More than a hundred years ago, a pioneering thinker changed the way we understand space and time. He told us that both are intertwined in a fabric that permeates the cosmos, comprising three dimensions of space and one dimension of time. The name of this now famous visionary? The mustachioed Hermann Minkowski, of course, Albert Einstein’s mathematics teacher. And no, he didn’t flunk Einstein, who then added gravity to flat “Minkowski spacetime” and “gave birth” to curved spacetime. In fact, it can be said that Einstein suspended Hermann, as Einstein considered Hermann’s way of thinking to be “superfluous knowledge.” At first, anyway. But why does the Universe have three spatial dimensions and one temporal dimension? A strange new mathematical theory offers a surprising possibility: it’s all because of the invisible building blocks, like puzzle pieces or LEGO (or even K’NEX) that make up the cosmos. In a preprint paper published on arXiv, which has not yet been peer-reviewed, a trio of physicists from the University of Belgrade in Serbia simulated different cosmic geometries, starting from four-dimensional virtual triangles, to see if they could give rise to our familiar combination of three dimensions of space and one of time. The answer is yes, absolutely. More or less. The authors used a toy model of quantum gravity, itself mysterious and debated, to investigate some complex cosmic mechanics without the complicated complications of the real Universe, such as the laws of physics. This framework modeled what one could consider an immensely miniature Universe, decreasing from four to zero dimensions, like a hierarchical house of cards. It started with the four-dimensional simple 4s, which are made of three-dimensional tetrahedra, which are made of two-dimensional triangles, which are made of one-dimensional edges, which meet at zero-dimensional vertices. Like a famous quote about turtles sustaining the world, it’s very simple! A four-dimensional simplex building block. (Djordjevic et al., arXiv, 2026) The researchers then randomized the edge lengths of these pieces, setting the minimum at the Planck length, a scale of 10 to 35 meters that represents the breakdown of our physical understanding. The upper limit of this scale is the point at which the Universe stops behaving as a smooth continuum and begins to act as an irregular puzzle. Observations from the Large Hadron Collider and the LIGO-Virgo gravitational wave network help establish the size range: from the size of the entire Universe, about 1026 meters, to a scale of 10 to 20 meters. Therefore, any irregularities would only appear on a scale much smaller than the size of an atom, which is not even visible. The researchers also considered three different topologies, or cosmic landscapes, composed of approximately 100,000 simplices in three configurations. First, a four-dimensional ball with a boundary. Secondly, a four-dimensional sphere without limits, because it twists around itself. And third, a disconnected set of simple four dimensions, like 100,000 scattered puzzle pieces used as a control. Finally, the researchers treated all edges of the pieces as spaces (similar to physical distances, represented by real numbers) or as temporal (similar to time intervals, represented by imaginary numbers, or a combination of both). In total, their final data set included more than 20 billion evaluations of these various simplex-based simulations. So, did a four-dimensional ‘Universe’ emerge? Surprisingly, yes. When you throw a bunch of random puzzle pieces into a blender, removing complex cosmic dynamics and forces and letting them assemble geometrically, up to about 85 percent of the time they organize themselves into a space-time with three spatial dimensions and one temporal dimension, based on the mathematical signatures the researchers assigned to these dimensions. Other strange configurations also arise. About 6 percent of the essays give a Euclidean signature: a frozen universe with four spatial dimensions and no time. And interestingly, about 8 percent of the tests yielded a divided Universe, with two dimensions of space and two dimensions of time. However, this is only when you treat the edge lengths as if they were spaces. Treating them as temporal, or as a mixture, produces signatures with two or even three dimensions of time, rather than the Minkowski-style Universe we perceive as reality. So this presented one of the biggest surprises: one would think that both spatial and temporal borders would be necessary. However, in this model, spatial edges alone were sufficient: edges of mismatched lengths can often only fit a geometry that includes a temporal direction. Equally surprising is that topology did not matter, making little difference whether the overall shape of the Universe was a ball, a sphere or simply a jumble of puzzle pieces, perhaps suggesting that the division between space and time is established locally. Either that topological differences are invisible or averaged out with enough puzzle pieces. Future research may include other dynamics, such as physical laws and various shapes, to further test “whether the spacetime signature can ultimately be understood as an emergent property of quantum geometry,” the researchers conclude. The research is available as a preprint on arXiv and has not yet been peer-reviewed. This article was fact-checked by Fiona MacDonald and edited by Fiona MacDonald. While we take pride in our process, we are human. If you spot an error, please let us know.
