Warp Drives and Closed Timelike Curves (2309.10072v3)

Abstract: It is commonly accepted that superluminal travel may be used to facilitate time travel. This is a purely special-relativistic argument, using the fact that for observers in two frames of reference, separated by a spacelike interval, the non-causal (spacelike) future of one observer includes part of the causal past of the other. In this paper we provide a concrete realization of this argument in a curved general-relativistic spacetime, using warp drives as the means of faster-than-light travel. By generalizing the usual warp drive metric to allow for a non-unit lapse function, we allow the warp drive to switch between reference frames in a purely geometric way. With an additional modification allowing the warp drive to have compact support, this permits us to glue two warp drives together to construct a closed timelike geodesic, such that a test particle following the geodesics of the two warp drives travels back to its own past. This provides a precise mathematical model for the connection between faster-than-light travel and time travel in general relativity, and the first such model to be explicitly formulated using two warp drives. We also give a detailed discussion of weak energy condition violations in the non-unit-lapse warp drive.

• The paper mathematically demonstrates that two sequential warp drives can create a closed timelike curve by guiding a test particle along a geodesic returning to its temporal origin.
• It introduces a generalized Alcubierre metric with a variable lapse function to reconcile superluminal travel with time travel within the framework of general relativity.
• The study reveals that violations of the weak energy condition are inherent in these models, highlighting ongoing challenges in achieving physically viable warp drive spacetimes.

An Analysis of "Warp Drives and Closed Timelike Curves"

The paper by Shoshany and Snodgrass titled "Warp Drives and Closed Timelike Curves" explores the fascinating field of general relativity to explore the theoretical feasibility of time travel using warp drives. It elaborates on a general-relativistic model that links faster-than-light (FTL) travel to the creation of closed timelike curves (CTCs), which are paths in spacetime returning to the original temporal coordinates.

Warp Drives: From Science Fiction to Scientific Inquiry

Warp drives, since Alcubierre's original proposal, have primarily been a theoretical construct, suggesting that FTL travel might be possible by warping spacetime. Despite substantial challenges, such as energy conditions violations and unsustainable energy requirements, warp drives remain a significant topic in theoretical physics, especially in relation to the fundamental aspects of causality in general relativity.

Time Travel Through Superluminal Travel

The paper posits a concrete model wherein two warp drives could facilitate time travel by navigating a curved spacetime. It extends previous conceptual ideas by providing a warp drive spacetime explicitly formulated using two sequentially linked warp bubbles. The authors employ a non-trivial spacetime metric, allowing the warp drive to transition between different reference frames, thereby potentially creating a CTC. This approach is geometrically expressed using a generalization of the Alcubierre metric with a variable lapse function and compact support.

Key Results and Theoretical Implications

By scrutinizing the underlying mechanism, the authors mathematically demonstrate that, under certain conditions, a test particle following the geodesics of two such warp drives would effectively form a closed timelike path. The conditions necessary for this include sufficiently superluminal velocities of the warp bubbles which, combined with a spatial displacement, allow the traveler to encounter the past. This result elegantly connects superluminal and time travel within the framework of general relativity.

The authors address the weak energy condition (WEC), a significant criterion in understanding the feasibility of such spacetime configurations in general relativity. Despite attempts to circumvent the known issue of energy condition violations via their generalized metric, they conclude that WEC violations appear inherent to this class of spacetimes as opposed to being uniquely associated with superluminal or timelike travel constructs. Here, they argue that any connection between warp drives and negative energy requirements does not necessarily implicate FTL travel in such violations.

Future Directions and Theoretical Speculation

This research intensifies discussions around the theoretical limits posed by general relativity on FTL and time travel. Given the formulation of a closed timelike geodesic purely through spacetime geometry, theoretical advancements may explore the implications on causality, potentially revealing insights into the nature of time. Further studies could also involve investigating the broader class of warp drive metrics that might fulfill energy conditions or examining alternative formulations that remain within the realms of classical physics.

In summary, this paper provides a rigorous exploration into how warp drives might theoretically facilitate time travel. It represents a thorough investigation into the equations governing spacetime and proposes viable constructions for CTCs entirely derived from relativistic principles, while highlighting the perennial challenges posed by energy conditions. These insights contribute to the fundamental understanding of spacetime and lay the groundwork for potential breakthroughs in theoretical physics.