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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