Introduction to the Theory of Relativity

Preface to the First Edition

Introduction


PART 1 The Special Theory of Relativity

CHAPTER I Frames of Reference, Coordinate Systems, and Coordinate Transformations
Coordinate transformations not involving time
Coordinate transformations involving tim

CHAPTER II Classical Mechanics
The law of inertia, inertial systems
Galilean transformations
The force law and its transformation propertie

CHAPTER III The Propagation of Light
The problem confronting classical optics
The corpuscular hypothesis
The transmitting medium as the frame of reference
The experiment of Mictielson and Morle
The ether hypothesis

CHAPTER IV The Lorentz Transformation
The relative character of simultaneity
The length of scales
The rate of clocks
The Lorentz transformation
The "kinematic" effects of the Lorentz transformatio
The proper time interval
The relativistic law of the addition of velocities
The proper time of a material body
PROBLEMS

CHAPTER V Vector and Tensor Calculus in an n Dimensional continuum
Orthogonal transformations
Transformation determinant
Improved notation
Vector analysis.
Tensors.
Tensor analysis
Tensor densities
The tensor density of Levi-Civita
Generalization
n dimensional continuum
General transformations
Vectors
Tensors
Metric tensor, Riemannian spaces
Raising and lowering of indices
Tensor analysis
Geodesic lines.
Minkowski world and Lorentz transformations
PROBLEMS

CHAPTER VI Relativistic Mechanics of Mass Points
Program for relativistic mechanics
The form of the conservation laws
A model exampl
Lorentz covariance of the new conservation laws
Relation between energy and mass
The Compton effect
Relativistic analytical mechanics
Relativistic force.
PROBLEMS

CHAPTER VII Relativistic Electrodynamics
Maxwell's field equation
Preliminary remarks on transformation properties
The representation of four dimensional tensors in three plus one dimensions.
The Lorentz invariance of Maxwell's field equations
The physical significance of the transformation laws.
Gauge transformations
The ponderomotive equations

CHAPTER VIII The Mechanics of Continuous Matter
Introductory remarks.
Nonrelativistic treatment
Tensor form of the equations
The stress-energy tensor of electrodynamics
PROBLEM

CHAPTER IX Applications of the Special Theory of Relativity
Experimental verifications of the special theory of relativity
Charged particles in electromagnetic fields
The field of a rapidly moving particle
Sommerfeld's theory of the hydrogen fine structure
PROBLEMS


PART II The General Theory of Relativity

CHAPTER X The Principle of Equivalence
Introduction.
The principle of equivalence
Preparations for a relativistic theory of gravitation.
On inertial systems
Einstein's "elevator."
The principle of general covariance
The nature of the gravitational field.

CHAPTER XI The Riemann-Christoffel Curvature Tensor
The characterization of Riemannian spaces
The integrability of the affine connectio
Euclidicity and integrability
The criterion of integrability
The commutation law for covariant differentiation, the tensor character of Rikl"
Properties of the curvature tensor.
Contracted forms of the curvature tensor.
The contracted Bianchi identities.
The number of algebraically independent components of the curvature tensor

CHAPTER XII The Field Equations of the General Theory of Relativity
The ponderomotive equations of the gravitational field
The representation of matter in the field equations.
The differential identities
The field equations
The linear approximation and the standard coordinate conditions.
Solutions of the linearized field equations
The field of a mass point.
Gravitational waves.
The variational principle
The combination of the gravitational and electromagnetic fields
The conservation laws in the general theory of relativity.

CHAPTER XIII Rigorous Solutions of the Field Equations of the General Theory of Relativity
The solution of Schwarzschild
The "Schwarzschild singularity."
The field of an electrically charged mass point
The solutions with rotational symmetry

CHAPTER XIV The Experimental Tests of the General Theory of Relativity
The advance of the perihelion of Mercury.
The deflection of light in a Schwarzschild field.
The gravitational shift of spectral lines

CHAPTER XV The Equations of Motion in the General Theory of Relativity
Force laws in classical physics and in electrodynamics.
The law of motion in the general theory of relativity
The approximation method.
The first approximation and the mass conservation law.
The second approximation and the equations of motion.
Conclusion
PROBLEM


PART III Unified Field Theories

CHAPTER XVI Weyl's Gauge-Invariant Geometry
The geometry.
Analysis in gauge-invariant geometry
Physical interpretation of Weyl's geometry
Weyl's variational principle
The equations G= 0.

CHAPTER XVII Kaluza's Five Dimensional Theory and the Projective Field Theories
Kaluza's theory
A four dimensional formalism in a five dimensional space.
Analysis in the p-formalism
A special type of coordinate system
Covariant formulation of Kaluza's theory
Projective field theories.

CHAPTER XVIII A Generalization of Kaluza's Theory
Possible generalizations of Kaluza's theory
The geometry of the closed, five dimensional world
Introduction of the special coordinate system
The derivation of field equations from a variational principle
Differential field equations


APPENDIX A Ponderomotive Theory by Surface Integrals
Invariance groups
Noether's theorem
The surface integral theorems
Ponderomotive laws.

APPENDIX B Supplementary Notes

Index