| |
| |
Preface | |
| |
| |
| |
Preface | |
| |
| |
| |
Bibliography | |
| |
| |
| |
The foundations of the special theory of relativity | |
| |
| |
| |
Historical background | |
| |
| |
| |
| |
The postulate of relativity | |
| |
| |
| |
The postulate of the constancy of the velocity of light | |
| |
| |
Ritz's and related theories | |
| |
| |
| |
The relativity of simultaneity | |
| |
| |
Derivation of the Lorentz transformation from the two postulates | |
| |
| |
Axiomatic nature of the Lorentz transformation | |
| |
| |
| |
Lorentz contraction and time dilatation | |
| |
| |
| |
Einstein's addition theorem for velocities and its application to aberration and the drag coefficient | |
| |
| |
The Doppler effect | |
| |
| |
| |
Mathematical Tools | |
| |
| |
| |
The four-dimensional space-time world | |
| |
| |
| |
| |
More general transformation groups | |
| |
| |
| |
Tensor calculus for affine transformations | |
| |
| |
| |
Geometrical meaning of the contravariant and covariant components of a vector | |
| |
| |
| |
"Surface" and "volume" tensors | |
| |
| |
Four-dimensional volumes | |
| |
| |
| |
Dual tensors | |
| |
| |
| |
Transition to Riemannian geometry | |
| |
| |
| |
Parallel displacement of a vector | |
| |
| |
| |
Geodesic lines | |
| |
| |
| |
Space curvature | |
| |
| |
| |
Riemannian coordinates and their applications | |
| |
| |
| |
The special cases of Euclidean geometry and of constant curvature | |
| |
| |
| |
The integral theorems of Gauss and Stokes in a four-dimensional Riemannian manifold | |
| |
| |
| |
Derivation of invariant differential operations, using geodesic components | |
| |
| |
| |
Affine tensors and free vectors | |
| |
| |
| |
Reality relations | |
| |
| |
| |
Infinitesimal coordinate transformations and variational theorems | |
| |
| |
| |
Special theory of relativity | |
| |
| |
Further elaborations | |
| |
| |
| |
Kinematics | |
| |
| |
| |
Four-dimensional representation of the Lorentz transformation | |
| |
| |
| |
The addition theorem for velocities | |
| |
| |
| |
Transformation law for acceleration | |
| |
| |
Hyperbolic motion | |
| |
| |
| |
Electrodynamics | |
| |
| |
| |
Conservation of charge | |
| |
| |
Four-current density | |
| |
| |
| |
Covariance of the basic equations of electron theory | |
| |
| |
| |
Ponderomotive forces | |
| |
| |
Dynamics of the electron | |
| |
| |
| |
Momentum and energy of the electromagnetic field | |
| |
| |
Differential and integral forms of the conservation laws | |
| |
| |
| |
The invariant action principle of electrodynamics | |
| |
| |
| |
Applications to special cases | |
| |
| |
| |
Integration of the equations for the potential | |
| |
| |
| |
The field of a uniformly moving point charge | |
| |
| |
| |
The field for hyperbolic motion | |
| |
| |
| |
Invariance of the light phase | |
| |
| |
Reflection at a moving mirror | |
| |
| |
Radiation pressure | |
| |
| |
| |
The radiation field of a moving dipole | |
| |
| |
| |
Radiation reaction | |
| |
| |
| |
Minkowski's phenomenological electrodynamics of moving bodies | |
| |
| |
| |
Electron-theoretical derivations | |
| |
| |
| |
Energy-momentum tensor and ponderomotive force in phenomenological electrodynamics | |
| |
| |
Joule heat | |
| |
| |
| |
Applications of the theory | |
| |
| |
| |
The experiments of Rowland, R�ntgen, Eichenwald and Wilson | |
| |
| |
| |
Resistance and induction in moving conductors | |
| |
| |
| |
Propagation of light in moving media | |
| |
| |
The drag coefficient | |
| |
| |
Airy's experiment | |
| |
| |
| |
Signal velocity and phase velocity in dispersive media | |
| |
| |
| |
Mechanics and general dynamics | |
| |
| |
| |
Equation of motion | |
| |
| |
Momentum and kinetic energy | |
| |
| |
| |
Relativistic mechanics on a basis independent of electrodynamics | |
| |
| |
| |
Hamilton's principle in relativistic mechanics | |
| |
| |
| |
Generalized coordinates | |
| |
| |
Canonical form of the equations of motion | |
| |
| |
| |
The inertia of energy | |
| |
| |
| |
General dynamics | |
| |
| |
| |
Transformation of energy and momentum of a system in the presence of external forces | |
| |
| |
| |
Applications to special cases | |
| |
| |
Trouton and Noble's experiments | |
| |
| |
| |
Hydrodynamics and theory of elastic | |