In one minute

L. H. Ford and Thomas Roman start from the fact that quantum fields can have negative energy density at a point, as in the Casimir effect and squeezed light. Their earlier bound for the massless scalar field limits how large negative energy density can be, and for how long, as seen by any inertial observer, in the style of an uncertainty principle. This paper gives a much simpler derivation using plane wave modes instead of spherical waves. They derive similar quantum inequality bounds for the electromagnetic field and for the massive scalar field in two- and four-dimensional flat spacetime. The energy-time uncertainty principle itself is not an input to these bounds.

Restrictions on Negative Energy Density in Flat Spacetime