Analogue non-causal Null Curves and Chronology protection in a dc-SQUID Array

TL;DR

This paper presents an analogue quantum simulator using a dc-SQUID array to emulate a 1+1 D spacetime with non-causal null geodesics, demonstrating a form of chronology protection consistent with theoretical predictions.

Contribution

It introduces a novel method to simulate non-causal spacetime regions with a dc-SQUID array, advancing analogue gravity research and understanding of chronology protection mechanisms.

Findings

Successfully simulated non-causal null geodesics

Did not simulate a full spacetime with a chronological horizon

Supported the theoretical chronology protection hypothesis

Abstract

We propose an analogue quantum simulator of a 1+1 D 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 analogue-gravity chronology protection mechanism by Barcel\'o et al.