The Relational Universe: Interaction and the Transition of the Possible to the Actual

We argue that quantum randomness is a logical necessity arising from the nature of intrinsically relational properties — properties lacking definite states outside specific contexts of causal interaction. This motivates Relational Actualism (RA), an ontological framework classifying physical properties as invariant, classical, or intrinsically relational.

The actualization criterion is physically grounded and mathematically precise: an interaction constitutes an actualization event when it produces an irreversible increase in the quantum relative entropy of the system with respect to the vacuum reference state, ΔS(ρ‖σ₀) > 0, generating a robust, redundant causal record. The on-shell condition pᵘpᵤ = m²c² is the implementation of this entropic criterion in weakly coupled perturbative QFT; it is not the fundamental definition and does not constitute a claim of sharp spacetime localization. This criterion is basis-independent, non-perturbative, and requires no new fundamental constants.

To reconcile a globally consistent wave function with special relativity, the Tomonaga–Schwinger equation establishes a foliation-independent global update mechanism. A derived consistency condition demonstrates that the RA actualization map preserves identical observable statistics at spacelike-separated points regardless of hypersurface choice, strictly forbidding superluminal signaling via algebraic microcausality.

Three specific, discriminating empirical predictions are stated: a finite actualization propagation velocity bounded by the Lieb–Robinson speed; an environment-dependent transition duration scaling as ħ/ΔE_env; and a sharp reversibility threshold at the actualization criterion.

RA is distinguished from Relational Quantum Mechanics (which relativizes facts to observers), dynamical collapse models (which ground collapse in stochastic gravitational thresholds), decoherence-only models (which leave the outcome problem open), and Everettian Many-Worlds (which denies definite events). Classical behavior emerges dynamically when continuous actualization events eliminate all unconstrained degrees of freedom.

Recent suite results: the Einstein field equations are the unique macroscopic description of the RA causal graph by Lovelock's theorem; c = l_P/t_P is derived as the maximum causal bandwidth rate; E = γmc² follows from discrete counting alone; α_s(m_Z) = 1/√72 is proved from BDG path weight geometry; and 101 results have been formally verified in Lean 4/Mathlib across three proof files with zero sorry tags.