Quantum Field Theory Constrains Traversable Wormhole Geometries

TL;DR

This work derives a quantum inequality bound on negative energy densities in Minkowski space and argues it extends to curved spacetimes on scales small compared to local curvature radii or boundaries. Applying this bound to static, spherically symmetric Morris–Thorne wormholes shows that macroscopic traversable geometries require either Planck-scale throats or extreme disparities among characteristic length scales, typically concentrating negative energy in ultra-thin bands. The analysis covers several explicit wormhole models (Φ=0 with various b(r), proximal Schwarzschild, MTY) and yields general bounds that generically preclude large, smoothly distributed exotic matter. Overall, quantum field theory thus imposes severe constraints on the existence of macroscopic traversable wormholes, with MTY-like configurations remaining only with substantial caveats about stability and practicality.

Abstract

Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable.