Foundations of Wave Electricity

1. Concept and Introduction

• Introduction to Wave Electricity
• Interactive Diagram of the Theory
• Unified Concept
• One-dimensional coordinate of electric interaction: two experiments with a moving charge

2. Idempotent Algebra and the New Cartesian Basis

• The Hidden Geometry of the Hyperbolic Unit
• Splitting of possibilities: channels and spatial ports
• 1. A New Cartesian Basis
• 2. Motion as Complex Modulation of the Cartesian Basis
• 3. Internal Motion of the Electron and the Origin of Its Magnetic Moment
• 4. The Schrödinger Equation in Split-Operator Geometry
• Commutative Algebra for the New Cartesian Basis

3. Wave, Particle, and Mass

• A Unified Geometric Model of Waves and Particles
• Mass as a Geometric Projection of a Closed Wave. Why the Photon Mass Is Zero

Motion and Relativistic Geometry

1. The Lorentz Factor and Observer Coordinates

• Origin of the Lorentz Factor from Infinite Idempotent Splitting
• Geometric Origin of the Lorentz Factor and the Energy Invariant
• Geometric Splitting of Coordinates Between Observers: A New View of Lorentz Transformations

2. Sum and Difference of Velocities

• 1. Identical Internal States
• 2. Different Internal States

3. Acceleration and Rotation

• Acceleration as a Projection of Uniform Motion in Higher Splittings. Why Acceleration Is an Illusion
• Application. Turning on and off acceleration as a projection of higher splitting
• Circular Motion as a Projection of Uniform Motions in Higher Splittings
• Rotation as a Projection of Acceleration-Free Splittings

4. Dynamics of the External Parameter

• Relativistic Force as a Change in the External Parameter

Elementary Particles

1. Internal Structure of the Electron

• 1. From the Idempotent Basis to a Geometric Model of the Electron's Internal Structure
• 2. The Electron's Double Internal Orbit, Spinor Periodicity, and Magnetic Precession

2. Spin, Polarization, and Deep Splitting

• Electron Spin as a Consequence of the Double Orbital Cycle in the Geometric Model
• Transition of Electron and Positron Spin into Photon Polarization
• Multilevel Splitting of Electron Geometry: Spin, Anomalous Magnetic Moment, and the Coulomb Gradient
• Anomalous Magnetic Moment of the Electron

3. i-Splitting and the Classification of Matter

• 1. Construction of Known Particles from Normalized Operators
• 2. Operator Classification of Matter

4. Particle Interactions

• 1. Operator states and transformation invariants
• 2. Geometric Rule of Particle Interaction
• 3. Sector restructuring of operator states
• 4. State space and probabilities of sector rearrangements

Quantum Phenomena

1. Quantum measurement and interpretations

• One Reality and Many Realities: The Unifying Geometry of Quantum Interpretations

2. Uncertainty and Correlated Phases

• Internal Phase Uncertainty as the Geometric Basis of the Heisenberg Principle
• Correlated Random Phases: From Particle Uncertainty to Two-Particle Interference
• Geometric origin of energy and time uncertainty from phase splitting

3. Particle Diffraction

• 1. Passage Through a Single Slit
• 2. Passage Through Two Slits

Atomic Physics

1. From the Electron to the Atom

• From the Geometric State of the Electron to the Orbit of the Hydrogen Atom
• Geometric Origin of the Square of the Fine-Structure Constant and the Parameters of the Bohr Atom

2. Orbits, Orbitals, and Electron Pairs

• 1. The First Orbit
• 2. Higher Orbits and Fine Splitting
• Atomic Orbitals as Projections of Split Phase Space
• Geometric Formation of an Electron Pair and the Pauli Exclusion Principle

3. Atomic Spectra

• Geometric Origin of the Rydberg Law

Electrodynamics

1. Electric Forces and Operator Correlation

• Geometric Origin of the Electric Force
• Attraction and Repulsion of Charges and Currents as Two Projections of Operator Correlation

2. Electromagnetic Fields and Waves

• Geometric Origin of Electric and Magnetic Fields
• Geometric Origin of a Propagating Wave

3. Electromagnetic Parameters of the Electron

• Geometric Meaning of the Electron's Capacitance and Inductance

Temporal Field and Cosmology

1. The Temporal Field and the Origin of Space

• 1. The Temporal Field and the Origin of Space
• 2. Projections of the Temporal Field: The Origin of Electric, Magnetic, and Wave Fields
• Splitting of Space and Motion as a Unified Process

2. Evolution and Expansion of the Universe

• From State to Time and Space: The Geometric Evolution of the Universe
• The Expansion of the Universe as an Upward Splitting of Space
• Dark Matter as a Geometric Scalar Mode

Additional Materials

1. Appendices

• The Fine-Structure Constant as the Basis of the Logarithmic Scale of Physical Quantities

2. Early Works

• The Second Magnetic Field in the Electron
• 2.1 Mathematical Model
• 2.2 Mathematical Model: Completion
• Coefficient-Free Coulomb's Law and Ampère's Law
• Wave Electricity (WEL). Part 1. Introduction
• Wave Electricity. Part 2. General Form of the Law of Interactions