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