I shall review the main points of combinatorial quantum gravity, a model for the emergence of dynamical geometric manifolds from random graphs, driven by the combinatorial Ollivier-Ricci curvature. In the simplest version, the manifold is a negative-curvature surface with two scales, an ultraviolet Planck length and an infrared radius of curvature. At scales larger than the latter, there appears an holographic Lorentzian picture with one additional dimension, in which geodesic observers move away from each other and see the residual slow dynamics of particles as 3D quantum mechanics.

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Combinatorial Quantum Gravity: Q-it From Bit?

  • Carlo A. Trugenberger

摘要

I shall review the main points of combinatorial quantum gravity, a model for the emergence of dynamical geometric manifolds from random graphs, driven by the combinatorial Ollivier-Ricci curvature. In the simplest version, the manifold is a negative-curvature surface with two scales, an ultraviolet Planck length and an infrared radius of curvature. At scales larger than the latter, there appears an holographic Lorentzian picture with one additional dimension, in which geodesic observers move away from each other and see the residual slow dynamics of particles as 3D quantum mechanics.