Space Time and Gravitation/Index

by Arthur Stanley Eddington

INDEX

• Absolute, approached through the relative, 82
• Absolute acceleration, 68, 154, 194
• Absolute past and future, 50
• Absolute rotation, 152, 164, 194
• Absolute simultaneity, 12, 51
• Absolute time, in cylindrical world, 163
• Acceleration, a simpler quality than velocity, 195; modifies FitzGerald contraction, 75
• Action, 147; atomicity of, 199; on Weyl's theory, 177
• Action, Principle of Least, 149, 178
• Addition of velocities, 59
• Aether, a plenum with geodesic structure, 164; identified with the "world," 187; non-material nature of, 39; stagnant, 210
• Artificial fields of force, 64
• Atom, vibrating on sun, 128
• Atomicity, law of, 199; of Action, 177
• Aviator, space and time-reckoning of, 23

• Bending of light, effect on star's position, 112; observational results, 118; theory of, 107, 207
• Beta particles, 59, 145
• Brain, constitution of, 191
• Brazil, eclipse expedition to, 117

• Causality, law of, 156
• Causation and free will, 51
• Centrifugal Force, compared with gravitation, 41, 65; debt at infinity, 157; not caused by stars, 153; vibrating atom in field of, 129
• Chess, analogy of, 184
• Christoffel, 89
• Circle in non-Euclidean space, 104
• Clifford, 77, 152, 192
• Cliquishness, 188
• Clock, affected by velocity, 58; on sun, 74, 128; perfect, 13; recording proper- time, 71
• Clock-scale, 58
• Clock-scale geometry, not fundamental, 73, 131, 191
• Coincidences, 87
• Comets, motion through coronal medium, 121; radiation-pressure in, 110
• Conservation of electric charge, 173; of energy and momentum, 139; of mass, 141, 196
• Content contrasted with structural form, 192, 200
• Continuous matter, 91, 140
• Contraction, FitzGerald, 19, 54
• Convergence of physical approximations, 154
• Coordinates, 77
• Coordinate velocity, 107
• Corona, refraction by, 121
• Cottingham, 114
• Crommelin, 114, 122
• Curvature, degrees of, 91; identified with action, 148; merely illustrative, 84; of a globe of water, 148; of space and time, 158; on Weyl's theory, 176; perception of, 190
• Cylinder and plane, indistinguishable in two dimensions, 81
• Cylindrical world, Einstein's, 161, 177

• Davidson, 114
• Deflection of light, effect on star's position, 112; observational results, 118; theory of, 107,207
• Density, effect of motion on, 62
• Displacement of spectral lines, 129; in nebulae, 161 ; in stars, 135
• Displacement of star-images, 112, 115
• Double stars and Einstein effect, 133
• Duration, not inherent in external world, 34
• Eclipse, observations during, 113
• Ehrenfest's paradox, 75
• Electrical theory of inertia, 61
• Electricity and gravitation, 167
• Electromagnetic potentials and forces, 172
• Electron, dimensions of, 177; geometry inside, 91; gravitational mass of, 178; inertia of, 61; Kaufmann's experiment on, 62, 146; singularity in field, 167
• "Elsewhere," 50
• Emptiness, perception of, 190
• Energy, conservation of, 139; identified with mass, 146; inertia of, 61, 146; weight of radio-active, 112
• Entropy, 149
• Eötvös torsion-balance, 112
• Equivalence, Principle of, 76, 131, 212
• Euclidean geometry, 1, 47, 73
• Euclidean space of five dimensions, 84
• Event, definition of, 45, 186
• Evershed, 130
• Extension in four dimensions, 37, 46

• Feeling, elements of, 192
• Fields of force, artificial, 64; due to disturbance of observer, 69; electromagnetic, 171; relativity of, 67
• Field of velocity, 195
• FitzGerald contraction, 19; consequences of, 22; modified by acceleration, 75; relativity explanation of, 54
• Flat space in two dimensions, 80
• Flat space-time, 83; at infinity, 84; conditions for, 89
• Flatfish, analogy of, 95
• Flatland, 57
• Force, compared with inertia, 137; electromagnetic, 172; elementary conception of, 63; fields of, 64; relativity of, 43, 67, 76
• Form contrasted with content, 192, 200
• Formalism of knowledge, 175
• Foucault's pendulum, 152
• Four-dimensional order, 35, 56, 186
• Four-dimensional space-time, geometry of, 45, 82; reality of, 181
• Fourth dimension, 13
• Frame, inertial, 156
• Frames of reference, "right" and "wrong," 42
• Freewill, 51
• Freundlich, 212
• Future, absolute, 50

• Galilean potentials, 83
• Gauge, effect on observations, 31; provided by radius of space, 177
• Gauge-system, 169
• Geodesic, absolute significance of, 70, 150; definition of, 75; motion of particles in, 138, 151; in regions at infinity, 157
• Geodesic structure, absolute character of, 155, 164; acceleration of, 195
• Geometrical conception of the world, 176, 183
• Geometry, Euclidean, 1; hyperbolic, 47; Lobatchewskian, 1, 9; natural, 2; non-Euclidean, or Riemannian, 6, 73, 84, 90; non-Riemannian, 169; semi-Euclidean, 47
• Ghosts of stars, 161
• Globe of water, limit to size of, 148
• Gravitation, Einstein's law of, differential formula, 90; integrated formula for a particle, 97; macroscopic equations, 140, 193
• Gravitation, Newton's law of, ambiguity of, 93; approximation to Einstein's law, 103; deflection of light, 109, 111
• Gravitation, propagation with velocity of light, 94, 147; relativity for uniform motion, 21, 125
• Gravitational field of Sun, 97; deflection of light, 107, 118, 207; displacement of spectral lines, 129; motion of perihelion, 122, 206; Newtonian attraction, 102; result of observational verification, 126
• Grebe and Bachem, 130
• Greenwich, Royal Observatory, 114
• Gyro-compass, 152

• Hummock in space-time, 97
• Hurdles, analogy of counts of, 104
• Hyperbolic geometry, 47
• Identities connecting $G_{\mu \nu }$, 141
• Identity permanent, 40, 193
• Imaginary intervals, 150, 187
• Imaginary time, 48, 181
• Inertia, compared with force, 137; electrical theory of, 61; in regions at infinity, 157; infinite, 56; Mach's views, 164; of light, 110; relativity theory of, 139
• Inertia-gravitation, 137
• Inertial frame, 156
• Infinity, conditions at, 157
• Integrability of length and direction, 174
• Interval, 46, 150, 187; general expression for, 82; practical measurement of, 58, 75
• Interval-length, geometrical significance essential, 127; identified with proper time, 71; tracks of maximum, 70, 150; zero for velocity of light, 71
• Invariant mass, 145; of light, 148

• Jupiter, deflection of light by, 133

• Kaufmann's experiment, 62, 146
• Kinds of space, 81

• Laplace's equation, 96, 140
• Larmor, 19, 211
• Length, definition of, 2; effect of motion on, 19; relativity of, 34
• Le Verrier, 124
• Levi-Civita, 89
• Lift, accelerated, 64
• Light, bending of, 107, 112, 118, 207; coordinate velocity of, 107; mass of, 62, 110, 148; voyage round the world, 161; weight of, 111
• Light, velocity of, an absolute velocity, 59; importance of, 60; system moving with, 26, 56
• Lobatchewsky, 1, 9
• Lodge, 32, 125, 211
• Longest tracks, 70
• Lorentz, 19, 211

• Mach's philosophy, 163
• Macroscopic equations, 92, 139; interval, 187
• Map of sun's gravitational field, 99
• Mass, conservation of, 141, 195; electrical theory of, 61; gravitational, 98; identified with energy, 146; invariant, 145; of light, 62, 110, 148; variation with velocity, 145
• Mathematics, Russell's description of, 14
• Matter, continuous, 91; definition of a particle, 98; extensional relations of, 8; gravitational equations in, 141; perception of, 190; physical and psychological aspects, 192
• Mercury, perihelion of, 123, 125
• Mesh-systems, 77; irrelevance to laws of nature, 87
• Michelson-Morley experiment, 18
• Minkowski, 30, 212
• Mirror, distortion by moving, 22
• Momentum, conservation of, 141; re-definition of, 144; of light, 111
• Moon, motion of, 93, 134
• Motion, insufficiency of kinematical conception, 194; Newton's first law, 136

• Natural frame, 155
• Natural gauge, 176
• Natural geometry, 2
• Natural tracks, 70
• Nebulae, atomic vibrations in, 161
• Newton, absolute rotation, 41; bending of light, 110; law of gravitation, 93; law of motion, 136; relativity for uniform motion, 40; super-observer, 68
• Non-Euclidean geometry, 6, 73, 84, 90
• Non-Riemannian geometry, 169

• Observer, an unsymmetrical object, 57
• Observer and observed, 30
• Orbits under Einstein's law, 123
• Order and dimensions, 14, 186
• Ordering of events in external world, 35, 54, 184

• Past, absolute, 50
• Perceptions, as crude measures, 10, 15, 31
• Perihelia of planets, motions of, 123
• Permanence of matter, 196
• Permanent identity, 40, 193
• Permanent perceptual world, 141, 198
• Poincaré, 9
• Point-event, 45, 186
• Potentials, 80; Galilean values, 83
• Potentials, electromagnetic, 172
• Principe, eclipse expedition to, 114
• Principle of Equivalence, 76, 131, 212
• Principle of Least Action, 149, 178
• Principle of Relativity (restricted), 20
• Probability, a pure number, 178
• Projectile, Jules Verne's, 65
• Propagation of Gravitation, 94, 147
• Proper-length, 11
• Proper-time, 71
• Pucker in space-time, 85

• Quanta, 60, 177, 182, 200

• Radiation-pressure, 110
• Real world of physics, 37, 181
• Receding velocities of B-type stars, 135; of spiral nebulae, 161
• Reflection by moving mirror, 22
• Refracting medium equivalent to gravitational field, 109
• Refraction of light in corona, 121
• Relativity of force, 43, 76; of length and duration, 34; of motion, 38; of rotation, 152, 155; of size, 33
• Relativity, Newtonian, 40; restricted Principle of, 20; standpoint of, 28
• Repulsion of light proceeding radially, 102, 108
• Retardation of time, 24, 55; in centrifugal field, 129; in spherical world, 160
• Ricci, 89
• Riemann, 2, 89, 167
• Riemann-Christoffel tensor, 89
• Riemannian, or non-Euclidean, geometry, 6, 73, 84, 90
• Rigid scale, definition of, 3
• Rotation, absolute, 152, 164, 194
• Rotation of a continuous ring, 194
• Russell, 14, 197

• St John, 130
• Semi-Euclidean geometry, 47
• Simultaneity, 12, 51
• de Sitter, 134, 159, 179
• Sobral, eclipse expedition to, 117
• Space, conventional, 9; kinds of, 81; meaning of, 3, 8, 15; relativity of, 34
• Space-like intervals, 60, 187
• Space-time, 45; due to Minkowski, 212; partitions of, 54
• Spherical space-time, 159
• Standard metre, comparison with, 168
• Stresses in continuous matter, 193
• Structure opposed to content, 197, 200
• Structure, geodesic, absolute character of, 155, 164; acceleration of, 195; behaviour at infinity, 157
• Super-observer, Newton's, 68
• Synthesis of appearances, 31, 182

• Tensors, 89, 189
• Thomson, J. J., 61
• Time, absolute, 163; depends on observer's track, 38, 57; for moving observer, 24; imaginary, 48; measurement of, 13; past and future, 51; "standing still," 26, 160
• Time-like intervals, 60, 187
• Tracks, natural, 70

• Vacuum, defined by law of gravitation, 190
• Vector, non-integrable on Weyl's theory, 174
• Velocity, addition-law, 59; definition of, 193; static character, 194
• Velocity of gravitation, 94, 147
• Velocity of light, importance of, 60; in gravitational field, 108; system moving with, 26, 56

• Warping of space, 8, 126
• Wave-front, slewing of, 108
• Weight, of light, 107, 111; of radio-active energy, 111; proportional to inertia, 137; vanishes inside free projectile, 65
• Weyl, 174
• World, 186, 187
• World-line, 87