Table of Contents

Preface

About the Author

Part I. The Atomic Structure

Chapter 1. Spherical Quantities in Two-Dimensional Spacetime
1.1. Introduction
1.2. Euclidean Space and Newtonian Time
1.3. Two-Dimensional Spacetime
1.3.1. General Harmonic Oscillation
1.3.2. Duality in a Helium Shell
1.3.3. Duality in an LC Circuit
1.3.4. The Duality Equation vs. Schrödinger’s Equation
1.4. Dynamic Calculus
1.4.1. Infinitesimal Calculus Definition
1.4.2. Dynamic Calculus Definition
1.4.3. Spacetime Continuity
1.4.4. Properties of Spherical Quantity
1.5. Linear Interpretation of Spherical Quantity
1.5.1. Spherical Quantity as a Rotatory Vector
1.5.2. Dimension Concepts of Space and Time
1.5.3. Spherical Quantities in Euclidean Space

Conclusion

References

Chapter 2. The Theory of Quaternity
2.1. Introduction to Four Space Dimensions
2.1.1. Four Geometric Elements in a Sphere
2.1.2. Orthogonality and Scalability of Four Space Dimensions
2.2. Quaternity Spacetime
2.2.1. Symmetry and Complementarity of Time and Space
2.2.2. Rotatory Operations in the Quaternity Equation
2.2.3. Electronic Orbitals in a Neon Shell
2.2.4. Dimension Encapsulation Mechanism
2.2.5. The Differential Chain Rule
2.3. Four-Dimensional Harmonic Oscillations
2.3.1. Harmonic Oscillation in One Dimension
2.3.2. Harmonic Oscillation in Two Dimensions
2.3.3. Harmonic Oscillation in Three Dimensions
2.3.4. Harmonic Oscillation in Four Dimensions
2.3.5. Four Kinds of Orbital Geometries
2.4. Compatibility with Classical and Quantum Mechanics

Conclusion

References

Chapter 3. Dynamic Calculus in Vector Calculus
3.1. Introduction
3.2. Vector Calculus in One-Dimensional Space
3.3. Vector Calculus in Quaternity Space
3.3.1. The Polor in the First Dimension
3.3.2. The Metor in the Second Dimension
3.3.3. The Vitor in the Third Dimension
3.3.4. The Scalor in the Fourth Dimension
3.4. Orbitals Synchronization
3.4.1. Green’s Theorem
3.4.2. Stokes’ Theorem
3.4.3. Gauss’s Theorem
3.5. Electronic Interaction through Virtual Photons
3.6. About Quaternity Space

Conclusion

References

Chapter 4. Quaternity, Relativity, and Quantum Mechanics
4.1. Introduction
4.2. Scope of Views
4.3. Quaternity on EPR Paradox
4.4. Special Relativity in Quaternity
4.5. Quaternity Solutions to Schrödinger’s Equations
4.5.1. Duality as a Solution to One-dimensional Schrödinger’s Equation
4.5.2. Quaternity as a Solution to Three-dimensional Schrödinger’s Equation

Conclusion

References

Chapter 5. The Structure of Atomic Shells
5.1. Introduction
5.2. Electronic Orbitals in an Argon Shell
5.2.1. Spherical Quantities for 3s3p Electrons
5.2.2. Complementary Orbitals due to a Clockwise Direction Shift
5.2.3. Dimension Factors as Operators
5.2.4. Electronic Ropes
5.3. Electronic Orbitals in a Krypton Shell
5.3.1. Coordination of Circular Complex Functions
5.3.2. Circular Complex Functions as Exponential Functions
5.3.3. Circular Complex Functions as Radian Angles
5.3.4. Spherical Quantities for 3d Electrons
5.3.5. Complementary Orbitals due to a Standpoint Shift
5.4. Electronic Orbitals in a Radon Shell and Beyond
5.4.1. Spherical Quantities for 4f Electrons
5.4.2. The Quaternity Periodic Table of Elements
5.4.3. Electronic Interactions and Waves in Atoms
5.4.4. The Atomic Shell Octet

Conclusion

References

Intermission

Part II. The Natural Pattern

Chapter 6. Anisotropic 2p Orbitals and a Chiral Carbon
6.1. Introduction to Anisotropic 2p Orbitals
6.1.1. Geometries of 2p Orbitals
6.1.2. Covalent Bonds in Methane, Ethene, and Ethyne
6.1.3. Nucleophilic Substitutions of Alkyl Halides
6.1.4. Covalent Bonds in Aromatic Rings
6.1.5. Electrophilic Substitutions of Mono-Substituted Benzenes
6.2. Molecular Chirality
6.2.1. The Density Gradient of 2s2p Orbitals
6.2.2. The Origin of Molecular Chirality
6.2.3. The Physical Principle of Optical Rotation
6.2.4. Chiral Disposition Induced by Electrophilic Groups
6.2.5. Selective Electron Transfer through Chiral Centers

Conclusion

References

Chapter 7. DNA Circuits and Waves
7.1. Introduction
7.2. DNA Electric Conductivity
7.2.1. DNA Electronic Components and Circuitry
7.2.2. Circuit Model Discussion and Prediction
7.3. DNA Wave Functions
7.3.1. Harmonic Oscillation between Base Pairs
7.3.2. Mathematical Formula of DNA.

Conclusion

References

Chapter 8. The Principle of Cells and Life
8.1. Introduction
8.2. The Helium Model for Rope Structure
8.3. The Carbon Model for Gene Expression
8.3.1. DNA Replication (1s to 1s)
8.3.2. DNA Transcription (2s to 2px)
8.3.3. RNA Translation (2px to 2py)
8.3.4. Enzymatic Catalyses (2py to 2pz)
8.3.5. Metabolism and ATP Cycle (2pz to 2s)
8.4. The Zinc Model for Endosymbiotic Organelles
8.5. The DNA Circuitry for the Human Lineage
8.6. Wave Functions as Biological Variables
8.7. The Rotatory Operation for the Mind and Body Relationship
8.8. The Poisson Distribution and Evolution
8.9. The Law of Nature and General Gyroscope
8.10. At the Dawn of Calculus Biology

Conclusion

References

Chapter 9. Circular Motion and Central Force
9.1. Introduction
9.2. Kepler’s Laws in Atomic Spacetime
9.3. The Energy Density and Coulomb’s Law.

Conclusion

References

Chapter 10. The Order of Physical Quantities
10.1. Introduction
10.2. Dimensions of Physical Quantities
10.3. Interpretation of Electromagnetic Quantities
10.4. The Unification of Physical Quantities
10.5. Dimensions of Thermodynamic Quantities

Conclusion

References

Chapter 11. The Rational Core of Chinese Medicine
11.1. Introduction to Yin and Yang
11.2. The Common Origin of “Yi Jing” and TCM
11.3. Literal Meanings of Four Spherical Quadrants
11.4. Geometrical Interpretation of Five Elements
11.5. Quaternity Interpretation of Eight Trigrams

Conclusion

References

Appendix I. Review Questions

Appendix II. Glossary of Key Concepts

Appendix III. The Law of Nature in Mathematics

Appendix IV. Special Meanings of Symbols

Index

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Author’s ORCID iD

Kunming Xu – 0000-0002-5418-6133