Spatially Averaged Quantum Inequalities Do Not Exist in Four-Dimensional Spacetime

TL;DR

This paper constructs specific quantum states in four-dimensional spacetime that demonstrate the non-existence of spatially averaged quantum inequalities by exhibiting arbitrarily large negative energy densities.

Contribution

It provides explicit counterexamples of quantum states that violate the concept of spatially averaged quantum inequalities in four-dimensional spacetime.

Findings

States can have arbitrarily large negative energy densities.

Counterexamples to spatially averaged quantum inequalities.

Negative energy can be localized in space at fixed times.

Abstract

We construct a particular class of quantum states for a massless, minimally coupled free scalar field which are of the form of a superposition of the vacuum and multi-mode two-particle states. These states can exhibit local negative energy densities. Furthermore, they can produce an arbitrarily large amount of negative energy in a given region of space at a fixed time. This class of states thus provides an explicit counterexample to the existence of a spatially averaged quantum inequality in four-dimensional spacetime.