Causality Violation and Nonlinear Quantum Mechanics

Abstract

It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must play an essential role in such cases. As a striking example, the logical paradoxes usually associated with causality violation can be resolved by quantum effects. We ask whether the explicit construction of a theory that allows causality violation might in turn teach us something about quantum gravity. Taking the toy model of Deutsch as a starting point, in Part I we argue that, despite being a nonlinear modification of quantum mechanics, the model does not imply superluminal signalling and its predictions can be operationally verified by experimenters within an appropriate ontological setting. In Part II we show that the model can be directly applied to scalar quantum fields, provided the fields are sent back in time by an amount much larger than the coherence time of the wavepackets. We propose a generalisation of the model that lifts this constraint and recovers the predictions of standard quantum field theory when the size of the temporal jump is much smaller than the coherence time of the wavepackets. Finally, we discuss an extension of the model to ordinary gravitational time dilation. The resulting model generalises and extends earlier work on the topic and can be tested experimentally using current technology.

PhD Thesis, The University of Queensland, 2013, 179 pages, 33 figures

References in corpus (13)

• Gaussian Quantum Information
• Quantum correlations with no causal order
• Closed timelike curves via post-selection: theory and experimental demonstration
• Spectral structure and decompositions of optical states, and their applications
• Linear Quantum Feedback Networks
• Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
• Nonlinear coupling of continuous variables at the single quantum level
• Quantum Connectivity of Space-Time and Gravitationally Induced Decorrelation of Entanglement
• Quantum Communication with an Accelerated Partner
• Relativistic quantum information and time machines
• Open timelike curves violate Heisenberg's uncertainty principle
• Quantum causal histories in the light of quantum information
• A General Framework for Nonlinear Quantum Dynamics

Cited by in corpus (3)

• Computational tameness of classical non-causal models
• Reality, Causality, and Quantum Theory
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories