This relativistic, time-travel spacetime is everywhere metrically flat, excepting a conical singularity. Observers following timelike geodesics can eventually encounter their past selves, aging in the opposite time sense. The spacetime is not time orientable.
“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 here.
Time is a construct that humans created to better understand our reality. Its a ruler, nothing more, nothing less.
That’s philosophically true, but mathematically, time is also an objective interval that exists regardless of our perspective. That interval doesn’t need humans to exist.
Time passes whether humans exist or not. All animals exist in time, and a consciousness is not required. Are you suggesting time didn’t exist when nothing but bacteria existed?
Time is an interval of spacetime, whether we exist to perceive it or not.
Math is another human invention, another ruler. It is the mind that experiences time, time is experienced differently based on many different inputs. Which doesn’t negate its usefulness, but it was invented by a literal Ape, with serious limitations, we have so much to learn.
It’s not. Maths is an objective measure of the world, and time exists beyond us. We define these things in our language, but they don’t need us. We didn’t create these things, we only describe them.