Christian Møller (1904–1980)

Indeholder "Preface to the second edition", "Preface to the first edition", "1. The foundations of the special theory of relativity. Historical survey", "1.1 The relativity principle of mechanics. The Galilean transformation", "1.2 The special principle of relativity", "1.3 Invariance of the phase of a plane wave", "1.4 Transformation of the characteristics of a plane wave", "1.5 The Doppler effect", "1.6 The velocity of light in vacuo", "1.7 The velocity of light in refractive media", "1.8 Hoek's and Fizeau's experiments", "1.9 Lorentz's theory of electrons", "1.10 Agreement between the ether theory and the principle of relativity as regards all effects of the first order. Fermat's principle", "1.11 The aberration of light", "1.12 Michelson's experiment", "1.13 The contraction hypothesis", "1.14 Validity of the principle of relativity for all physical phenomena", "2. Relativistic kinematics ", "2.1 Simultaneity of events", "2.2 The relativity of simultaneity", "2.3 The special Lorentz transformation", "2.4 The most general Lorentz transformation", "2.5 Contraction of bodies in motion", "2.6 The retardation of moving clocks. The clock paradox", "2.7 Transformation of particle velocities", "2.8 Successive Lorentz transformations. The Thomas precession", "2.9 Transformation of the characteristics of a wave according to the theory of relativity", "2.10 The ray velocity in moving bodies", "2.11 The Doppler effect, the aberration of light, and the dragging phenomenon according to the theory of relativity", "3. Relativistic mechanics", "3.1 Momentum and mass of a particle", "3.2 Force, work, kinetic energy", "3.3 Transformation equations for momentum energy and force", "3.4 Hyperbolic motion. Motion of an electrically charged particle in a constant magnetic field", "3.5 Equivalence of energy and mass", "3.6 Inelastic collisions. Mass of a closed system of particles", "3.7 Experimental verification of relativistic mechanics", "4. Four-dimensional formulation of the theory of relativity: Tensor calculus", "4.1 Four-dimensional representation of the Lorentz transformation", "4.2 Lorentz contraction and retardation of moving clocks in four-dimensional representation", "4.3 Covariance of the laws of nature in four-dimensional formulation", "4.4 The four-dimensional line element or interval. Four-vectors", "4.5 Four-velocity and acceleration. Wave number vector. Four-ray velocity", "4.6 Four-momentum. Four-force. Fundamental equations of point mechanics in four-dimensional vector form", "4.7 Tensors of the second rank", "4.8 Angular momentum and moment of force in four-dimensional representation", "4.9 Tensors of arbitrary rank", "4.10 Pseudo-tensors", "4.11 The Levi-Civita symbol", "4.12 Dual tensors", "4.13 Infinitesimal Lorentz transformations. Lorentz transformations without rotation", "4.14 Successive Lorentz transformations", "4.15 Successive rest systems of a particle in arbitrary rectilinear motion and in constant circular motion", "4.16 Tensor and pseudo-tensor fields. Tensor analysis", "4.17 Gauss's theorem in four-dimensional space", "4.18 The fundamental equations of mechanics for incoherent matter", "4.19 The kinetic energy-momentum tensor", "5. Electrodynamics in the vacuum", "5.1 The fundamental equations of electrodynamics in vacuum. Four-current density for electric charge", "5.2 Covariance of the fundamental equations of electrodynamics under Lorentz transformations. The electromagnetic field tensor", "5.3 The four-potential. Gauge transformation", "5.4 Four-dimensional integral representation of the four-potential", "5.5 Retarded potentials. Lienard-Wiechert's potentials for point charges", "5.6 The field of a uniformly moving point charge", "5.7 The electromagnetic forces acting on charged matter", "5.8 Variational principle of electrodynamics", "5.9 The electromagnetic energy-momentum tensor", "5.10 The total energy-momentum tensor", "6. General closed systems. Mechanics of elastic continua. Field theory", "6.1 The conservation laws for a closed system", "6.2 Four-momentum and angular momentum four-tensor for a closed insular system", "6.3 Centre of mass", "6.4 The fundamental equations of mechanics in elastic continua", "6.5 Principal form of the stress tensor and the energy-momentum tensor. Transformation properties", "6.6 Perfect fluids", "6.7 Scalar meson fields. General field theory", "7. Non-closed systems. Electrodynamics in dielectric and paramagnetic substances. Thermodynamics", "7.1 General properties of non-closed systems", "7.2 Static non-closed systems", "7.3 Electrostatic systems. Classical models of the electron", "7.4 The fundamental equations of electrodynamics in stationary matter", "7.5 Minkowski's field equations in uniformly moving bodies", "7.6 The constitutive equations in four-dimensional language. Boundary conditions", "7.7 Electromagnetic energy-moment tensor and four-force density", "7.8 The propagation velocity of the energy of a light wave in a moving refractive body", "7.9 Continuously distributed matter with internal heat conduction", "7.10 The first law of relativistic thermodynamics. Transformation properties of the four momentum of supplied heat", "7.11 The second law of relativistic thermodynamics", "7.12 The thermodynamical potentials of a homogeneous isotropic body", "7.13 Ideal gas. Black-body radiation", "8. The foundations of the general theory of relativity", "8.1 The general principle of relativity", "8.2 The principle of equivalence", "8.3 Uniformly rotating systems of coordinates. Space and time in the general theory of relativity", "8.4 Non-Euclidean geometry. The metric tensor", "8.5 Geodesic lines ", "8.6 Determination of the metric tensor by direct measurements. Geometry in n-dimensional space", "8.7 General accelerated systems of reference. The most general admissible space-time transformations", "8.8 Space and time measurements in an arbitrary system of reference. Experimental determination of the functions g_ik", "8.9 The spatial geometry in the rotating system of reference", "8.10 The time tracks of free particles and light rays", "8.11 The dynamical gravitational potentials", "8.12 The rate of a moving standard clock in a gravitational field", "8.13 Transformation of coordinates inside a fixed system of reference ", "8.14 Further simple examples of accelerated systems of reference", "8.15 Rigid systems of reference with an arbitrary motion of the origin", "8.16 Rigid frames of reference moving in the direction of the X-axis ", "8.17 The clock paradox", "9. Permanent gravitational fields. Tensor calculus in a general Riemannian space", "9.1 Four-dimensional formulation of the general principle of relativity and of the principle of equivalence", "9.2 Contravariant and covariant components of a four-vector", "9.3 Tensor algebra", "9.4 Pseudo-tensors. Dual tensors", "9.5 Geodesic lines. Christoffel's formulae", "9.6 Local pseudo-Cartesian coordinates and local systems of inertia", "9.7 Parallel displacement of vectors", "9.8 Absolute derivative. Fermi-Walker transport", "9.9 Locally rigid non-rotating systems of reference with an arbitrary motion of the origin. Fokker precession", "9.10 Tensor analysis. Covariant differentiation", "9.11 Covariant differentiation of tensor densities", "9.12 Integral theorems", "9.13 The curvature tensor", "9.14 The contracted forms of the curvature tensor", "9.15 Special systems of coordinates in finite regions of space-time", "9.16 Gauge-invarian quantities. Standard four-tensors", "10. The influence of gravitational fields on physical phenomena", "10.1 The fundamental equations of point mechanics", "10.2 The physical interpretation of the equations of point mechanics. Standard equations of motion. Standard simultaneity", "10.3 Coordinate form of the equations of motion", "10.4 Lagrangian and Hamiltonian forms of the equations of motion", "10.5 Propagation of light signals. Fermat's principle", "10.6 Propagation of light waves. Photons", "10.7 The Doppler shift and the Einstein shift of spectral lines", "10.8 Mechanics of continuous systems", "10.9 The electromagnetic field equations", "10.10 Electromagnetic force and energy-momentum tensor", "11. The fundamental laws of gravitation in the general theory of relativity", "11.1 The gravitational field equations and the laws of mechanics", "11.2 The linear approximation for weak fields", "11.3 Simple applications of the linear equations for weak fields.", "11.4 Equivalent systems of coordinates. Systems with spherical symmetry", "11.5 Static systems with spherical symmetry", "11.6 Schwarzschild's exterior solution", "11.7 Schwarzschild's solution for the interior of a perfect fluid", "11.8 The variational principle for gravitational fields", "11.9 The energy-momentum complex and the laws of conservation of energy and momentum for isolated insular systems", "11.10 The superpotential. The total momentum and energy of an isolated system", "11.11 Non-isolated insular systems. Gravitational radiation", "11.12 Other expressions for the energy-momentum complexes", "11.13 The four-angular momentum of isolated systems", "12. Experimental verification of the general theory of relativity. Cosmological problems", "12.1 The Einstein shift or gravitational shift of spectral lines", "12.2 The advance of the perihelion of Mercury", "12.3 The gravitational deflexion of light", "12.4 Further tests of general relativity", "12.5 Cosmological models", "12.6 The Einstein universe", "12.7 The de Sitter universe", "12.8 Non-static models of a homogeneous isotropic universe", "12.9 Models of the universe compatible with general relativity. The Friedmans universe", "12.10 Relations between observable astronomical quantities", "Appendixes", "1. Gauss's theorem", "2. The transformation equations for the four-current density", "3. Plane waves in a homogeneous isotropic substance", "4. The Christoffel symbols in terms of the variables and their derivatives", "5. The condition for flat space", "6. The derivatives of the function Omega with respect to g im _,k and g im and expressions for the superpotential", "Bibliography", "Author index", "Subject index".

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