New research involving one of physics’ most enduring mysteries—whether time travel can be practically achieved—has revealed a new condition that may mean those hoping to travel back in time are out of luck.
In a new study by researcher Hongsheng Zhang, investigating the mathematical foundations of time travel, suggests that journeys to the past are likely to be impossible, at least according to certain theoretical models of spacetime.
The research, featured in a recent study uploaded to the preprint server arXiv, examined what physicists call closed time-like curves, a kind of hypothetical pathway through spacetime that, according to some models, may allow a prospective time traveler to travel into its own past, potentially creating the kinds of paradoxes long associated with such theoretical temporal journeys.
The Mathematics of Time Travel
While such travel through time has long been recognized as a theoretical possibility consistent with Einstein’s general theory of relativity, such trajectories are only permitted under certain mathematical conditions. However, a key issue involves determining which spacetimes can support them.
In Zhang’s recent research, he introduces a new and surprisingly simple mathematical basis for excluding closed time-like curves. At the heart of this is a single equation, which Zhang uses to describe a function whose gradient is everywhere light-like, or null.
“We prove that a spacetime admitting a globally defined function whose gradient is everywhere null cannot contain a closed timelike curve, and that the hypothesis is logically independent of stable causality rather than weaker than it,” Zhang writes.
But what, precisely, does this mean?
In simple terms, Zhang argues that certain kinds of spacetime have a built-in mathematical rule that prevents time from looping backward on itself, and that, relatively speaking, he has found a simple way to demonstrate it.
A Staircase Through Time
As an example, imagine someone walking up a staircase within a building, which, as it ascends, may allow you to turn corners and change direction, or even walk in circles around the building’s interior.
However, an important rule exists here: as long as you are proceeding up the staircase, you are also required to be moving a little farther upward. Under such conditions, you could never follow a path that would ever bring you back to where you started—no matter how many times you walk around the interior of the building, following the staircase will always only carry you to higher levels, and never back to your starting point.
In essence, Zhang’s mathematics demonstrates a similar idea, but with relation to spacetime: it is a mathematical quantity that must continually increase as an object moves along any physically possible “staircase” or path through time. The result is that an object following such pathways is unable to eventually come back to its starting point in spacetime.
What Makes This Approach Different?
In the past, physicists have often relied on much more complicated mathematical tests to try and decipher whether certain spacetime conditions may permit time loops.
By contrast, Zhang’s approach looks for a single mathematical feature—a quantity that changes in a very specific way across all spacetime—as opposed to examining all the different properties of a hypothetical universe.
By describing its mathematical gradient as “null,” Zhang essentially means it is associated with the geometry of light-like directions.
Of fundamental significance to Zhang’s theory is that if this quantity does exist consistently throughout the spacetime region in question, it must always change in one direction along the path of a prospective time traveler moving slower than light.
Because of this unique constraint determined in Zhang’s calculations, he argues that researchers are provided a new method of ruling out time loops without having to rely on many past assumptions about the theoretical mechanics of time travel.
A New Perspective on Time Loops
Applying this approach, Zhang establishes that two significant “families” of theoretical spacetimes, which physicists call Kundt and Robinson–Trautman geometries, are not likely to contain closed time-like curves in cases where the required “null” coordinate is globally defined.
“We establish for the first time that no Kundt spacetime and no Robinson–Trautman spacetime can contain a closed timelike curve on any region where the null coordinate is globally single valued, whatever the cosmological constant and the rotation one form, which settles a question left open for gyratonic waves,” Zhang writes.
Zhang’s findings present a new approach to past studies involving mathematical models where hypothetical time loops are present.
Overall, while his research does not eliminate every theoretical scenario enabling time travel, per se, it does present a new mathematical tool that could help physicists determine conditions when spacetime geometries essentially make travel through time into the past an impossibility.
Zhang’s study, “A no-go theorem for closed timelike curves in globally null-foliated spacetimes,” appeared at arXiv.org on October 24, 2026.
Micah Hanks is the Editor-in-Chief and Co-Founder of The Debrief. A longtime reporter on science, defense, and technology with a focus on space and astronomy, he can be reached at micah@thedebrief.org. Follow him on X @MicahHanks, and at micahhanks.com.