## Quantum Theory: Concepts and MethodsThere are many excellent books on quantum theory from which one can learn to compute energy levels, transition rates, cross sections, etc. The theoretical rules given in these books are routinely used by physicists to compute observable quantities. Their predictions can then be compared with experimental data. There is no fundamental disagreement among physicists on how to use the theory for these practical purposes. However, there are profound differences in their opinions on the ontological meaning of quantum theory. The purpose of this book is to clarify the conceptual meaning of quantum theory, and to explain some of the mathematical methods which it utilizes. This text is not concerned with specialized topics such as atomic structure, or strong or weak interactions, but with the very foundations of the theory. This is not, however, a book on the philosophy of science. The approach is pragmatic and strictly instrumentalist. This attitude will undoubtedly antagonize some readers, but it has its own logic: quantum phenomena do not occur in a Hilbert space, they occur in a laboratory. |

### Contents

Quantum Tests | 24 |

Complex Vector Space | 48 |

Continuous Variables | 79 |

CRYPTODETERMINISM AND QUANTUM INSEPARABILITY | 113 |

Bells Theorem | 148 |

Contextuality | 187 |

Spacetime Symmetries 81 What is a symmetry? 82 Wigners theorem 83 Continuous transformations 84 The momentum operator 85 The Euclidean g... | 215 |

260 | 260 |

298 | 298 |

The Measuring Process 373 121 The ambivalent observer | 373 |

430 | |

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### Common terms and phrases

angle arbitrary atom basis beam bosons canonical CHSH inequality commute complete components consider correlated corresponding defined degrees of freedom denote density matrix detector diagonal domain dynamical variables eigenstates eigenvalues eigenvectors elements energy entropy equations of motion evolution example Exercise experimental fermions finite follows given Hamiltonian Heisenberg Heisenberg picture Hermitian hidden variables Hilbert space identical initial interaction invariant Kochen-Specker Kochen-Specker theorem Likewise Liouville density macroscopic magnetic maximal test meaning measurement observable obtain operator orbit orthogonal orthonormal outcomes pair parameters particles phase space photons Phys physical system Poisson brackets possible POVM predict preparation probability projectors properties pure Pµm quantization quantum mechanics quantum system quantum test quantum theory rays represented result right hand side rotation satisfy Schrödinger Show spin statistical Stern-Gerlach experiment symmetry theorem unitary matrix unitary transformation vector wave function wave packet