Models for Chronology Selection

TL;DR

This paper derives a partition function for a rotating scalar field in the Einstein universe, showing that quantum mechanics enforces chronology protection by preventing states beyond critical velocities or boosts, thus avoiding causality violations.

Contribution

It introduces a novel expression for the grand canonical partition function in rotating and boosted scalar fields, linking quantum state suppression to chronology protection.

Findings

Number of states tends to zero at critical rotation speed.

Number of states tends to zero at the formation of closed timelike curves.

Quantum mechanics enforces causality by superselecting non-violating configurations.

Abstract

In this paper, we derive an expression for the grand canonical partition function for a fluid of hot, rotating massless scalar field particles in the Einstein universe. We consider the number of states with a given energy as one increases the angular momentum so that the fluid rotates with an increasing angular velocity. We find that at the critical value when the velocity of the particles furthest from the origin reaches the speed of light, the number of states tends to zero. We illustrate how one can also interpret this partition function as the effective action for a boosted scalar field configuration in the product of three dimensional de Sitter space and $S^1$. In this case, we consider the number of states with a fixed linear momentum around the $S^1$ as the particles are given more and more boost momentum. At the critical point when the spacetime is about to develop closed timelike curves, the number of states again tends to zero. Thus it seems that quantum mechanics naturally enforces the chronology protection conjecture by superselecting the causality violating field configurations from the quantum mechanical phase space.