The Ontological Status of Physical Reality

The Ontological Status of Physical Reality Antonios Valamontes Kapodistrian Academy of Science Theorem 1. Let Mbe a mathematical structure whose internal relations generate all empirically accessible observables. If no additional non-mathematical substrate alters these relations or predictions, then identifying physical reality with Mis the most coherent and economical ontology: W ≡ M. Proof. (1) Structural Representation. All physical quantities—position, momentum, charge, spin, fields, states—are represented entirely by mathematical objects: real vectors, Hilbert rays, bundle sections, operator algebras. (2) Historical Direction. Physics consistently replaces intuitive “physical primitives” with deeper mathematical structure: particle →T∗Q, field →Γ(E),state →P(H),spacetime →Sol(Gµν ). (3) Law as Structure. Dynamics in every theory is a map within a mathematical space: Hamiltonian flow, Schrödinger evolution, geometric field equations, operator constraints. (4) Quantum-Gravity Form. Canonical quantum gravity defines the universe by the constraint ˆ HΨ = 0, a purely mathematical condition on a space of geometries. (5) No Empirical Surplus. If a substrate never changes any observable, it is ontologically idle. By parsimony, only the predictive structure need be taken as real. A structure that predicts all phenomena is, by coherence and economy, the structure that exists. 1