`Operational' Energy Conditions

TL;DR

This paper introduces an 'operational' weak energy condition for quantum fields, suggesting that local measurement limitations prevent negative energy densities from producing exotic spacetime effects, thus impacting theories involving wormholes and cosmic censorship.

Contribution

It proposes an operational perspective on energy conditions in quantum fields, demonstrating that measurement constraints prevent negative energy densities from causing exotic phenomena.

Findings

Operational energy condition holds for quantum fields in Minkowski space.

Quantum measurement limitations prevent verification of negative energy densities.

Negative energy effects are likely self-defeating due to measurement constraints.

Abstract

I show that a quantized Klein-Gordon field in Minkowski space obeys an `operational' weak energy condition: the energy of an isolated device constructed to measure or trap the energy in a region, plus the energy it measures or traps, cannot be negative. There are good reasons for thinking that similar results hold locally for linear quantum fields in curved space-times. A thought experiment to measure energy density is analyzed in some detail, and the operational positivity is clearly manifested. If operational energy conditions do hold for quantum fields, then the negative energy densities predicted by theory have a will-o'-the-wisp character: any local attempt to verify a total negative energy density will be self-defeating on account of quantum measurement difficulties. Similarly, attempts to drive exotic effects (wormholes, violations of the second law, etc.) by such densities may be defeated by quantum measurement problems. As an example, I show that certain attempts to violate the Cosmic Censorship principle by negative energy densities are defeated. These quantum measurement limitations are investigated in some detail, and are shown to indicate that space-time cannot be adequately modeled classically in negative energy density regimes.