Motion of inertial observers through negative energy

Recent research has indicated that negative energy fluxes due to quantum coherence effects obey uncertainty-principle-type inequalities of the form $\left|\Delta E\right|\Delta \tau \lesssim 1$. Here $\left|\Delta E\right|$ is the magnitude of the negative energy which is transmitted on a time scale $\Delta \tau$. Our main focus in this paper is on negative energy fluxes which are produced by the motion of observers through static negative energy regions. We find that although a quantum inequality appears to be satisfied for radially moving geodesic observers in two- and four-dimensional black hole spacetimes, an observer orbiting close to a black hole will see a constant negative energy flux. In addition, we show that inertial observers moving slowly through the Casimir vacuum can achieve arbitrarily large violations of the inequality. It seems likely that, in general, these types of negative energy fluxes are not constrained by inequalities on the magnitude and duration of the flux. We construct a model of a nongravitational stress-energy detector, which is rapidly switched on and off, and discuss the strengths and weaknesses of such a detector.