acceleration, 14–15, 48, 71, 257, 300
action at a distance. See spooky action at a distance
AdS/CFT correspondence, 303–304
Aesop’s fables, 4–5
Aharonov, Yakir, 177
amoeba dividing analogy, 123–124
amplitudes
description of, 19–20
probabilities and, 86–87, 130–131, 142–146
probability distribution and, 187
unequal, 147–148
wave functions and, 33
angular momentum, 55
Anscombe, Elizabeth, 129
anti—de Sitter space, 303, 304
arrow of time, 158–159
atoms
austere quantum mechanics and, 34
blackbody radiation and, 49–50
branching and, 138–139
compatibilism and, 218
Dalton on, 45
description of, 18
electrons and, 45–46
entropy and, 158, 160, 276, 297–298
GRW theory and, 184
history of, 45
matter and, 48
obeying quantum mechanics rules, 36
radioactive decay of, 120
Rutherford’s model, 45–46, 52–55
statistical mechanics theory, 29
austere quantum mechanics (AQM), 32–36, 104, 245. See also Everett formulation of quantum mechanics; Many-Worlds theory
Banks, Tom, 285
Bauer, Edmond, 222
Bayes, Thomas, 136
Bayesian inference, 198
Bayesianism, 136
Bekenstein-Hawking entropy, 297–299
Bell states, 102–103
Bell’s theorem on entanglement, 102–106, 190, 233
black hole information puzzle, 294
black holes
complementarity, 304–306
degrees of freedom inside, 298–299
description of, 291–292
dynamical nonlocality and, 296
emitting radiation, 293–296
entropy and, 297–299
evaporation, 295
event horizon and, 293
in general relativity, 293, 301–302
general relativity and, 270, 297, 305
holography for, 302–303
maximum-entropy nature of, 300–301
membrane paradigm, 305
no-cloning theorem and, 296
as region of spacetime, 293, 299
representing highest-entropy states, 299–300
temperature of, 293
blackbody radiation, 49–50
blackbody spectrum, 50
Bohm, David, 30, 103, 178, 189–190
Bohmian mechanics
as alternative formulation of quantum mechanics, 192–193
Einstein on, 194
haphazard construction of, 202
Heisenberg on, 194
nonlocality and, 191
Oppenheimer on, 194
particle observation and, 41, 190–194
particles momenta, 195
Pauli on, 194
problems in, 194–195
uncertainty principle in, 195–196
wave functions in, 193
Bohr, Niels, 28, 31, 35, 54–58, 66–67, 74–75, 109
Boltzmann, Ludwig, 158–163, 276
Born, Max, 20, 33, 58–59, 65–66, 67
Born rule
description of, 19–20
in Many-Worlds theory, 146–148
particle locations and, 191–193
probabilities and, 130–131, 145, 167–168
as Pythagoras’s theorem, 87, 142
self-locating uncertainty, 171
Bousso, Raphael, 300
brains, as coherent physical systems, 220
branch counting, 142–144
branching
atoms and, 138–139
cause of, 213–214
decision making and, 213–216
decoherence and, 119–120, 122–123, 137–138, 183, 186
description of, 157–161
as emergent worlds, 239
with four consecutive spin measurements, 134
in Many-Worlds theory, 169–172
Many-Worlds theory and, 138–140
as nonlocal process, 171–172
quantum systems and, 216
Schrödinger’s equation and, 116
Bunn, Ted, 117
Cao, ChunJun (Charles), 285
categorical imperative (Kant), 210
Caves, Carlton, 198
CFT (conformal field theory), 303
choice-making. See free will
classical electromagnetism, 250, 269
classical mechanics
atoms (See atoms)
fields (See fields)
Hamiltonian, 64, 196, 239–240, 281–282
Newton and, 14–15
particles (See particles)
rules of, 21–22
closed universe, 287–288
Coleman, Sidney, 129
collapse theory, 212
compatibilism, 218
complementarity, 74–79, 304–306
composite particles, 46–47
conformal field theory (CFT), 303
consciousness, 122–123, 219–224
consequentialism, 210
Copenhagen interpretation of quantum mechanics, 23, 57, 110, 116, 221
cosmological constant, 256–257
cosmological constant problem, 258–259
credences, 136–137, 141–142, 211
curved spacetime. See general relativity
Dalton, John, 45
Davies, Paul, 256
de Broglie, Louis, 28, 30, 60, 62–65, 188
de Broglie—Bohm theory, 41. See also Bohmian mechanics
decision making, as classical events, 213–216
decoherence
branching and, 119–120, 122–123, 137–138, 183, 186
description of, 117–120
linking austere quantum mechanics to the world, 245
multiple worlds and, 233–234
Penrose and, 186
as rapid process, 140
reversal of, 160
Schrödinger’s cat thought experiment, 241–243
worlds interference with one another, 157
Zeh and, 178–179
degrees of freedom, 71, 262–263, 283–284, 298–299
Democritus, 44
demon thought experiment (Laplace), 16, 57, 63, 162–163, 235
Dennett, Daniel, 238–239
deontology, 210
determinism, 216–218
Deutsch, David, 126, 148, 174, 194
Dirac, Paul, 65
disappearing worlds theory, 117
distribution of probabilities. See probability distributions
double-slit experiment, 75–79, 120–123, 191
dualism, 223
dynamical locality, 233, 281–282
dynamical nonlocality, 296
dynamical-collapse models, 181–186
effective field theory, 320–321
Einstein, Albert
Bohm and, 189–190
on Bohmian mechanics, 194
Bohr debate with, 28–29, 31, 109
compass story, 310
on cosmological constant, 256–257
death of, 309
general relativity work, 110, 112, 185, 230–231, 279–280. See also general relativity
on Heisenberg’s approach to quantum theory, 271
at Institute for Advanced Study, 110
labeling quantum mechanics as spooky, 11
light quantum proposal, 51–52, 60, 66
on matrix mechanics, 59
physical theory, 102
Podolsky and, 101
quantum entanglement and, 31
on quantum mechanics, 96, 102, 268
as relativity pioneer, 31
on spacetime, 269–270
special relativity theory, 99, 233
on uncertainty principle, 91, 109
Einstein-Podolsky-Rosen (EPR) thought experiment, 96–102, 109, 191, 233, 285
electric charge, 48n
electric fields, 47–48
electricity, 46
electromagnetic field
Feynman diagrams and, 315
gravitons and, 274
leading to particle-like photons, 255
Maxwell on, 47–48
electromagnetic radiation, 49–50, 66. See also light
electromagnetic waves, 60, 249–250
electromagnetism, classical, 250, 269
electrons
atoms and, 45–46
Bohr’s quantized orbits, 55–58, 66–67
cloud of probability, 19
definition of, 18
discovery of, 45
double-slit experiment, 75–79
Feynman diagrams and, 315
interference bands, 121
interference pattern of, 77–78
in natural habitat, 18
orbiting, 46
in superposition, 34
elementary particles, 46–47
elements of reality, 100
emergence, 234–239
empirical theories, 155–156
empty space
energy of, 256–257
entropy and, 278
no particles in, 260–261
quantum vacuum in, 256–257, 259–261
quantum version of, 302
as stationary, 260
energy, 173, 184, 253, 256–257, 281–282, 291. See also vacuum energy
entangled superposition, 114–116
entanglement. See also Bell’s theorem on entanglement
in action, 94–95
to define distances, 276–277
degrees of freedom in, 263, 283–284
in different regions of space, 261–265
Einstein and, 31
entropy and, 160
with environment, 118–119
examples of, 91–92
in GRW theory, 182–183
momentum and, 92
nonlocal nature of, 178
no-signaling theorem, 97–99
in quantum field theory, 249
quantum states and, 118, 261–262
quantum systems and, 159–160
Schrödinger’s equation and, 38
two-qubit system, 95–96
vacuum energy and, 262–265
entanglement entropy, 160, 277, 283
entropic arrow of time, 158–159
entropy
area and, 285
arrow of time, 158–159
atoms and, 158, 160, 276, 297–298
Bekenstein-Hawking, 297–299
of black holes, 297–299
Boltzmann formula for, 158–163
in closed systems, 158
cutoffs, 278
of empty space, 278
entanglement, 160
event horizon as similar to, 297
limits on, 300
low, 159
from objective to subjective feature, 161–162
quantum mechanics and, 276–278
of quantum subsystems, 277
within thermodynamics, 279
in vacuum state, 279
epistemic probabilities, 135–140
equal probability, 144–146
equal-amplitudes-imply-equal-probabilities rule, 144–146
ER=EPR conjecture, 285n
ERP. See Einstein-Podolsky-Rosen (EPR) thought experiment
event horizon, 293, 296–297, 301–305
Everett, Hugh
death of, 127
DeWitt and, 126
leaving academia, 178
lifestyle choices, 127
Many-Worlds formulation and, 39
Petersen and, 125
on quantum gravity, 111–114, 122–125, 272
on quantum immortality, 207
on quantum measurements, 164–165
at Weapons Systems Evaluation Group, 125–126
Everett, Mark, 127
Everett formulation of quantum mechanics
as assault on Bohr’s picture, 123–124
implications of, 41
ingredients for, 40–41
measurements and, 104–105, 114–117, 123–125
overview of, 38–40
as simple and elegant, 202
Everett phone, 180
fatness measure, 141
Feynman, Richard, 2, 27n, 111, 314
Feynman diagrams
description of, 314–316
electromagnetic field and, 315
explicit cutoff, 320
infinities in, 319
internal closed loop, 317–318
particle physicists’ use of, 315–317
particles and, 314–316
renormalization, 318–319
virtual particles in, 316
field metric, 273
fields
defining feature of, 47
definition of, 44
in GRW theory, 185
in quantum field theory, 250–252
Fifth International Solvay Conference, 27–28
firewall proposal, 296–297n
Fischler, Willy, 285
forces, examples of, 16
formalism of quantum mechanics, 30, 152–153
foundations of quantum mechanics
Albert and, 177
Bell’s theorem on entanglement, 102, 105
Bohr-Einstein debates on, 109
consensus on, 178
measurement problems and, 17
Nobel prize awarded for, 59
physicists response to, 196–197, 272, 311
Popper and, 157
spacetime and, 6
Franklin, Benjamin, 48n
free will, 216–218
frequency, measuring, 50–51
frequentism, 133–135. See also Bayesianism
Geiger counters as quantum systems, 221–222
general relativity. See also quantum gravity; special relativity
behavior of spacetime in, 280
Big Bang and, 287
black holes and, 270, 293, 297, 301–302, 305
Einstein’s work on, 110, 112, 185, 230–231, 269–270
expansion of the universe and, 270
gravitons and, 273–274
loop quantum gravity and, 275
metric field, 273
Penrose’s work on, 185–186
predictions in, 156
replacing Laplace’s theory, 248
universe’s zero energy and, 287–288
Wheeler’s work on, 110
generic quantum state, 282
Gerlach, Walter, 80
Ghirardi, Giancarlo, 181
“ghost world” scenario, 120
Giddings, Steve, 285
gluons, 46
Gospel of Matthew, 27n
Goudsmit, Samuel, 178
gravitational fields, 48, 248, 273–274
gravitational waves, 53–54
gravitons, 273–274
gravity, 6–7, 165, 185–186, 230, 267, 270–273. See also general relativity; quantum gravity; relativity theory
Green, Michael, 274
GRW theory, 181–186, 196–197, 202–203
Habicht, Conrad, 52
Hamilton, William Rowan, 64
Hamiltonian formulation of classical mechanics, 64, 196, 239–240, 281–282
Hammeroff, Stuart, 219
Hawking, Stephen, 113, 291–292, 293
h-bar version, 56
Heisenberg, Werner, 28, 35, 57–59, 63, 67, 194
Heisenberg cut, 35
Heisenberg method, 271
hidden variables, 187–190
hidden-variable theories, 188–189, 190, 260
Hilbert space, 85, 154, 164–166, 263, 306
Hobbes, omas, 218
holographic principle, 302–304
Hooft, Gerard ’t, 302
horizontal spin, 81–83
House Un-American Activities Committee, 189
human choice-making. See free will
human consciousness, 219–224
Hume, David, 177
idealism, 223–225
imposing a cutoff, 258
indeterminism, 216–218
infinities, in Feynman diagram calculations, 317–319
Institute for Advanced Study, Princeton, New Jersey, 110
interpretation of quantum mechanics. See Copenhagen interpretation of quantum mechanics
Jacobson, Ted, 279
Jumpers (play), 129
Laplace, Pierre-Simon, 16, 48, 235, 248
Lewis, David, 175
light, 49–50
light quanta (Einstein), 51–52, 60, 66
LIGO gravitational-wave observatory, 53
locality principle, 99, 171–172, 232–233, 240, 292
London, Fritz, 222
loop quantum gravity, 275
low-probability worlds, 168
magnetic fields, 47
“making a decision,” 213–216
Manhattan Project, 189
Many-Worlds theory. See also austere quantum mechanics (AQM); Everett formulation of quantum mechanics
attaching probabilities to, 132
Born rule in, 146–148
branching and, 138–140, 169–170
Everett and, 39
formula simplicity, 179
frequentism and, 133–135
life-span of a person and, 139–140
as local theory, 171–172
low-probability worlds, 168
measurement and, 122, 169, 179
as morally relevant, 212–213
as nonlocal process, 233
overview of, 38–40
quantum-first perspective of, 231–232
seeds of, 113
as simple and elegant, 203–204
wave function in, 234
matrix mechanics, 57–59, 63, 65, 67
Matthew Effect, 27n
Maxwell, James Clerk, 47–48, 269
measurement locality, 233
measurement problem of quantum mechanics
altering Schrödinger equation for, 180–181
austere quantum mechanics and, 36
collapsing wave systems, 22–24, 112
consciousness and, 224
consensus on, 17
definite vs. indefinite outcomes, 104–105
Everett’s theory on, 104–105, 114–117, 123–125
GRW theory and, 184
Hume on, 177
Many-Worlds theory of branching and, 179
Oppenheimer on, 178
textbook approach to, 242
membrane paradigm, 305
Mermin, N. David, 27, 198, 200, 201
Merton, Robert, 27n
metric, field, 273
Michalakis, Spyridon, 285
microtubules, 219–220
Milky Way galaxy, 298–299
Misner, Charles, 113
mode of the field, 253–254
modes of the string, 60–61
momentum
in classical mechanics, 16, 70–71, 239
entanglements and, 92
position and, 69
in wave functions, 71–72
momentum space, 240
morality, 210–213
multiple worlds, 6, 39, 119, 180, 184, 233–234
nature
quantum field theory and, 229–230
quantum mechanics describing, 174–175
neuroscience, 224
neutrons, 46
new quantum theory, 57. See also quantum mechanics
Newton, Isaac, 14–15, 24, 48, 239, 247–248
Newtonian gravity, 247–248
Newtonian mechanics, 14–15
Newton’s laws of motion, 21, 195, 238
no-cloning theorem, 296
nonlocal process, 171–172, 178, 191, 233
no-nonsense utilitarianism, 211
no-signaling theorem, 97–99
nuclear fission, 110
observable universe, 94, 164–166, 182, 299, 301
observer, 122–123
Occam’s razor, 152
old quantum theory, 52–56
ontological commitments, 152
Oppenheimer, Robert, 178, 189–190, 194
Padmanabhan, Thanu, 280
Page, Don, 288
Parfit, Derek, 139
participatory realism, 200
particles
behaving like gravitons, 274
Bohmian mechanics and, 41, 190–194
composite, 46–47
defining feature of, 47
definition of, 44
double-slit experiment, 75–79
of Earth, 236
elementary, 46–47
Feynman diagrams and, 314–316
in quantum field theory, 250
virtual, 316
Pauli, Wolfgang, 28, 57, 63, 188, 194
personal identity through time, 137–140
physical reality, 100–102
physics, 13–15
pilot wave, 187–188
pilot-wave theories, 194
Polchinski, Joe, 180
Popper, Karl, 154–157
position
in classical physics, 16, 70–71, 239
momentum and, 69
in quantum mechanics, 70–71
positrons, Feynman diagrams and, 314–315, 317
post-decoherence wave function, 234
preferred-basis problem, 241–245
Principia Mathematica (Newton), 14
probabilities
amplitudes and, 86–87, 130–131, 142–146
Born rule and, 130–131, 145, 167–168
credences and, 136–137
decision-theoretical approach to, 212
epistemic, 135–140
equal probability, 144–146
fatness measure, 141
frequentism and, 133–135
given by amplitudes squared, 131, 145, 147
self-locating uncertainty and, 140–142, 149
probability distributions, 29–30, 187, 198
probability rule, 59
protons, 46
Pythagoras’s theorem, 86, 87, 142, 146–147, 273
quantum arrow of time, 158–159
Quantum Bayesianism (QBism), 41, 198–201
quantum entanglement. See entanglement
quantum field theory
entanglement in, 249
fields in, 250–252
lowest-energy state of, 253
mode of the field, 253–254
nature and, 229–230
particles in, 250
pointer states of, 255
transitions between states, 255
wave functions in, 250–252, 254
quantum fluctuations, 259–260
quantum gravity. See also gravity
conceptual issues, 272–273
constructing theory of, 292
Everett on, 111–114, 122–125, 272
location in space, 196
loop quantum gravity, 275
number of quantum states and, 165
problem of time in, 288
spacetime and, 271–272
string theory and, 274–275
technical challenges of, 113
quantum immortality, 207–209
quantum logic, 74
quantum measurement process, consciousness and, 164–165, 222–224
quantum mechanics
alternative formulation of (See Bohmian mechanics; GRW theory)
atoms and, 36
discarding classical physics’ framework, 16–17
Einstein-Bohr debate, 28–29, 31
electromagnetic waves, 249–250
entropy and, 276–278
lack of understanding of, 24–25
as one specific physical system, 229
position in, 70–71
presentations of, 13
rules of, 22–23
spacetime and, 271–272
special relativity and, 269
spookiness of, 11–12
understanding of, 1–4
violating logic, 73–74
quantum random number generator, 205–206
quantum states. See also Bell states
disappearing worlds theory and, 117
entanglement and, 118, 261–262
evolving under Schrödinger equation, 232, 243, 287–288
as fundamental, 241
uncertainty principle and, 73–74, 89
quantum subsystems, 277
quantum suicide, 208
quantum systems
branching and, 216
classical divide with, 18, 35–36
entangled, 159–160
Geiger counters as, 221–222
GRW theory and, 182
mathematical description of, 3
measuring, 117–118
wave functions describing, 21
quantum utility maximizing device (QUMaD), 211
quantum vacuum, 254, 256–257, 259–261
quantum/classical divide, 35–36
quarks, 46
radiation, black holes emitting, 293–296
radioactive decay, 120
radioactive emissions, 242
randomness, 294–295
random-number generator, 134
Reeh-Schlieder theorem, 264
region of space, 65, 156, 261–265, 280–284, 299–300
relativity theory, 30–31, 97–99, 112, 268–269. See also general relativity; spacetime; special relativity
renormalization, 318–319
Rimini, Alberto, 181
Rosen, Nathan, 96
Ryu, Shinsei, 303–304
Sagittarius A*, 299
Schack, Rüdiger, 198
Schrödinger, Erwin, 28, 59, 62
Schrödinger’s Cat thought experiment, 241–245
Schrödinger’s equation
altering, 180
beam splitter, 206
branching and, 116
description of, 21
entanglement and, 38
formula for, 63–64
Geiger counters and, 221
measurement problems and, 180–181
quantum states evolving under, 232, 243, 287–288
space and time treatment by, 286–287
time defined in, 281
wave functions and, 21–22, 32, 64, 86, 94
Schwartz, John, 274
scientific theories, characteristics of, 155–156
second law of thermodynamics, 158, 297
the self, 137–139
self-locating uncertainty, 140–142, 149, 171, 211
“Shut up and calculate!,” 27
Solvay Conference, 27–31, 67, 96, 109, 188
space and time
degrees of freedom in, 263
locality and, 240
measurement outcomes of, 85–86
in superposition state, 288–289
treatment of, 286–287
spacetime
applying quantum mechanics to, 271–272
black holes as regions of, 293, 299
curvature of (See general relativity)
degrees of freedom, 298
Einstein on, 269–270
foundations of quantum mechanics and, 6
maximum entropy in, 300
metric in, 273
quantum gravity and, 271–272
unified, 269
warping of, 305
wormholes in, 285n
special relativity, 99, 170, 233, 269–270, 273. See also general relativity
speed of light restrictions, 97–98, 99
spin, 79–83
spin outcomes, 80–83, 87–89, 97–99, 101
spin+apparatus system, 114–116
spin-measuring apparatus, 118
spontaneous collapse of wave functions, 181, 184–185, 192
spooky action at a distance, 98, 99, 105, 247–248, 309
Standard Model of particle physics, 31, 180–181
statistical mechanics theory, 29–30
Stern, Otto, 80
Stern-Gerlach experiment, 133
Stoppard, Tom, 129
string theory, 274–275
superdeterminism, 104
superpositions
description of, 34–38
of macroscopic objects, 116
Schrödinger’s Cat thought experiment, 243
as separate worlds, 117
space and time in, 288–289
time in, 288–289
Susskind, Leonard, 285n, 302, 304–305
Swingle, Brian, 303–304
symmetries, 222
Taj Mahal theorem, 264
Takayanagi, Tadashi, 303–304
Tegmark, Max, 207
Thomson, J. J., 45
Thorn, Charles, 302
Thorne, Kip, 111
thought experiment
Einstein-Podolsky-Rosen (EPR), 96–102, 109, 191, 233, 285
ideal world of, 260–261
Schrödinger’s Cat, 241–245
time. See space and time
tin oxide, 44–45
two-qubit system, 95–96
ultraviolet catastrophe, 50
uncertainty principle (Heisenberg)
Bohmian mechanics and, 195–196
empty space and, 260
locality and, 240
unified “you,” 138–139
universal wave function, 113–114, 118–119
Universe Splitter, 205–206
utilitarianism, no-nonsense, 211
utility, 210–212
vacuum energy
cosmic acceleration and, 257
cosmological constant problem, 258–259
of empty space, 256–257
entanglement and, 262–265
gravitational influence of, 256–257
negative, 304
positive, 304
size of, 257–258
vacuum state
area and, 284
empty space in, 278
entropy in, 279
entropy proportional to boundary area, 299–300
in quantum field theory, 254, 256–257, 260, 264
Vaidman, Lev, 140
Van Raamsdonk, Mark, 303–304
vector fields
electric field as, 47–48
magnetic field as, 47
velocity
in classical physics, 16–17, 239
measuring, 18–19
probability of measuring, 71
Verlinde, Erik, 280
vertical spin, 81–83
Virgo gravitational-wave observatory, 53
virtual particles, 316
volition, attributing, 218
von Neumann, John, 74, 159–160, 188–189, 276–278
Wallace, David, 129, 163, 202, 239
wave functions
as abstract, 79
amplitudes and, 33
assigning an amplitude, 33
Bohmian mechanics and, 193
Born on, 65–66
branching of, 137–138, 213–214
changing with time, 62–63
collapse of, 22–24, 33, 112, 219–220, 222
consciousness and, 222
de Broglie’s view, 65
description of, 19–21
distinct persons on branches of, 208–209
double-slit experiment, 120–123
Hamiltonian, 64
influencing itself, 120
in Many-Worlds theory, 234
measurement outcomes of, 30–31
momentum and, 71–72
for one particle, 94
pilot wave role, 187–188
in quantum field theory, 250–252, 254
quantum systems and, 21
of a qubit, 84
representing density of mass in space, 65
Schrödinger’s equation and, 21–22, 32, 64, 86, 94
for single particles, 71
space within, 276
spontaneous collapse of, 181, 184–185, 192
for two particles, 91–93
unifying particles and fields into, 44
as vectors, 86–88
wave-function-is-everything view, 33–34
waves
double-slit experiment, 75–79
Weapons Systems Evaluation Group, 125–126
Weber, Tullio, 181
Weinberg, Steven, 180–181
Wheeler, John Archibald, 110–111, 123–126, 270–272, 281, 288
Wheeler-DeWitt equation, 288
Wilson, Kenneth, 319–320
The Wire (television show), 5
Wittgenstein, Ludwig, 129
Wootters, William, 288
wormholes, 285n