NEGATIVE ENERGIES AND THE LIMIT OF CLASSICAL SPACE–TIME

Abstract

Relativistic quantum field theories predict negative energy densities, contravening a basic tenet of classical physics and a fundamental hypothesis of the deepest results in classical general relativity. These densities may be sources for exotic general relativistic effects, and may also lead to pathologies. Combining Ford's "quantum inequality" with quantum restrictions on measuring devices, we present an argument that these densities nevertheless satisfy a sort of "operational" positivity: the energy in a region, plus the energy of an isolated device designed to detect or trap the exotic energy, must be non-negative. This will suppress at least some pathological effects. If we suppose also that Einstein's field equation holds, then no local observer can measure the geometry of a negative energy density regime accurately enough to infer a negative energy density form the curvature. This means that the physics of a negative energy regime cannot be adequately modeled by a classical space–time.