Emergent Gravity from Information Relation Networks via Loop Holonomy

From Loop Phase Structures to Emergent Geometry and Curvature

抄録

We propose a framework in which both gauge structures and gravity emerge from an underlying information relation network. In our previous work, we showed that minimal relational configurations naturally generate gauge symmetries through loop phase structures.
In this paper, we extend the framework toward geometry and gravity. We demonstrate that loop phase transport along closed paths defines holonomy, which provides a natural notion of discrete curvature.
By introducing an effective distance derived from relational strength, we construct an emergent metric structure from the network.
Within this formulation, curvature arising from nontrivial holonomy is interpreted as a source of effective energy, leading to an Einstein-like relation between geometry and energy.
This suggests that gravity can be understood as a macroscopic manifestation of microscopic relational curvature.
The overall picture establishes a unified origin of interactions: gauge fields arise from phase connections, while gravity arises from curvature of the same underlying relational structure.
This provides a minimal and coherent route toward unifying gauge theory and gravity from an information-theoretic perspective.