The model reveals geometric unification of key physical theories and phenomena in the universe, suggesting new insights.
In 1899, Max Planck introduced the fundamental constants that now bear his name, combining the gravitational constant G, the speed of light c, and the reduced Planck's constant ħ to define natural units of length, time, and mass. The Planck length and Planck mass emerged as the scales at which quantum effects of gravity should become dominant — a transition zone where classical general relativity (GR) and quantum mechanics (QM) intersect. Planck himself viewed these units as theoretical curiosities, unaware that they hinted at a discrete structure underlying spacetime. We propose that spacetime at the Planck scale is composed of a grid — a lattice — of rhombic dodecahedral voxels with fractal boundaries. The unique properties of this shape impart it with the specific qualities and characteristics of the observed universe through emergent geometric rules. Through this single geometric structure, the Fractal Planck Voxel model (FPV) fully realizes the transition zone that Planck’s work hinted at over 125 years ago. The FPV model derives general relativity, quantum mechanics, the Standard Model gauge groups, three generations, particle masses, and mixing angles, all from voxel symmetry and triangular modes on rhombic faces, with the cosmological constant serving as the energy of fractal subdivision. The model also addresses numerous longstanding problems and questions in physics — from the collapse of the wave function to neutrino masses, dark matter, dark energy, the origin of the Higgs, and more. The fact that the FPV model does all of this while remaining consistent with all current observations — without additional fields, particles, dimensions, or fine-tuned parameters — lends strong credence to its validity as a unifying theory.
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Carignan et al. (2026) studied this question.
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