Analogue Non-Causal Null Curves and Chronology Protection in a dc-SQUID Array

We propose an analogue quantum simulator of a 1 + 1D spacetime containing non-causal curves, in particular null geodesics going back in time, by means of a dc-SQUID array embedded on an open superconducting transmission line. This is achieved by mimicking the spatial dependence of the metric with the propagation speed of the electromagnetic field in the simulator, which can be modulated by an external magnetic flux. We show that it is possible to simulate a spacetime region containing non-causal null geodesics, but not a full spacetime containing a chronological horizon separating regions with non-causal null geodesics and regions without them. This is in agreement with a recent suggestion of an analogue-gravity chronology protection mechanism by Barcelo et al.

Automated summary

We propose an analogue quantum simulator that can simulate a 1+1D spacetime with non-causal curves, specifically null geodesics going back in time. This is achieved by mimicking the spatial dependence of the metric using the propagation speed of the electromagnetic field in the simulator, which can be controlled by an external magnetic flux. While it is possible to simulate a spacetime region containing non-causal null geodesics, it is not possible to simulate a full spacetime with a chronological horizon separating regions with and without non-causal null geodesics, in agreement with recent suggestions of an analogue-gravity chronology protection mechanism by Barcelo et al.