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References
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Further Reading
Favrhold, D. 1992. Niels Bohr’s philosophical background. Copenhagen: Det Kongelige DanskeVidenskabernes Selskab.
Faye, J. 1991. Niels Bohr: His heritage and legacy. An anti-realist view of quantum mechanics.Dordrecht: Kluwer.
Faye, J., and H. Folse, eds. 1994. Niels Bohr and contemporary philosophy. Dordrecht: Kluwer.Folse, H.J. 1985. The philosophy of Niels Bohr: The framework of complementarity. Amsterdam:
North Holland.French A.P., and P.J. Kennedy, eds. 1985. Niels Bohr: A centenary volume. Cambridge, MA:
Harvard University Press.Heisenberg, W. 1962. Physics and philosophy: The revolution in modern science. New York:
Harper & Row.Heisenberg, W. 1971. Physics and beyond: Encounters and conversations. London: G. Allen &
Unwin.Honner, J. 1987. The description of nature: Niels Bohr and the philosophy of quantum physics.
Oxford: Clarendon, 1987.Jammer, M. 1989. The conceptual development of quantum mechanics: Interpretations of
quantum mechanics in historical perspective. Melville, NY: American Institute of Physics.Murdoch, D. 1987. Niels Bohr’s philosophy of physics. Cambridge: Cambridge University Press.Pais, A. 1991. Niels Bohr’s times, in physics, philosophy, and polity. Oxford: Clarendon.Petruccioli, S. 2006. Atoms, metaphors and paradoxes: Niels Bohr and the construction of new
physics (trans: I. McGilvray). Cambridge: Cambridge University Press.Rozental, S. 1967. Niels Bohr: His life and work as seen by his friends and colleagues.
Amsterdam: North-Holland.
186 References
Author Index
AAbel, N.H., 178Amati, D., 113n5, 183Aspect, A., 109, 181Aspelmeyer, M., 185Atmanspacher, H., 159n6, 181
BBeckett, S., 160–165, 181Bell, J. S., 107, 113n5, 123, 181Beller, M., 27n1, 181Bertlmann, R. A., 113n5, 118Bethe, H., 97Bohr, A., 82n6, 182, 185Bohr, H., 175Bohr, N.Boltzmann, L., 160Born, M., 2, 13, 29–33, 36–38, 81, 90, 92, 110,
130, 150, 155–157, 163, 182Bothe, W., 3, 108Brown, H. R., 170n1, 182
CCantor, G., 178Cauchy, A-L., 173Cayley, A., 137Coleman, S., 161Cushing, J. T., 113, 182
DDalibard, J., 181Darwin, C., 160
De Broglie, L., 44, 56, 77n4, 81, 84Dedekind, R., 178Democritus, x, 148, 149Derrida, J., 160n7, 182Dirac, P. A. M., x, 2, 2n1, 8, 30, 35–38,
41, 49, 51, 54, 55, 84, 90–94,98–105, 182
Dirichlet, G. L., 173–175Dostoyevsky, F., 162Dyson, F., 97–99, 182
EEinstein, A.Ellis, J., 113, 183
FFaraday, M., 91Favrhold, D., 19n1, 175, 186Faye, J., 2n1, 181, 182, 186Fermi, E., 91, 93Ferreirós. J., 177, 178n4, 183Feynman, R., 74n3, 77, 97, 140, 164, 183Folse, H., 2n1, 148n5, 181–183, 186French, A. P., 184, 186Freud, S., 159n6
GGalileo, 5, 19, 30, 37, 40, 158Galois, E., 178Gauss, K. F., 177, 178Geiger, H., 3, 108, 156Gieser, S., 159, 167, 183
A. Plotnitsky, Niels Bohr and Complementarity, SpringerBriefs in Physics,DOI: 10.1007/978-1-4614-4517-3, � Arkady Plotnitsky 2013
187
G (cont.)Gomatam, R., 27n1, 183Gottfried, K., 113n5, 183Gray, J., 177n3, 183Greenberger, D.M., 109, 183
HHardy, L., 109, 183Haydn, J., 160Hegel, G.W.F., 13, 13n6Heidegger, M., 40, 50, 183Heisenberg, W.Held, K., 113n5, 184Hermite, C., 37Hoffding, H., 50, 164Honner, J., 186Horne, M. A., 109, 183Howard, D., 27n1, 184Hume, D., x, 13, 13n6, 152, 160
JJaeger, G., 109, 184James, W., 10, 159n, 6, 184Jammer, M., 186Jennewein, T., 185Jordan, P., 2, 8, 29–40, 90–92, 182Joyce, J., 160, 162Jung, K. G., 159n6
KKafatos, M., 113n5, 183, 184Kafka, F., 160, 162Kalckar, J., 42n1, 47n3Kant, I., x, 9, 13, 13n6, 64, 152, 153,
160, 165, 184Kennedy, P. J., 184, 186Kierkegaard, S., xKlein, O., 90Kramers, H., 3, 32, 90, 97, 98, 182Kronecker, L., 178
LLandau, L., 90, 91, 95, 96, 184Locke, J., 13n6Lucretius, T. C., 10
MMaxwell, J. C., 76, 91, 92, 160McMullin, E., 182
Mehra, J., 36, 108, 113n5, 184Mermin, N. D., 109, 113n5, 123n10,
124n11, 184Metzinger, J., 160Minkowski, H., 176Mottelson, B. R., 82n6, 182Murdoch, D., 111n4, 184, 186Musil, R., 160
NNewton, Isaac, Sir., 5, 13, 101Nietzsche, F., 13, 159n6
PPais, A., 3n3, 18, 21, 22, 90n1, n2, 105, 106,
160, 184, 186Pauli, W., vii, 2, 4, 60, 90–93, 95, 101, 141,
159n6, 184Peierls, R., 90, 91, 95, 96, 184Peres, A., 85, 113n5, 123n10, 184Petersen, A., 142n2, 171, 182, 184Petruccioli, S., 42n1, 184, 186Planck, M., x, xii, 1, 2n1, 3, 13, 17, 18, 20, 46,
59, 62, 65, 69, 77, 148, 152, 160Plotnitsky, A., 28n1, 109n1, 122n9, 124n12,
160, 162, 177n2, 184, 185Podolsky, B., 6, 107, 124, 183Pooley, O., 170n1, 182Primas, H., 159n6, 181
RRandall, L., 162, 185Rechenberg, H., 36, 108, 113n5, 184Riemann, G. B., x, 15, 173, 175–179, 185Roger, G., 181Ron, S., 178n4Rosen, N., 6, 107, 124, 183Rosenfeld, L., xi, 18, 89–91, 91n3, 95–99, 171,
182, 185Rozental, S., 184–186Rudinger, E., 171, 182Rutherford, E., 17–23, 49
SSchilpp, P. A., 111, 138, 167, 183, 185Schlosshauer, M., 80n5, 145n4, 185Schoenberg, A., 160Schrödinger, E., ix–x, 1, 2, 2n1, 8, 10, 28–30,
34n2, 38, 41, 44, 46, 54–56, 71, 89–93,93n5, 109, 150, 163, 185
188 Author Index
Schweber, S. S., 91n4, 97n7, 99, 185Schwinger, J., 97Shakespeare, W., 162Shelley, P. B., 164Shimony, A., 113n5, 185Slater, J., 3, 128, 182Sommerfeld, A., 30, 160Stapp, H., 148n5, 185Stravinsky, I., 160
TTeller, P., 91n4, 97n7, 185t’Hooft, G., 97, 100Tomonaga, S-I., 97
UUlfbeck, O., 82n6, 182, 185
VVan der Waerden, B. L., 2n1, 185Veltman, M., 97, 100
Volta, A., 42Von Neumann, J., 2n1, 37, 55, 93n6, 146, 185
WWeber, W., 177Weihs, G., 185Weinberg, S., 91n4, 185Weizsäcker, von, C. F., vii, viii, 185Weyl, H., 178, 178n4Wheeler, J. A., 5, 15, 50, 82, 82n7, 133, 135,
161, 164, 178n4, 182–185Whitehead, A. N., 148n5, 185Wilczek, F., 105, 185Wittgenstein, L., 11, 153, 185
YYukawa, H., 93
ZZurek, W., 5, 15, 80n5, 145n4, 182–185
Author Index 189
Subject Index
AAbstraction, 56, 94, 99, 179
the concepts of particle and wave as, 29,44, 55, 56, 82n6
mathematical, 94, 99, 179Ambiguity, 49, 57, 83, 109, 143, 149
of EPR’s criterion of reality (according toBohr), 57, 114, 117, 124–127, 168
Amplification, irreversible amplification, 66,81, 144, 145, 145n4
Amplitude, or probability amplitude, 33, 34,34n2, 81, 150
Atomicity (Bohr’s concept of), v, vii, 28, 43,45, 46, 55, 57, 94, 104, 105, 137, 138,147, 148, 148n5, 149–153
BBell’s theorem, 109, 112, 113, 113n5, 131, 156Biology, 6, 158, 159BKS (Bohr, Kramers, and Slater) theory
(see Bohr, Kramers, and Slater [BKS]theory)
Black holes, 171Bohmian mechanics, theories (see also hidden
variables theories), 2n1, 9, 14, 27n1,54n4, 77n4, 81, 112, 142
The Bohr–Einstein debate, vi, 19, 78, 86,131–136, 167
concerning the EPR and related experi-ments (see also Bohr’s reply to EPR’sand related arguments by Einstein), 86,107–136, 153–157
Bohr’s interpretation ofquantum mechanics
Como version (argument, lecture), v, 4, 7,8, 27–29, 34, 41–57, 59–65, 67, 69, 71,78–79, 84, 90, 92, 93, 116, 138, 143,145n4, 147, 151, 172
different versions of, v–viii, 27, 28, 42–44,53, 78
the intermediate (pre-EPR) version(of 1929), 28, 59–70
the ultimate (post-EPR) version, 4, 10, 28,29, 45, 60, 78, 79, 137–165
Bohr, Kramers, and Slater (BKS)theory, 3, 29, 108
Bohr’s reply to EPR’s and related argumentsby Einstein, 107–136, 153–157
ambiguity of EPR’s criterion of reality(see also Ambiguity: of EPR’s criterionof reality [according to Bohr]), 57, 114,117, 124–127, 168
complementarity and the EPR experiment,111, 122, 124, 127
completeness/incompleteness of quantummechanics, 5, 14, 56, 69, 77, 78, 86, 87,95, 107–131, 136–138, 144, 153–158,164
disturbance, 112, 114, 116, 118, 120,124–129, 126
Einstein’s commentaries on, 6, 111, 112,129, 155, 167
influence (Bohr’s concept of), 124–129locality/nonlocality, 9, 78, 86, 107–131,
153–158measurement and measuring instruments,
109–112, 114–131probability and statistics, 110, 116, 123,
123n111, 124, 153–158
A. Plotnitsky, Niels Bohr and Complementarity, SpringerBriefs in Physics,DOI: 10.1007/978-1-4614-4517-3, � Arkady Plotnitsky 2013
191
B (cont.)the uncertainty relations, 111, 112, 114,
117, 119, 121, 122, 129, 131, 134, 155Born’s probabilistic interpretation of the wave
function (see Wave or probabilityfunction (w): Born’s probabilisticinterpretation of)
Born’s rule, 33, 34, 34n2, 81, 115n8, 129, 146,150, 163
CCausality (and/vs. noncausality), ix, x, 4, 5, 7,
8, 10–15, 21, 22, 28, 41, 43–57, 60–63,65, 69, 78, 79, 110, 128, 138, 142, 143,149–161, 163–165, 168, 169, 171
causal interpretations of quantum mechan-ics and causal quantum theories, 4,12–14, 54n4, 128, 157
in classical physics, 3, 5, 8, 11, 12, 117, 150definition of, 10, 11vs. determinism, 1012, 153local causality, 110mathematical causality or determination, 53in philosophy, 13, 152, 159, 160, 165and reality, realism, 8, 10–15, 50, 56, 151,
153, 154, 157, 159, 161, 171and relativity, 169, 171of undisturbed quantum behavior vs.
observational disturbance, 79, 14, 44,51–56, 60
Chance or randomness, 9, 12, 15, 150and probability, 9, 12, 87, 150
Chaos theory, 11‘‘Choice of nature’’, 21, 22, 47, 49, 50
Classical (or Newtonian) mechanics, ix,2n1, 3, 5, 8, 11, 12, 21, 23, 31–39, 43,46, 53, 55, 62, 77, 78, 86, 92, 96, 101,103, 110, 114, 116–118, 123, 143,146–147, 151, 152, 157
causal and/or realist character of, 5, 8, 11,12, 53, 92, 117
descriptive character of, 5, 11, 53, 78, 92,110, 116, 117
deterministic character of, 11, 117Classical physical concepts in quantum theory
(according to Bohr), 65–69Classical physics, theory, v, 1, 2n1, 3–10,
10n5, 11, 14, 15, 18, 21–23, 31, 40, 43,45–47, 51–53, 54n4, 56, 62–68, 73–77,79, 82n6, 83, 83n8, 93, 96, 99,101–104, 110, 114, 116–118, 123, 130,131, 140–147, 150–152, 154, 163, 168,169, 173, 178
causal and/or realist character of, 48, 10,10n5, 11, 39, 40, 53, 117–119
descriptive character of, 4, 11, 32, 39, 40,53, 117, 118
Classical statistical physics (or mechanics), 3,11, 12, 30, 34, 34n2, 35, 53, 62, 69,110, 150–152, 156, 157
Complementarityand ‘‘the basic principles of science,’’, 124,
127, 128, 169definition of, 6, 52of experimental arrangements, 45, 60, 79,
117, 121, 122, 130, 133–136, 143, 155,156
and idealization of observation and defini-tion, 44, 45
of particles and fields, 93of position and momentum, 7, 52, 79of space–time coordination and the claim
of causality, 89, 14, 28, 43–45, 51–54,60, 61, 63, 65, 78
of space–time coordination and conserva-tion laws, 59, 60, 65, 78, 79, 85, 143, 144
and the uncertainty relations, 59, 79, 85,143, 144
wave-particle complementarity, 8, 44, 45,93, 140
Completeness/incompleteness of quantummechanics, 5, 14, 56, 69, 77, 78, 86, 87,95, 107–131, 136–138, 144, 153–158,164
and locality/nonlocality, 77, 78, 86,107–131, 136, 154–157
Complex numbers (also imaginary numbers),34n2, 48, 56, 92, 101, 172–176
Concept(s)the definition (or concept) of, 6role in defining observation, 13, 13n6, 24classical (see Classical physical concepts in
quantum theory [according to Bohr];Measurement, measuring instruments:classical aspects of measuringinstruments)
Conservation laws, 3, 7, 28, 33, 37, 43, 45, 52,58, 65, 79, 85, 108, 122, 143, 144
Copenhagen interpretation of quantummechanics, v, 27n1
vs. ‘‘the spirit of Copenhagen’’, v, 27n1Correlations (see also Entanglement, quan-
tum), 12, 86, 101–103, 109, 110, 123,123n11, 150, 151, 153
as order or pattern, 12, 86, 153quantum nature of, 12, 109, 110statistical nature of, 101–103, 110, 123n11
192 Subject Index
Correspondence principle, 31, 33, 35–38, 96,99, 101, 143, 147
and the cut, 37, 147mathematical form of, 31, 35, 36, 99, 101pre-quantum-mechanical form of, 31, 35, 36in quantum electrodynamics, 101
Counterfactual argumentation, 123, 123n10Creation and annihilation (birth and dis-
appearance) of particles in quantumfield theory (see also Virtual particleformation), 104–106
The Cut, 37, 146, 147
DDecoherence, 80n5, 145n4Delayed-choice experiment, 50, 82, 133, 135Detached observer, 95, 140, 141Determinism, deterministic, 4, 10–14, 44, 51,
117, 143, 153and causality, 10–14, 51, 117, 153
Dirac’s equation, 90, 102, 103Discontinuity (see also Atomicity [Bohr’s
concept of]), 1, 3, 20, 45, 46, 55, 62,148, 149
and Bohr’s concept of phenomena oratomicity, 148, 149
and individuality, 46, 148, 149Discreteness, (see also Atomicity [Bohr’s
concept of]), 1, 46, 148, 149and Bohr’s concept of phenomena or
atomicity, 148, 149and individuality, 148, 149
Disturbance, of quantum objects by measure-ment, 8, 9, 43, 44, 47, 51, 54, 54n2, 67,74, 112–114, 116, 118, 124–129,136, 141
Bohr’s critique of the concepts of‘‘creation’’ and ‘‘disturbance’’by measurement, 43, 47
and the EPR experiment, 112–114, 116,118, 124–129, 136, 141
vs. interference, 51, 53Double-slit experiment, 15, 28, 34n2, 49, 59,
61, 71–88, 122, 133–136, 139–140and probability, 86–88and the uncertainty relations, 79, 84–88
EEffects (quantum), 8, 9, 31, 38, 44, 46, 50, 56,
62–64, 67, 73–79, 81, 82, 84, 87, 100,102, 105, 133–138, 141, 144, 145,148–150, 165
amplification effects, 81, 144individuality of quantum effects, 64, 82,
84, 148of the interaction between quantum objects
and measuring instruments (see Mea-surement, measuring instruments:interaction, effects of the interactionbetween quantum objects and measur-ing instruments and other macro-objects)
language and concept of effects in Bohr,63, 133, 144
particle-like (discrete) individual effects, 8,77, 78, 81, 82
wave or interference collective effects, 8,76–78, 81, 82, 133, 134
Einstein–Podolsky–Rosen’s (EPR) argument(see EPR’s [Einstein, Podolsky, andRosen’s] argument and related argu-ments by Einstein)
Einstein–Podolsky–Rosen’s (EPR) experiment(see EPR’s [Einstein, Podolsky, andRosen’s] and related experiments)
Electrodynamics, classical (also Maxwell’s),20, 76, 77, 83n8, 152, 160
Electrodynamics, quantum (see Quantumelectrodynamics)
Electron(s), 2–4, 11, 12, 17, 20–22, 30, 34–36,49, 71n1, 74, 78, 80–81, 82n7, 83n8,89–92, 96–106, 120, 133, 135, 139,145, 150, 152, 163
Empiricism, 13, 13n6, 19, 20, 24, 31and positivism, 13n6
Entanglement, quantum, 109, 110, 115, 115n7Epistemology
Bohr’s, 4, 9, 10, 23, 29, 38, 43, 47, 51, 61,63, 64, 79, 89, 94, 95, 100, 104–106,108, 111, 113n6, 119, 131, 132, 137,141, 142n2, 146, 148n5, 150–153,158–179
Bohr’s and/vs. Kant’s, 9, 10, 64, 153classical, 80, 104Heisenberg’s, 23, 29, 38Kant (phenomena vs. noumena or things in
themselves), 9, 10, 64, 153of quantum electrodynamics and quantum
field theory, 89, 94, 95, 98, 100, 102,104–106
EPR’s (Einstein, Podolsky, and Rosen’s)argument and related arguments byEinstein, 6, 41, 57, 63, 86, 90, 91, 94,107–116, 131–137, 153–158
completeness/incompleteness of quantummechanics, 86, 114–134
Subject Index 193
E (cont.)completeness/incompleteness vs. locality/
nonlocality of quantum mechanics, 86,114–137
criterion of completeness, 114criterion of reality, 112, 114–137, 154disturbance, 112, 114, 116, 118, 120,
124–129, 126locality/nonlocality of quantum mechanics,
9, 78, 86, 114–134statistical nature of quantum mechanics in
Einstein’s arguments of the EPR-type,153–158
and the uncertainty relations, 112, 117,131, 134, 155
EPR’s (Einstein, Podolsky, and Rosen’s) andrelated experiments, 9, 15, 68, 71n1,73n2, 78, 86, 107–137
Bohm’s version, 70n1, 109, 123, 123n11Bohr’s argument concerning (see Bohr’s
reply to EPR’s [Einstein, Podolsky, andRosen’s] and related arguments byEinstein)
as distinguished from EPR’s argument, 107Heisenberg on, 73n2, 146probability and statistics in EPR-type
experiment and measurements, 110,116, 123, 123n11, 124, 153–158
Equations of motion, 30, 31, 33descriptive classical vs. predictive quantum-
mechanical use of (see also Heisen-berg’s ‘‘new kinematics’’), 30, 31, 33
Exclusion principle (Pauli’s), 104
FFeynman diagrams, 103, 104Field theory
classical (see also Electrodynamics;classical or Maxwell’s), 91, 92, 96, 97
quantum (see Quantum field theory)
GGravity, gravitation, 97, 99, 106, 176
quantum (see Quantum gravity)
HHawking’s radiation, 171Heisenberg’s microscope, 67, 84Heisenberg’s ‘‘new kinematics’’, 32, 35
vs. classical kinematics, 32
Heisenberg’s (matrix) quantum mechanics (seeMatrix or Heisenberg’s quantummechanics)
Hidden variables theories (see also Bohmianmechanics, theories), 27n1, 112, 113
Hilbert space, 32, 93n6, 101, 103, 104, 115n8,121, 175, 178
in quantum field theory, 101, 103, 104
IIdealization, idealized models, 5, 8–11, 53, 74,
83n7, 96, 98, 99, 101, 102, 116, 128,142, 146, 171, 178
classical (causal and realist, or descriptive)idealization and models, 5, 6, 8–11, 53,74, 76, 83n7, 102, 116, 128, 142,146, 178
difficulty/impossibility of classical-likeidealization and models in quantumtheory, 10, 102, 128, 178
of observation and definition (in Bohr), 44,45, 51–53
in quantum electrodynamics and quantumfield theory, 96, 98, 99
in quantum mechanics, 9–11, 83n7,101, 102
in relativity, 171, 178Imaginary numbers (see Complex numbers)Individuality (see also Atomicity [Bohr con-
cept of]; Quantum phenomena, alsoatomic phenomena, as defined by therole of Planck’s constant h: Bohr’sconcept of)
Bohr’s concept of individuality, 46, 69,123, 148–151, 153
individual vs. collective phenomena inquantum physics, 85, 139, 140
individual quantum objects, processes,behavior, phenomena, and events, 3, 4,11–15, 24, 32, 34, 35, 35n3, 38, 53, 62,69, 78, 80–87, 105, 108–110, 116, 123,137, 139, 140, 148–150, 153–157,162, 168
and probability in quantum theory, 4, 12,14, 15, 24, 32, 35, 60, 80, 81, 108, 109,140, 151, 153–157, 162
of quantum effects, 64, 82, 84, 148, 150Indivisibility or wholeness of quantum
phenomena (see also Atomicity [Bohr’sconcept of]; Quantum phenomena, alsoatomic phenomena, as defined by therole of Planck’s constant h: in Bohr’s
194 Subject Index
sense, Bohr’s concept of [definition]),50, 67, 145–153
Interference, interference effects or pattern,34n2, 49, 75–86, 133, 134, 139
as correlational pattern, 76Intuition (see also Visualization, pictorial
representation, conception), 39, 40, 171as Anschaulichkeit, 39, 40, 171
JJosephson’s junctures, 63
KKinematics (see Heisenberg’s ‘‘new
kinematics’’)Klein–Gordon equation, 89Knowledge, nature of knowledge (see also
Epistemology), 9, 10, 13n6, 15, 24, 49,56, 176
as changed by quantum physics, 15, 49, 56in quantum physics, 15, 49, 56, 62, 64, 84,
87, 128, 164, 176unity (harmonies) of knowledge in Bohr,
169–171The Kochen–Specker theorem, 109, 113,
113n5, 113n6, 123n10
LLocality/nonlocality, 9, 10n5, 14, 54n4, 77,
78, 85, 86, 107–131 , 136, 148n5,154–157
and completeness/incompleteness of quan-tum mechanics (see Completeness/incompleteness of quantum mechanics:and locality/nonlocality)
MMany-worlds interpretation of quantum
mechanics, 54n4Mathematics
Bohr on mathematics in quantum theory,vii, 37–40, 89, 94
mathematics, physics, and philosophy inBohr, 171, 173, 177–179
Matrices, matrix variables (see also Matrix orHeisenberg’s (quantum) mechanics),23, 32, 33, 37, 92, 101, 104, 178
multiplication rules for, 32, 33
Matrix or Heisenberg’s quantum mechanics,ix, 1, 28, 29, 32–36, 46, 55, 56, 90, 92,93, 93n5, 100
mathematical equivalence to wave orSchrödinger’s quantum mechanics,93n5
and wave or Schrödinger’s quantummechanics, ix, 1, 28, 35, 55, 56, 93,93n5
Measurement, measuring instruments (see alsoDisturbance [of quantum objects bymeasurement]; Uncertainty relations[also the uncertainty principle, indeter-minacy relations, indeterminacy prin-ciple]: and measurement and measuringinstruments), 7–9, 11, 14, 29, 31–32,35, 37, 39, 40, 43, 44, 46, 47, 50–57,63–69, 73, 78–85, 87–105, 109–151,154, 155, 157, 163, 168–171, 173
classical aspects of measuring instruments,14, 29, 31, 32, 43, 54n5, 56, 66–68, 79,80, 130, 144, 147, 151
in classical physics, 47, 54n5, 145, 169discrimination between measuring instru-
ments and quantum objects, 68, 117, 118erasure by measurement, 68, 130, 134, 146,
163‘‘finite and uncontrollable interaction’’
between quantum objects and measur-ing instruments, 118, 122, 124, 127, 142
identical preparation of measuring instru-ments, 14, 110
interaction, effects of the interactionbetween quantum objects and measur-ing instruments and other quantumobjects (see also Quantum phenomena,also atomic phenomena, as defined byPlanck’s constant h: Bohr’s conceptof), 8, 9, 31, 44, 46, 50, 56, 63, 64, 67,73, 79, 82, 84, 87, 100, 102, 105, 117,135–138, 144–150, 157, 173
irreducible role of, in quantum physics, 39,40, 44, 47, 51, 53–55, 66, 68, 69, 109,112, 116–125, 129, 131–134, 138, 140,142, 145, 147, 154, 163, 171
quantum (or atomic) aspects of measuringinstruments, 66, 67, 80, 94–100, 104,110, 117, 132, 133, 141, 144, 147, 169
in quantum field theory, 89–105, 141and relativity, 169–171and the uncertainty relations, 85–87
Mechanics
Subject Index 195
M (cont.)classical (see Classical mechanics)the concept of, 3, 38, 86, 110quantum (see Quantum mechanics)
Models (see Idealization, idealized models)
NNoncommutativity (of multiplication in quan-
tum-mechanical formalism), 32, 33Nonlocality (see Locality/nonlocality)
OObject(s)
classical, physical (of classical physics), 6,11, 32, 53, 63, 77, 80, 82, 83n8, 92,102, 23
as idealization (vis-à-vis nature) inclassical physics, 6, 10–12, 83n2
quantum (see Quantum objects andprocesses)
as noumenon or things in itself (vs.phenomenon) in Kant, 64, 153
Objectivity, 9, 63, 64, 140–142, 161,167–170, 173
as unambiguous communication in Bohr,64, 140, 167–170
Old quantum theory, 1–3, 21, 29–36, 53, 108,149, 160
Ontology, ontological, ix, 9, 13, 14, 50, 79, 80,161, 164
Orbits, orbital motion of electrons in atoms(see also Stationary states, of electronsin atoms), 11, 20, 21, 30–32, 173
PParticle(s), 3, 8, 29, 33, 44, 46, 55, 56, 64, 66,
74, 76–83, 90–93, 99, 100, 103–106,127, 133–135, 149, 150, 160
as abstraction, 29, 44, 55, 56, 82n6in classical physics, the classical concept
of, 74, 76, 77, 83, 92elementary particles, 79, 83n8, 99, 149, 150and fields in quantum field theory, 92, 93particle-like behavior, 46, 74, 76–83, 92,
93n8, 140particle-like phenomena or effects, 44, 45,
76, 82, 83and/vs. waves, 8, 44, 77, 77n4, 81, 160
Phenomena
and noumena or things in themselves(in Kant), 64
quantum (see Quantum phenomena, alsoatomic phenomena, as defined by therole of Planck’s constant h)
Philosophy, v, 6, 13, 13n6, 18, 19, 23, 39, 152,159, 160, 165, 171, 173, 177–179
and physics (see Physics: physics and phi-losophy; mathematics, physics, andphilosophy in Bohr)
of physics (also of quantum theory), vii, ix,xi, 19, 23, 24, 91n4
of quantum field theory, 91n4Photon(s), 4, 12, 20, 22, 50, 53, 73–76, 78,
80–83, 91, 94, 103, 105, 120, 133, 164the concept of, 20, 81relativistic motion of, 171
Photon-box experiment (of Einstein),134–136, 176
Physics (see also Classical mechanics;Classical physics; Classical statisticalphysics [or mechanics]; Quantummechanics)
physics and philosophy; mathematics,physics, and philosophy in Bohr, 19,20, 171, 173, 177–179
Planck’s constant (h), the quantum of action, 1,2n1, 7, 37, 46, 49, 51, 55, 55n5, 62, 63,65, 66, 68, 69, 81, 144, 148, 152, 169
irrationality of, 49, 63symbolic nature of, 46, 55, 65
Planck’s discovery of quantum physics, xii, 3,13, 46, 62, 65, 77, 148, 152, 160
Planck’s (black-body radiation) law, 1, 3, 150Planck’s discreteness postulate, 12, 46Positivism, positivist, 1313n6, 19, 20, 24, 31Prediction(s)
EPR predictions, the special character of(see also Bohr’s reply to EPR’s andrelated arguments by Einstein; EPR’s[Einstein, Podolsky, and Rosen’s]argument and related argument byEinstein, EPR’s [Einstein, Podolsky,and Rosen’s] and related experiments),112, 114, 115, 118–123, 125–133,135–136, 154
probabilistic or statistical nature of quantumpredictions, 3–5, 9, 11, 12, 14, 24, 29,32–35, 38, 54, 55, 64, 68–69, 80–81, 84,86, 87, 92, 96, 100–103, 108–111, 117,120, 123, 128, 134, 139, 140, 142n2,144, 149–158, 162, 163, 173
196 Subject Index
quantum vs. those of classical and classicalstatistical physics, 4, 5, 11, 32, 34, 38,69, 150, 151
and verification, 119, 130Pre-Socratic philosophy, 19, 50, 159, 162Probability
and the Bohr-Einstein debate, 110, 111,153–158
definition of, 12and/vs. chance or randomness (see Chance
or randomness: and probability)Kant on, 165probabilistic nature of quantum theory (see
Prediction(s): probabilistic or statisticalnature of quantum predictions; Predic-tion(s): quantum vs. those of classicaland classical statistical physics)
propagation of (in Born), 163in quantum electrodynamics and quantum
field theory, 96, 101–106quantum rules for probability (see Ampli-
tude, or probability amplitude)and quantum waves (see Wave or prob-
ability function (w))and/vs. statistics, 12
Probability amplitude (see Amplitude, orprobability amplitude)
QQ-numbers (in Dirac’s formalism), 36, 92Quantum of action (see Planck’s constant (h),
the quantum of action)Quantum chromodynamics, 91Quantum electrodynamics (see also Quantum
field theory), 2, 2n1, 6, 37, 62, 74, 74n3,89–106
Quantum field theory, 89–106measurement in, 89–106epistemology of, 89–91, 93–95, 98, 100,
102, 104–106philosophy of, 91n4vs. quantum mechanics, 89–91, 91n4,
93–94, 98, 102, 104–106Quantum gravity, 100, 171Quantum information theory, 109Quantum jumps (see Transitions between
stationary states)Quantum measurement paradox, 76Quantum mechanics
debate concerning, ix, 5, 19, 105, 107, 109,115n8, 167
matrix (see Matrix or Heisenberg’squantum mechanics)
as probabilistically predictive theory (seePrediction(s): probabilistic or statisticalnature of quantum predictions; quan-tum predictions vs. those of classicalphysics and classical statistical physics)
as a rational theory, 29, 32, 37, 48, 172and relativity (see Relativity: and/vs.
quantum theory)symbolic nature of, 23, 46, 54–56, 62, 92,
139, 143wave mechanics (see Wave or Schrödin-
ger’s quantum mechanics)Quantum objects and processes
inaccessible, inconceivable, unthinkablenature of, 9, 10, 15, 20, 24, 31, 35, 39,40, 47, 48, 60, 63, 64, 73, 100, 112,137, 138, 145, 147–149, 151, 153, 157,160, 164, 168, 172, 176
independent existence of, 9, 10, 31, 79macroscopic or composite, 54n5, 63, 73, 79and measuring instruments (see Measure-
ment, measuring instruments: dis-crimination between measuringinstruments and quantum objects;‘‘finite and uncontrollable interaction’’between quantum objects and measur-ing instruments; interaction, effects ofthe interaction, between quantumobjects and measuring instruments andother macro objects)
Quantum phenomena, also atomic phenomena,as defined by the role of Planck’s con-stant h (see also Atomicity [Bohr’sconcept of ]); Individuality: individualquantum objects, processes, behavior,phenomena, and events; Indivisibility orwholeness of quantum phenomena;Measurement, measuring instruments:discrimination between measuringinstruments and quantum objects; inter-action, effects of the interaction,between quantum objects and measuringinstruments and other macro objects)
Bohr’s concept of, v, viii, 28, 29, 43–46,50, 57, 59, 60, 67, 82, 83, 94, 105, 108,111n3, 130, 131, 133, 137–153, 158,167, 168
Bohr’s concept of (definition), 138, 139vs. classical phenomena, 62, 103, 117, 118,
154
Subject Index 197
Q (cont.)closed (in Bohr’s sense), 141, 145, 148as defined by Planck’s constant, 2n1individual (see Individuality: individual
quantum objects, processes, behavior,phenomena, and events; individualityof quantum effects)
vs. quantum objects (see Quantum objectsand processes: inaccessible, inconceiv-able, unthinkable nature of)
Quantum postulate, 41, 44–51, 55, 62, 172‘‘irrationality’’ of, 47, 48, 172
Quantum states (state vectors), 115n8, 145n4Quantum statistics, 3, 12, 104, 150, 157Quantum theory
definition of the term, vi (n3)and relativity (see Relativity: and/vs.
quantum theory)
RRandomness (see Chance, or randomness)Realism, realist, 4, 5, 8, 9–15, 19, 22, 80, 108,
128, 157, 161, 169–171definition of realism, 9, 10
Reality, ix, 9, 10, 13, 24, 47, 49, 50, 62, 64, 107,110, 112, 114–120, 122, 124–130, 135,143, 154, 159, 161, 165, 168, 169, 173
element(s) of reality (according to Einsteinand EPR), 112, 114–119, 122, 125
EPR’s criterion of, 112, 114–120, 122,124–130, 135, 154, 168
Real numbers, 33, 34n2, 173and/vs. complex numbers, 34n2, 173
Reciprocity (as complementarity) in Bohr, 60,61, 64, 67, 68
Relativity theory, v, ix, 1, 3, 4, 9, 10n5, 12, 14,18, 31, 47, 51, 62–64, 66, 77, 86, 91,92, 101, 102, 106, 107, 110, 110n2,113, 113n5, 129, 131, 141, 161,169–171, 173, 171–179
general theory, 106, 134, 169, 171,176–179
and/vs. quantum theory, 51, 63, 66, 101,102, 131, 141, 169–171, 178, 179
special theory, 1, 91, 106, 171, 176Renormalization, 97–102Retroaction in time, 77Riemann’s geometry, 176–179Riemann’s surfaces, 173–177Riemann’s theory of functions of complex
variables, x, 15, 173–175
SSchrödinger’s or wave equation, 44, 53–55,
89, 93n5, 99–101, 103Schrödinger’s mechanics (see Wave or
Schrödinger’s quantum mechanics)Spectra, atomic, 3, 21, 23, 30, 92Spin, 71n1, 92, 101, 109, 115n7, 121, 123,
123n11‘‘Spooky actions at a distance’’ (according to
Einstein), 86, 110, 128, 129Spooky predictions at a distance (as opposed
to ‘‘spooky actions at a distance’’), 128,129
Standard model (of particle physics), 91, 97Stationary states, of electrons in atoms, 20–22,
30, 31, 33, 34, 49, 150Statistical physics (see Classical statistical
physics, or mechanics)Statistics (see Probability: and/vs. statistics)String and brane theories, 100, 105, 179
TThermodynamics, 152, 160Transformation theorems, 146Transformation theory (of Dirac and Jordan),
30, 49, 51, 54, 84, 93, 100Transition between stationary states, 3, 2021,
24, 32–34, 150probabilities of, 33, 34, 150
UUncertainty relations (also the uncertainty
principle, indeterminacy relations), 7, 8,14, 24, 28–39, 33, 37, 41, 43–45, 52,54, 56, 57, 59–61, 65–69, 71, 72, 78,79–81, 83–87, 90, 91, 95, 99, 103, 111,121, 122, 134, 140, 142–145, 155
in Bohmian theories, 14and classical physical concepts, 65–69and complementarity, 7, 8, 28, 29, 30, 43,
45, 52, 59–61, 64, 67, 79, 84, 85, 140and the double-slit experiment, 71, 72, 80,
81, 85, 86and the EPR experiment, and in EPR’s
argument and Bohr’s reply to EPR,111, 112, 114, 117, 119, 121, 122, 155
as a law of nature, 86and measurement and measuring instru-
ments, 65–69
198 Subject Index
physical meaning or interpretation of, 71,72, 122
and probability and statistics, 65–69, 80,81, 84–87, 144
and quantum field theory, 91, 95, 99and quantum-mechanical formalism, 84and quantum randomness, 8, 60, 66–69,
85–87relativistic invariance of, 129
VVisualization, pictorial representation, con-
ception (see also Intuition), 38–40, 56,64, 93, 104, 156, 159, 170, 171, 173
Virtual particle formation, 95
WWaves, wave phenomena in quantum physics,
8, 29, 44, 45, 55, 56, 75–77, 80, 81,82n6, 83, 84, 92, 93, 104, 160
as abstraction, 29, 44, 55, 56, 82n6in Bohmian theories, 77n4vs. classical waves, 74, 83and particles (see Particle(s): and waves)pattern (see Interference, interference effects
or pattern)
and/as probabilities (see Wave (w) or proba-bility function)symbolic, 80, 81, 92
wave or wave-like attributes, features, behav-ior, processes, 8, 44–46, 56, 75, 76, 80,81, 140
wave or wave-like phenomena or effects (seealso Interference, interference effects orpattern), 76, 82
Wave-particle complementarity (see Com-plementarity: wave-particlecomplementarity)
Wave or probability function (w), 34n2, 53,101, 103, 116, 121, 128, 129, 150, 163
Born’s probabilistic interpretation of, 34n2,81, 150, 163
as expectation catalogue, 163Wave or Schrödinger’s quantum mechanics,
ix, 1, 8, 28–30, 35, 41, 44, 46, 54, 92,93, 93n5, 150
and matrix mechanics (see Matrix or Hei-senberg’s quantum mechanics: mathe-matical equivalence to wave orSchrödinger’s quantum mechanics; andwave or Schrödinger’s quantummechanics)symbolic, 55, 98
Subject Index 199