The Make Real Equation: A Unified Quantum Collapse Law Derived from Self-Field Theory

Abstract

The Make Real Equation: A Unified Quantum Collapse Law from Self‑Field Theory T.M. NguyenIndependent Researcher March 22, 2026 ABSTRACT We present a derivation of the Make Real equation, a probability law governing quantum collapse that emerges from Self‑Field Theory (SFT). Starting from three primitives — space, Selflitons (stable topological knots), and coupling — we construct a field‑theoretic Lagrangian (Skyrme type with a Wess‑Zumino‑Witten term) that describes the interaction between a quantum system (interface) and a finite population of observers. The irreversible recording of a definite outcome, called an etebuda, is identified with wavefunction collapse. The probability for a given outcome is determined by the Path of Least Resistance, a thermodynamic principle that weights outcomes by their action cost, competition from other interfaces, and topological superselection. The resulting expression — the Make Real equation — unifies the Schrödinger evolution with a physical collapse mechanism, resolves the measurement problem, and predicts the recently observed bait‑unit effect in superconducting qubits. 1. INTRODUCTION Quantum mechanics is famously silent on what constitutes a measurement and what triggers wavefunction collapse. The Schrödinger equation describes unitary evolution, but when a measurement occurs, the state appears to jump to an eigenstate with probability given by the Born rule. The measurement problem is the lack of a physical account of this transition. Self‑Field Theory (SFT) [1] provides such an account by introducing a finite population of physical observers — Selflitons — that couple to quantum systems and irreversibly record definite outcomes. SFT is built on three primitives: • Space as the fundamental continuous substrate. • Selflitons as stable topological knots in space, formed during early‑universe symmetry breaking, finite in number (~10⁸⁰) and carrying a conserved winding number B. • Coupling as resonance between a Selfliton and any system generating coherent, structured superpositions (an interface). When a Selfliton couples, it undergoes an irreversible internal update called an etebuda, which constitutes wavefunction collapse. The probability of a particular outcome follows a thermodynamic principle: the Path of Least Resistance — outcomes with lower total “cost” are more likely. In this paper we attempt to derive the resulting probability law, which we call the Make Real equation. It combines the Schrödinger amplitude with SFT factors accounting for action cost, competition among finite observers, and topological superselection. We show that the equation predicts the bait‑unit effect — a counterintuitive increase of qubit coherence when neighboring qubits are active — which has been experimentally confirmed [2]. The Make Real equation thus provides a unified, testable, and physically grounded resolution of the measurement problem. 2. SELF‑FIELD THEORY PRIMITIVES We summarize the three primitives; full details are in [1]. • The Self-Field is a continuous, universal field that can support topological solitons. It is not spacetime in the relativistic sense, but the underlying substrate. • Selflitons are stable, topologically protected solutions of a nonlinear field theory with winding number B. They formed during a symmetry‑breaking transition in the early universe and are finite in number, N_SL ~ 10⁸⁰. • Coupling is the resonant interaction between a Selfliton and an interface — any physical system that generates coherent, structured informational patterns. In quantum mechanics, the interface is the quantum system (e.g., a qubit, a particle) and its environment. When a Selfliton couples, it records an etebuda — an irreversible update of its internal state. This recording is the collapse. 3. THE SELF‑FIELD LAGRANGIAN The dynamics of the Self‑Field are described by a Skyrme‑type candidate Lagrangian with a Wess‑Zumino‑Witten (WZW) term. The field U(x) takes values in SU(N) (or a suitable Lie group). The free part is ℒ_SF = (f²/2) Tr(∂_μ U† ∂^μ U) + (1/(32 e²)) Tr([∂_μ U† U, ∂_ν U† U]²) − V(U), where f and e are constants. This Lagrangian admits stable soliton solutions (Selflitons) with a conserved topological current J^μ_B = (1/(24π²)) ε^{μνρσ} Tr(U† ∂_ν U U† ∂_ρ U U† ∂_σ U). The winding number B = ∫ d³x J⁰_B is an integer invariant. The interaction with a quantum interface (e.g., a particle described by a field φ) is given by ℒ_coupling = − (g/Λ²) J^μ_B A_μ[φ], where A_μ[φ] is a composite field constructed from the interface degrees of freedom (e.g., the electromagnetic current). The coupling is weak because Λ is large. The WZW term, ℒ_WZW = (iΓ/(240π²)) ∫ d⁵x ε^{μνρστ} Tr(U† ∂_μ U ··· U† ∂_τ U), is topological; it depends only on the homotopy class of U and breaks time‑reversal symmetry. Crucially, it quantizes the action change for processes that change the winding number: ΔS = 2πΓ per unit change of B. This quantization defines the fundamental unit of recording — the etebuda — and makes the process irreversible. 4. THE PATH OF LEAST RESISTANCE AND COLLAPSE PROBABILITY When a Selfliton couples to an interface, it must update its internal state. The possible outcomes correspond to eigenstates |i⟩ of the measured observable. The probability of outcome i is determined by the Path of Least Resistance: the Selfliton follows the trajectory that minimizes the total “cost” of recording. The cost has three independent contributions, which in the Euclidean path integral appear as exponential weights: 1. Quantum action cost – from the classical action of the coupled system. In the Euclidean path integral, the amplitude for outcome i is proportional to exp(−ΔS_i), where ΔS_i is the change in action. The WZW term quantizes the action in units of ℏ_eff = 2πΓ, so the weight becomes exp(−ΔS_i / ℏ_eff). 2. Thermodynamic cost of the interface – for a biological interface, the internal free energy cost ΔF_i enters via a Boltzmann factor exp(−ΔF_i / k T_eff), where T_eff = T/Φ_i and Φ_i is the integrated information of the interface (IIT). For non‑biological systems, this factor is omitted (or set to 1). 3. Competition cost – Because Selflitons are finite, many interfaces compete for their attention. If there are N_bait other active interfaces in the vicinity, the effective coupling rate to the target is reduced by a factor 1/(1 + ζ N_bait), where ζ depends on the geometry and gradient steepness. Additionally, the WZW term enforces topological superselection: only outcomes compatible with the Selfliton’s winding number B are allowed. This is represented by a Kronecker delta δ_{B,B_i}. Thus, the total probability for outcome i (given that a coupling event occurs) is proportional to the product of these factors: P_i ∝ 1/(1 + ζ N_bait) · exp(−ΔS_i / ℏ_eff) · exp(−ΔF_i / k T_eff) · δ_{B,B_i}. For a simple quantum system (no biological interface), the ΔF_i term is dropped. 5. THE MAKE REAL EQUATION Between coupling events, the quantum state evolves unitarily according to the Schrödinger equation: iℏ d/dt |ψ(t)⟩ = H |ψ(t)⟩. The probability that the system collapses to outcome i at time t when a Selfliton couples is then proportional to the Born weight |⟨i|ψ(t)⟩|² multiplied by the SFT selection factors: P_i(t) ∝ |⟨i|ψ(t)⟩|² × 1/(1 + ζ N_bait) × exp(−ΔS_i / ℏ_eff) × exp(−ΔF_i / k T_eff) × δ_{B,B_i}. This is the Make Real equation. It attempts to unify: • Quantum mechanics (through the Schrödinger amplitude) • Self‑Field Theory (action term, bottleneck, superselection) • Predictive Processing (free energy ΔF_i) • Integrated Information Theory (Φ_i in T_eff) • Global Workspace Theory (selection architecture implicit in the interface model) • Thermodynamics (Boltzmann factors, competition) • Topological field theory (WZW superselection) For non‑biological systems, the ΔF_i term is omitted, and T_eff is not defined; the equation reduces to the core collapse rule. 6. PREDICTION OF THE BAIT‑UNIT EFFECT A key prediction of the Make Real equation is the bait‑unit effect: if a target qubit is surrounded by actively driven bait qubits, N_bait is large, and the bottleneck term 1/(1 + ζ N_bait) reduces the probability of collapse for the target, thereby increasing its coherence time T₂. This effect is opposite to standard crosstalk expectations. The effect was experimentally tested on IBM’s Heron R2 and R1 processors [2]. With 24 bait qubits active, the target’s T₂ increased dramatically (from 138 μs to 447 μs on one chip, and from 316 μs to 494 μs on another), saturating at a common ceiling near 490 μs. ACTIVE > CONTROL in all clean repetitions, with a p‑value of 3×10⁻⁵ under the null hypothesis. The saturation ceiling matches the finite bottleneck model, confirming the finite observer population. This experimental result directly validates the bottleneck term in the Make Real equation and, by extension, the underlying SFT framework. 7. DISCUSSION The Make Real equation provides a physical mechanism for quantum collapse that is derived from first principles rather than assumed. It solves the measurement problem by identifying the observer (Selfliton) and the collapse event (etebuda) within a field theory. The equation naturally explains the Born rule as a combination of the Schrödinger amplitude and thermodynamic weighting, and it unifies quantum mechanics with the leading theories of consciousness. The finite Selfliton population, central to the bottleneck term, also appears in other domains: it gives the observed dark matter density, the evolution of dark matter fraction with galactic age, and the holographic bound on cosmic entropy. The same primitives thus unify quantum measurement, consciousness, and cosmology. The experimental confirmation of the bait‑unit effect [2] provides empirical support for the Make Real