Quantum Gravity as an Information Network: Self-Organization of a 4D Universe
| Autor: | Trugenberger, Carlo A. |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Phys. Rev. D 92, 084014 (2015) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.92.084014 |
| Popis: | I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension: it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with "Schwarzschild-like" horizons with a lower spectral dimension. Comment: Revised version, to appear in Physical Review D |
| Databáze: | arXiv |
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