Einstein's Apple

The following sections are included:

• DEDICATION
• PREFACE
• CONTENTS
• FIGURES

The following sections are included:

• The Principle of Equivalence
• Where the Principle of Equivalence Leads
• The Reference System
• The Physical Principle of Equivalence
• Newton, Mach, and Einstein

The following sections are included:

• Born Motion
• A Homogeneous Gravitational Field
• A Homogeneous Gravitational Field in the Minkowski Plane
• The Newtonian Gravitational Field
• Relativistic Equivalence

The following sections are included:

• Cartan's Torsion
• The Gravitational Frequency Shift
• Fermi's Torsion
• Reference Frames

The following sections are included:

• Inertial Frames of Reference in Minkowski Spacetime
• General Leg Transformations
• Inertial Fields
• The Rigidly Rotating Frame in Minkowski Spacetime
• Gravitational Fields

The following sections are included:

• The Meaning of Einstein's First Principle of Equivalence
• The Use of Frames
• Einstein's Torsion
• The Notion of Torsion
• Conclusion

The following sections are included:

• Outline
• Definition of the Frame Bundle for a Surface
• Local Homogeneous Fields
• Surfaces of Zero Curvature
• Surfaces of Constant Negative Curvature
• Remarks on Curvature
• Indefinite Two-Dimensional Metrics
• The Field Concept
• The de Sitter Metric (K < 0)
• Geodesics of the de Sitter Spacetime (K < 0)
• Anti-de Sitter Spacetime (K > 0)

The following sections are included:

• Existence
• Positive Definite Metrics
• Lorentz Manifolds
• De Sitter Space
• Anti-de Sitter Space
• Minkowski Space
• Potentials in Minkowski Space
• Vacua Defined
• Force Fields
• Conservation Laws
• The Minkowski Potentials

The following sections are included:

• Overview
• Homogeneous Fields on Positive Definite Spaces
• Homogeneous Fields on 3-Dimensional Minkowski Spacetime

The following sections are included:

• Overview
• Three-Dimensional Minkowski Spacetime
• Spacetime Interpretation of the Scalar Product
• Lorentz Transformations in Three-Dimensional Spacetime
• Lorentz Transformations Characterized in Three-Dimensional Spacetime
• The Null Rotations of SO(2,1)
• The Redshift and Superluminal Velocities

The following sections are included:

• Introduction
• About Ricci Coefficients
• Levi-Civita's Constant Gravitational Field
• Minkowski Spacetime as an Infinite Mass Limit of Schwarzschild Spacetime
• The Constant Electric or Magnetic Field as a Limit of the Spherically Symmetric Field of a Point Charge
• The Reissner-Nordstrom Limit Procedure Near m = e
• The Levi-Civita Limit
• Isotropic Reissner-Nordstrom Solution
• Reissner-Nordstrom Force Field - Rest Case
• Reissner-Nordstrom Force Field - General Case
• Schwarzschild's Field in Isotropic Coordinates
• Schwarzschild Spatial Acceleration
• Schwarzschild Energy Loss
• The de Sitter Isotropic Form
• De Sitter Analysis
• Geodesic Equation

The following sections are included:

• Subalgebras for the Lie Algebra of the Poincaré Group
• Null Rotations and Translations in the (2+N)–Dimensional Minkowski Space M^2+N
• Specialization to Three-Dimensional Minkowski Spacetime
• Specialization to Circular Orbits
• The Hyperbolic Analogue of Minkowski Circular Motion in Homogeneous Fields
• Geodesic Motion in Homogeneous Fields

The following sections are included:

• Definition of Homogeneous Fields in Euclidean Three-Space
• Curvature Form
• Jacobi Identity
• Classification of Homogeneous Fields
• Euclidean Three-Space
• Curvature Form Calculation
• Riemann Tensor
• Ricci Tensor
• Ricci Tensor Eigenvectors (c_r ≠ 0)
• Ricci Tensor Eigenvectors (c_r = 0)
• Homogeneous Field Components
• Ricci Tensor in Field Strengths
• Ricci Tensor (continued)
• Homogeneous Gravitational Fields in Euclidean ℝ³
• ADDENDUM: Ricci Tensor Calculation from Field Strengths
• ADDENDUM: Ricci Tensor and Ricci Coefficients - The Vector Free Case

The following sections are included:

• Discussion of Homogeneous Gravitational Fields
• Homogeneous Fields in N Dimensions
• Homogeneous Fields in Two Dimensions
• Homogeneous Fields in Three Dimensions
• Vanishing Ricci Tensor in Three Dimensions

The following sections are included:

• Mathematics
• Physics
• Equivalence Principle

The following sections are included:

• APPENDIX A. Basic Concepts
• APPENDIX B. A Non-trivial Global Frame Bundle
• APPENDIX C. Geodesics of the Poincaré Half-Plane
• APPENDIX D. Determination of Homogeneous Fields in Two-dimensional Riemannian Spaces
• APPENDIX E. Space Expansion
• APPENDIX F. The Reissner-Nordstrom Isotropic Field
• APPENDIX G. The Cremona Transformation
• APPENDIX H. Hessenberg's “Vectorial Foundation of Differential Geometry”
• APPENDIX K. Gravitation Is Torsion
• APPENDIX R. References
• APPENDIX X. Index
• APPENDIX N. Notations and Conventions