Closed timelike curves and chronology protection in quantum and classical simulators

Abstract

In principe, General Relativity seems to allow the existence of closed timelike curves (CTC). However, when quantum effects are considered, it is likely that their existence is prevented by some kind of chronological protection mechanism, as Hawking conjectured. Confirming or refuting the conjecture would require a full quantum theory of gravity. Meanwhile, the use of simulations could shed some light on this issue. We propose simulations of CTCs in a quantum system as well as in a classical one. In the quantum simulation, some restrictions appear that are not present in the classical setup, which could be interpreted as an analogue of a chronology protection mechanism.

Relativistic Quantum Motion of an Electron in Spinning Cosmic String Spacetime in the Presence of Uniform Magnetic Field and Aharonov-Bohm Potential

“…CTCs are one of the most controversial aspects of modern physics [82]. It is possible to find in the literature works dealing with the concepts of causality [83], chronology protection [84], time travel [85], and flow information [86] in the framework of closed timelike curves. In our study, we consider the quantum motion only in regions such that α 2 r 2 − a 2 > 0.…”

Towards Quantum Simulation of Black Holes in a dc-SQUID Array

“…being the inductance of a single SQUID, where I c is its critical current, φ 0 = h/2e is the magnetic flux quantum, φ ext is the external magnetic flux and ψ is the SQUID phase difference, which gives rise to nonlinearities. Therefore, we will work on the weak signal limit linear regime, where we assume cos ψ 1 [13][14][15]. When no flux is applied, the effective speed of propagation all along the array is…”

“…However, to search for situations in which quantum fields are involved, we are compelled to turn instead to quantum simulators, where quantum gravitational effects could, in principle, arise. Some proposals for quantum simulations include traversable wormholes [12,13], and searching for a chronology protection mechanism [14] or other exotic spacetimes, such as warp drives, Gödel spacetimes or extreme Kerr black holes [15]. These simulations can be performed in very different quantum setups, depending on the simulated system or what is expected to be achieved.…”

“…These simulations can be performed in very different quantum setups, depending on the simulated system or what is expected to be achieved. For example, the previously cited simulations were proposed for a Bose-Einstein condensate [12] or a dc-SQUID array [13][14][15]. A simulation of Hawking radiation has been successfully achieved in a laboratory with Bose-Einstein condensates [16], and theoretical proposals with superconducting circuits can be found in the literature [17,18].…”

Quantum Simulation of Black Holes in a dc-SQUID Array

“…But to search for situations in which quantum fields are involved we are compelled to turn instead to quantum simulators, where quantum gravitational effects could, in principle, arise. Some proposals for quantum simulations include traversable wormholes [12,13], a search for a chronology protection mechanism [14] or other exotic spacetimes like warp drives, Gödel spacetimes or extreme Kerr black holes [15]. These simulations can be performed in very different quantum setups, depending on the simulated system or what is expected to be achieved.…”