The dream of time travel, which has inspired generations of writers and filmmakers, is one step closer to a definitive scientific verdict. Physicist Hongsheng Zhang from Jinan University (China) has published a study on the arXiv preprint server proposing a concise mathematical justification for why returning to the past is physically impossible. The fundamental feature of the new approach is its simplicity: the proof, according to the author, fits in just three lines and does not require exotic matter, negative energy, or complex quantum anomalies that previous attempts to formalize the prohibition of time loops relied upon.
The Equation That Forgives No Loops
At the core of the proof lies the so-called "null eikonal equation"—a classical mathematical tool long used in physics to describe the propagation of light in various media and spacetime geometries. Zhang applies it to the hypothetical trajectory of a time traveler and derives a simple geometric constraint: a light beam can never move at a right angle to the path of an object undertaking temporal displacement. It follows that a certain scalar indicator along the trajectory inevitably increases monotonically, making a closed loop—returning to the starting point—mathematically unattainable. The author compares this geometry to a one-way highway where it is physically impossible to make a U-turn and head back.
Four Paths to a Single Prohibition
The new work does not emerge in a vacuum. Physics already had three main approaches explaining why closed timelike curves (CTCs) do not manifest in nature. The first is the concept of universal time: if global "clocks" always ticking forward exist in the universe, loops are ruled out a priori. The second is energy constraints: creating a time loop requires exotic matter with negative energy density, the existence of which has not been confirmed. The third is topological criteria associated with the global shape and connectedness of spacetime itself. Zhang's method occupies a fourth niche: it rejects the possibility of loops through pure algebra and differential geometry, without delving into specific cosmological models or requiring knowledge of the universe's global topology.
Light Surfaces Instead of Time Slices
Another methodological device proposed in the paper is to "slice" spacetime not along the usual surfaces of constant time, but along light surfaces—hypersurfaces determined exclusively by the geometry of the metric. This approach avoids choosing a specific coordinate system or tying the result to any observer, making the proof invariant and applicable to a wide class of metrics. Essentially, the author shows that the ban on time loops is not a consequence of some special cosmological model, but a direct consequence of the local structure of the light cone embedded in the radiation propagation equations.
When Loops Are Still Possible
It is important to emphasize that the study does not claim the absolute impossibility of CTCs in every conceivable geometry. The author explicitly points out two scenarios in which closed timelike trajectories could arise: first, near an extremely massive rotating black hole (the Kerr solution), where the spacetime structure "wraps" around the event horizon; second, if the global topology of the entire universe forms a closed loop by nature. However, in both cases, realizing the loop would require violating the basic properties of light propagation enshrined in the null eikonal equation. Thus, if anyone ever builds a "time machine," it will have to violate not just engineering constraints, but the fundamental laws of optics in curved spacetime.
Status of the Work and What's Next
At the time of publication, the study is at the preprint stage on arXiv and has not yet undergone peer review in a scientific journal. This means the formal status of the proof remains preliminary: peers may point out assumptions not covered by the proof or limitations in the class of metrics to which the argument applies. Nevertheless, the very fact of publication and the transparency of the mathematical apparatus (three lines, one classical tool) allow the community to quickly verify or refute the result. For the general audience, the conclusion of the work is simply formulated: time travel will most likely remain the realm of science fiction rather than an engineering task of the coming decades.
