A Novel Approach to Relativistic Dynamics: Integrating Gravity, Electromagnetism and Optics

Preface
Contents
Notation
List of Figures
List of Tables
1 Introduction
	1.1 Physics via Geometry–A Historical Perspective
	1.2 Unification and Simplicity
	1.3 Overview of the Model
	1.4 Outline of the Book
	1.5 Alternative Theories
2 Classical Dynamics
	2.1 Classical Fields
	2.2 Motion in the Classical Fields
	2.3 The Euler–Lagrange Equations
3 The Lorentz Transformations and Minkowski Space
	3.1 Inertial Frames
	3.2 Spacetime Transformations that Satisfy the Principle of Relativity
		3.2.1 The Galilean Transformations
		3.2.2 The Lorentz Transformations
	3.3 Einstein Velocity Addition and Applications
		3.3.1 Velocity Addition
		3.3.2 Fiber Optic Gyroscopes and the Sagnac Effect
	3.4 Minkowski Space
	3.5 Four-Vectors, Four-Covectors, and Contraction
	3.6 Relativistic Energy-Momentum
	3.7 Relativistic Doppler Shift
	3.8 Lorentz-Covariant Functions for a Single-Source Field
4 The Geometric Model of Relativistic Dynamics
	4.1 The Relativity of Spacetime and the Extended Principle of Inertia
	4.2 Geodesics on the Globe
	4.3 The Geometric Action Function and Its Properties
	4.4 Simple Action Function
	4.5 Universal Relativistic Equation of Motion
		4.5.1 The Equation of Motion Using Proper Time
		4.5.2 The Equation of Motion Using tildeτ
5 The Electromagnetic Field in Vacuum
	5.1 The Electromagnetic Field Tensor
	5.2 The Four-Potential of a Single-Source Electric Field
	5.3 The Electromagnetic Field of a Moving Source
	5.4 The Electric and Magnetic Components of the Field …
	5.5 The Energy-Momentum of an Electromagnetic Field
	5.6 The Radiation Field
	5.7 The Four-Potential of a General Electromagnetic Field
	5.8 The Field of a Current in a Long Wire
	5.9 Maxwell\'s Equations
	5.10 Orbits of Charged Particles in a Static, Single-source Field
	5.11 Circular Orbits
6 The Gravitational Field
	6.1 The Gravitational Field of a Stationary, Static, Spherically …
	6.2 Precession of Orbits in a Stationary, Static, Spherically Symmetric Gravitational Field
	6.3 Periastron Advance of Binary Stars
	6.4 Orbits in the Strong Field Regime
		6.4.1 Circular Orbits
		6.4.2 Elliptical Orbits
		6.4.3 Hyperbolic-Like Orbits
	6.5 Gravitational Lensing
	6.6 Shapiro Time Delay
	6.7 The Gravitational Field of Multiple Sources
	6.8 The Gravitational Field of a Moving Source
	6.9 Gravitational Waves
7 Motion of Light and Charges in Isotropic Media
	7.1 The Photon Action Function of Rest Media
	7.2 The Photon Action Function in Moving Media
	7.3 Refraction of Light
	7.4 Motion of a Charge in an Isotropic Medium at Rest
8 Spin and Complexified Minkowski Spacetime
	8.1 History of the Spin of Particles
	8.2 The State Space of an Extended Object Moving Uniformly
	8.3 Complexified Minkowski Space as the State Space of an Extended Object
	8.4 The Representation of the Spin of an Electron
	8.5 Transition Probabilities of Spin States and Bell\'s Inequality
	8.6 Motion of Particles with Spin in a Slow-varying Electromagnetic Field
9 The Prepotential
	9.1 The Prepotential and the Four-Potential of a Field Generated by a Single Source
	9.2 Representations of the Lorentz Group on Mc
	9.3 Lorentz Invariance of the Prepotential and the Conjugation
	9.4 The Four-Potential of a Moving Source
	9.5 The Symmetry of the Complex Four-Potential
	9.6 The Prepotential and the Wave Equation
	9.7 The Electromagnetic Field Tensor of a Moving Source and its Self-Duality
	9.8 The Prepotential of a General Electromagnetic Field
Appendix  References
Index