## Interpreting the Quantum WorldThis 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 |

268 | |

286 | |

### Common terms and phrases

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