This paper extends Complexity Binding Theory (CBT) from galactic dynamics to quantum mechanics, cosmology, and black hole physics. I demonstrate that Born's probability rule P = |ψ|² emerges naturally from entropy maximization in the binding field framework, without requiring it as an axiom. Entanglement entropy is identified with binding entropy, providing a unified information-theoretic interpretation. The binding field is shown to saturate at event horizons, recovering Bekenstein-Hawking entropy. Crucially, I prove that the binding field's entropic potential is quadratic near its minimum, yielding a sound speed cs² ≈ 0 — making it dynamically equivalent to cold dark matter at cosmological scales while producing modified dynamics at galactic scales. This establishes compatibility with CMB acoustic peaks. Additionally, I explore a heuristic connection between the galactic binding parameter α₀ = 1/e and quantum decoherence scales, yielding predictions consistent with experimental coherence times in superconducting qubits and trapped ions. This work suggests that quantum probability, entanglement, decoherence, cosmological structure, and black hole thermodynamics may share a common entropic origin through a single scalar binding field.
This paper extends Complexity Binding Theory (CBT) from galactic dynamics to quantum mechanics, cosmology, and black hole physics. I demonstrate that Born's probability rule P = |ψ|² emerges naturally from entropy maximization in the binding field framework, without requiring it as an axiom. Entanglement entropy is identified with binding entropy, providing a unified information-theoretic interpretation. The binding field is shown to saturate at event horizons, recovering Bekenstein-Hawking entropy. Crucially, I prove that the binding field's entropic potential is quadratic near its minimum, yielding a sound speed cs² ≈ 0 — making it dynamically equivalent to cold dark matter at cosmological scales while producing modified dynamics at galactic scales. This establishes compatibility with CMB acoustic peaks. Additionally, I explore a heuristic connection between the galactic binding parameter α₀ = 1/e and quantum decoherence scales, yielding predictions consistent with experimental coherence times in superconducting qubits and trapped ions. This work suggests that quantum probability, entanglement, decoherence, cosmological structure, and black hole thermodynamics may share a common entropic origin through a single scalar binding field.
The Total Entropic Quantity (TEQ) framework derives quantum mechanics from entropy-driven selection principles, unifying entropy, emergent time, and thermodynamic evolution. TEQ decomposes total entropy into realized entropy (macroscopic disorder), latent entangled entropy (quantum correlations), and latent classical entropy (stable classical records), clarifying how classical irreversibility arises from global quantum coherence. A central result is \textit{Universal Entropic Time} (UET), defined by the monotonic growth of realized entropy. UET aligns the thermodynamic arrow of time with cosmological expansion, linking decoherence to macroscopic irreversibility. TEQ offers a unified epistemic-ontological interpretation of measurement, reconciling the Copenhagen and Many-Worlds views as complementary facets of entropy redistribution. It also provides an entropic explanation for quantum stability---especially in Majorana qubits---and suggests that spacetime and causal structure emerge from entropy gradients.TEQ yields two testable predictions: (1) Majorana qubits should exhibit extended coherence due to suppressed entropy flow; and (2) the entropic driver f(Λ(t)) has a unique global maximum, implying that dark energy peaked in the past---a result consistent with recent DESI observations. Future work will derive quantum dynamics from an entropy-weighted variational principle, aiming to recover the Schr\"odinger equation, the Born rule, and quantum suppression from entropic constraints.
Abstract We demonstrate that the axioms of quantum mechanics -- superposition, the Born rule, and the projection postulate -- are not independent assumptions but theorems derivable from the Four-Sector Cosmological (FSC) structure. Sector-II, the dark matter sector, acts as a universal environment: tracing it out from the global FSC state generates the mixed density matrix of Sector-I (baryonic matter), from which quantum probabilities emerge as Schmidt coefficients (Theorems 3.1-3.4). The Schmidt coefficient spectrum is determined within the FSC modular framework: the ratio R = Omega_DM/Omega_b = 5.4 (Planck 2018) fixes the FSC parameter p = -6 ln R/pi = -3.221, and the S-transformation of the partition function Z_I(tau) = |eta(tau)|^{-2p} mathematically derives Omega_Lambda/Omega_b = <|tau|^{-p}>_F = 13.6, yielding Omega_b = 1/20 = 0.05 in agreement with Planck 2018 observations (1.4% accuracy, Theorem 4.5). A number-theoretic observation emerges: 1/Omega_b = 20 = c_Monster - |Z_4| = 24-4, connecting the baryonic density to the Monster moonshine central charge and the FSC Z_4 symmetry (Corollary 4.5.1). The monotonic increase of entanglement entropy S_ent(t) reproduces the arrow of time consistent with Paper E (Theorem 5.1). Five open questions for future work are identified (OQ-1 through OQ-5). This paper initiates the FSC & Baryon World (FBW) series, focusing on the interface between FSC cosmological structure and quantum information.
The Born rule, assigning probabilities via |ψ|², is traditionally introduced as an independent axiom of quantum mechanics. Despite its empirical success, its foundational origin remains unresolved. In this paper we derive the Born rule as a necessary consequence of configurational stability in a timeless, pre-metric configuration space. Physical states are described by field configurations Φ, weighted by a stability functional S[Φ]. Quantum states ψ arise as representational coordinates encoding relative stability rather than as ontological wave objects. We show that requiring: projective invariance, factorizability for independent subsystems, and classical additivity under phase degradation, uniquely selects the quadratic probability map |ψ|², without assuming Hilbert space structure, Gleason-type theorems, or temporal dynamics. Measurement is identified as a topological transition at a stability threshold Σ*, where the Hessian spectrum becomes marginally stable. This leads to a distinctive, non-analytic “kink” in decoherence behavior. Unlike stochastic collapse models, the framework predicts pure dephasing without energy injection, avoiding existing experimental heating constraints. The theory yields explicit, falsifiable experimental signatures, including structure-dependent decoherence effects in mesoscopic systems, accessible to current matter-wave interferometry and levitated nanosphere experiments. The framework is fully timeless at the fundamental level; laboratory time emerges only as an epistemic ordering parameter. This work is self-contained and does not rely on gravitational, cosmological, or dark-matter assumptions. Keywords quantum foundations; Born rule; measurement problem; decoherence; timeless physics; configuration space; stability theory; quantum-classical boundary
The Born Rule is central to quantum mechanics, yet it remains a postulate: a probabilistic rule grafted onto the deterministic evolution of the Schrödinger equation. This work derives the Born Rule as an emergent statistical law grounded in thermodynamic principles. We propose that quantum probability reflects the survival likelihood of a branch under decoherence, determined by its informational reversibility, structural fragility, and exposure to entropy.In this formulation, reversibility quantifies the mutual information retained during measurement, entropy reflects environmental disruption, and buffering represents the system’s capacity to absorb it. In low-entropy, high-buffering conditions typical of laboratory systems, the survival probability of a branch closely approximates the squared amplitude of its wavefunction — recovering the Born Rule as a limiting case.This approach reframes quantum amplitude as a measure of structural persistence and interprets wavefunction collapse as a form of thermodynamic selection. The result unifies concepts from measurement theory, thermodynamics, and information theory into a coherent physical framework, while also predicting conditions under which deviations from the Born Rule could arise — offering new directions for theoretical and experimental inquiry.
The Total Entropic Quantity (TEQ) framework derives quantum mechanics from entropy-driven selection principles, unifying entropy, emergent time, and thermodynamic evolution. TEQ decomposes total entropy into realized entropy (macroscopic disorder), latent entangled entropy (quantum correlations), and latent classical entropy (stable classical correlations), clarifying how classical irreversibility emerges from global quantum coherence. A key result is Universal Entropic Time (UET), a synchronized temporal structure governed by realized entropy growth. UET aligns the thermodynamic arrow of time with cosmological evolution, linking decoherence to macroscopic irreversibility. TEQ provides a unified epistemic and ontological perspective on quantum measurement, reconciling the Copenhagen and Many-Worlds interpretations as complementary descriptions of a single entropy-driven selection mechanism. Additionally, entropy minimization explains the stability of quantum systems such as Majorana qubits, while entropy gradients suggest a mechanism for spacetime emergence and causal order. Entropy redistribution in TEQ acts as an active selection principle, stabilizing preferred trajectories while suppressing unstable quantum states. Future work will develop an entropy-weighted variational principle to formalize path selection in TEQ, aiming to derive quantum dynamics---including the Born rule, wavefunction suppression, and the Schrödinger equation---from entropic constraints. This approach is expected to clarify how path weights relate to entropy redistribution and selection, offering a thermodynamic basis for quantization. Notably, TEQ makes its first concrete prediction: Majorana qubits should exhibit extended coherence times due to suppressed entropy redistribution, offering an experimentally testable signature of the framework.
We propose that the unobservability of absolute scale constitutes a foundational principle of physics. Starting from the requirement that physical predictions must be invariant under rescalings of the action, we show that only phase-based quantities remain well defined. This requirement uniquely selects a complex amplitude description, leading directly to the structure of quantum mechanics, including linear superposition, Hilbert space, and the Born rule. Within this framework, the classical notion of action loses absolute meaning, and physical observables arise from invariant phase relations. Quantum mechanics is therefore not postulated, but emerges as the minimal consistent description of systems in which scale cannot be directly observed. The formal structure of quantum theory is shown to follow from this principle without additional axioms. We further demonstrate that the same principle implies the existence of a dynamical scale field, which governs the effective quantum scale and connects naturally to cosmological models with a time- dependent Planck mass. In this way, the structure of quantum mechanics and the large-scale dynamics of the Universe are linked through a common origin. This framework provides a unified perspective in which quantum behavior and cosmological evolution arise from a single underlying principle, suggesting a new approach to the relationship between fundamental physics and cosmology.