A new model of time travel by a conical singularity
DOI: 10.1063/10.0035455
A new model of time travel by a conical singularity lead image
The concept of time travel has long fascinated both fiction writers and physicists. The acceptance of Einstein’s general theory of relativity made time travel physically respectable, because it allows spacetimes in which the timelike curves of observers can form a closed loop. While some theories suggest exotic physics that open wormholes, author John D. Norton has proposed a simpler model in which observers, tracing out timelike curves, might meet their past selves.
An interesting difference between author Norton’s model and that of others is that the model presented here is not time-orientable, which means that it does not have a uniform, forward definition of time. Furthermore, it is matter-free and flat everywhere except for a two-dimensional singularity analogous to the singular point of a paper cone.
“A conical singularity is unlike more familiar curvature singularities,” said Norton. “No matter how close you come to the singularity in this spacetime, the spacetime geometry remains flat and regular with no indication locally of something pathological.”
A spaceship, traveling in a well-behaved region of spacetime, might then encounter this singularity and find its timelike geodesic to be deflected into its past. It would then return to the earlier, well-behaved region of spacetime and the spaceship occupants would encounter their past selves aging in the opposite time sense.
The author anticipates this model being a useful tool for teaching technical aspects of relativity theory.
“The full geometry of this spacetime model can be recovered using rather simple methods,” said Norton. “In addition to seeing the nature of the conical singularity, the analysis requires that students treat spacetime coordinates with extreme care, since they do not have their usual default physical meanings.”
Source: “A simple Minkowskian time-travel spacetime,” by John D. Norton, American Journal of Physics (2025). The article can be accessed at https://doi.org/10.1119/5.0224022 .
