the ideal gas
8.7.4.2: Combined successive variation
8.7.4.3: Incorporating interaction
8.7.4.4: Repetition: Derivation of the diffusion equation
8.8: Centers of Gravity and Quantum Centers
8.8.1: Quantum Centers
8.8.2: Centers of Gravity or Metric Centers
8.8.3: Summing up: Centers of Gravity and Quantum Centers → Thermodynamics
8.9: Repetition: The Infinity Options Principle or What Happens in Infinitely Many Dimensions
8.10: Appendix A: The Derivation of the Scaled Ricci Scalar R*
8.11: Appendix B: Derivation of the Scaled Ricci Tensor
8.12: Appendix C: First Steps for a Tensor-Scaled Metric
8.13: Appendix D: Further Generalization to R* with Scaling Fq
8.13.1: Variation of the Laplace Operator with R*-Scaling
8.13.2: Back to the Total Variation of Our Scaled Metric Ricci Scalar with Scaling Factor Fq
8.13.3: Variation of the Scaled Ricci Tensor Term Together with the New Factor Fq
8.13.4: Back to the Total Variation of Our Scaled Metric Ricci Scalar with Action Factor Fq
8.14: Appendix E: Quantum Centers with Scaled Lagrange Density Fq
The Fifth Day: Let There Be a Dirac Equation
Chapter 9: The Metric Dirac Equation Revisited and the Geometry of Spinors
9.1: Abstract: Why Dirac Again?
9.2: A Few Basics
9.2.1: Extended (Quantum Gravity) Einstein Field Equations
9.2.2: Example in 6 Dimensions
9.2.3: Can We Now Understand Quantum Theory in a Truly Illustrative Manner?
9.3: Derivation of the Metric Dirac Equation
9.3.1: Dirac’s “Luck” in Connection with the Scaled Ricci Scalar
9.3.2: Repetition: Dirac in the Metric Picture and Its Connection to the Classical Quaternion Form
9.3.3: Intermediate Sum-Up: The Classical and the Intrinsic Dirac Approach
9.3.4: Dirac’s “Luck” and the Flat Space Condition
9.3.5: Mass and Its Metric Dimensional Origin
9.3.6: A Possible Origin of Spin l = 1/2
9.3.7: Connection to the Classical Picture
9.3.8: Seeds for Particles
9.3.9: Several Time-Like Dimensions and More Origins of Mass
9.3.9.1: To Dirac in 6 dimensions
9.3.9.2: To Dirac from 6 dimensions in a simpler (luckier) way
9.3.9.3: The infinity options principle
9.3.10: More Discussion and a Bit Redundancy
9.3.10.1: Vectorial root extraction
9.3.10.2: Decomposition of the metric Eq. (1184) → generalized metric Dirac
9.3.11: Further Factorization
9.3.11.1: Insertion: The classical way to obtain curved Dirac equations
9.3.11.2: The connection to the metric from
9.3.11.3: An asymmetry
9.3.11.4: Generalization
9.3.12: A Multitude of Options and the Collapse of the Wave Function
9.3.13: Application to the Schwarzschild Metric → Getting Rid of the Singularity
9.4: Adaptation of the Dirac Approach
9.4.1: More Tedious Work
9.4.2: The Klein−Gordon Option
9.4.3: About Higher Order Quaternions
9.4.4: A Few Words about the Metric Form(s) and Its Connection to the Dirac Approach
9.4.5: Decomposition of the Ricci Scalar and Tensor
9.4.6: A Potentially Problematic Issue
9.4.7: Back to Intrinsically Structured Wave Functions
9.4.8: From Tetrads or Base Vectors to Real Vectors
9.4.9: Example in n = 6, n = 8 and Higher Dimensions
9.4.10: The Substitution Approach
9.4.11: Metric Dirac Equation—An Outlook
9.5: Higgs with F[f]
9.6: Conclusions Regarding Our “Dirac Trials” Here So Far
9.7: Appendix A: The Derivation of the Scaled Ricci Scalar R*
9.7.1: For Illustration
9.8: Appendix B: Derivation of the Scaled Ricci Tensor—With an Extension
Chapter 10: The Dirac Miracle
10.1: Abstract: Toward a Variety of Dirac Paths
10.2: Quantum Einstein Field Equations
10.2.1: A Side-Note
10.2.2: Back to the Main Section and Eq. (1431)
10.3: Quantum Einstein Field Equations in Their Simplest Form
10.4: Where Does Hilbert’s Matter Come From?
10.5: Solving an Inconsistency Problem with the Quantum Einstein Field Equations
10.6: The Classical Dirac Equation, Derived from the Einstein−Hilbert Action
10.6.1: Insertion: The Classical Way to Obtain Curved Dirac Equations
10.6.2: Back to the Main Section
10.6.3: Extension to Arbitrary n and Non-Vacuum Einstein Compatible Space-Times
10.6.3.1: The Ricci-flat space-time
10.6.4: Instead of the Quaternions—The Stamler-Approach
10.6.4.1: The factorization problem and simple derivation of the Dirac equation in its classical form
10.6.4.2: The Laplace condition
10.6.4.3: The F' = 0-condition
10.6.4.4: The H[f]-approach from chapter 9, section 9.4.10
10.6.5: A Note
10.6.6: Excursion: The n = 1 − Case
10.7: Brief Sum-Up: “The Dirac Miracle”
10.8: Is There a Gravitational Dirac Equation?
10.9: The Other “Dirac Equation”
10.9.1: The Other Origin of a “Dirac Equation”
10.9.2: For Completeness
10.9.2.1: A consistency-check
10.9.2.2: Another derivation
10.9.2.3: Brief example: Flat space—Minkowski-like
10.9.3: Incorporation of the Volume Split-Up Option
10.9.4: Extension of Eq. (1604) to Arbitrary n and non-Vacuum-Einstein-Compatible Space-Times
10.9.5: A Note about Potential Simplifications and Evaluation Techniques
10.9.6: Generalization
10.10: The Gravity Dirac Equation
10.11 Conclusions
The Sixth Day: A Math for Body, Soul, and Universe
Chapter 11: A Curvy Math to Salvation
11.1: Personal Note and Motivation
11.2: Abstract
11.3: What We Will Need
11.3.1: Repetition: Extended (Quantum Gravity) Einstein Field Equations
11.3.2: Repetition: Can We Now Understand Quantum Theory in a Truly Illustrative Manner? Part I
11.4: About the Derivation of the Metric Dirac Equation
11.4.1: Toward Metric Dirac Equation: About the Starting Point
11.4.2: The Simplest Way to Derive a Metric Dirac Equation from the Scaled Ricci Scalar R*
11.4.3: What Does the Occurrence of Spinors in Quantum Gravity Mean?
11.5: The Meaning of the Occurrence of Spinors: A Suggestion
11.5.1: A Spherical Object in Cartesian Coordinates Regarding Its Position
11.5.2: Spherical Symmetry around the Sphere and an r-Connection
11.5.3: A Possible Origin of Spin l = 1/2
11.5.4: An Adapted Half Spin Metric and a Bit of Interpretation Work
11.5.5: Connection to the Classical Picture
11.5.6: Seeds for Particles
11.6: The Simpler Route
11.6.1: Checking Ricci-Flat and Vacuum Conditions for (1771)
11.6.2: Checking Non-Ricci-Flat Conditions for (1771)
11.6.3: Checking Non-Ricci-Flat-Non-Vacuum Conditions for (1771)
11.6.4: Generalizing the Langrangian of the Einstein–Hilbert Action, but Keeping the R-Linearity
11.6.5: The Hilbert Dimension
11.6.6: Looking for Suitable Solutions: The Quantum Einstein Field Equations
11.6.7: Can We Now Understand Quantum Theory in a Truly Illustrative Manner? Part II
11.6.8: Scaling Options
11.6.9: Origin of the Energy–Momentum Tensor in the General Theory of Relativity
11.6.10: The Quantum Origin of the Energy–Momentum Tensor to the Scale-Split-Up (1820)
11.7: The Special Situation in 2 Dimensions
11.8: Repetition: A Funny Inconsistency Resolved
11.9: Quantum Black Hole Solutions → Inner Black Hole Metrics without Singularities
11.9.1: Discussion of the Missing Smoothness Conditions
11.10: Metric Observables
11.11: The Gravity Dirac Equation Revisited
11.12: The Math for Body, Soul, and Universe?
11.13: Appendix
11.13.1: Appendix A1: Derivation of the Metric Klein–Gordon Equation from the Scaled Ricci Scalar R*
11.13.2: Appendix A2: Derivation of the Metric Dirac Equation from the Scaled Ricci Scalar R*
11.13.3: Appendix B: Derivation of the Metric Schrödinger Equation from the Scaled Ricci Scalar R*
11.13.4: Appendix C: A Few Words about Spin 1/2, 3/2, 5/2 and So On
Chapter 12: About the Flatness Problem in Cosmology
12.1: The Flatness Problem in Cosmology
12.2: Robertson–Walker Metric
12.3: Toward a Simple Quantum Cosmology
12.4: The Sub-Space Idea and the Global Time
12.5: Discussion
12.5.1: Repetition: A Quantum Origin of the Classical Energy–Momentum Tensor
Chapter 13: Mathematical Tools for Socioeconomic and Psychological Simulations
13.1: Mass Formation Psychosis as an Example
13.1.1: About Math as a Tool in Psychology and Socioeconomics
13.1.2: Mass Formation Psychosis
13.1.3: Illustrative “Mathematical,” Quantum Gravity Discussion of the Process of Mass Formation Psychosis
The Seventh Day: Give It Some Rest
Chapter 14: About the Origin of the Minimum Principle
14.1: Brief Story about the Minimum Principle—Part II
Index