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Reexamining the Quantum-Classical Relation

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Reexamining the Quantum–Classical Relation
Cambridge University Press
9780521857208 - Reexamining the Quantum–Classical Relation - Beyond Reductionism and Pluralism - By Alisa Bokulich
Index

Index

abgeschlossene theorie

See closed theories

analogy 51, 52, 53 n. 12, 53, 54–5, 82, 91, 92, 163

See also Dirac, methodology of analogy extension

Archive for History of Quantum Physics 30, 32 n. 10, 50

Ballentine, Leslie 19, 24, 25, 26

Balmer series, the 88

Batterman, Robert 85 n. 25, 93 n. 40, 101 n. 49, 102, 135, 160

beauty 61 n. 21

Dirac on 50 n. 4, 50, 52, 60, 61–2

Heisenberg on 60

Beller, Mara 30 n. 3, 30, 44, 45 n. 26

Belot, Gordon 12, 93 n. 40, 135

Berry, Michael 4, 15, 127

Bethe, Hans 111

billiard system, stadium

classical 125–6, 126 (fig. 5.5), 126 (fig. 5.6)

quantum 106, 125–6, 128 (fig. 5.7), 138, 147, 153

Bohmian interpretation of QM 125 n. 31, 138 n. 6

Bohr, Niels 2, 36, 44, 50, 56, 63, 76 (fig. 4.1), 159–61, 175

comparison with Dirac

See Dirac, comparison with Bohr

comparison with Heisenberg 96, 158 n. 4

comparison with semiclassical theorists 160–1,

complementarity 67, 95–6, 96 n. 43, 97, 161

continuity of classical/quantum theories 81, 94, 95, 159–60,

correspondence principle

See correspondence principle, Bohr’s

definition of “classical concepts” 97–8

development of old quantum theory

See quantum theory (old)

indispensability of classical concepts 37, 45, 97 n. 45, 98–9, 161

Kantian/neo-Kantian interpretation of 98

rational generalization thesis 2, 94–7, 98

selection rule

See correspondence principle, Bohr’s

Bohr–Dirac tradition 174

Born, Max 31, 45 n. 26, 64, 79, 80

bow–stern enigma 133

break time 21–2, 23, 25

Bueno, Otávio 166, 167–8

Cartwright, Nancy 10, 12, 29, 41–2,

chaos,

classical 1, 2, 13, 16, 22, 23, 78, 106, 109, 111, 115, 123, 125, 126 (fig. 5.5), 131, 163

quantum 2 n. 2, 2, 77–8, 102–3, 105, 114–15, , 117, 123, 125, 131, 160

Chevalley, Catherine 30 n. 3

classical limit 2, 8, 14–18, 16 n. 22, 20, 24, 127

combined limits 18

Heisenberg on 45–7

in Feynman’s path integral formulation 53 n. 11

in terms of large quantum numbers 17–18, 82, 84, 100, 102

in terms of Planck’s constant 14–17

inadequacy of to characterize quantum–classical relation 20–1, 28, 62, 156, 157, , 160 n. 8, 162 n. 11

See also reductionism2 and, semiclassical limit and, Ehrenfest’s theorem

classical mechanics (Newtonian mechanics) 1, 2, 34, 50, 124, 157

as a closed theory 31, 34

as an open theory 50, 56, 162, 163

Hilbert space formulation of 13

Lagrangian formulation of 52

Clifton, Rob 150

closed theory 2, 31, 41, 49, 60, 93, 158–9

as an axiomatic system 31–2, 33–4, 43

characteristics of 32, 34–7,

definition of 29–30

examples of 31

collapse of the wavefunction 30 n. 5

commutation/non-commutation 13, 51

algebra 51, 52, 62 n. 22, 92

of limits 17

completeness, causal 10 n. 12, 10

Copenhagen–Göttingen school 51, 55, 56, 71

Copenhagen interpretation 30 n. 5, 30, 37 n. 15, 44, 63, 67

correspondence principle(s) 56 n. 16, 161 n. 9, 175

as commonly misinterpreted 18, 25, 82, 84, 101 n. 49, 101, 127

as expression of structural continuity 62, 102, 173–4

Bohr’s 17, 71, 74–5, , 81–90, 84 n. 24, 85 (fig. 4.2), 85 n. 25, 86, 88, 94–5, 101, 159–60, 162 n. 12

as a law of quantum theory 89

as Bohr’s selection rule 85, 88, 89, 92, 101

as formalized in matrix mechanics 89–90, 92 n. 38

Batterman on Bohr’s 160

Heisenberg on Bohr’s 90, 92–3, 93 n. 39, 93 n. 40

not an asymptotic limit 87–9, , 101, 175

Sommerfeld on Bohr’s 93–4

Dirac’s (Poisson bracket) 59, 62, , 162, 172

for finite-resolution spectra 120, 160

frequency correspondence 84, 86, 88, 91

general 55 n. 14, 55, 90 n. 36

generalized 55 n. 14, 127, 172 n. 27

in Lagrangian formulation 53, 162

intensity–amplitude correspondence 86–7

inverse 55, 56 n. 15, 163

polarization correspondence 87 n. 32, 87

reciprocal correspondence principle methodology 55–8, 56 n. 16, 58–9, 112 n. 15, 121 n. 28, 162 n. 12, 162, 164

semiclassical relations as 160–1

Craver, Carl 143–4

Cvitanović, Predrag 110 n. 13, 111

Darrigol, Olivier 30 n. 6, 62, 80, 85 n. 25, 87 n. 33, 90 n. 35, 92 n. 38

de Broglie, Louis 63

decoherence

as solution to divergence of quantum/classical predictions 21–4, 25–7

definition of 21,

Delos, John 119–23, , 138, 153, 160

determinism/indeterminism 1, 64, 67, 68, 70

Dirac, Paul 2, 3, 47, 48 (fig. 3.1), 161–4, 175

comparison with Bohr 50–1, 57, 63, 66–72, , , 96, 161–2

comparison with Heisenberg 47, 49 n. 3, 49–50, , 51, 56, , 58

comparison with semiclassical theorists 162–4

methodology of analogy extension 53, , 54–5, , 162, 173

See also analogy

on open theories

See open theory

physics as engineering 49–50, 50 n. 4

reciprocal correspondence principle methodology

See correspondence principle(s)

reintroduction of an aether 58–9

reintroduction of particle trajectories 55

structural continuity thesis 52, 58

See also structure, continuity of

thesis of transferability 57, 58

disunity of science 8, 10, 11, 12, 47

See also pluralism

Dupré, John 10

Ehrenfest, Paul 63, 64, 65, 66

Ehrenfest’s theorem 18–20

Einstein, Albert 20, 63, 119

criticism of modern quantum mechanics 63–6, 66 n. 25

on statistical/ensemble interpretation 64

quantum condition for old quantum theory 77–8, 108,

Einstein–Bohr debate 63–6, , 87 n. 29

Dirac on 67–71

electrodynamics

classical 50 n. 5, 57, 59

quantum 56 n. 17, 56, 58, , 59, 70

eliminativism (theory replacement) 7, 10, , 24, 33, 44, 100, 157

empirical adequacy 12, 39, 98, 146 n. 18

ensemble interpretation

See statistical interpretation

EPR (Einstein, Podolsky, Rosen paper) 65–6, , 68

See also photon box

Epstein, Paul 76

explanation, scientific 3, 133, 175

asymptotic 136

causal 3, 150

Salmon’s 139

Woodward’s 145

deductive–nomological 3, 139, 146 n. 18, 150, 154 n. 27

explanatory depth 152–3

in semiclassical mechanics 117–18, 122, 128–30, 137, 138, 147–9, , , 150–1, 153,

model 137, 139–40, 140 n. 8, 143–7, , 175

conditions for model explanation 145, 146

causal model explanation 140–2, , 143, 148

covering-law model explanation 142–3, 143 n. 13, 143 n. 14, 148

mechanistic model explanation 143–4, 144 n. 15, 148

structural model explanation 150–1

examples of 147–8,

structural 141 n. 11, 149 n. 22, 149–50

understanding’s role in 151–2

Ezra, Gregory 163

Feyerabend, Paul 9

Feynman, Richard 53 n. 11, 53 n. 12, 53

fictions 106, , 111, 124–5, 131, 137–9, , 148, 176

See also models

Fine, Arthur 64 n. 24, 66

fine structure constant 69

Fodor, Jerry 5, 11

Ford, Joseph 24, 101

Frappier, Mélanie 31, 32, 45

French, Steven 167, 168

Friedman, Michael 151

Frisch, Mathias 57 n. 18

Galison, Peter 12

Garton and Tomkins experiments 115, 122

Goethe, Wolfgang von 41 n. 23

Göttingen

See Copenhagen–Göttingen school

Green’s function 53 n. 10, 119–20, 121

Gutzwiller, Martin 109–10

Gutzwiller’s trace formula

See semiclassical mechanics, periodic orbit theory

Hanson, N. R. 44

Healey, Richard 149

Heller, Eric 127, 128–30

Heisenberg, Werner 2, 29, 48 (fig. 3.1), 158–9, 175

as a pluralistic realist 30–1, 31 n. 7, 34 n. 12, 38–9, 40–2

comparison with Bohr

See Bohr

comparison with Cartwright 29 n. 2, 41–2, 47

comparison with Dirac

See Dirac

comparison with Kuhn 30, 37–8, 42–4, , 158

comparison with semiclassical theorists 158–9

emphasis on “observables only” 38, 59, 90 n. 35, 90,

half-integer solution to the helium atom 79 n. 16, 79 n. 17, 79

influence of Hilbert on 31–2

misinterpreted as positivist and instrumentalist 30–1, 31 n. 7, 38, 44

on closed theories

See closed theory

on incommensurability 37–8

on nonuniversality of theories 33–4, 158–9

See also pluralism, Heisenberg’s

on phenomenological theories 39, 43

on “pragmatic philosophy” (instrumentalism) 39, 40

Heisenberg–Kuhn tradition 174

helium atom 2, 78–81, 79 n. 16, 79 n. 17, 105, 111, 113 (fig. 5.1), 154

semiclassical solution of 110–13, 154

Hempel, Carl 139, 146 n. 18, 151

Hesse, Mary 167 n. 18

heuristics 55, 90, 172–3

Hilbert, David 32

Hitchcock, Chns 152–3

Hoag, Barton 39

holism 34–5, 43

Hooker, Clifford 135

Howard, Don 30 n. 5, 65, 66, 97 n. 45

Hughes, R. I. G. 149

Hylleraas, Egil 81, 110

Hyperion 23 (fig. 1.1), 23–4, 25–7

idealization 141

de-idealization 142, 143, 146–7

imperialism, theoretical

See reductionism

incommensurability 3, 9, 12, 13, 37, 42, 43, 132, 158

Infeld, Leopold 59

integrability vs. separability 107 n. 7

interstructuralism 3, 62, 173–4, 176

as distinct from reductionism and pluralism 174

as dynamic 173

defined for quantum–classical relation 173

intertheory relations 1 n. 1, 1, , 3, 4, , , 7, 12, 102, 171, 174, 175

challenges from semiclassical mechanics 133–4, 157

See also reductionism and, pluralism and, quantum–classical relation

isolationism, theoretical

See pluralism

Jalabert, Rodolfo 131

Jammer, Max 14, , 74

Keller, Joseph 107–9

Kemeny, John 7

Kleppner, Daniel 117, 133, 138, 153

Koopman, Bernard 13

Kragh, Helge 56 n. 15, 63

Kramers, Hendrik 78

Kuhn, Thomas 9, 10 n. 11, 30, 33, 42–4, 158, 165

Ladyman, James 166, 167

Lakatos, Imre 49 n. 2

laws 7, 8, 10, 35, 41, 47, 51, 82

Leopold, J. 110

limits

noncommuting 17

singular 15–16, 16 n. 22

See also classical limit

logic, mathematical 32, 50

Lyapunov exponent 22 n. 31, 129, , 130

Mach, Ernst 30 n. 6

Maslov index 108 n. 9, 110, 111, 119

matrix mechanics

See quantum mechanics, matrix mechanics

McMullin, Ernan 140–2, 143

measurement problem, the 21 n. 30, 21, 27 n. 41, 27

mesoscopic 2, 117

methodology, scientific 9, 38, 56 n. 16, 71

Bohr on 90

Dirac on 51, 56, 58

See also correspondence principle, reciprocal

Heisenberg on 38, 56, 90, 92

See also Heisenberg, emphasis on observables

methodology of analogy extension

See Dirac, Paul

models 33, 167 n. 20

de-idealization of 142, 143, 146–7

explanatory

See explanations, model

falsity of 140 n. 9

non-explanatory 140 n. 10, 146 n. 18

not just as calculational devices 138

See also fictions and, idealization

Morrison, Margaret 145

Nagel, Ernest 6

natural kinds 10

pluralism of 11

Nickles, Thomas 8, 20

nonlocality 64, 68

open theory 31 n. 9, 47, 49, 57, 58–9, 61, 68–9, 69 n. 29, 70, 173

Oppenheim, Paul 7

Pauli, Wolfgang 56, 57, , 79, 81, 114

Paz, Juan Pablo 21

Percival, Ian 110

Peres, Asher 27

photon box thought experiment 65–6

as proto-EPR argument 65–6

Planck, Max 14, 34, 73, 95

Planck’s constant 14, 69 n. 29, 97

Planck’s formula 14

planetary quantum dynamics 28

platonism

Heisenberg on

See realism, Heisenberg on

in mathematics 137 n. 5

pluralism 1, 3, 5, 8–13, , , 24, 100–1

Carwright’s 10, 11, 29

Feyerabend’s 9

Fodor’s 11

Heisenberg’s 29, 33–4, 158–9

isolationism of 5, 12, , 13, 176

problems for 9

type-I 8, 9, 10, 11,

type-II 9, , 11

type-III 9, , 11

Poisson bracket 22, 59, 62 n. 22, 62, 162

Popper, K. 30 n. 4

Post, Heinz 55 n. 14, 172

potential barrier problem 15–16

Ptolemaic astronomy 30, 42–43 n. 25, 42–3

quantization 59, 77 n. 12, 109

See also quantum theory, old, quantum conditions

quantum flesh on classical bones 104 n. 2, 104

See also semiclassical mechanics

quantum mechanics 1

alternative formulations of 22 n. 32

as a closed theory 31

as an open theory 47, 57, 68–9, 70

Feynman path integral formulation of 53 n. 11, 53, 54 n. 13, 139

Heisenberg vs. Schrödinger picture 55, 90–2

interpretations of

See Bohmian or, statistical or, Copenhagen

Lagrangian formulation of 52–4, 72

matrix mechanics 81, , 89–92

phase space formulation of 13, 22, 25

quantum–classical relation 1, 2, , 3, 12, 14, 20–1, 27–8, 138–9, 156–7, 160, 171

Bohr on 99–101, , , 159–61

See also Bohr, rational generalization thesis

Dirac on 51, 62–3, 161–4,

Heisenberg on 45–7, 158–9

interstructuralism as best account of

See interstructuralism

quantum–classical, divergence of predictions 13, 21–4, 26–7,

See also break time

quantum condition

See quantum theory, old

quantum dots 2, 131–2

quantum electrodynamics

See electrodynamics, quantum

quantum number 17, 84

See also classical limit, in terms of large quantum numbers

quantum theory, old 73, 111, 112, 114

consistency of 74–5, 97

crisis of 79–80

differences from classical theory 83–4

failure to model helium atom 78–81

postulates of 73–4

problem of quantum chaos in 77–8, 102–3

quantum conditions 74, 75–8, 77 n. 12, 106–7, , 108, 109

use of half-integer 79, 107, 110

Railton, Peter 149

Raleigh–Jeans formula 14

random eigenstate hypothesis 127, 129

realism, scientific 125, 157 n. 3, 164, 176

Heisenberg on 39 n. 22, 39–40

See also Heisenberg, as pluralistic realist

Kuhn on 43–4

pessimistic meta-induction argument 165, 166

“promiscuous” 10

structural

See structural realism

“success of science” argument 165

reciprocal correspondence principle methodology

See Dirac, Paul

Redhead, Michael 93 n. 40, 135, 170

reductionism 1, 3, 4–5, 6–8, 100, 157

diachronic 6

Kemeny–Oppenheim 6, 7–8

imperialism of 5, 11, 176

Nagelian (“reductionism1”) 6–7, , 11, 170

ontological 4 n. 1

“reduction2” 6, 8, 14, 20–1, , 28, 62, 82, 100, 156, 170, , 171, 172

inadequacy of for quantum-classical relation

See classical limit, inadequacy of

synchronic 6

relativism 9

relativity theory 31 n. 9, 31, 50, 59 n. 20, 64, 69 n. 29, 149

renormalization

See electrodynamics, quantum

resonances, quasi-Landau 117–22

See also Rydberg atoms, diamagnetic

Rosenfeld, Léon 101

Rutherford, Ernest 73

Rydberg, Johannes 115

Rydberg atom 2, 115 n. 21, 115, 123, 137, 157

diamagnetic 105–6, 115–18, 116 (fig. 5.2), 118 (fig. 5.3), 124 (fig. 5.4), 138, 147, 153, 154

explanation of 117–18, 122, 147, 153

See also Zeeman effect

in Stark effect 123

Salmon, Wesley 139, 152

Sánchez-Ron, José 55

Saunders, Simon 172

scarring, wavefunction 2, 106, 125, 128 (fig. 5.7), 153

as unexpected classically 127

definition of 127

explanation of 128–30, 137, 138, 147–8, 153

Scheibe, Erhard 35 n. 13, 37 n. 16

Schrödinger, Erwin 55, 63, 67, 100

Schrödinger cat states

See superposition

Schwarzschild, Karl 76

Schweber, Silvan 51

semiclassical limit 16 n. 22

See also classical limit

semiclassical mechanics 2, 3, 16, 28, 54, 104 n. 1, 104, 172

as correspondence principles 160–1

as Dirac’s reciprocal correspondence methodology 163–4

challenges for philosophy of science 133–4, 175

closed orbit theory 105, 119–23, , , 139, 156

EBK quantization 105, 107–9, 119, 156, 160,

history of 106–10

motivations for 104–5

periodic orbit theory 105, 109–10, 139, 148, 156, 160, , 161, 163, 172

relation to old quantum theory 106–9,

theoretical importance of 112–13, 130–1, 132–3, 153, , 154–5, 156–7, , 175

torus quantization

See EBK quantization

WKB method 106–7

Sober, Elliott 142–3, 143 n. 13

Sommerfeld, Arnold 75, 76 (fig. 4.1), 93–4

Stark effect, the 77, 123

statistical interpretation 20, 64

Stoppard, Tom vi, 115

structure

continuity of 2, 3, , 47, 51–3, , , , 54–5, 60, 61, 62–3, 106, 127, 130, 131–3, , 139, 156, 157, 159, 162, , 165, 171–2

dynamical 3, 105, , 106, 125, 130–1, 137 n. 5, 139, 171–2

insight into provided by semiclassical mechanics 112–13, 130–1, 154–5

interstructuralism

See interstructuralism

structural empiricism 166

Bueno’s partial structures approach 167–8

continuity defined in 168, 170–1

criticism of 168–71,

van Fraassen’s “requirement upon succession” 170–1

See also structural realism

structural realism 164–6

continuity defined in 168, 170

continuity thesis 165, 170

criticism of 168–71,

epistemic vs. ontic 166

partial structures approach 167

quasi-structural continuity 168

realism thesis 165, 166

See also structural empiricism

superposition 21 n. 30, 21, 24, 25, 27

Tanona, Scott 85 n. 25, 99 n. 46

theories

closed

See closed theory

nonuniversality of

See pluralism

open

See open theory

patchwork of 4

See also pluralism

“serial monogamy” of 10, 44

universality of 10, 13, 24, 33, 100,

theory change

Dirac’s model of 50

Heisenberg’s model of 35, 90

thesis of transferability

See Dirac, Paul

Tomsovic, Steven 132

trace formula

See semiclassical mechanics, periodic orbit theory

“trading zones” 12

trajectories, particle 55, 81, 102, 105, 114, 130, 131, 157 n. 2

as a way of modeling quantum dynamics 138, 147 n. 21

closed orbits 117–19, 118 (fig. 5.3), 124 (fig. 5.4), 157

experimentally determined electron 123–5

explanatory power of 128–30, 131–2, , 147–9, 150–1

ontological status of 125, 128, 130, 137 n. 5, 137–9,

periodic orbits 109–10, 126 (fig. 5.6), 126

uncertainty principle 59, 64–5, 66 n. 25, 68, , 69, 96 n. 43, 122, 123, , 137

unity of science 59–62, 162, 174

universal phenomena 136

van Fraassen, Bas 157 n. 3, 166, 170–1

van Vleck, John 78

w-questions 145, 147, 151, 152, 154

Weinberg, Steven 5 n. 2

Wigner, Eugene 13, 169

Wigner function

See quantum mechanics, phase space formulation

Wimsatt, William 140 n. 9

Wintgen, Dieter 111, 112, 154

Wise, M. Norton and D. Brock 130

Woodward, James 145 n. 17, 145, 149, 152–3

Worrall, John 165, 167 n. 16, 170

Zeeman effect 114 n. 19, 114–15, 117

Zurek, Wojciech 21, 101




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