Simulating the Geometry of the Cosmos
Physicists at the University of Belgrade have proposed a new mathematical toy model simulating quantum gravity to explain why our universe features three spatial dimensions and one temporal dimension. Published as a preprint on arXiv on November 2, 2026, and reported by ScienceAlert, the simulation reveals that randomized building blocks assemble into a spacetime with three spatial dimensions and one time dimension roughly 85 percent of the time. This finding suggests that the familiar dimensional mix of our reality may emerge naturally from fundamental geometric constraints rather than fine-tuned physical laws.
For more than a century, theoretical physics has relied on the foundational framework established by Hermann Minkowski, Albert Einstein’s mathematics teacher. Minkowski spacetime wove space and time into a four-dimensional continuum comprising three spatial dimensions and a single temporal dimension. While Einstein initially dismissed Minkowski’s geometric formulation as superfluous learning, he later incorporated it to build his theory of general relativity. Yet, despite centuries of scientific progress, the fundamental reason behind this specific 3+1 dimensional split has remained an enduring mystery in theoretical physics.
Building Blocks of Quantum Gravity
To investigate this cosmic puzzle without the complications of standard physical laws, the research team from Serbia constructed a toy model of quantum gravity. This framework simulated a miniature universe scaling down from four dimensions to zero, utilizing virtual four-dimensional triangles known as 4-simplices. These geometric building blocks are composed of three-dimensional tetrahedra, two-dimensional triangles, and one-dimensional edges converging at zero-dimensional vertices. The investigators randomized the edge lengths of these pieces, establishing a lower bound at the Planck length—approximately 10 to the power of minus 35 meters—where conventional physical understanding breaks down and spacetime transitions from a smooth continuum into a jagged configuration.
To contextualize these microscopic scales, researchers noted that experimental observations from the Large Hadron Collider and the LIGO-Virgo gravitational wave network constrain our physical understanding across ranges spanning from the scale of the entire universe down to 10 to the power of minus 20 meters. Consequently, any geometric jaggedness at the Planck scale remains far below atomic dimensions and completely imperceptible to current instruments. The Belgrade team tested approximately 100,000 simplices across three distinct global topologies: a four-dimensional ball with a boundary, a four-dimensional sphere without a boundary, and a disconnected control set of scattered simplices.
Emergence of Familiar Spacetime Signatures
The researchers treated the edge lengths of the geometric pieces either as space-like, representing physical distances through real numbers, or as time-like, representing intervals through imaginary numbers. Across more than 20 billion individual simulation evaluations, the randomized geometric pieces assembled into a 3+1 dimensional spacetime roughly 85 percent of the time. The analysis also uncovered alternative configurations, including frozen universes with four spatial dimensions and no time in about 6 percent of trials, and split universes featuring two spatial and two temporal dimensions in approximately 8 percent of trials, provided the edge lengths were treated strictly as space-like.
A major surprise in the findings was that space-like edges alone were sufficient to generate time dimensions, as mismatched lengths frequently fit together exclusively through geometries that incorporate a time direction. Furthermore, the global topology made little difference, indicating that the split between space and time is established locally rather than being dictated by the universe’s overall shape. The authors note that future research must incorporate complex physical laws and varied shapes to confirm whether spacetime signatures represent a truly emergent property of quantum geometry.