A Stubbornly Persistent Illusion
Page 47
length and time, relativity of, 7–9
moving rigid bodies and moving clocks, equations from, 14–16
simultaneity, definition of, 5–7
velocities, composition of, 16–18
moving frames, transformations between. See Lorentz transforms
multiplication of tensors, 60–62, 274
N
n-dimensional metrical spaces, 371–372
negative electrical fluid, 303
negative electrical masses, 168
Newton, Sir Isaac
absolute space theory, 351
co-ordinate system, 397
corpuscular theory, 308
cosmological difficulties of theories
mass densities, 256–257
universe as a whole, considerations, 210–211
equation of motion of material point, 93–94
field-law of gravitation, 372
finite universe, 106
as foundation of physics, 437–438
gravitation, law of, 166, 190, 237, 391, 400, 411
heat phenomena, 414
immediate action at a distance, 366
light, particle properties of, 284, 415
material phenomena, 92–94
motion, laws of, 2, 178, 263, 346, 355
sound-transmission theory, 347
Nishijima, Kazuhiko, 283
nodes, standing wave, 319
non-symmetrical tensor, 380
nuclear physics, 306
nuclear transformation processes, 166
nucleus, 306, 444
O
object, primitive concept of, 334
observable fact of experience, 48
optical phenomena, 414–415
orbit, mass-point in reference to inertial system, 371
orientation, rigid body, 268
outer multiplication of tensors, 60
Out of My Later Years (Einstein), 383–456
common language of science, 448–450
defining theory of relativity, 396–400
ethics, laws of science and, 451–452
general theory of relativity, 388–395
mass and energy, elementary derivation of equivalence, 453–455
physics and reality
corpuscles, relativity theory and, 431–433
field concept, 414–418
mechanics and, 406–414
method of science, general consideration concerning, 401–406
quantum theory and, 424–431
scientific system, stratification of, 404–406
theory of relativity, 418–424
theoretical physics, fundaments of, 436–447
theory of relativity, 385–395
P
pans on a gas range example, 183–184
parallel displacement vectors, 381
partial differential equations, 413, 417, 425
particles
attraction, 285–286
division, finite, 283–284
electrical elementary, describing, 254–255
motion of
equations of, 277
generally covariant equations, mathematical aids to formulation of, 66–68
neutral, 433
physics, beginning of, 334
probability waves, 283, 330–331
waves, appearance as, 284
wave versus, 322–323
pendulum example, mass and energy, 392
perceptions, comparing experiences, 265–266
perfect reflectors, theory of the pressure of radiation exerted on, 23–26
perihelion motion, Mercury, 226–227, 391
perpetuum mobile, 364–365
philosophy, effect on scientific thought, 266, 401
photoelectric effect, 284, 307–308, 320
photographic plate, 311–312, 322
photons, 284, 308
emission, 313–314
light as shower of, 309–310
probability waves, 330–331
X rays, 315
physical nature of gravitational field, hypothesis of, 35–37
physical space, universal law of, 371
physics
classical mechanics and, 411–412
education, 346–351
mathematics versus, 246
reality and
appearances, totality of physical, 349
corpuscles, relativity theory and, 431–433
field concept, 414–418
mechanics and, 406–414
method of science, general consideration concerning, 401–406
phenomenological, 413–414
quanta, 333–335
quantum theory and, 424–431
scientific system, stratification of, 404–406
theory of relativity, 418–424
pinhole
electrons and photons velocity through, 323–324
light beam through, 311–312, 322
Planck, Max, 308–309, 424–425
heat radiation investigations, 356–359
radiation of bodies as a function of temperature, 443
Poincaré, H., 252
changes of state and changes of position, 407
experience, relation to concepts, 266
Poisson’s equation, 105, 372
poles at rest, 293–294
Popper, Karl, 247
position, changes in, 266–267, 407
positive electrical fluid, 303
positive magnetic force, 288
potential energy, 353, 430
Poynting, 91
pressure
law of, 453
minimum, 121
primary concepts, 404
The Principle of Relativity (Einstein), 1–124
Cosmological Considerations, 105–116
boundary conditions, 108–111
calculation and result, 115–116
Newtonian theory, 105–107
spatially finite universe with uniform distribution of matter, 111–115
electrodynamics of moving bodies, 4–31
electrodynamical part, 18–31
kinematical part, 5–18
generally covariant equations, mathematical aids to formulation of, 55–77
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
divergence of a mixed tensor of the second rank, 74–75
divergence 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
tensors of second and higher ranks, 58–60
gravitational field, theory of
absence of matter, field equations for, 78–80
conservation in the general case, laws of, 84–85
field-components, expression for, 77–78
field equations of gravitation, general form of, 82–84
Hamiltonian function, 80–82
material point, equations of motion of, 77–78
momentum and energy for matter, laws of, 85–86
momentum and energy, laws of, 80–82
gravitation fields, 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
Hamilton’s Principle
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
light, influence of gravitation on the propagation of, 35–45
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
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
postulate of relativity, fundamental considerations
extension, need for, 47–50
four co-ordinates to measurement in space and time, 53–55
general laws of nature, general co-variance for the equations expressing, 50–53
observations, 46–47
space-time continuum, 50–53
principle of relativity, restricted sense, 138–140
principle of variation and field-equations of gravitation and matter, 99–100
principle–theories, 396–397
probability, 326
probability waves
particles, defining, 283
quanta, 323–333
propagation of light, apparent incompatibility with principle of relativity, 142–144
proposition, truth of, 344
Pythagorean theorem, 342
Q
quanta
continuity-discontinuity, 300–301
elementary quanta of matter and electricity, 301–306
of light, 306–312
light spectra, 312–316
physics and reality, 333–335
probability waves, 323–333
waves of matter, 316–323
Quantum Field Theory, 236
Quantum Mechanics, 383–384
quantum physics, 327–328
quantum theory
field theory, limitations of, 435
particles, appearance as waves, 284
physics and reality, 424–431
R
radiation
acceleration, freedom of, 38–39
of bodies as a function of temperature, 443
density, 359
diminishing energy, 34
increasing energy, 164–165
light spectra, 312
photoelectric effect, 307–308
pressure, law of, 453
thermodynamics, 356, 362–363
transparent bodies, refraction-indices of, 349–350
radioactive disintegration, 326–327
railroad embankment examples
distance, relativity of the conception of, 151–152
nonuniform motion, 176
reference-body, choosing, 174–175
relativity of simultaneity, 148–150
retardation of motion, 182
simultaneity and time, 145–147
uniformly moving co-ordinate system, 138–140
velocities, addition of, 141
ray of light, moving, 8, 11–13
real things, measuring, 249–253
rectilinear and uniform motion, body in, 387
red, displacement of spectral lines towards, 230–232
refraction-indices of transparent bodies, 349–350
Reissner, Hans, 423
relativity, general theory of
autobiographical notes, 369–371, 374–375
mechanics, 139
Out of My Later Years, 388–395
relativity, special theory of, 364–369
mechanics, 46
physical interpretation of space and time in classical mechanics, 386–388
relativity, theory of
defining, 396–400
ether and, 237–248
geometry and experience, 249–262
physics and reality, 418–424
Relativity—The Special and General Theory (Einstein), 125–234
addition of the velocities, theorem of (experiment of Fizeau), 159–161
classical mechanics and, unsatisfactory aspects of, 183–184
clocks and measuring–rods on a rotating body of reference, 189–191
co-ordinate, system of, 132–134
distance, relativity of conception of, 151–152
equality of inertial and gravitational mass, 179–182
Euclidean and non-Euclidean continuum, 192–194
exact formulation, 203–205
experience and, 167–170
experimental confirmation, 225–232
light, deflection by gravitational field, 228–229
Mercury, motion of the perihelion of, 226–227
red, displacement of spectral lines towards, 230–232
Galilean system of co-ordinates, 137
Gaussian co-ordinates, 195–197
general results, 163–166
geometrical propositions, physical meaning of, 129–131
gravitational field, 177–178
gravitation, solution of problem of, 206–209
heuristic value of theory of relativity, 162
inferences, 185–188
Lorentz transformation, 153–156, 218–222
measuring-rods and clocks in motion, behavior of, 157–158
Minkowski’s four-dimensional space, 171–173, 223–224
principle of relativity, restricted sense, 138–140
propagation of light, apparent incompatibility with principle of relativity, 142–144
simultaneity, relativity of, 148–150
space and time in classical mechanics, 135–136
space-time continuum as Euclidean continuum, 198–199
space-time continuum is not Euclidean continuum, 200–202
special and general principle, 174–176
structure of space, 233–234
theorem of addition of velocities in classical mechanics, 141
time, idea of in physics, 145–147
universe as a whole, considerations
“finite” and “unbounded” universe, possibility of, 212–215
Newton’s theory, cosmological difficulties of, 210–211
structure of space, 216–217
religion, experience with, 339–340
resonators, oscillation of all, 358–359
rest
bodies at, 9
geometry, 47
poles at, 293–294
result, calculation and, 115–116
Riemann, Bernhard
four-dimensional continuum of space-time, 254
metric, 443
n-dimensional metrical spaces, 371–372
tensor of curvature, 118
Riemann-Christoffel tensor, 75–77
rigid bodies
changes in position, 266–267
distance, 408
distance between two points, 130–131
interval, 267–268
moving, 14–16
in nature, 409
orientation, 268
rigid surfaces. See coordinates, system of
rods
analytic geometry, 386
ideal, 364
kinematics, 47
length of interval, 268
marble slab example, 192–193
temperature, 193–194
in motion, behavior of, 157–158
moving, length of, 8–9, 14
objects above surface of earth, 132–133
on a rotating body of reference, 1–2, 189–191
static gravitational field, 94–96
Rosen, Robert, 423, 431
rotation
co-ordinate, system of, 251–252
Mercury, 98
S
scalar field, 367–368
covariant law for, 374
scalar of curvature, 121
&n
bsp; scalars, field equations freed of
covariant law, 374
gravitation fields, role in structure of elementary particles of matter, 119–122
Schrödinger, Erwin, 425–428, 444, 445
Schwarzschild, Karl, 126, 423, 432–433
scientific description, basis of, 132
scientific system, stratification of, 404–406
sense experiences, 401–403
simultaneity
clocks, 147
definition of, 5–7, 386–387
events, 366
railroad embankment examples, 145–147
relativity of, 148–150, 410
six-vector, divergence of, 73–74
size, atoms, 357–358
skew-symmetry tensors, 275, 282
solenoid, magnetic field, 291–292, 295
solid bodies, Euclidean geometry, 251
space
curvature, Euclidean geometry and, 399
empty as seat of field, 416–417
empty, equations of, 379–380
structure in universe as a whole, 216–217
structure of, 233–234
in time in pre-relativity physics, 265–282
space and time
absent gravitational fields, 187–188
accelerated frames, bending lightbeams, 2
in classical mechanics, 135–136
geometrical behavior, 400
in geometry, 386
Newtonian basis, 437–438
rigid bodies and, 409
space-time continuum
character, note on, 64–65
ether, role of, 244–245
Euclidean geometry, 51, 198–199, 409
four-dimensional, 111–112, 116, 254
nature versus, 430
not as Euclidean continuum, 200–202
postulate of relativity, fundamental considerations, 50–53
spark produced when current disconnected, 298–299
spatial infinity, 110–111
constant limit, 105–106
spatially finite universe with uniform distribution of matter, 111–115
special and general principle, 174–176
special theory of relativity. See relativity, special theory of
spectral lines, displacement towards red, 230–232
spectroscope, 312–313
speed of light, 1, 5, 366–367, 386
sphere, lines in space model, 286
standing wave, 318–319, 320
stars
Boltzmann’s law of distribution for gas molecules, 106–107
distribution, 256–257
lines of light from surface, 96
state, changes of, 407
statement of set of rules, 403
stationary charges, 1
stationary system, 9–14, 363
statistical quantum theory
merits of, 378–379
relativity, theory of, and, 375–376
Riemann’s n-dimensional metrical spaces, 371–372
u-function (insert symbol please), 376–377
statistics, method of, 325–326
quantum physics, 327–328