Einstein's Unfinished Revolution
Page 32
relationalism, 237, 253, 265, 302
relational model, of universe, 242
relational quantum theory, 193, 197, 302
relational spacetime geometry, special relativity and, 235
relationships, 231–32, 236
relativistic field theory, pilot wave theory and, 213
relativity, general, 9, 93, 227, 229
Einstein and, 230
nads and, 254
as nonlinear, 138
Penrose and, 134–39
planets and, 75
quantum theory and, 136–38
solution to, 255n
spacetime and, 256
superposition and, 138
relativity, special, 9, 47, 133, 230, 303
collapse and, 141
Einstein and, 226
energy and, 261
momentum and, 261
nonlocality and, 212
pilot wave theory and, 212
quantum equilibrium and, 121
realism and, 215
relational spacetime geometry and, 235
relativity, theory of, xx, 8, 16, 303
collapses and, 133
collapse theory and, 133
of Einstein, 137, 227
equation, 72
pilot wave theory and, 211
spacetime and, 226
speed of light and, 47
wave function and, 142
religion, xxiv
restriction, 45, 46, 55, 184, 215, 298
retrocausality, 216–17, 217, 303
reversibility, 158, 214, 268, 268n
Roger, Gérard, 45
rolled-up dimensions, 233
Rosen, Nathan, 43, 44. See also Einstein-Podolsky-Rosen state
Rosenfeld, Léon, 113–14
rotations, 263–64, 263n
Rovelli, Carlo, 193–94, 196, 197
Rule 0, 203, 303
Rule 1, 31–36, 35n, 54, 54, 63–64, 99, 121
Born’s rule and, 171
decoherence and, 158, 159–60
definition, 303
lack of, 148n
measurement and, 33–34
pilot wave theory and, 101, 116
quantum information theory and, 188
quantum theory and, 154
realism and, 145, 149
reversibility of, 158
Rule 2 and, 64, 129–31, 141, 158
as universal, 148n
wave function and, 116, 118
Rule 2, 35–36, 35n, 41–42, 50, 51, 53–54, 63–64, 99
definition, 303
Everett and, 164–65
invention of, 128
irreversibility of, 158
measurement and, 144
outcomes and, 172
pilot wave theory and, 101
probabilities and, 150
quantum theory and, 172
Rule 1 and, 64, 129–31, 141, 158
wave-function collapse and, 215
Rutherford, Erenst, 74
Saunders, Simon, 171
Schrödinger, Erwin
background of, 82
de Broglie, L., and, 82
equation of, 31, 239, 241, 247, 303
Nobel Prize of, 83
Schrödinger’s cat, 49–54, 54, 121–24, 145–48, 152, 156–57, 201
wave-particle duality and, 83–84
Schrödinger-Newton law, 141
science, xix, xxiii–xxiv, xxiv–xxv, xxvi, 27, 85, 90–91
scientific method, 273
scientific mind, xiv
second law of thermodynamics, 159, 303
self- reference, 28
semantics, information and, 189–90
senses, xiv
shadow theory, xvii
Shannon, Claude, 189, 191n
Shimony, Abner, 158, 198
Shore, Peter, 185
similar systems, 251
solar system, xv, 74, 75, 244
Solvay Conference, 98, 101–2, 117
Sorkin, Rafael, 218, 257–58
sound waves, 98
space
configuration, 122–24, 123, 217–18
dimensions of, 233
as emergent, 236–37, 238, 264, 269
entanglement and, 238
as fundamental, 263
geometry of, 229–30
as illusion, 204
locality and, 245
networks and, 240
relationships within, 236
spacetime, xxvi, 4
adding together, 138
atoms, 257–59
backgrounds and, 269
causality and, 134
causal relations and, 257
Einstein and, 226
as emergent, 269
entanglement and, 135
general relativity and, 256
geometry of, 130, 134, 257
information and, 259–60
inverse problem and, 258
quantum, 256
quantum mechanics and, 228
relational principle of, 232
theory of relativity and, 226
wave function and, 140
Specker, Ernst, 56
spectrograph, measurements of photons, 87
spectrum, 59–61, 78, 83, 89
speed, 303
speed of light, 43, 46–47, 57, 121. See also locality
spin, 303
spin networks, 135–36, 238n, 303
splitting
Bohr and, 193–94
problem, 152–54, 157, 174
process in Many Worlds Interpretation, 149–50, 150n, 152, 153–54
spontaneous collapses, 131–33, 141, 143, 213, 214
standard deviation, 62
standard model of particle physics, 304
stars, 4
starvation, 178
states. See also quantum states
of atoms, 49–51, 60–61, 77–78, 146–47
classical, 30
contrary, 38–43, 45, 123, 298
correlated, 51, 145–47, 146n, 149
definition, 15, 304
of electrons, 78
superposing, 32–33
stationary states, 77, 87, 92
stochastic quantum mechanics, 223
Stoppard, Tom, 15
string theory, 189, 234n, 278, 304
subjective probabilities, 162, 163n, 170, 172, 174, 193, 208
subjectivity, entropy and, 191n
subsystem principle, 26, 27
superdeterminism, 220–22
superposition, 4–5
of atoms, 6–7, 50, 139–40, 146, 152, 156–57
of electrons, 152
entanglement and, 195
general relativity and, 138
gravity and, 140
measurement and, 64
of molecules, 6
of objects, 139
of particles, 4–5
of photons, 50
pilot wave theory and, 214
quantum, 6
quantum mechanics and, 37, 138–39
quantum states and, 32–33
of quantum systems, 37, 137–38
reality and, 147
Schrödinger’s cat, 49–53
of states, 32–33, 196–97
wave function and, 139–40, 213
superposition principle, 33, 137–39
symmetry, 104n, 255n, 263, 263–64
’t Hooft, Gerard, 221–22
technology, entanglement, 48
temperature, 29, 30
t
emporal relationalism, 237, 253, 265
thermodynamics, 120, 159, 177, 191n, 214, 303
time
capsules, 203
causality and, 204, 236
as emergent, 237
events and, 266
gravity and, 137, 140
as illusion, 202–4
irreversibility of, 236, 236n
laws of, 265
laws of nature and, 265
moments and, 201–3
momentum and, 262
nature and, 265
quantum mechanics and, 63, 137
quantum state and, 31
retrocausality, 216–17, 217
topological field theories, 193–94
transactional interpretation, 216–17
truth, xx, xxvi, 276–77
Tumulka, Roderich, 107
Turing machine, 185
twistor theory, 136
tyranny, 178
uncertainty principle, 18–22, 32, 58, 61, 90, 92–93, 117, 145, 304
Unger, Roberto Mangabeira, 265
unification, 216, 229
unification of forces, xvii
unitary law, 31
universal quantum computer, 185
universe
as causal set, 260
chosen aspect of, 221
expansion of, 4
information and, 189
living mirror of, 245
nadic, 242–43, 243
observation and, 166–67, 231
parallel, 145, 148, 247
physics in early, 175–76
pilot wave theory and, 121
quantum mechanics and, 28, 159n, 231
quantum states and, 193, 197, 231
quantum theory and, 27–28
relational model of, 242
theory of, 27
wave function and, 231
Valentini, Antony, 120, 121, 210
variety, 244, 247
velocity, 20–21, 21, 23, 81, 262n, 304
views, causal theory of, 269–71
Vigier, Jean-Pierre, 114
von Neumann, John, 93–94, 104–5, 110
water, xv
wave function, 31n, 32, 99n, 176
atomic systems and, 141, 213
beables and, 224
definition of, 304
information and, 193, 249n
particles and, 99–100, 109, 118–20, 209, 210
phases of, 214n
pilot wave theory and, 125–26, 210
probabilities and, 124, 128, 151, 165
Rule 1 and, 116, 118
spacetime and, 140
spontaneous collapses and, 143
squaring, 99–100, 100, 151
superposition and, 139–40, 213
theory of relativity and, 142
universe and, 231
wave-function collapse, 35–36, 129–30, 139, 186
definition, 298
drawbacks of, 214–15
ghost branches and, 213
lessons from, 213–16
measurement problem and, 213
Rule 2 and, 215
wavelength, xxviii, 22
wave mechanics, 304
wave-particle duality, 86, 97–98
de Broglie, L., and, 83–84, 103
decoherence and, 156
definition of, 304
double slit experiment and, 98, 199–200, 210–11
Einstein and, 83–84
electrons and, 98–99
light and, 84
measurement problem and, 223
pilot wave theory and, 142, 208–10, 222
realism and, 89
Schrödinger and, 83–84
waves
in electric field, 40
electrons as, 79–80, 82, 83
frequency of, 22, 61
height of, 34
light as, 68, 68, 72, 80
matter as, 5, 23, 84
particles and, 21–24, 34, 60, 66, 79–80, 81, 83–84, 99–100, 213
photons as, 69
sum of, 124
wave theory, 67
Weinberg, Steven, 179
Weyl, Hermann, 82–83
Wheeler, John Archibald, xxvii, 37, 145, 187–88
Wheeler-DeWitt equation, 203
Wigner, Eugene, 195–96
Wigner’s friend, 196n
Witten, Edward, 136
Wittgenstein, Ludwig, 72n
World War I, 12
wormholes, 240, 240n
X-rays, 79–80
Young, Thomas, 67–68
ABCDEFGHIJKLMNOPQRSTUVWXYZ
ABOUT THE AUTHOR
Lee Smolin has made influential contributions to the search for a unification of physics. He is a founding faculty member of the Perimeter Institute for Theoretical Physics. His previous books include Time Reborn, The Trouble with Physics, and Three Roads to Quantum Gravity.
* A note to my expert readers: Quantum foundations is presently a very lively subject, with many exciting developments both experimental and theoretical. Many proposals compete to resolve the puzzles we will meet here. I should warn the reader that our path through these frontiers will be a narrow one, and there are many exciting ideas and results that I do not mention here. Had I tried to review the whole field, or include all the latest supremely clever advances, the result would have been a less accessible book. My first aim is to introduce the world of quantum phenomena, not the full spectrum of competing interpretations of those phenomena. I apologize in advance to those experts who don’t find their preferred version of quantum physics here, and encourage them to write their own books. I also apologize to the historians. I am not a scholar, and the stories I tell are creation myths, handed down from teacher to student, originating, in some cases, with the founders themselves.
* The metaphor of the universe as a computer is helpful for illustrating determinism, but is on the whole misleading, as I will argue below.
* Momentum will be defined shortly, but roughly, a body’s momentum is proportional to both its speed and mass.
* > means “is larger than.”
* When a wave represents a quantum state, we sometimes call it a wave function.
* But you knew as soon as I mentioned Rule 1 that there had to be a second one. I should point out that in some textbooks, Rules 1 and 2 are switched.
* For more on how Planck misappropriated Boltzmann’s methods, see Thomas Kuhn’s Black-Body Theory and the Quantum Discontinuity, 1894–1912, or a wonderful biography of Paul Ehrenfest by Martin Klein, both listed in the Further Reading section.
* Unfortunately, this came too late for Boltzmann, who, depressed at his failure to convince his colleagues of the reality of atoms, committed suicide the next year. And as a footnote to a footnote: a young Viennese physics student called Ludwig Wittgenstein was so dismayed by news of Boltzmann’s suicide that he switched to philosophy.
* I am oversimplifying a bit. The particle follows a part of the wave function called its phase.
* Antony Valentini gave me a copy of that paper of Einstein’s during a speech at my wedding, which I promptly lost.
* Noether is one of the greatest twentieth-century mathematicians; among her many discoveries was a seminal theorem on symmetry in physics, which we will come to.
* If I can be permitted a purely personal remark, I am a grandchild of a Marxist who remained a lifelong member of the American Communist Party long after the dream had died, and I am also the son of seekers who spent many years in the Gurdjieff work. To a large extent, the errors of my parents and grandparents inoculated me against falling in love with organized seekers, running after visions of transcendence. It is
easy for me to criticize Bohm and others of his generation for the astounding naiveté they showed in the face of the peculiar combination of genuine compassion for human suffering and extraordinary dishonesty and narcissism that gurus like Gurdjieff and Krishnamurti shared with the “revolutionary” leaders on the vanguard of the left. But at the same time, there is, I believe, the shadow of something real behind the teachings of the likes of Gurdjieff and Krishnamurti, who brought distillations of Eastern spiritual practices to westerners.
* Which was completed in a PhD thesis of a student of Penrose’s called John Moussouris, which also remained unpublished, and was also passed hand to hand.
* Notice that the two contingent statements, which together express the content of the correlated state IN-BETWEEN, do not require or imply that the atom has decayed, releasing a photon that passes through and triggers the detector. At each time, it may have decayed or it may have yet to decay. This is why I refer to “the photon’s possible passage through the detector.”
* We can think of Everettian quantum mechanics as pilot wave theory without the particles. In both cases, there is no Rule 2; both make Rule 1 universal. So in both cases, the wave function continually branches, creating alternative histories, such as the ones where I stayed in London or perished off Peggy’s Cove with the Swissair flight. The difference is that pilot wave theory has particles, which take only one of the alternate branches.
* There is an operational reading of Everett that sees the theory purely as a method for producing sets of contingent statements such as I described above, but makes no claims to what is real beyond that. This seems to me a consistent way to read Everett’s thesis. (Lee Smolin, “On Quantum Gravity and the Many Worlds Interpretation of Quantum Mechanics,” in Quantum Theory of Gravity: Essays in Honor of the Sixtieth Birthday of Bryce S. DeWitt, eds. Steven Christensen and Bryce S. DeWitt [Bristol, UK: Adam Hilger, 1984].)
* In the next chapter, we will see that some experts argue that splitting requires a macroscopic process called decoherence. This happens far less often; this has the effect of decreasing “vast” in this sentence to merely very large.
* That is, wave functions with small amplitudes.
* To put it more precisely, while the measure of all those branches with statistics not obeying the Born rule goes to zero, in the limit of an infinite number of trials, the number of those branches does not.