Dynamics and the Emergence of Geometry in an Information Mesh

Abstract

The idea of a graph theoretical approach to modeling the emergence of a quantized geometry and consequently spacetime, has been proposed previously, but not well studied. In most approaches the focus has been upon how to generate a spacetime that possesses properties that would be desirable at the continuum limit, and the question of how to model matter and its dynamics has not been directly addressed. Recent advances in network science have yielded new approaches to the mechanism by which spacetime can emerge as the ground state of a simple Hamiltonian, based upon a multi-dimensional Ising model with one dimensionless coupling constant. Extensions to this model have been proposed that improve the ground state geometry, but they require additional coupling constants. In this paper we conduct an extensive exploration of the graph properties of the ground states of these models, and a simplification requiring only one coupling constant. We demonstrate that the simplification is effective at producing an acceptable ground state. Moreover we propose a scheme for the inclusion of matter and dynamics as excitations above the ground state of the simplified Hamiltonian. Intriguingly, enforcing locality has the consequence of reproducing the free non-relativistic dynamics of a quantum particle.

References in corpus (12)

• Thermodynamics of Spacetime: The Einstein Equation of State
• On the Origin of Gravity and the Laws of Newton
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Minimal Length Scale Scenarios for Quantum Gravity
• Nonperturbative Quantum Gravity
• Quantum Graphity: a model of emergent locality
• Loop quantum gravity: an outside view
• The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree
• Combinatorial Quantum Gravity: Geometry from Random Bits
• Random Holographic "Large Worlds" with Emergent Dimensions
• Gauge fixing in Causal Dynamical Triangulations
• Critical Space-Time Networks and Geometric Phase Transitions from Frustrated Edge Antiferromagnetism

Cited by in corpus (5)

• Enhanced Forman curvature and its relation to Ollivier curvature
• Accelerated Particle Detectors with Modified Dispersion Relations
• Fundamental length scale and the bending of light in a gravitational field
• Dispersive vacuum as a decoherence amplifier of an Unruh-DeWitt detector
• The Quantum Vacuum of Spacetime with a Fundamental Length