Relational Transition Networks: Toward an Atemporal Foundation of Physics

We introduce Relational Transition Networks (RTN), an atemporal framework for fundamental physics in which time is not treated as a primitive entity. Physical reality is modelled as a small category whose objects are relational states and whose morphisms are admissible transitions governed by local transition programs. Within this framework, temporal order, causality, simultaneity (as incomparability in a partial order), and spatial geometry are proposed to emerge from the relational structure of transitions. RTN admits a quantum formulation based on transition amplitudes and suggests a formal correspondence between an atemporal path-sum construction and the Feynman path integral in the continuum limit, motivated by the Trotter–Kato theorem. A transition cost function defined on the network further induces an emergent information-geometric structure. The framework is presented as a foundational proposal toward an atemporal description of physical reality and identifies several open problems connecting quantum theory, geometry, and quantum gravity.