Three physicists at the University of Belgrade in Serbia have published a preprint on arXiv suggesting that the familiar split between three dimensions of space and one of time may emerge naturally from the way tiny geometric building blocks assemble. The paper, posted to the arXiv server and not yet peer-reviewed, reports that in roughly 85 percent of their simulated trials, randomized four-dimensional simplices organized into a spacetime with the same dimensional signature we observe, according to ScienceAlert.
Why it matters
Physics has long taken for granted that the cosmos has three spatial directions and one temporal one, a structure formalized by Hermann Minkowski, Einstein's former mathematics teacher, more than a century ago. Minkowski described space and time as a single interwoven fabric, and Einstein later added gravity to that flat picture, producing curved spacetime. What has never been settled is why the mix should take exactly this form rather than some other arrangement.
The Belgrade work does not claim to answer that question definitively. It is a toy model of quantum gravity, a framework that remains unsettled and widely debated, and it deliberately strips away real-world complications such as the laws of physics. But the authors' results hint that the dimensionality of spacetime might not need to be imposed from outside. It may instead be a byproduct of how quantum geometry fits together at the smallest scales, ScienceAlert reports.
A house of cards built from triangles
The team constructed what amounts to a miniature universe that steps down from four dimensions to zero. At the top sit four-dimensional 4-simplices, which are composed of three-dimensional tetrahedra, which in turn are made of two-dimensional triangles, then one-dimensional edges, meeting finally at zero-dimensional vertices. The structure is nested all the way down, like a hierarchical stack of cards.
The researchers then assigned random lengths to the edges of these pieces. The lower limit was set at the Planck length, about 10⁻³⁵ meters, the scale at which current physical understanding breaks down. The upper bound was drawn from the point where the Universe stops looking like a smooth continuum and begins to behave like a jagged jigsaw puzzle. Data from the Large Hadron Collider and the LIGO-Virgo gravitational wave network helped constrain the range, from the size of the observable Universe at roughly 10²⁶ meters down to about 10⁻²⁰ meters. Any jaggedness in the model would therefore appear only far below the scale of an atom, well beyond anything visible.
The simulations covered three different topologies, each built from approximately 100,000 simplices. One was a four-dimensional sphere with no boundary, because it loops back on itself. Another was a disconnected collection of four-dimensional simplices, essentially 100,000 scattered puzzle pieces, used as a control. The third configuration is described in the preprint alongside these.
The edges were then treated either as space-like, analogous to physical distances and represented with real numbers, or as time-like, analogous to time intervals and represented with imaginary numbers, or as some combination of the two. In total, the final dataset comprised more than 20 billion evaluations across the various simulations.
What the simulations turned up
When the randomized pieces were allowed to assemble purely on geometric grounds, without complex cosmic dynamics or forces, about 85 percent of runs produced a spacetime with three spatial dimensions and one temporal dimension, judged by the mathematical signatures the researchers assigned to each dimension.
Other outcomes also appeared. Roughly 6 percent of trials yielded a Euclidean signature: a frozen Universe with four spatial dimensions and no time at all. About 8 percent produced a split Universe with two dimensions of space and two of time.
These proportions held when edge lengths were treated as space-like. Treating them as time-like, or as a mixture, instead produced signatures with two or even three dimensions of time, rather than the Minkowski-style Universe we perceive.
One of the more striking findings concerned which type of edge was needed. Intuition might suggest that both space-like and time-like edges would be required to generate a temporal direction. In this model, space-like edges alone sufficed. The researchers note that edges of mismatched lengths often can only fit together in a geometry that includes a time direction.
Equally surprising, the global topology made little difference. Whether the overall shape of the Universe was a ball, a sphere, or simply a jumble of pieces had minimal effect on the outcome. That may suggest the division between space and time is set locally, or that topological differences are invisible at this level, or that they average out once enough pieces are included.
The authors conclude that future work could incorporate additional dynamics, including physical laws, and a wider variety of shapes to test "whether the spacetime signature can ultimately be understood as an emergent property of quantum geometry," as ScienceAlert reports.
The research is available as a preprint on arXiv and has not yet been peer-reviewed.
Watch for peer review and for follow-up work that adds physical dynamics to the model, which would be the next step in testing whether the 3+1 dimensional structure of our Universe really can arise from quantum geometry alone.
