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Staicu V. (ed.) — Differential Equations, Chaos and Variational Problems
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Íàçâàíèå: Differential Equations, Chaos and Variational ProblemsÀâòîð: Staicu V. (ed.) Àííîòàöèÿ: Differential equations are a fast evolving branch of mathematics and one of the mathematical tools most used by scientists and engineers. This book gathers a collection of original articles and state–of–the–art contributions, written by highly distinguished researchers working in differential equations, delay–differential equations, differential inclusions, variational problems, Young measures, control theory, dynamical systems, chaotic systems and their relations with physical systems. The forefront of research in these areas is represented in this volume.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2008Êîëè÷åñòâî ñòðàíèö: 435Äîáàâëåíà â êàòàëîã: 10.12.2009Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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"Bare" theory 116—125 "Bare" theory, "effective" knowledge in 119—120 "Bare" theory, emergence of "probabilities" in 120—123 "Bare" theory, self-measurement in 180—186 "Color" (as a property of electrons) 1 "Hardness" as a property of electrons 1 "Ignorance" interpretation of probabilities in Bohm's theory 135 139—140 "Ignorance" interpretation of superpositions 15 "Modal" interpretations of quantum mechanics 191—197 Action at a distance (in Bohm's theory) 159—160 see Aharonov — Bohm effect 11—12 Aharonov, Yakir 12n 195n Aicardi, F. 106 Albert, D. 101 129n 131n 133n 185n 189n 191n Barrett, J. 115 123n Basis of a state space 31 33 40—41 Basis of a vector space 21—25 40—41 Bell's theorem 66—70 131 158 Bell, J. 61 68 70 134 160n Bohm's theory 134—179 Bohm's theory, contextuality 153—155 Bohm's theory, effective collapse 161—164 Bohm's theory, epistemology 164—169 Bohm's theory, metaphysics 134—135 Bohm's theory, nonlocality 155—161 Bohm's theory, probability 135 140 Bohm's theory, relation to "modal" (Kochen — Healy — Dieks) interpretations of quantum mechanics 191 194 Bohm's theory, relation to many-minds theories 176—179 188n Bohm's theory, self-measurement 187—188 Bohm, D. 12n 134 Bohr, Neils 17 Borsellino, A. 106 Brain states, discoverability of, by introspection 116—120 Brain states, relation to mental states 77 104—110 126—132 170—176 180—189 Brain states, time evolution of 77—79 104—110 119—125 180—189 Brain surgery, science-fictional 107—108 170—173 Brains, observables of 180—186 Causality 64—65n Classical mechanics 43—44 134—135 Collapse of the wave function 36 37 51—53 Collapse of the wave function, effective (in Bohm's theory) 161—164 Collapse of the wave function, effective (in the "bare" theory) 119—120 Collapse of the wave function, effective (in the single-mind theory) 127—129 Collapse of the wave function, empirical consequences of 75—76 78 84—92 176n Collapse of the wave function, for systems consisting of more than a single particle, or with more than one degree of freedom 51—53 Collapse of the wave function, lack of experimental evidence for 110—111 Collapse of the wave function, theories of 80—84 92—111 Commutators/commutation relations and compatibility 42—43 182—184n Commutators/commutation relations and compatibility, the case of position and momentum 44 Compatible/incompatible observables 7 14—15 32—33 42—43 Compatible/incompatible observables, simultaneous knowability/unknowability of 7 165—170 183—188 Complex numbers/vector spaces 39—41 Contextuality, of deterministic replacements for quantum mechanics 153—155 Coordinate space 18—19 Coordinate space, quantum-mechanical formalism for 43—47 140—141 142—143 Copenhagen interpretation of quantum mechanics 17 38 Correspondence, principle of 43—44 Cosmology 133 D'Espagnat, B. 127n Daneri, A. 91n 124n deBroglie, L. 134 Decoherence see "Environmental decoherence effects" Degrees of freedom 53 Determinism of Bohm's theory 135 137 187—188 Determinism of the quantum-mechanical equations of motion 34 36 37 Deutsch, David 115n DeWitt, B. 113 Dieks, D. 191 Dualism, mind-body 81—82 126 130—132 Eigenstates 31 Eigenvalues/eigenvectors 29 Einstein — Podolsky — Rosen (EPR) argument 61—66 69 Einstein, A. 61 69 Elementary particles 93—94 Empirical equivalence/inequivalence/incommensurability of theories 176—179 Energy non-conservation (in the GRW theory) 97—98 Environmental decoherence effects 88—92 161—164 Epistemology of Bohm's theory 165—170 183—186 187—188 Epistemology of the many-minds theory 132—133 183—187 Equation of motion (Schroedinger equation) 34 Everett, H., III 112—113 Fields, force 135 Fields, relativistic quantum 59—60 160n Gell-Mann, M. 91n 124n Ghirardi, G.C. 96 106 Ghirardi, Rimini, and Weber (GRW) theory of the collapse of the wave function 92—111 153n 176n Ghirardi, Rimini, and Weber (GRW) theory of the collapse of the wave function, nonconservation of energy 97—99 Ghirardi, Rimini, and Weber (GRW) theory of the collapse of the wave function, significance of position 93 101—104 153n see Gleason, A.M. 155n Gottfried, K. 91n 124n Grassi, R. 106 Hartle, J. 91n 124n Healy, R. 191 Hermitian operators 40—41 Inner product, of two vectors 20 introspection see "Brain states" Kochen and Specker theorem 154n Kochen, S. 155n 191 Light, speed of 65n Linearity, as a property of dynamical laws 34 Linearity, as a property of operators 26 Locality 64—65 Locality, of the many-minds theory 131—132 see Lockwood, Michael 124n Loewer, B. 129n 131n 191n Loinger, A. 91n 124n Macroscopic systems/superpositions 83—84 see principle "Environmental Many-minds theory 130—132 Many-minds theory and locality 131—132 Many-minds theory and self-measurement 186—187 Many-minds theory and the vacuum 133 Many-minds theory, relation to Bohm's theory 176—179 188n Many-stories interpretation of quantum mechanics 115—116 Many-worlds interpretation of quantum mechanics 113—115 187 Matrices 27—28 Measurement 34—38 39 50—53 see Measurement, approximate 194—197 Measurement, forms of outcomes of 92—93 99 100—111 170—179 191—197 Measurement, interactions 73—79 Momentum, observable of 44 see Newman, J. 124n Norm, of a vector 21 Normalized vectors, use of, in quantum mechanics 30 Observables 30—31 see "Operators" Observables, complete 40—41 Operators 25—30 31—32 36 Operators, Hermitian 40—41 Orthogonal vectors 21 Orthonormal bases 21 Orthonormal bases, theorems about 40—41 Peres, A. 91n 124n photons 101 102—104 Podolsky, B. 61 69 POSITION 170—176 Position, observable of 44—47 Position, special role of, in Bohm's theory 134—135 Position, special role of, in the Ghirardi — Rimini — Weber theory 93 100—111 Privacy, the quantum mechanics of 184—186 187—188 Probability in Bohm's theory 135 139—140 Probability in Kochen — Healy — Dieks-type theories 193 Probability in many-worlds and many-stories theories 114—116 Probability in single-mind and many-minds theories 126—129 130 Probability in the Ghirardi — Rimini — Weber theory 93—95 97—98 Probability in the standard formulation of quantum mechanics 34—36 46 Projection postulate see "Collapse of the wave function" Prosperi, G.M. 91n 124n Putnam, Hilary 187 Quantum mechanics, coordinate-space formalism 43—47 Quantum mechanics, general formalism 30—43 Quantum mechanics, multiple degree-of-freedom formalism 53 Quantum mechanics, multiple-particle formalism 47—52 142—143 Quantum mechanics, relativistic formalism 60—61 quantum states 30 Relativity and Bohm's theory 160—161 169 see Relativity and locality 65n Retinas 105 Rimini, A. 96 Rosen, N. 61 69 Schroedinger's cat 73—80 Schroedinger's equation see "Equation of motion" Senses, human 103 105—106 Senses, nonhuman 107 Senses, superhuman 107—111 170—176 Separability/nonseparability 49 see "Nonlocality" Simultaneity see "Relativity" see Single-mind theory 126—130 Space see "Coordinate space" see "State "Vector Space-time structure, and the foundations of quantum mechanics 177 Specker, E.P. 155n Spin angular momentum 1 33 State space 30—33 40—41 State vector 30 State vector reduction see "Collapse of the wave function" State, quantum-mechanical 30 Statistical mechanics 135 Superposition 11 Superposition, phenomenology of 116—125 see Supervenience of the mental on the physical see "Brain states" Time evolution see "Equation of motion" Two-slit experiment 12—14 Uncertainty principle 7 see "Compatible/incompatible Underdetermination of theory by experiment see "Empirical equivalence/inequivalence/incommensurability of theories" Vacuum, quantum-mechanical 133 Vaidman, L. 101 van Fraassen, B. 196 Vector/vector space 17—25 von Neumann, J. 80 Wave functions see "Quantum mechanics coordinate-space Weber, T. 96 Wigner's friend 76—79 Wigner, E.P. 81—82
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