van Vleck determinants: traversable wormhole spacetimes

TL;DR

This paper computes the van Vleck determinant in traversable wormhole spacetimes, revealing that attempts to create time machines generally lead to disruptive vacuum effects, supporting Hawking's chronology protection conjecture, with complex configurations possibly evading it.

Contribution

It extends junction condition formalism to compute the van Vleck determinant in wormholes, analyzing implications for chronology protection and time machine feasibility.

Findings

Single wormholes produce large vacuum polarization effects disrupting time travel.

Multi-wormhole configurations can suppress vacuum effects, approaching Planck scale physics.

Full quantum gravity analysis is needed for definitive conclusions.

Abstract

Calculating the van Vleck determinant in traversable wormhole spacetimes is an important ingredient in understanding the physical basis behind Hawking's chronology protection conjecture. This paper presents extensive computations of this object --- at least in the short--throat flat--space approximation. An important technical trick is to use an extension of the usual junction condition formalism to probe the full Riemann tensor associated with a thin shell of matter. Implications with regard to Hawking's chronology protection conjecture are discussed. Indeed, any attempt to transform a single isolated wormhole into a time machine results in large vacuum polarization effects sufficient to disrupt the internal structure of the wormhole before the onset of Planck scale physics, and before the onset of time travel. On the other hand, it is possible to set up a putative time machine built out of two or more wormholes, each of which taken in isolation is not itself a time machine. Such ``Roman configurations'' are much more subtle to analyse. For some particularly bizarre configurations (not traversable by humans) the vacuum polarization effects can be arranged to be arbitrarily small at the onset of Planck scale physics. This indicates that the disruption scale has been pushed down into the Planck slop. Ultimately, for these configurations, questions regarding the truth or falsity of Hawking's chronology protection can only be addressed by entering the uncharted wastelands of full fledged quantum gravity.