Quantum Field Theory Constrains Traversable Wormhole Geometries

TL;DR

This paper uses quantum field theory constraints on negative energy to argue that macroscopic traversable wormholes are highly unlikely due to the required energy conditions.

Contribution

It extends quantum energy bounds to curved spacetimes and applies them to wormholes, revealing fundamental limitations on their size and energy distribution.

Findings

Traversable wormholes must be Planck-sized or have extreme scale discrepancies.

Negative energy must be confined to very thin regions, making large wormholes improbable.

Quantum bounds strongly restrict the feasibility of macroscopic traversable wormholes.

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.