A University of Jinan physicist has shown that closed timelike curves cannot exist in spacetimes with a particular global structure, limiting the result to mathematical models that meet the condition.
Hongsheng Zhang submitted a 39-page preprint to arXiv on Oct. 24. For his theorem to apply, a single-valued function must be defined throughout the spacetime, and its gradient must be lightlike and nonzero everywhere.
The proof tracks the function along a timelike path: its value keeps changing in one direction. A closed timelike curve—a path a traveler can follow as their own time advances, returning to the event where they started—would require the function to regain its starting value. That conflicts with the required one-way change.
The theorem concerns timelike paths; it does not rule out every kind of closed curve. Some closed null curves, which follow lightlike directions, remain possible under the result.
Zhang applies the test to Kundt and Robinson–Trautman spacetimes when the required coordinate is globally single-valued. A twisting lightlike direction or a coordinate that wraps around can keep this particular test from applying if no other qualifying global coordinate exists. The paper also discusses a wrapped-coordinate example where another coordinate allows the test to work. Falling outside the test does not by itself show that a closed timelike curve exists.
Time dilation is a separate effect: motion or gravity can make clocks tick at different rates. In 2010, the U.S. National Institute of Standards and Technology (NIST) reported different ticking rates for clocks separated vertically by 33 centimeters. NIST also reported a rate change after researchers altered the motion of an ion inside one clock. Those measurements concern differences in clock rates, not a return to an earlier event.
Zhang's proof establishes its result for mathematical spacetimes that meet the stated condition. The paper does not show that the real universe has the required structure.
