## 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 | |

### Other editions - View all

### Common terms and phrases

2-valued homomorphism associated atoms Bohm Bohm's Bohmian mechanics Bohr Boolean algebra Boolean lattice Boolean sublattice classical mechanics collapse colouring commute compatible composite system configuration space constraint correlations corresponding decoherence defined denotes density operator determinate properties determinate sublattice determinate values disjunction dynamical variables eigenspaces eigenstates eigenvalues eigenvectors Einstein elements environment equivalent evolution false follows hidden variables Hilbert space idempotent interpretation of quantum Kochen and Specker lattice linear matrix maximal measurement interaction measurement problem measuring instrument modal interpretation non-Boolean non-ideal measurement noncommuting nonzero orthodox interpretation orthogonal triples outcome pair partial Boolean algebra particle phase space physical plane pointer observable position in configuration possible preferred determinate observable preferred observable probability projection operators quantum mechanics quantum propositions quantum world ray spanned reduced density representation self-adjoint operator similarly singlet statistical independence stochastic subsets subspaces subsystems superposition theory truth values uniqueness theorem unit vectors value assignments yields