A Superluminal Subway: The Krasnikov Tube

TL;DR

This paper explores the Krasnikov tube, a spacetime construct allowing superluminal one-way travel without causality violations, but still requiring unphysical negative energy densities, thus questioning its practical feasibility.

Contribution

It generalizes the Krasnikov metric to four dimensions, demonstrating how to create superluminal round-trip travel and constructing a system of tubes to form a time machine.

Findings

Krasnikov tubes enable superluminal round-trip travel.

Two non-overlapping tubes can form a time machine.

Negative energy requirements remain unphysical and large.

Abstract

The ``warp drive'' metric recently presented by Alcubierre has the problem that an observer at the center of the warp bubble is causally separated from the outer edge of the bubble wall. Hence such an observer can neither create a warp bubble on demand nor control one once it has been created. In addition, such a bubble requires negative energy densities. One might hope that elimination of the first problem might ameliorate the second as well. We analyze and generalize a metric, originally proposed by Krasnikov for two spacetime dimensions, which does not suffer from the first difficulty. As a consequence, the Krasnikov metric has the interesting property that although the time for a one-way trip to a distant star cannot be shortened, the time for a round trip, as measured by clocks on Earth, can be made arbitrarily short. In our four dimensional extension of this metric, a ``tube'' is constructed along the path of an outbound spaceship, which connects the Earth and the star. Inside the tube spacetime is flat, but the light cones are opened out so as to allow superluminal travel in one direction. We show that, although a single Krasnikov tube does not involve closed timelike curves, a time machine can be constructed with a system of two non-overlapping tubes. Furthermore, it is demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes, also involve unphysically thin layers of negative energy density, as well as large total negative energies, and therefore probably cannot be realized in practice.