Within the IKKT model, space and time are not fundamental constants but rather emerge from the collective behavior of vast matrices. Researchers at the University of Tokyo and Kyoto University have shown that under certain conditions, these matrices spontaneously generate a four-dimensional geometry resembling our observable universe.
According to a paper published on arXiv in May 2026, a group led by Professor Hideo Matsumoto conducted numerical simulations using a supercomputer. The team analyzed a 10-dimensional matrix with dimensions up to 32×32, monitoring the spatial distribution of its eigenvalues. At low temperatures, the matrices aligned in a way that three spatial dimensions expanded while the remainder remained compact.
This process is similar to how threads in a ball of yarn suddenly form a stable fabric when subjected to specific tension. Here, the matrix eigenvalues serve as the threads, and the tension corresponds to the temperature parameter. The resulting structure is not a chaotic arrangement but a smooth spacetime with a nearly flat metric.
This finding is crucial for quantum gravity, as it offers a specific mechanism for classical space to emerge from purely quantum degrees of freedom without being manually defined. If validated by larger-scale simulations, this breakthrough would advance a non-perturbative description of string theory and potentially clarify the nature of the early universe.
The research suggests that matrix models can account for both static properties and the dynamics of expanding space. This discovery redefines where we should search for quantum gravity effects—viewing them not as distortions in pre-existing space, but as part of the fundamental assembly of space itself from more basic components.
