Causality violation and nonlinear quantum mechanics

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.