Interpreting the Quantum World

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Cambridge University Press, Aug 26, 1999 - Science - 290 pages
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This is a book about the interpretation of quantum mechanics, in particular how to resolve the measurement problem introduced by the orthodox interpretation of the theory. The heart of the book is a new result that shows how to construct all possible "no collapse" interpretations, subject to certain natural constraints and the limitations imposed by the hidden variable theorems. From this perspective one sees precisely where things have gone awry and what the options are. Various interpretations, including Bohm's causal interpretation, Bohr's complementarity interpretation, and the modal interpretation are shown to be special cases of this result, for different choices of a "preferred" observable. A feature of the book is a novel treatment of the main hidden variable theorems, and an extended critique of contemporary "decoherence" theories of measurement. The discussion is self-contained and organized so that the technical portions may be skipped without losing the argument.
 

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Contents

From classical to quantum mechanics
8
12 States and properties in classical mechanics
13
13 States properties and probabilities in quantum mechanics
22
14 Schrödingers cat and quantum jumps
32
Bells no go theorem
40
22 The GreenbergerHorneZeilinger counterargument
48
23 Stochastic hidden variables
52
24 Deterministic hidden variables
58
55 Proof of the tridecompositional theorem
159
Quantum mechanics without observers II
163
62 The modal interpretation
173
63 Proof of the modal recovery theorem
181
Orthodoxy
184
72 Some formal constructions
199
The new orthodoxy
207
82 Many worlds
218

25 Locality and separability
64
The Kochen and Specker no go theorem
71
32 Schüttes tautology
82
33 Fourdimensional uncolourable configurations
95
34 Proofs and constructions
102
The problem of interpretation
115
42 A uniqueness theorem for no collapse interpretations
126
Quantum mechanics without observers I
131
52 The evolution of property states
133
53 Nonideal measurements
141
54 Environmental monitoring
150
83 Consistent histories
227
Coda
232
Some mathematical machinery
239
A2 Quantum states
247
A3 The Dirac notation
254
A4 Spin
258
A5 Composite systems
263
Bibliography
268
Index
286
Copyright

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