Quantum interest for scalar fields in Minkowski spacetime

TL;DR

This paper proves the quantum interest conjecture for scalar fields in 4D Minkowski spacetime, showing that negative energy fluxes are always balanced by larger positive fluxes, with implications for thermodynamics and potential extensions to other fields.

Contribution

It provides a rigorous proof of the quantum interest conjecture for scalar fields in flat spacetime, extending understanding of negative energy constraints in quantum field theory.

Findings

Quantum interest holds for scalar fields in 4D Minkowski spacetime.

Negative energy fluxes are always preceded or followed by larger positive fluxes.

Implications for the second law of thermodynamics and potential applicability to other fields.

Abstract

The quantum interest conjecture of Ford and Roman states that any negative energy flux in a free quantum field must be preceded or followed by a positive flux of greater magnitude, and the surplus of positive energy grows the further the positive and negative fluxes are apart. In addition, the maximum possible separation between the positive and negative energy decreases the larger the amount of negative energy. We prove that the quantum interest conjecture holds for arbitrary fluxes of non-interacting scalar fields in 4D Minkowski spacetime, and discuss the consequences in attempting to violate the second law of thermodynamics using negative energy. We speculate that quantum interest may also hold for the Electromagnetic and Dirac fields, and might be applied to certain curved spacetimes.