RUI: Constraints on Negative Energy in Field Theory and Gravitation

Central Connecticut State University, New Britain CT

Investigators

Abstract

The research discussed here deals with the implications of a very unusual form of energy. The existence of this so-called "negative energy" is allowed by the laws of quantum field theory, which describe the behavior of matter and energy on microscopic scales. Since negative energy would have repulsive gravitational effects, this work lies at the intersection of quantum field theory and Einstein's theory of gravity, general relativity. The focus of the research is the extended investigation of restrictions imposed by the laws of physics on negative energy. These generalized restrictions would involve the placement of constraints on the distribution of negative energy in both time and space. In addition, the scope of the constraints would be extended to include the effects of gravitation. Regions of negative energy also appear to be accompanied by large fluctuations in energy density, which could perhaps lead to large fluctuations in the gravitational fields produced by the negative energy. How this would affect the description of gravity, given in Einstein's theory as the curvature of the geometry of space and time, in these circumstances is currently not well understood. It is hoped to investigate this issue as well. These topics are of interest for several reasons. Situations involving negative energy, such as the Casimir effect and squeezed states of light, have been produced in the laboratory. The amounts of negative energy generated in these experiments are extremely tiny. However, if the laws of physics impose no constraints on negative energy, then one might be able to create large amounts of it and thereby produce bizarre macroscopic effects. Such effects could include: traversable wormholes (tunnels connecting otherwise distant regions of space and time), warp drives (for faster-than-light travel), time machines for travel into the past, violations of the second law of thermodynamics (e.g., refrigerators requiring no power sources), and the destruction of black holes (the remains of collapsed dead stars). However, research by Larry Ford and the author has shown that quantum field theory does impose some rather strong restrictions on negative energy. These constraints have come to be known as "quantum inequalities", and yield severe limitations on the macroscopic effects of negative energy mentioned above. Loosely speaking, they say that large negative energies can exist for only short periods of time. It has recently been realized that even the currently known quantum inequalities, although formulated as restrictions in time, can be used to rule out or constrain the ways in which negative energy can be distributed in space as well. These results, together with some explicit examples of spatial distributions of negative energy which are allowed by the laws of physics, indicate that negative energy must be subtly intertwined with positive energy in space. Must this always be the case? A major focus of the proposed investigation will be to narrow the gap between distributions which can be ruled out and those which are definitely allowed. The latter will involve the construction and analysis of additional explicit examples. This represents a continuation of my previous research and essentially aims to extend the scope of all of these results.