in tube, electricity discharge, 312–313
Gaussian co-ordinates, 195–197, 203–205
Gell-Mann, Murray, 283
general laws of nature, general co-variance for the equations expressing, 50–53
generally covariant equations, mathematical aids to formulation of, 55–77, 421
antisymmetrical extension of a six-vector, 73
contravariant and covariant four-vectors, 56–58
curl of a contravariant vector, 73
divergence
of a contravariant vector, 72–73
of a mixed tensor of the second rank, 74–75
of a six-vector, 73–74
fundamental tensor (uv) (insert correct symbols, please), 62–66, 71–72
geodetic line, equation of, 66–68
multiplication of tensors, 60–62
particle, motion of, 66–68
Riemann-Christoffel tensor, 75–77
tensors
formation by differentiation, 68–71
of second and higher ranks, 58–60
general theory of relativity. See relativity, general theory of
geodetic line
equation of, 66–68
movement in gravitational field, 78
geometrical invariant, 271–272
geometrical propositions, physical meaning of, 129–131
geometry
bodies at rest, 47
experience and, 249–262
as intermediary between physical sciences and math, 247–248
physical standpoint, 386
space and time, 386
globe, unbounded continuum, 258–261
gravitation
field equations, deducing from laws of conservation, 104
mechanics and, 36–37
Newton’s law of, 166, 190, 237, 391, 400, 411
gravitational field, 177–178, 237
absence of matter, field equations for, 78–80
acceleration, imparting, 49, 389
bending of light rays in, 43–45
centrifugal force, 189–191
clocks and, 42–43
conservation in the general case, laws of, 84–85
describing, 431–432
electricity, combined equations with, 433
electromagnetic field and, 78–79, 422–423
ether and, 245
field-components, expression for, 77–78
field equations of gravitation, general form of, 82–84
Hamiltonian function, 80–82
law of, 372
light, deflection by, 228–229
lines of force, 286
material point, equations of motion of, 77–78
momentum and energy for matter, laws of, 85–86
momentum and energy, laws of, 80–82
Newton’s theory, divergence from, 400
pure, 375
ray of light, transmitting curvilinearly, 185–186
role in structure of elementary particles of matter, 117–124
cosmological question, 122–124
defects in present (1919) view, 117–119
scalars, field equations freed of, 119–122
separate existence (Hamilton’s Principle), 101
space and time absent, 187–188
gravitational lensing, 126
gravitational mass, 181, 368–369
gravitation, solution of problem of, 206–209
Grommer, J., 109
H
Hamilton’s Principle
gravitational field, theory of, 80–82
invariants, theory of, conditioning properties of field equations of gravities, 101–104
principle of variation and field–equations of gravitation and matter, 99–100
separate existence of gravitational field, 101
Hawkings, Stephen, ix–xi
heat
phenomena, 393, 394, 413, 414
radiation investigations of Planck, 356–359
wires between charged plates, 304
Heisenberg, Werner, 425
Hertz, G., 428
Hertz, Heinrich, 239–240, 416, 439–440. See also Maxwell-Hertz equations
heuristic value of theory of relativity, 162
Hilbert, D.
defects in theory, 117
variation, theory of relativity from, 99
homogeneity of space, 276
Hubble, Edwin, 3, 126
Huyghen’s principle, 43–45, 97
hydrodynamics, 347, 413
hydrogen atom, 304–305
I
indivisible steps, change, 301–306, 324
induced currents, 295–299
induction, 297, 405
inertia, 351
of a body, dependence on energy content, 32–34
β-rays, 168
constant controlling, 399
co-ordinates, system of, 335
disk, centrifugal force acting on, 189–190
law of, 137, 388, 411
law of constancy of light velocity, 419
light and, 387
Mach’s theory, 351–352, 367, 438
magnetic field and, 417
material point of mass, 111
radiation conveying between emitting and absorbing bodies, 34
inertial mass, 181
classical mechanics problem, 420
constant of accelerated body, 178
energy increasing, 368–369
equivalence, principle of, 389
gravitational, equality with, 179–182
gravitation of energy, 37–40
Infield, Leopold. See The Evolution of Physics
infinity, spatial, 105–106
inner multiplications of tensors, 61–62
intervals
Cartesian co-ordinate system, 268–269
rate of, 254
rigid body, 267–268
two points on rigid body, 267
invariants, theory of, 101–104
isotropy of space, 276
J
Jacobi’s theorem, 272
Jupiter, 45
K
Kaluza, Theodor, 423
kinematics
electrodynamics of moving bodies, 5–18
as laws regarding measuring bodies and clocks, 47
length and time, relativity of, 7–9
moving rigid bodies and moving clocks, equations from, 14–16
simultaneity, definition of, 5–7
special theory of relativity and, 398, 400
velocities, composition of, 16–18
kinetic energy, 353
of the body, 166
mass, material point of, 163–164
kinetic theory, gas particles, 357, 358, 414
Kirchhoff, Gustav, 356
L
Laser Interferometer Gravitational wave Observatory (LIGO), 248
Laser Interfoerometer Space Antenna (LISA), 248
later events, 265
law of conservation of momentum and of energy for the gravitational field, 81–82
law of constancy of light velocity, 419
law of constancy of velocities, 142
law of inertia, 137, 388, 411
law of motion, 168–169, 352, 375, 411
law of pressure, 453
law of the constancy of the velocity of light, 144
law of the parallelogram of velocities, 17
law of the transmission of light in vacuo, 155–156
laws of conservation. See conservation
length
distance, relativity of the conception of, 151–152
of interval, 268
measurements of, 132
of moving rods, 8–9, 14
and time, relativity of, 7–9
wave listed by color, 314–315
LeVerrier, Urbain, 98
light
aberration of, 453
bending, 2
clock, using as, 263–264
comp
act fields from which can’t escape, 126
curving by action of gravitational fields, 400
deflection by gravitational field, 228–229
Ether, theory of, 238
gravitation and propagation of
bending of light rays in gravitational field, 43–45
gravitation of energy, 37–40
physical nature of gravitational field, hypothesis of, 35–37
time and velocity of light in gravitational field, 40–43
homogeneous, extracting electrons from metal, 307–308
law of constancy of velocity, 419
law of the constancy of the velocity of, 144
in liquid, traveling with particular velocity, 160–161
measuring height of clouds, 133
motion of material points, 415
particle properties of, 284
phenomenological physics, 413–414
quanta, 306–312
radiation, 312
ray
curvature of, 97
transformation of the energy of, 23–26
velocity of, 8, 11–13
as shower of photons, 309–310
source of, inertia and, 387
spectra, 312–316
speed of, 1, 2, 5, 366–367, 386
stars, lines of light from, 96
transmitting rectilinearly, 185–186
in vacuo, constancy of, 398
wave-motion of, 347, 438
lightning strike, simultaneity of, 145–146, 148
LIGO (Laser Interferometer Gravitational wave Observatory), 248
lines of force
of the gravitational field, 286
induction phenomena, 297
magnetic field, 288–289
metal plates, 303–304
line, straight, 130
movement
not subject to external forces, 77–78
relative to two different points, 138
properties of, 268
liquid, light traveling through, 160–161
LISA (Laser Interfoerometer Space Antenna), 248
longitudinal mass, 29
Lorentz contraction, 51
Lorentz, Hendrick A., 144, 170. See also Maxwell-Lorentz theory
covariant law for scalar field, 374
electrodynamic theory, 161, 240
empty space as seat of field, 416–417
field-theory of gravitation and, 373–374
stationary charges, 1
theory of matter, 354–356
variation, theory of relativity from, 99
Lorentz transformation, 26–27, 153–156
addition of velocities, 160
conditions, 198–199
demand, 387–388
Galileo’s versus, 263
limiting velocity, 157–158
simple derivation of, 218–222
space-time variables, replacing, 203
velocities, 153–154
Luminiferous Ether, 235, 238
M
Mach, Ernst, 47, 184, 348, 414
inertia, 351–352, 367, 438
mean acceleration, 243–244
magnetic field, 177
asymmetries, 4
current acting upon magnetic pole, 287–288
electrical current, 287, 294
inertia and, 417
lines of force, 288–289
masses, 415
in motion, 18–23
positive force, 288
magnetomotive forces, 21
maps, distances and, 300
marble slab rods example, 192–194
mass
conservation of, 164, 392
defined, 393–394
densities, 256–257
discontinuous nature of, 302
electric, introduction of, 350
and energy, equivalence of, 392–393, 394, 453–455
hydrogen atom, 304–305
inertia, 111
inertial and gravitational, equality of, 179–182
kinetic energy of a material point of, 163
magnetic field, 415
negative electrical, 168
reciprocal action between, 256
material particle. See particles
material phenomena, 86–98
free space, Maxwell’s electromagnetic field equations for, 88–91
frictionless adiabatic fluid, Euler’s equations for, 87–88
Newton’s theory as a first approximation, 92–94
rods and clocks, behavior in static gravitational field, 94–96
material point
describing, 410–411
equations of motion of, 77–78
forces on, 412
mathematics
antisymmetrical extension of a six-vector, 73
contravariant and covariant four-vectors, 56–58
curl of a contravariant vector, 73
divergence
of a contravariant vector, 72–73
of a mixed tensor of the second rank, 74–75
of a six-vector, 73–74
education in autobiographical notes, 344–346
fundamental tensor (uv) (insert correct symbols, please), 62–66, 71–72
geodetic line, equation of, 66–68
multiplication of tensors, 60–62
particle, motion of, 66–68
physics versus, 246
real things, measuring, 249–253
Riemann-Christoffel tensor, 75–77
tensors
formation by differentiation, 68–71
of second and higher ranks, 58–60
matter
absence, field equations for, 78–80
density defining energy-tensor, 93–94
elementary particles, gravitational field and structure of, 119–122
elementary quanta, 301–306
Lorentz’s theory, 354–356
molecular structure of, 435
uniform distribution in spatially finite universe, 111–115
waves of, 316–323
Maxwell-Hertz equations
for currents, 330
electromagnetic waves, 440
for empty space, 32
mechanics as basis of physics, 347
transformation, 18–23
Maxwell, James Clerk
asymmetries in moving bodies, 4
electric field theory, 415–416
electricity and magnetism theory, 1, 338, 367
electrodynamics, 187
electromagnetic action at distance, 166, 350, 415–416, 439–440
autobiographical notes, 353–354
as foundation of electron theory of Lorentz, 281, 441–442
fundamental equations of electrodynamics, 164–165
speed of light and, 5
empty space, equations of, 379–380
fields as fundamental variables, 353–354
free space, electromagnetic field equations for, 88–91
Maxwell-Lorentz theory
body moving uniformly, 169
electron, theory of, 119
ether and, 239
experimental arguments in favor of, 167–168
Maxwell-Poynting expressions, 91
mean acceleration, 243–244
The Meaning of Relativity (Einstein), 263–282
measurable distance between two points, 271
measurement
distance, 132
of events, 386
real things with mathematics, 249–253
measuring rods. See rods
mechanics
as basis of physics, 351–353
electricity and, 414–415
force laws and, 411
gravitation and, 36–37
inertial mass problem, 420
natural phenomena, insufficiency to describe, 139
observable fact of experience, 48
physics and reality, 406–414
phy
sics, inadequacy as basis of, 349–351
potential energy as function of configuration, 412
relativity principle, 139
space and time, 135–136
special theory of relativity, 46
unsatisfactory aspects of, 183–184
Mercury
ellipses of planetary orbits, 400
mass density, 256
perihelion motion, 226–227, 391
rotation, 98
metal plates
electrons, extracting, 307–308
lines of force, 303–304
method of statistics, 325–326
quantum physics, 327–328
metrical character (curvature), four-dimensional space-time continuum, 111–112, 116
Michelson, Albert, 169–170, 235
Mie, G., 117, 119
Milky Way
distribution of stars, 256–257
mean density, 256
Millikan, Robert, 428
Minkowski, Peter, 89
four-dimensional space, 171–173, 223–224, 365
objects to which motion cannot be applied, 242
space-time continuum as Euclidean continuum, 198–199
mixed multiplications of tensors, 61–62
mixed tensors, 59
molecules
elementary quanta of matter, 301–302
matter, structure of, 435
momentum
conservation of, 366, 453
gravitational field, theory of, 80–82, 85–86
money, change and, 300–301
Morley, Edward, 170
Ether, 235
speed of light, 1
motion. See also kinematics; wave
clocks and, 204
coordinate systems in any state of, 443
corpuscles, 320
describing, need for second body and, 397
distant masses, 48
law of, 2, 168–169, 178, 263, 346, 352, 355, 375, 411
magnetic field creating electricity, 294
material particle, equations of, 277
of material point, 77–78, 93–94, 201–202, 415
neutral particle, 433
Newton’s law of, 2, 178, 263, 346, 355
nonuniform, 176
rectilinear and uniform, body in, 387
retardation, 182
rigid bodies and moving clocks, equations from, 14–16
tensors, equations of, 278–279
theory of relativity and, 385
uniform acceleration, 420
uniform rectilinear, 185
motion of uniform translation. See relativity, special theory of; special theory of relativity
movement
chest against gravitational field, 179–182
straight line, 138
moving bodies
electrodynamical part
convection-currents, transformation of Maxwell-Hertz equation with, 26–31
light rays, transformation of the energy of, 23–26
magnetic field in motion, 18–23
negative electrical masses, 168
perfect reflectors, theory of the pressure of radiation exerted on, 23–26
kinematical part
co-ordinates and times, converting from stationary system, 9–14