The Meaning of Relativity/Index
INDEX
A
Accelerated massesinductive action of, 113.
Addition and subtraction of tensors, 14.
— theorem of velocities, 40.
B
Biot-Savart force, 46.
C
Centrifugal force, 67.
Clocks–moving, 39.
Compressible viscous fluid, 22.
Concept of space, 3.
– – time, 30.
Conditions of orthogonality, 7.
Congruence–theorems of, 3.
Conservation principles, 55.
Continuum–four-dimensional, 33.
Contraction of tensors, 15.
Contra-variant vectors, 72.
– – tensors, 75.
Co-ordinates–preferred systems of, 8.
Co-variance of equation of continuity, 22.
Co-variant, 12 et seq.
– – vector, 72.
Criticism of principle of inertia, 65.
Criticisms of theory of relativity, 31.
Curvilinear co-ordinates, 68.
D
Differentiation of tensors, 76, 79.
Displacement of spectral lines, 101.
E
Energy and mass, 48, 51.
– tensor of electromagnetic field, 52.
– – of matter, 56.
Equation of continuity–co-variance of, 22.
Equations of motion of materia particle, 52.
Equivalence of mass and energy, 51.
Equivalent spaces of reference, 26.
Euclidean geometry, 4.
F
Finiteness of universe, 110.
Fizeau, 29.
Four-dimensional continuum, 33.
Four-vector, 43.
Fundamental tensor, 74.
G
Galilean regions, 65.
– transformation, 28.
Gauss, 68.
Geodetic lines, 86.
Geometry, Euclidean, 4.
Gravitational mass, 63.
Gravitation constant, 98.
H
Homogeneity of space, 17.
Hydrodynamical equations, 56.
Hypotheses of pre-relativity physics, 77.
I
Inductive action of accelerated masses, 113.
Inert and gravitational mass–equality of, 63.
Invariant, 10 et seq.
Isotropy of space, 17.
K
Kaluza, 108.
L
Levi-Civita, 77.
Light-cone, 42.
Light ray–path of, 102.
Light-time, 34.
Linear orthogonal transformation, 7.
Lorentz electromotive force, 46.
– transformation, 32.
M
Mach, 62, 109, 110, 111, 113, 119.
Mass and Energy, 48, 51.
– equality of gravitational and inert, 63.
– gravitational, 63.
Maxwell’s equations, 23.
Mercury–perihelion of, 103, 107.
Michelson and Morley, 29.
Minkowski, 34.
Motion of particle–equations of, 52.
Moving measuring rods and clocks, 39.
Multiplication of tensors, 14.
N
Newtonian gravitation constant, 98.
O
Operations on tensors, 14 et seq.
Orthogonality–conditions of, 7.
Orthogonal transformations–linear.
P
Path of light ray, 102.
Perihelion of Mercury, 103, 107.
Poisson's equation, 90.
Preferred systems of co-ordinates, 8.
Pre-relativity physics–hypotheses of, 27.
Principle of equivalence, 64.
– – inertia – criticism of, 65.
Principles of conservation, 55.
R
Radius of Universe, 118.
Rank of tensor, 14.
Ray of light–path of, 102.
Reference–space of, 4.
Riemann, 72.
– tensor, 82, 85, 110.
Rods (measuring) and clocks in motion, 39.
Rotation, 66.
S
Simultaneity, 17, 30.
Sitter, 29.
Skew-symmetrical tensor, 15.
Solar Eclipse expedition (1919), 103.
Space–concept of, 3.
– homogeneity of, 17.
– Isotropy of, 17.
Spaces of reference, 4; equivalence of, 26.
Special Lorentz transformation, 36.
Spectral lines–displacement of, 101.
Straightest lines, 86.
Stress tensor, 22.
Symmetrical tensor, 15.
Systems of co-ordinates–preferred, 8.
T
Tensor, 12 et seq, 72 et seq.
– Addition and subtraction of, 14.
– Contraction of, 15.
– Fundamental, 74.
– Multiplication of, 14.
Tensor, operations, 14 et seq.
– Rank of, 14.
– Symmetrical and Skew-symmetrical, 15.
Tensors–formation by differentiation, 76.
Theorem for addition of velocities, 40.
Theorems of congruence, 3.
Theory of relativity, criticisms of, 31.
Thirring, 113.
Time-concept, 30.
Time-space concept, 33.
Transformation–Galilean, 28.
– Linear orthogonal, 7.
U
Universe–finiteness of, 110.
– radius of, 118.
V
Vector–co-variant, 72.
– contra-variant, 72.
Velocities–addition theorem of, 40.
Viscous compressible fluid, 22.
W
Weyl, 77, 103, 108.