PIRSA:15050020

Self-organization of a 4D universe

APA

Trugenberger, C. (2015). Self-organization of a 4D universe. Perimeter Institute. https://pirsa.org/15050020

MLA

Trugenberger, Carlo. Self-organization of a 4D universe. Perimeter Institute, May. 07, 2015, https://pirsa.org/15050020

BibTex

          @misc{ pirsa_15050020,
            doi = {10.48660/15050020},
            url = {https://pirsa.org/15050020},
            author = {Trugenberger, Carlo},
            keywords = {Quantum Gravity},
            language = {en},
            title = { Self-organization of a 4D universe},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {may},
            note = {PIRSA:15050020 see, \url{https://pirsa.org}}
          }
          

Carlo Trugenberger InfoCodex Semantic Technologies AG , Switzerland

Collection
Talk Type Scientific Series
Subject

Abstract

I propose a quantum gravity model in which the fundamental degrees of freedom are pure 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 arising between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension. The model has three quantum phases: a mean field phase in which the spectral and Hausdorff dimensions coincide and are larger then 4. A fluctuations-dominated phase in which the Hausdorff dimension can only be 4 and the spectral dimension is lower than the Hausdorff dimension and a disordered phase in which there is no space-time interpretation. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. An ultraviolet fixed point at the lower critical dimension of the Ising model implies the absence of space-time at very small scales. At finite temperatures the universe 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 unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits also macroscopic black hole configurations corresponding to graphs containing holes with no space time inside and around which there are "Schwarzschild-like horizons" with a lower spectral dimension and an entropy proportional to their surface.