Classical and quantum flux energy conditions for quantum vacuum states

TL;DR

This paper develops classical and quantum flux energy conditions based on flux measurements by observers, showing the quantum version (QFEC) holds broadly for vacuum states, unlike the classical FEC.

Contribution

It introduces flux energy conditions (FEC and QFEC) as alternatives to classical energy conditions, with the quantum version applicable to a wide range of vacuum states.

Findings

Classical FEC is satisfied in some situations.

Quantum FEC (QFEC) holds for natural quantum vacuum states.

The applicability of these conditions to nonvacuum states remains uncertain.

Abstract

The classical energy conditions are known to not be fundamental physics -- they are typically violated by semiclassical quantum effects. Consequently, some effort has gone into finding possible semiclassical replacements for the classical energy conditions -- the most well developed being the Ford-Roman quantum inequalities. In the current article we shall instead develop classical and quantum versions of a "flux energy condition" (FEC and QFEC) based on the notion of constraining the possible fluxes measured by timelike observers. The naive classical FEC will be seen to be satisfied in some situations, and even for some quantum vacuum states, while its quantum analogue (the QFEC) is satisfied (for naturally defined quantum vacuum states) under a rather wide range of conditions. The situation for completely general (nonvacuum) quantum states is less clear.