  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.
