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 (RAQM), an ontological framework classifying physical properties

as invariant, classical, or intrinsically relational. RAQM grounds wave function actualization in

physical interaction rather than observer-relative facts. 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

pμ pμ = 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

(see Section 3.2.1 for the explicit response to Reeh-Schlieder and LSZ concerns). 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. We derive a consistency condition demonstrating

that RAQM’s actualization map preserves identical observable statistics at spacelike-separated points

regardless of hypersurface choice—a derived result, not a postulate—strictly forbidding superluminal

signaling via algebraic microcausality. The no-signaling result applies rigorously to the non-selective

(outcome-averaged) actualization map; conditioned branches are treated explicitly. 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/ΔEenv, and a sharp

reversibility threshold at the actualization criterion. RAQM is distinguished from Relational Quantum

Mechanics (which relativizes facts), dynamical collapse models (which ground collapse in stochastic

gravitational thresholds rather than causal interaction), 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. The companion papers RAGC and RACI extend these results to gravity, cosmology,

and biological complexity; RAHC [Sandeman, 2026d] extends the framework to the emergence of

agentic intelligence. Recent results: the Einstein field equations are the unique consistent macroscopic

description of the RA causal graph by Lovelock’s theorem [Sandeman, 2026b]; c = lP/tP is derived as

the maximum causal bandwidth rate and E = γmc2 from discrete counting alone; the Causal Firewall

threshold is proved via the Erd˝os-R.nyi percolation theorem; and the Poisson-CSG generative measure

makes the causal graph dynamics local and environment-dependent for the first time in any sequentialgrowth

formulation. Key theorems have been formally verified in Lean 4/Mathlib. A second Lean 4 file

(RA_AQFT_Proofs_v10.lean) formalises the finite-dimensional AQFT proof program and proves

the frame-independence and Rindler stationarity theorems; see the note on formal verification in the

companion paper RAGC [Sandeman, 2026b].