A Philosopher's Understanding of Quantum Mechanics: Possibilities and Impossibilities of a Modal Interpretation

by Pieter E. Vermaas

• ISBN13: 9780521651080
• ISBN10: 0521651085
• Format: Hardcover
• Copyright: 2000-01-28
• Publisher: Cambridge University Press

Summary

This book is about how to understand quantum mechanics by means of a modal interpretation. Modal interpretations provide a general framework within which quantum mechanics can be considered as a theory that describes reality in terms of physical systems possessing definite properties. Quantum mechanics is standardly understood to be a theory about probabilities with which measurements have outcomes. Modal interpretations are relatively new attempts to present quantum mechanics as a theory which, like other physical theories, describes an observer-independent reality. In this book, Pieter Vermaas summarises the results of this work. The book will be of great value to undergraduates, graduate students and researchers in philosophy of science, and physics departments with an interest in learning about modal interpretations of quantum mechanics.

Table of Contents

Preface	ix
Introduction	1	(8)
Quantum mechanics	9	(13)
The standard formulation	9	(7)
The need for an interpretation	16	(6)
Modal interpretations	22	(15)
General characteristics	22	(5)
Starting points	27	(2)
Demands, criteria and assumptions	29	(8)
Part one: Formalism	37	(134)
The different versions	39	(24)
The best modal interpretation	39	(4)
Van Fraassen's Copenhagen modal interpretation	43	(3)
The bi modal interpretation	46	(8)
The spectral modal interpretation	54	(2)
The atomic modal interpretation	56	(2)
Bub's fixed modal interpretation	58	(1)
Some measurement schemes	59	(4)
The full property ascription	63	(24)
Some logic and algebra	63	(4)
The full property ascriptions by Kochen and by Clifton	67	(4)
Conditions on full property ascriptions	71	(3)
A new proposal	74	(3)
Results	77	(2)
Definite-valued magnitudes	79	(8)
Joint property ascriptions	87	(12)
A survey	87	(1)
Snoopers	88	(5)
A no-go theorem	93	(4)
The atomic modal interpretation	97	(2)
Discontinuities, instabilities and other bad behaviour	99	(36)
Discontinuities	99	(6)
Continuous trajectories of eigenprojections	105	(11)
Analytic trajectories of eigenprojections	116	(11)
Instabilities and other bad behaviour	127	(8)
Transition probabilities	135	(24)
Introduction	135	(2)
Freely evolving systems: determinism	137	(5)
Interacting systems: stochasticity	142	(9)
Stochastic processes	151	(3)
Two proposals by Bacciagaluppi and Dickson	154	(5)
Dynamical Autonomy and Locality	159	(12)
Introduction	159	(2)
The violation of Dynamical Autonomy	161	(8)
The violation of Locality	169	(2)
Part two: Physics	171	(36)
The measurement problem	173	(22)
Introduction	173	(4)
Bacciagaluppi and Hemmo: decoherence	177	(4)
Exact solutions for the atomic modal interpretation	181	(8)
Exact solutions for the bi and spectral modal interpretations	189	(3)
Degeneracies and a continuous solution	192	(3)
The Born rule	195	(12)
Probabilities for single outcomes	195	(2)
Correlations between multiple outcomes	197	(6)
Correlations between preparations and measurements	203	(4)
Part three: Philosophy	207	(73)
Properties, states, measurement outcomes and effective states	209	(15)
Noumenal states of affairs	209	(3)
Relations between properties, states and measurement outcomes	212	(6)
States and effective states	218	(6)
Holism versus reductionism	224	(28)
Holistic properties of composite systems	224	(5)
The violations of holism and of reductionism	229	(8)
Holism with observational reductionism	237	(10)
Reductionism with dispositional holism	247	(5)
Possibilities and impossibilities	252	(21)
Indefinite properties and inexact magnitudes	252	(2)
Correlations and perspectivalism	254	(4)
Discontinuities and instabilities	258	(2)
Determinism and the lack of Dynamical Autonomy and of Locality	260	(4)
The measurement problem and empirical adequacy	264	(2)
The lack of reductionism and of holism	266	(3)
An elusive ontology	269	(4)
Conclusions	273	(7)
Appendix A From the bi to the spectral modal interpretation	280	(4)
Glossary	284	(3)
Bibliography	287	(6)
Index	293