Quantum Inequalities and Singular Energy Densities

TL;DR

This paper examines the limitations of quantum inequalities in the context of singular negative energy densities, proposing refined formulations with compact support sampling functions to uphold their validity.

Contribution

It introduces a new approach to quantum inequalities using compact support sampling functions to address singular energy densities.

Findings

Quantum inequalities can be formulated with compact support sampling functions.

Such inequalities remain valid even with singular energy densities.

The approach helps constrain negative energy in extreme conditions.

Abstract

There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of apparent failures of the quantum inequalities, which involve passage of an observer through regions where the negative energy density becomes singular. We argue that this type of situation requires one to formulate quantum inequalities using sampling functions with compact support. We discuss such inequalities, and argue that they remain valid even in the presence of singular energy densities.