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COVERAGE AND ABBREVIATIONS
This index covers the Prologue, Chapters, Epilogue, and Notes.
Additional information about subjects will be found in the Glossary (pages 547–60) and Chronology (pages 537–46).
Letters appended to page numbers have the following meanings:
b—box
f—figure or photograph
n—footnote
N—in the Notes, the page to which the note refers; for example, 561N26 means “the note to page 26, which will be found on page 561”
Absolute interval in spacetime, 90, 92, 91b–92b, 414
Absoluteness of space and time:
Newton’s concepts of, 62–63
Einstein’s rejection of, 72
implies speed of light is relative, 63, 79
experimental evidence against, 65–66
theoretical arguments against, 66–68
see also Relativity of space and time
Absoluteness of speed of light:
not true in Newtonian physics, 63, 79, 133
Einstein’s conception of, 72–73, 79
consequences of, 73–76, 77b, 82
tested by Michelson-Morley experiment, 64, 78–79
tested in modern particle accelerators, 83–84
Acceleration radiation and accelerated viewpoint, 443–46, 444b
Accelerators, particle, 83–84, 86, 237, 339, 340
Accretion disk around black hole:
concept of, 46, 47f, 346
anchoring by black hole’s spin, 346–47
possible roles in quasars and jet production, 346–54
Accretion of gas onto black hole:
in science fiction scenario, 24–25, 24f
as source of X-rays and other radiation, 307–9, 307f, 308f, 318
see also Accretion disk
Accretion of gas onto neutron star, 241–43, 242f
Active galactic nuclei (AGN), 351–53
Adiabatic index, 149, 200b; see also Resistance to compression
Aether:
Newtonian concept of, 63, 564N63
and Michelson–Morley experiment, 64–65, 565N64, 565N65
Einstein’s rejection of, 72, 82, 85
Angular momentum, 27
Antimatter, 173, 173n, 340, 359, 439n, 445
Ants:
T. H. White’s Society of, 137, 285
parable of the, 246–49, 247f
Astronomers contrasted with other scientists, 319–21, 328, 341–42
Astrophysicists contrasted with other scientists, 319–21, 341–42
Atom, structure of, 170b; see also Nucleus, atomic
Atomic bomb, see Nuclear weapons research
Bekenstein’s conjecture about black-hole entropy, 425–26, 442, 445–46
Bets by Thorne:
with Chandrasekhar, about black-hole stability, 296, 298, 298n
with Hawking, about Cyg X-1, 314–15, 315f
with Hawking and Preskill, about cosmic censorship, 481–82, 481f
with Zel’dovich, about black-hole evaporation, 433, 435, 438–39
no bet about time machines, 521
Big bang:
like time reversed stellar implosion, 268–69, 450
singularity at beginning of, 465, 478, 487f, 525
gravitational waves from, 380
tiny black holes created in, 50–51, 447–48
wormholes created in, 497
nonlinearity in, 363b
failure of general relativity in, 86
quantum gravity as key to, 525
speculations on what preceded, 456, 525
topology as a tool for studying, 464f–65f, 471
Big crunch, 450, 454–55, 464f, 465f, 465, 468, 487f, 525, 581N465
Black-hole binary:
and observational search for black holes, 304–9, 305f, 308f, 315–19, 315f
inspiral and coalescence, 48–49, 358–59, 359f, 394–95, 413
as source of gravitational waves, 48–49, 357–61, 379, 393–96, 413
embedding diagrams for, 358f, 359f
Black hole, eighteenth-century version of, 122–24, 123f, 132, 133, 138, 251–53, 252f, 568N122, 568N123
Black-hole evaporation:
overview of, 50–51
presaged by Wheeler’s speculations, 210–11, 21 1f, 244–45, 253–54
presaged by Zel’dovich, 429–35
predicted by Hawking, 435–36; see also
Hawking radiation
details of, 446–48
endpoint of, 482
observational search for, 447–48
Black-hole evolution:
Hawking’s area-increase theorem, 413, 413n, 416–17, 422–23, 427, 462
laws of black-hole mechanics and thermodynamics, 427, 436, 442, 445–46
Black hole, fall of objects into, 33, 291–92, 292f;
see also Accretion disk around black hole;
Accretion of gas onto black hole
Black-hole formation by stellar implosion, see
Implosion of star to form black hole
Black hole, gigantic:
formation of, 354–55, 396
serendipitous discovery of, 322, 326, 355
as power source for quasars and radio galaxies, 346–54; see also Quasars; Radio galaxies; Radio jets; Radio waves, cosmic
number of in Universe, 354
in center of our Milky Way galaxy, 354
rate of swallowing Universe’s matter, 355–56
Black-hole interior:
summary of current understanding, 29–32, 36, 472–73
details of current understanding, 473–80
Oppenheimer–Snyder description of, 450–53, 452f, 473
Khalatnikov–Lifshitz claim of no singularity, and their retraction, 453–56, 455f, 459, 466–69, 473–74
singularity at center, overview of, 29–32
Penrose’s theorem that hole contains singularity, 462–63
BKL (mixmaster) singularity, 468–69, 474–76, 475f
foam-like structure of singularity, 476–79, 478f, 525
aging of tidal gravity in, 479–80
speculations on travel to another universe, 456–58, 457f, 473–74, 484
see also Singularity
Black hole, names for:
Schwarzschild singularity, 121, 136–37, 244, 250, 255
frozen star, 255–56, 291
collapsed star, 256
black hole, coined by Wheeler, 256–57
Black hole, observational searches for:
by blot-out of starlight, 303
by gravitational focusing of light, 303–4, 303f
in binary star systems, 304–9, 305f, 308f, 315–19, 315f
by X-rays from gas accreting onto hole, 307–9, 307f, 308f, 309–14
using gravitational waves, 360–61, 393–96
serendipitous discovery by radio telescopes, 322, 326
no definitive signature as yet, 317–19, 360–61
signature in gravitational waves, 360–61
Black hole, predictions of and resistance to predictions:
Schwarzschild’s prediction of, 131–34
Chandrasekhar’s prediction of, 160
Oppenheimer-Snyder prediction of, 211–19
Einstein’s rejection of, 121, 134–37, 523
Eddington’s rejection of, 134–35, 161–63, 523
Wheeler’s temporary rejection of, 209–11, 21 1f, 238, 523
Wheeler’s acceptance and advocacy of, 239–40, 244–45, 253
widespread resistance to, 138–39, 196–97, 219
astronomers’ resistance, 196–97
Black hole, primordial, 50–51, 447–48
Black-hole properties:
overview of properties, 23–56, 258–59
circumference, 28–29, 28n
radius, 30–33
shape, 28, 51–52, 293, 293f
blots out light from stars behind it, 26, 41, 303
warpage of space, 43; see also Embedding diagrams
tidal gravity, 34–37
spin and swirl of space, 27–28, 50–52, 289–94, 291f, 292f, 346–48, 408f; see also Kerr solution
gyroscopic action, 346–48
orbits, 38–40, 52, 291–92, 292f
gravitational acceleration, 40, 43
gravitational focusing of light, 41–44, 42f, 303–4, 303f
gravitational blueshift of light, 44
electric charge and field, 286, 288–89
rotational energy, 53, 294
entropy, 423–26, 442, 445–46
atmosphere, 443–46, 444b
superradiance, 433
pulsations, 295–99
stability, 296–98
Hawking’s area-increase theorem, 413, 413n, 416–17, 422–23, 427, 462
laws of black-hole mechanics and thermodynamics, 427, 436, 442, 445–46
uniqueness of, see “Hair” on black holes as described by membrane paradigm, 405–11, 443, 445; see also Membrane paradigm
see also Critical circumference; Embedding diagrams; ”Hair“; Hawking radiation; Horizon; Schwarzschild geometry; Schwarzschild singularity; Singularity
Blandford-Znajek process, 53–54, 54f, 349f, 350–53, 407–9, 408f, 577N350
Chain reactions, nuclear:
concept of, 220, 222, 222b
Zel’dovich–Khariton theory of, 223
Chandrasekhar–Eddington confrontation, 158–63
Chandrasekhar limit, 151–52, 154f, 156b–57b, 161f, 175
Chaos, 362b
Chemical reactions, 183b, 339–40
Chronology protection conjecture, 521
Clocks, perfect and rubbery, 397–403, 398b, 399f
Cold, dead matter, 197–98, 200b–202b, 203n
Cold fusion, 64
Conservation laws, 284
Cosmic censorship conjecture, 36, 481, 524
Cosmic rays, 165, 173–74, 173n, 174f, 189, 192, 231, 574N239
Critical circumference:
for eighteenth-century black hole, 122, 123f, 252f
predicted by Schwarzschild geometry, 132–38, 132f, 214–15
role in stellar implosion, 214, 217–19, 244, 248–55, 266, 274, 279–81, 329, 415b
role in accretion onto black hole, 139, 418b
and frequencies of gravitational waves, 367
and hoop conjecture, 266, 267f
see also Horizon
Cygnus A:
discovery of, 325f
identification of galaxy, 330–33, 332f–33f
discovery of double lobes, 333, 332f–33f
discovery of jets, 343–45
radio pictures of, 332f–33f, 344f
Cygnus X-1, 314–21, 316f
Dark star (eighteenth-century version of black hole), 122–24, 123f, 132, 133, 138, 251–53, 252f, 568N122, 568N123
Degeneracy of electrons:
concept of, 145n, 145–46, 148
relativistic vs. nonrelativistic, 150–51
in an atom, 170b
Eddington’s views on, 158–60
prevents small black holes from forming, 447
see also Pressure, nonthermal, degeneracy
Degeneracy of neutrons and protons:
in an atomic nucleus, 169
in a neutron star, 170
Differential equation, 153n–54n
Differential geometry, 113–14, 471
Doppler shift, 32, 100, 101b, 103b, 304, 305f, 506–7
Einstein field equation, formulation of:
Einstein’s struggle to discover, 113–17
Hilbert’s discovery of, 117, 119
details of, 118b–19b, 567Nl18–19
see also General relativity
Einstein’s legacy, overview of, 523–25
Einstein X-ray telescope, 314
Electric field lines:
around a charged black hole, 284, 286, 288–89, 289f, 294, 405–7, 406f
see also Magnetic field lines
Electromagnetic laws, see Maxwell’s laws of electromagnetism
Electromagnetic radiation, spectrum of, 25f
Embedding diagrams:
introduced and explained, 126–31, 129f, 127f
as part of a “paradigm,” 401
for star near critical circumference, 129f, 132f, 135
for imploding star, 213–14, 214f, 246–50, 247f
for black hole, 31f, 397, 399f
for electrically charged black hole, 288–89, 289f
for spinning black hole, 291, 291f
for binary black hole emitting gravitational waves, 357, 358f
for binary black hole merging, 359f
for travel to another universe, 456, 457f
for quantum foam, 487f, 495f
for a wormhole, 484–85, 485f, 501f
for creation of a wormhole, 496f
Entropy:
definition of, 423, 424b
increase of, 422–26, 424b
of black hole, 423–26, 442, 445–46
Equation of state:
concept of, 153, 193b
of white-dwarf matter, 150–53, 154f, 156b–57b, 200b–201b
of nuclear matter, 193b–95b, 200b–202b
of cold, dead matter, 200b–202b
Equivalence principle, 44–45, 97–98, 99f, 100, 103b, 109, 371
ETH (Zurich Politechnikum), 60, 62, 68, 69, 71, 93, 113, 115
Exotic material:
nature of, 488–90, 508
vacuum fluctuations as, 491–92, 498, 583N491, 583N492
required to hold a wormhole open, 488, 489b, 490–91, 493–94, 498, 504
required when creating a time machine, 499n
Experimental physicists contrasted with other scientists, 319–21, 328
Fifth force, 64
Fission, nuclear:
concept of, 221b–22b
discovery of, 220
Bohr–Wheeler theory of, 220–23
see also Chain reactions
Free will, 509
Fusion, nuclear:
concept of, 183b, 221b–22b
keeps stars hot, 182, 184, 191
as possible power source for quasars, 340
cold fusion, 64
Gamma rays:
as part of electromagnetic spectrum, 25f
emitted by gas accreting into black hole, 26
emitted in black-hole evaporation, 447–48
General covariance, 114n
General relativity:
Einstein’s struggle to formulate, 96–117
domain of validity, 84–85
experimental tests of, 57–58, 116–17, 393, 563N57–58, 568N131
marriage with quantum mechanics, see Quantum gravity
see also specific concepts: Einstein field equation; Equivalence principle; Gravitational time dilation; Gravity, tidal; Relativity, principle of; Space warpage; Spacetime curvature; Time warpage
Geodesic, 108–12, 108f, 118b, 126–27, 401
Global methods, 465, 490, 490n, 491
Golden age, 258–61, 260f, 299, 341, 346, 370, 426
Grandfather paradox, 508n
Gravitational collapse, see Implosion of star
Gravitational lens and focusing, 41–43, 42f 303–4m 303f, 489b, 507
Gravitational redshift of light:
description of, 32, 131–33, 132f, 142–43, 213f, 214–15, 445, 562N44
deduced from gravitational time dilation, 131, 214
astronomical observations of, 131, 143, 148
Gravitational time dilation:
Einstein’s inference of, 100, 102b–3b
near surface of a star or Sun, 130–31, 214
Gravitational waves:
nature of, 48–49, 358, 362–65, 364f
contrasted with electromagnetic waves, 379–81
strength of, 365
frequencies of, 367, 386, 393
sources of, 379–80
emission of, 379–80
polarizations of, 393–94
from black-hole binaries, 48–49, 357–61, 393–96, 413
waveforms of, 393–96, 394f
information carried by, 49, 360–61, 394–96, 524
extraction of information from, 393–96, 394f
may revolutionize our understanding of Universe, 378–81, 524
observational proof they exist, 392–93
1940s and 1950s skepticism about, 523
Gravitational-wave detectors:
Weber’s invention of, 366–69
bar detectors, 367–69, 368f, 372, 374–78, 385–87
interferometric detectors, 382–96, 383f, 384b–85b, 388f, 392f; see also LIGO; VIRGO
bars and interferometers compared, 385–87
Braginsky’s standard quantum limit, 372, 374–76, 386
quantum nondemolition, 375–76, 377f, 386–87 see also LIGO; VIRGO
Gravitational-wave recoil (kick-back), 48, 358–59, 393
Gravity, Einstein’s laws of, see General relativity
Gravity, Newton’s law of:
description of, 61, 93–94, 403, 405
Einstein’s objections to, 96
Gravity, tidal:
Newtonian explanation of, 34–35, 104–6, 104f, 106b
Einstein’s explanation—spacetime curvature, 110–12, 110f, 112f
due to Moon, 105, 106b, 111–12f, 362–65, 362b, 364f, 451
in a gravitational wave, 362–65, 364f near singularity inside black hole, see Singularity, tidal gravity near
Great Terror, 181, 185–86, 233b, 268
“Hair” on black holes:
no-hair conjecture, 274f, 275, 277
first evidence of hairlessness, 273–75
Israel’s theorem (proof of hairlessness for nonspinning holes), 279–80
proof for spinning, charged holes, 285
Price’s theorem (how the hair gets lost), 280–85, 282f, 283f, 350
implications of hairlessness: “black-hole uniqueness,” 27, 286, 425
quantum hair, 284
Hawking radiation from a black hole:
Zel’dovich’s discovery of, for a rotating hole, 429–35
Hawking’s discovery of, in general, 435–36
Zel’dovich’s acceptance of, 439
based on quantum field theory in curved
spacetime, 436–39
properties of, 435–36
relationship to superradiance, 433n
as evaporation of black-hole atmosphere, 443–45, 443f
see also Black-hole evaporation
H-bomb: see Nuclear weapons research
Hoop conjecture:
formulation of, 266–67, 267f
evidence for, 264–67
Horizon of black hole:
overview of, 26, 28–30
name coined, 255
circumference of, 28–29, 28n
spin of, 291–94
maximum spin rate, 51–52, 293–94
shape of, 28, 51, 293, 293f
entropy of, 423–26, 442, 445–46
surface gravity of, 436
temperature of, 427, 436, 442, 445, 446
freezing of things near, 217–18, 239, 244–49, 255–56, 291–92
makes quantum fields exotic, 491–92
membrane-paradigm description of, 405–11, 406f, 41 0f, 443, 445
Hawking’s area-increase theorem for, 413, 413n, 416–17, 422–23, 427, 462
laws of evolution of, 427, 436, 442, 446
apparent horizon vs. absolute horizon, 414–17, 415b
teleological evolution of absolute horizon, 417, 418b
apparent horizon as harbinger of singularity, 462–63
see also Critical circumference
Hyperspace, 55, 55f, 128–30, 214, 214f, 289, 291, 456–58, 457f, 458f, 484–86, 487f, 496f, 500–501, 501f
Implosion of star to form black hole:
overview, 27
limited by white-dwarf and neutron-star
masses, 159–61, 161f, 175–78, 177f
prevented by mass ejection, 196–97, 205–6, 210–11, 211f, 238
masses of parent stars, 205–6
Oppenheimer-Snyder predictions of, 211–19
Finkelstein’s reference frame for, 245–46, 249, 255
simulations on a computer, 238–39, 240–41
parable of the ants describing, 246–49, 247f
freezing of implosion as seen from outside, 217–18, 239, 244–49, 255–56
non-freezing as seen in the star, 218, 239, 244–49
creation of singularity, 250, 251, 253–56; see also Singularity
like time-reversed big bang, 268–69, 268n
as proposed power source for quasars, 341
see also Hoop conjecture
Implosion of star to form neutron star, 171, 172f, 173–75; see also Supernovae
Inertial reference frame, 80, 96–98, 99f, 106, 109, 249
Infrared radiation, 25f
Interferometry:
principles of, 384b–85b
and Michelson–Morley experiment, 64
and radio telescopes, 329f, 330
and gravitational-wave detection, 382–84, 383f, 384b–85b; see also Gravitational-wave detectors; LI GO
Interval in spacetime, 90, 92, 91b–92b
Kerr solution for spinning black hole, 289–90, 294, 341–42, 359–61, 359f, 575N289
Laser, invention of, 366, 366n
Laws of physics:
nature of, 57–58, 84–86
logical meshing of, 236–37, 437–38
force the universe to behave as it does, 27, 27n, 57, 86
permitted versus compulsory predictions, 137–38, 285–86; see also Stability and instability
metaprinciples obeyed by, 82–83, 94
should be beautiful, 66, 79, 82, 85
domains of validity of, 38–39, 57–58, 84–86, 193, 405, 514–15, 525
see also Newtonian laws of physics; Paradigm
Length contraction due to relative motion, 65–66, 68, 71, 76, 78, 84, 130, 565N66, 565N68
Les Houches, France, physics summer school, 369–70, 426–28, 433, 434f, 580N426
Light:
as part of electromagnetic spectrum, 25f
Newton’s corpuscular description of, 122–23
Huygens’ wave description of, 123, 147b
Einstein’s wave/particle duality of, 147b
see also Absoluteness of speed of light; Maxwell’s laws of electromagnetism
LIGO:
genesis of, 381–83, 394–91
description of, 391–93
organization of, 391, 391n
Linearity, 373b, 384b–85b; see also Nonlinearity
Magnetic field lines:
depicted, 67f, 262, 263f
“no ends” law, 66, 67f, 79, 81–82, 85, 565N66
magnetic repulsion between, 262
gravitational attraction between, 262–65 around
an imploding star, 273–74
around a black hole, 295, 348, 349f, 350–51, 408–9
in radio sources, 338–39, 342, 348, 349f, 350–51, 408–9
see also Electric field lines
Manhattan project, 223
Mass-energy equivalence and conversion (“E = Mc2”):
details of, 172b, 441n
as consequence of principle of relativity, 82
as implying that energy curves spacetime, 488
as power source for supernovae, 173
Matricide paradox, 56, 508–9, 508n
Matterhorn project, 229
Maxwell’s laws of electromagnetism, 62, 66, 67f, 71, 79, 81–82, 85, 147b, 433, 525, 565N66, 565N68
Membrane paradigm for black holes, 405–11, 443, 445
Mercury, perihelion shift of, 94, 95b, 103, 107, 116–17, 119b
Metaprinciple, 82–83, 94
Michaelson–Morley experiment, 64–66, 72–73, 78, 85, 383f, 565N64, 565N65
Microwave radiation, 25f
Mledina and Serona, tale of, 88–90
apparent anomaly in orbital motion, 94, 567N94
as source of tides on Earth’s oceans, 105, 106b, 111–12f, 362–65, 362b, 364f, 451
search for X-rays from, 311, 312f
Naked singularity, 480–82
NASA, 321, 354, 390,
National Science Foundation (NSF), 389–90
Neptune, 94
Neutron, discovery of, 169, 171
Neutron stars:
Zwicky’s prediction of, 165–66
Zwicky’s computations of, 207
Landau’s neutron cores, 182, 182f, 184–86, 191
Oppenheimer–Volkoff–Tolman computations of, 193b–96b
Harrison–Wakano–Wheeler computations of, 198–206
formation in supernovae, 171, 172f, 173–75, 174f
minimum mass, 190–91
maximum mass, 192, 195b
maximum mass determines fates of dying stars, 176–78
observations of, see Pulsar
in binary system, 58, 313, 379, 393, 571N191
as source of gravitational waves, 380, 393–94, 403
see also Pulsar
Newtonian laws of physics:
nature of and applications of, 61–63
foundations of, 61–63
crumbling of foundations of, 63–72
domain of validity of, 84–85
Newton’s laws of motion, 61, 81, 93, 563N61
see also Gravity, Newton’s law of; Maxwell’s laws of electromagnetism
Nobel prize awarded to:
Einstein, 69, 83, 103, 147b
Chandrasekhar, 149
Landau, 187
Townes, Basov, and Prokharov, 366
Hulse and Taylor, 393
Nonlinearity:
concept of, 361, 362b–63b
of black holes’ spacetime warpage, 361
see also Linearity
Novae, 166–68
Nuclear burning (fusion), see Fusion
Nuclear force:
concept of, 169
compared to gravitational force, 184
compared to electromagnetic force, 221b
in atomic nuclei, 170b, 183b
at high densities, 205, pressure due to, 177, 190–92, 194b–95b, 203f, 202b, 571N196
Nuclear weapons research:
American A-bomb project, 223–24
Soviet A-bomb project, 224–26
American H-bomb (super bomb) project, 226–29, 231–32
Soviet H-bomb (super bomb) project, 229–32, 233b–34b
Teller–Ulam/Sakarov–Zel’dovich secret, 241–43, 243f
relation to astrophysics research, 238–43
Nucleus, atomic, 169, 170f, 171, 183b, 221b
Oppenheimer security clearance hearings, 232, 234–35
Oppenheimer–Wheeler confrontation:
background of, 220, 223–24, 226–27, 234–35
confrontation, 209–11, 223–24, 238, 240
Orbit around gravitating body:
in science fiction scenario, 24
used to compute body’s mass, 26, 561N26, 563N61
explained by Newton’s laws, 61
Paradigm, 402–11, 416
concept of, 401
flat-spacetime paradigm for gravity, 401–5
curved-spacetime paradigm for gravity, 401–3
Newtonian paradigm for gravity, 403–5
membrane paradigm for black holes, 405–11, 443, 445
Pauli exclusion principle, 170b
Perturbation methods, 275, 276b, 296–98
Photoelectric effect, 147b
Photon:
and wave-particle duality, 146, 147b, 322
virtual, 439–41, 440f
spontaneous emission of, 431b
see also Gamma rays; Light; X-rays
Physical laws, see Laws of physics
Piezoelectric effect, 368f, 369, 372
Planck-Wheeler length, time, and area, 426, 426n, 442, 446, 476n, 494, 494n, 518, 520, 563N55, 582N476
Plasma, 349f, 350, 353, 408–9, 408f
Plutonium, 199, 222–25, 222b, 573N220, 221
Polarization:
of light, 406n
of a gravitational wave, 393–94, 406n
of metal or a black-hole horizon, by electric charge, 405–7, 406f
Polchinski’s paradox, 509–15, 510f, 512f, 513b–14b
Power notation for large numbers, 29b
Pressure:
physical cause of, 143–45
in rocks, 145, 201b
thermal, 144–45, 159–60
nonthermal, degeneracy 145–46, 148–52, 159–60, 169, 170b, 175–78, 193b, 200b–203b
nuclear, 177, 190–92, 194b-95b, 203f, 202b, 571N196
creates spacetime curvature, 118b–19b, 567N118–19
balances gravity in star, 135f, 137, 143–45, 144f, 151, 154f, 156b–57b, 160, 161f, 175–77, 190, 199, 202, 253
see also Equation of state
Probability, quantum mechanical, 147b, 477, 478f, 495f,496, 515
Pulsar:
nature of, 317–18
discovery of, 174, 468
as proof that neutron stars exist, 317
and tests of general relativity, 58, 393
radio waves from, 379
see also Neutron star
Quanta, 141
Quantum electrodynamics, 433
Quantum fields, 284
Quantum fields in curved spacetime, 436–39, 444b, 447–48, 482, 492, 517, 524
Quantum foam, 55–56, 477–78, 478f, 494–97, 495f
Quantum gravity:
Wheeler’s motivation for, 210, 236–37, 244, 253–56, 262, 301, 449
Wheeler–DeWitt and Hartle–Hawking approach to, 479n
realm of validity, 85–86
nonexistence of time in, 476–77, 518–19
quantum foam of space (wormholes) in, 55–56, 477–78, 478f, 494–97, 495f
at endpoint of stellar implosion, 210, 476–79
in singularity inside black hole, 453, 476–79
and time-machine destruction, 518–20
what we may learn from in future, 52–25
Quantum limits on measurement accuracies, 372–75, 386
Quantum mechanics:
discovery of the laws of, 141, 147b, 162, 180–81
nature of and domain of, 50, 141, 372, 510–11, 514–15
as primary, with classical physics secondary, 514–15
and matter at high densities, 145–46, 147b, 150–52
and atoms, molecules, crystals, 166, 169, 372
and atomic nuclei, 169, 184, 199; see also
Fusion; Nuclear force; Nucleus, atomic
and superconductivity, 231, 339
and superfluidity, 186–87, 186n, 208
and spectral lines of light, 335
and entropy, 423, 445–46
and quantum hair on black holes, 284
and time machines, 515, 517–23
on macroscopic scales, 372–76,
marriage with special relativity, 150–52, 160
marriage with general relativity, see Quantum gravity
speculations about failure of, 184, 207
see also other Quantum entries: Degeneracy;
Hawking radiation; Probability; Uncertainty
principle; Vacuum fluctuations;
Wave-particle duality
Quantum nondemolition, 375–76, 377f, 386–87
Quarks, search for, 370–71
Quasars:
overview of, 45–48, 47f
discovery of, 335–37
variability of, 337–38
energy of, 339
speculations about power source, 273, 339–41
gigantic black holes as power source, 346–54, 407–10, 408f
role of accretion disks in, 346–54
detailed model of, 351–53, 352f
Radio galaxies:
discovery of, 330–31
discovery of double radio lobes, 333
further observations of, 334
energy requirements of, 339
speculations about power source, 273, 339–41
gigantic black holes as power source, 346–54, 407–10, 408f
role of accretion disks in, 346–54
detailed model of, 351–53, 352f
see also Cygnus A; Quasars; Radio jets
Radio jets:
discovery of, 343–45
gyroscopic stability of source, 345
gigantic black hole as source, 345–54, 407–10, 408f
Radio telescopes:
Jansky’s and Reber’s, 323–24, 234f–25f
relation to radar, 327
interferometers, principle of, 328–30, 329f
Jodrell Bank, 331–33, 332f–33f
Greenbank and Owens Valley, 334
Very Large Array (VLA), 343, 344f, 345
VLBI, 345
improvements in angular resolution, 328, 330, 335, 342, 345
as key to revolution in understanding the Universe, 378–79
Radio waves, as part of electromagnetic spectrum, 25f, 322–23, 379
Radio waves, cosmic:
discovery of by Jansky, 323, 324f–25f
observations by Reber, 324–26, 324f–25f, 327–28
difficulty explaining, 323–24
explained as synchrotron radiation, 338–39, 338f
see also Cygnus A; Radio galaxies; Radio jets; Radio telescopes
Rayleigh–Taylor instability, 241–42, 242f
Reference frame:
concept of, 80
inertial (freely moving or freely falling), 80, 96–98, 99f, 106, 109, 249
non-inertial, 114
Finkelstein’s, for stellar implosion, 245–46, 249, 255
accelerated, near black hole, 443–46, 444b
Reissner–Nordström solution af Einstein field equation, 286, 458, 473, 581N458, 582N473, 582N473–74
Relativity of space and time:
Einstein’s conception of, 72–78
deduced from principle of relativity, 73, 77b
explained in terms of spacetime, 88–92, 91b–92b
see also Absoluteness of space and time; Length contraction; Time dilation
Relativity, principle of:
formulated in absence of gravity, 73, 81
as a metaprinciple, 82
consequences of, 76–78, 82
generalized to include gravity, 98, 100, 99f, 114
Relativity theory, see General Relativity; Special Relativity
Relativists contrasted with other scientists, 319–21, 341–42
Research methods and styles:
relation between experimental and theoretical, 64–65
interaction of theorists and experimenters/observers, 207–8, 315–17, 319–21, 326, 372, 376
interactions between various communities of researchers, 319–21, 326, 328, 341–43
interaction between individual researchers, 70–71, 187–89, 193b–96b, 240, 429, 499–500, 505
“small science” style vs. “big science” style, 388–91
massive, worldwide research efforts, 315–17, 319–21
solitude and introspection, 370, 499–500, 505 competition, 369–70
mathematical manipulations of laws, 61, 119–20, 563N61
attitudes toward mathematics, 469–72
different mathematical representations of same physics, 402
order-of-magnitude calculations, 193b
mind flips, 403, 404f, 405, 410–11
mental blocks, 71, 82, 244, 255, 295, 335, 338–39, 417
physical intuition, 79, 96, 119–20, 269, 279, 429
role of subconscious mind, 462
curiosity, 207, 236–37
self-confidence, 207–8
role of a first quick survey, 193b, 212
choice of physical laws, 193b
level of rigor, 441–42, 469
idealizations, 215–17, 217f
approximations, 194b–95b, 276b
perturbation methods, 275, 276b, 296–98
arguments by analogy, 429–30
thought experiments, 110–11, 122, 128, 445–46, 492–93, 496, 500–503, 503n
Sagan-type questions, 493, 496, 497, 508
pedagogy as tool in research, 96
examples of deductive reasoning, 102b–3b, 77b
influence of names, definitions, and viewpoints, 254–56, 295–96, 401–11, 416–17
paradigms, 401–11, 416; see also Paradigm
mentors and their styles, 261–62, 269–72
Resistance to compression:
concept of, 149–50
of white-dwarf matter, 149–53, 154f, 156b–57b, of nuclear matter, 193b–95b, 200b–202b
of cold, dead matter, 200b–202b
see also Equation of state
Rockefeller Foundation fellowships, 179, 220
Rulers, perfect and rubbery, 397–400, 398b, 399f
Sagan-type questions, 493, 496, 497, 508
Schwarzschild geometry for black hole or star:
Schwarzschild’s discovery of, 124
space warpage of, 128–30, 129f, 132–34, 132f
time warpage of, 130–31, 132–34, 132f
Schwarzschild singularity (black hole), 121, 136–37, 244, 250, 255; see also Black hole
Scientific revolution, 401, 403, 405
Sensor, for gravitational-wave detector, 368–69, 372, 374–76, 377f, 386
Shock waves, 173, 215–16, 217f, 238–40, 301, 307, 307f, 453
Singularity, naked, 36, 470–72, 524
Singularity, quantum gravity description of, 476–79, 478f
Singularity theorems:
black holes contain singularities (Penrose), 462–63, 468, 472
Universe began in singularity (Hawking–Penrose), 465
physicists’ reactions to, 524
Singularity, tidal gravity near:
perfectly spherical (Oppenheimer–Snyder), 451–53, 452f
mixmaster, 474–76, 475f
BKL, 30–31, 468–69, 474–76, 475f
aging of, 479–80
see also Black-hole interior
Sirius, 142, 159–60, 161f, 176–77, 177f, 205, 302
Sirius B, 142–43, 143f, 145, 148, 150, 152, 155, 160, 568N143
Soviet Union:
science under Lenin, 179–81
control on travel abroad, 181, 277–78, 466
organization of science in, 287b-88b, 382
influence of Landau on science in, 181, 470–71
attitudes toward topology, 469–72
see also Great Terror: Nuclear weapons research
Space:
foamlike structure in quantum gravity, 477–78, 478f, 494–97, 495f
contraction of: see Length contraction
see also Absoluteness of space and time; Relativity of space and time; Space warpage
Space warpage (curvature):
concept deduced by Einstein, 107
concept explained, 108–9, 108f
as due to rubbery rulers, 397–400, 399f
see also Black-hole properties; Embedding diagrams; Gravitational waves; Wormholes
Spacetime:
concept formulated by Minkowski, 87–88, 92–93, 414
absoluteness of, 90, 92, 91b-92b, 414
space and time derived from, 90, 92
Spacetime curvature (warpage):
concept deduced by Einstein, 107–8
equivalent to tidal gravity, 110–12, 110f, 112f
produced by mass, energy, and pressure, 113–19, 118b-19b
as due to rubbery clocks and rulers, 397–400
objects made from, overview of, 523–24
Spacetime diagrams:
in flat spacetime, 74–76, 75f, 77b, 91b
in curved spacetime, 249–51, 251f
for a star that implodes to form a black hole, 249–51, 251f, 281, 282f, 415b
for the growth of a black hole when matter falls in, 418b
for the fall of an astronaut into a black hole, 452f
for the expanding universe, 460–61
Special relativity:
Einstein’s formulation of, 80–83
experimental tests of, 78, 83–84, 566N78
Spectrum of electromagnetic waves, 25f, 379
Speed of light:
as maximum speed anything can travel, 82
see also Absoluteness of speed of light
Stability and instability:
of cold, dead stars, 203–5, 204b
of black holes, 296–98
of formation of singularity by imploding star, 453–56, 455f, 459, 466, 473–74
of travel through black hole to another universe, 473–74
Star:
laws governing structure of, 143–44, 144f
squeeze/pressure balance in, 135f, 137, 143–45, 144f, 151, 154f, 156b-57b, 160, 161f, 175–77, 190, 199, 202, 253
origin of heat, 182, 184, 191; see also Fusion, nuclear
cold, dead stars, 198, 203f, 202–6, 203n, 204b
unstable stars, 203–5, 204b
supermassive stars, 341
see also Black holes; Neutron stars; Sun; White dwarf stars
Stroboscopic sensor, 376
Strong force, see Nuclear force Sun:
compared with Earth and white dwarf, 143
origin of its heat, 182, 184, 191
fate when it dies, 159, 161f, 175, 177f
Super bomb, see Nuclear weapons research
Superconductivity, 231, 339
Superfluidity, 186–87, 186n, 208
Supernovae:
Baade–Zwicky discovery of, 166–68
photograph of, 167
energy of, 168, 171, 174f
powered by stellar implosion to form neutron star, 171, 172f, 173–75
as sources of gravitational waves, 380
Superradiance, 433n
Synchrotron radiation, 338–38, 338f
Tensor analysis, see Differential geometry
Texas Symposium on Relativistic Astrophysics, 240, 341–42, 498, 577N341, 577N342
Theoretical Minimum, Landau’s, 470–71
Theory:
misleading concept, so not used in this book, 86
see instead Laws of physics
Thermodynamics:
concept of, 422
laws of, 422–23, 436
second law of, 422–26, 424b
of black holes, 427, 436, 442, 445–46; see also Entropy; Horizon; Hawking radiation
Thermonuclear burning and evolution, 197–98, 228–29, 573N229; see also Fusion
Thought experiments, 110–11, 122, 128, 445–46, 492–93, 496, 500–503, 503n
Tidal gravity, see Gravity, tidal
Tides on ocean, 35, 57, 61, 93, 105, 106b, 111–13, 112f, 362–65, 364f, 451
Time, besides the following entries, see
Absoluteness of space and time; Quantum gravity, nonexistence of time in; Relativity of space and time
Time dilation:
due to relative motion, 37, 66, 68, 71, 76, 78, 84, 565N66, 565N68
gravitational, see Gravitational time dilation
Time machines (for backward time travel):
creation of requires exotic material, 499n
as solutions to the Einstein field equation, 499n
based on rapidly spinning matter, 499n, 521
based on cosmic strings, 521, 521n
based on wormholes, 55–56, 502–4, 503f
must accompany non-quantum creation of a wormhole (Geroch theorem), 497
possible if one can travel faster than light, 498–99
paradoxes due to, 508’-15
publicity about, 516
Time machines, destruction of when first activated:
by radiation? No, 505–7, 506f
by vacuum fluctuations? Probably yes, 56, 516–21, 518f
quantum gravity controls the answer, 521, 524
Time warpage:
due to high-speed motion or gravitational
acceleration, see Time dilation
concept deduced by Einstein, 107
as due to rubbery clocks, 397, 400–401, 403
see also Time machines
Topology:
concepts of 463–65, 464b–65b
as foundation for global methods, 465
use of to prove that singularities must occur, 462–63, 465
why introduced into physics by British, 469–77
abortive introduction in Russia, 471–72
Uhuru X-ray telescope, 311f, 312f, 314, 316
Ultraviolet radiation, 25f
Uncertainty principle, 372, 373b-74b, 375
Unification of all physical laws, 525
Universe:
origin of, see Big bang
expansion of, 337
structure of, 301, 302f
ultimate fate of, 355–56; see also Big crunch
speculations on travel to another, 456–58, 457f, 473–74, 484
steady-state theory of, 460
Uranium, 199, 220–23, 221b-22b, 225, 230
Uranus, 94
Vacuum fluctuations:
concept of, 430–31, 430b-31b, 491–92
as cause of spontaneous emission of radiation, 431b, 432–33
and virtual particles, 439–45, 440f, 441n, 444b
as form of exotic material, 491–92
as destroyers of time machines, 516–21
VIRGO, 392–93
Virtual particles, 439–45, 440f, 441n, 444b
Wave-particle duality:
concept of, 146
history of ideas on, 147b
illustrated by X-rays and radio waves, 322
and the uncertainty principle, 373b
and electron degeneracy, 146
and vacuum fluctuations, 439
Weak energy condition, 508
White dwarf stars:
mystery of, 142–45
observations of, 142
Chandrasekhar’s computations of, 153–55
properties of, 142, 143f, 150, 154f, 167f
maximum mass determines fates of dying stars, 159–60, 161f, 176–78, 177f
maximum mass, 151–52, 154f, 156b-57b, 161f
see also Sirius B
World War I, 124
World War II, 166, 197, 219, 222–24, 300, 309, 324, 327, 366, 469
Wormholes, classical:
overview of, 54–56, 55f
brief summary of present status, 524
embedding diagrams of, 485f, 501f
as solutions of Einstein field equation, 486, 488, 490
probably do not occur naturally in Universe, 486
pinch-off if not threaded by exotic material, 486–88, 487f, 491
creation of, by extraction from quantum foam, 56, 494–96, 497–98
creation of, by non-quantum means, 496–97, 497–98
travel through, 500–501, 500f, relative motion of mouths, 501–4, 501f
the hookup of time through, 500–502
time machine based on, 502–4, 503f
Wormholes, quantum (in quantum foam), 55–56, 494–96, 495f
X-ray astronomy and telescopes, 309–14, 311f, 312f, 378–79; see also Cygnus X-1
X-rays:
as part of electromagnetic spectrum, 25f, 322, 379
as high-energy photons, 146 emitted by gas accreting into black hole, 25, 307–9, 307f, 308f, 318, 379
as key to revolution in our understanding of Universe, 378–79
role in hydrogen bomb, 243, 243f