## Quantum Systems under Gravitational Time DilationThis thesis introduces a new theoretical tool to explore the notion of time and temporal order in quantum mechanics: the relativistic quantum "clock" framework. It proposes novel thought experiments showing that proper time can display quantum features, e.g. when a “clock” runs different proper times in superposition. The resulting new physical effects can be tested in near-future laboratory experiments (with atoms, molecules and photons as "clocks"). The notion of time holds the key to the regime where quantum theory and general relativity overlap, which has not been directly tested yet and remains largely unexplored by the theory. The framework also applies to scenarios in which causal relations between events become non-classical and which were previously considered impossible to address without refuting quantum theory. The relativistic quantum "clock" framework offers new insights into the foundations of quantum theory and general relativity. |

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### Contents

1 | |

2 Classical Clocks in General Relativity | 9 |

3 Quantum Clocks in General Relativity | 29 |

4 Quantum Complementarity and Time Dilation | 37 |

5 Interference of ClocksExperimental Proposals | 47 |

6 Decoherence from Time Dilation | 70 |

7 Quantum Formulation of the Einstein Equivalence Principle | 81 |

8 Clocks Beyond Classical SpaceTime | 98 |

9 Conclusions and Outlook | 115 |

Appendix Appendix A | 119 |

Appendix Appendix B | 121 |

Appendix Appendix C | 123 |

Appendix Appendix D | 127 |

Appendix Appendix E | 129 |

Appendix Appendix F | 136 |

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ˆHint,r ˆHs amplitudes atoms Bell inequality Bell’s causal central extension centre of mass classical coherence configuration considered coordinates corresponding decoherence defined degrees of freedom denoted described detector discussed dynamical mass eigenstate entangled equivalence principle evolving experimental framework Galilei group gravitational field gravitational phase shift gravitational potential gravitational time dilation Hamiltonian Hrest inertial interference experiment interference pattern interferometer interferometric visibility internal degrees internal dynamics internal Hamiltonian Lagrangian Lett mass parameter mass-energy equivalence measured metric modes Newtonian non-relativistic limit observers particles with internal paths photon Phys physical point-like predictions probing Publishing AG 2017 quantised quantum field quantum formulation quantum gravity quantum mechanics quantum superposition Quantum Systems quantum theory reads realised redshift regime relativistic relativistic effects respect rest frame scenario setup space space-time Springer International Publishing subsystems Systems Under Gravitational temporal order test theory trajectories unitary validity violations world line Zych