The Quantum Interest Conjecture

TL;DR

This paper proves the quantum interest conjecture, which states that positive energy pulses must overcompensate negative energy pulses increasingly with separation, based on quantum inequalities in massless scalar fields in flat spacetime.

Contribution

It provides a proof of the quantum interest conjecture for massless scalar fields, linking it to quantum inequalities in flat spacetime.

Findings

Quantum interest conjecture is proven for massless scalar fields.

Positive energy pulses overcompensate negative pulses with increasing separation.

Quantum inequalities imply the quantum interest condition.

Abstract

Although quantum field theory allows local negative energy densities and fluxes, it also places severe restrictions upon the magnitude and extent of the negative energy. The restrictions take the form of quantum inequalities. These inequalities imply that a pulse of negative energy must not only be followed by a compensating pulse of positive energy, but that the temporal separation between the pulses is inversely proportional to their amplitude. In an earlier paper we conjectured that there is a further constraint upon a negative and positive energy delta-function pulse pair. This conjecture (the quantum interest conjecture) states that a positive energy pulse must overcompensate the negative energy pulse by an amount which is a monotonically increasing function of the pulse separation. In the present paper we prove the conjecture for massless quantized scalar fields in two and four-dimensional flat spacetime, and show that it is implied by the quantum inequalities.