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, Δ S(ρ\|σ₀) > 0, generating a robust, redundant causal
record. The on-shell condition pμpμ = 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 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/Δ
Eeₙv, 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 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;
c = lP/tP is derived as the maximum causal bandwidth rate and
E = γ mc² from discrete counting alone; the Causal Firewall
threshold is proved via the Erdős-Rényi percolation theorem;
and the Poisson-CSG generative measure makes the causal graph
dynamics local and environment-dependent for the first time in any
sequential-growth 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.