A Simple Minkowskian Time-Travel Spacetime

Summary

This paper presents a simple, relativistic time-travel spacetime that is everywhere metrically flat, except for a conical singularity. Observers following timelike geodesics can encounter their past selves, aging in the opposite time sense.

Highlights

• The spacetime is not time-orientable.
• The singularity is a two-dimensional surface enclosed within a four-dimensional space.
• Timelike geodesics are deflected around the singularity and reversed in their direction.
• Observers can travel back in time without acceleration.
• The spacetime is constructed by identifying events in a Minkowski spacetime.
• The light cone structure is deflected around the singularity.
• The metrical structure is singular at the origin.

Key Insights

• The spacetime presented in this paper is a novel example of a time-travel spacetime that is everywhere metrically flat, except for a conical singularity. This singularity is a two-dimensional surface enclosed within a four-dimensional space, and it plays a crucial role in enabling time travel.
• One of the most interesting features of this spacetime is that observers following timelike geodesics can encounter their past selves, aging in the opposite time sense. This means that an observer can travel back in time and meet their younger self, but they will be aging in the opposite direction.
• The spacetime is constructed by identifying events in a Minkowski spacetime, which is a well-known spacetime in general relativity. This construction method allows for the creation of a spacetime with a conical singularity, which is necessary for time travel to occur.
• The light cone structure in this spacetime is deflected around the singularity, which means that light and other forms of radiation will be bent around the singularity. This deflection is crucial for time travel to occur, as it allows observers to move through the spacetime in a way that would not be possible in a flat spacetime.
• The metrical structure of this spacetime is singular at the origin, which means that the curvature of the spacetime is infinite at this point. This singularity is a result of the conical structure of the spacetime and is necessary for time travel to occur.
• The spacetime presented in this paper is not time-orientable, which means that it is not possible to define a consistent arrow of time throughout the spacetime. This is a result of the conical singularity and the deflection of the light cone structure around it.
• The fact that observers can travel back in time without acceleration is a result of the deflection of the light cone structure around the singularity. This deflection allows observers to move through the spacetime in a way that would not be possible in a flat spacetime, and it enables time travel to occur.

Mindmap

Citation

Norton, J. D. (2024). A Simple Minkowskian Time-Travel Spacetime (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.16272