Can quantum mechanics breed negative masses?

TL;DR

This paper investigates whether quantum effects like the Casimir effect can lead to negative masses, concluding that under realistic conditions, the total mass remains positive due to energy conditions.

Contribution

It establishes conditions under which the total mass in a quantum field theory setting remains non-negative, linking quantum effects to classical energy conditions.

Findings

Total mass remains positive when additional matter satisfies the dominant energy condition.

Quantum negative energy densities do not lead to negative total mass in equilibrium.

Energy conditions prevent the formation of negative masses despite quantum effects.

Abstract

The Casimir effect realizes the existence of static negative energy densities in quantum field theory. We establish physically reasonable conditions for the non-negativity of the total mass of a Casimir apparatus held in equilibrium in the Minkowski background, irrespective of any condensed matter consideration. Specifically, the dynamical equilibrium requires the presence of additional matter to hold the system apart. As long as this extra matter satisfies the dominant energy condition, the mass of the combined system is positive. Thus, the very same reason why energy cannot travel backwards in time could be the underlying mechanism behind the positivity of the mass. We discuss the takeaways from the Casimir setting to more general circumstances.