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.
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.
v1.1 (2026-09-28): Corrigendum applied to Appendix A. Correction: The erroneous approximation beta approx ln2/ln(4/3) (which evaluates to 2.409, not 0.716) has been replaced by the numerically verified expression beta approx 4*ln(R)/(3*pi) = 2*|p|/9 = 0.7158 (Delta = 0.03%), where |Z_4| = 4 is the FSC discrete symmetry group order and Sub(Z_4) = 3 counts the distinct subgroups. The three-phase symmetry-breaking chain Z_4 -> Z_2 -> {e} is identified as the structural candidate for OQ-1. Main theorems (Theorems 3.1-5.1) are unchanged. Original abstract: Quantum mechanical axioms -- superposition, Born rule, projection postulate -- are not independent assumptions but theorems derivable from the Four-Sector Cosmological (FSC) structure. Sector II (dark matter) acts as a universal environment; tracing out Sector II from a global FSC state generates a mixed density matrix for Sector I (baryonic matter), with quantum probabilities emerging as Schmidt coefficients (Theorems 3.1-3.4). The Schmidt coefficient spectrum is fixed within the FSC modular framework. 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} yields Omega_Lambda/Omega_b = 13.6, giving Omega_b = 1/20 = 0.05 (1.4% agreement with Planck 2018, Theorem 4.5). The entanglement entropy S_ent(t) reproduces the arrow of time consistent with Paper E (Theorem 5.1). Five open questions (OQ-1 to OQ-5) are presented.
v1.1 (2026-09-28): Corrigendum applied to Appendix A. Correction: The erroneous approximation beta approx ln2/ln(4/3) (which evaluates to 2.409, not 0.716) has been replaced by the numerically verified expression beta approx 4*ln(R)/(3*pi) = 2*|p|/9 = 0.7158 (Delta = 0.03%), where |Z_4| = 4 is the FSC discrete symmetry group order and Sub(Z_4) = 3 counts the distinct subgroups. The three-phase symmetry-breaking chain Z_4 -> Z_2 -> {e} is identified as the structural candidate for OQ-1. Main theorems (Theorems 3.1-5.1) are unchanged. Original abstract: Quantum mechanical axioms -- superposition, Born rule, projection postulate -- are not independent assumptions but theorems derivable from the Four-Sector Cosmological (FSC) structure. Sector II (dark matter) acts as a universal environment; tracing out Sector II from a global FSC state generates a mixed density matrix for Sector I (baryonic matter), with quantum probabilities emerging as Schmidt coefficients (Theorems 3.1-3.4). The Schmidt coefficient spectrum is fixed within the FSC modular framework. 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} yields Omega_Lambda/Omega_b = 13.6, giving Omega_b = 1/20 = 0.05 (1.4% agreement with Planck 2018, Theorem 4.5). The entanglement entropy S_ent(t) reproduces the arrow of time consistent with Paper E (Theorem 5.1). Five open questions (OQ-1 to OQ-5) are presented.
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.
Standard quantum mechanics separates unitary time evolution from non-unitary measurement collapse, creating a severe foundational bottleneck when applied to closed cosmological systems where no external classical observer exists to collapse primordial quantum fluctuations. Simultaneously, modern cosmology faces unexplained dark-sector anomalies, including dark energy, dark matter, and Hubble/structure growth tensions. In this paper, we establish the Dynamical Quantum Measurement and Cosmological Quantum-to-Classical Transition (DQMCQT) framework, unifying and upgrading items #6 (Dynamical Foundations of Quantum Measurement), #5 (Early Universe and Quantum-to-Classical Transition), and #4 (Dark Sector and Cosmological Effective Laws) of the 20 Emergent Physics Agenda. Anchored in our 71-page ZFC Master Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) and synthesized with the SVKES and HDGPS frameworks, we formulate coupled system–apparatus–gravity evolution on the Takesaki Type II₁ factor (ℳ_ground, τ_ground) with τ_ground(1_ℳ) = 1, governed by the URRHC idempotent modal reflection monad T_URRHC (T_URRHC² = T_URRHC) and universal constants 𝔘 = (𝒯_0x8A2C, C_UPTC, η_friction, ε_SHID). We establish six core axioms (DQMCQT-1 through DQMCQT-6) and prove six fundamental theorems: (1) Objective Pointer-State Contraction ‖ρ̂_t − T_URRHC(ρ̂_t)‖_tr ≤ η_friction in finite Lambert W₀ time τ_freeze = −(C_UPTC / Γ_dec) W₀(−Γ_dec η_friction / C_UPTC) < ∞ without ad-hoc collapse postulates, recovering the exact Born rule p_k = τ_ground(ρ̂_t Π̂_k); (2) Quantitative Visibility Deviation ΔV(t) = V_QM(t) − V_DQMCQT(t) > 0 from standard linear Lindblad decoherence when entanglement information crosses I_ent > ε_SHID, testable in macroscopic matter-wave interferometry; (3) Primordial Quantum-to-Classical Freezing of Mukhanov–Sasaki curvature perturbations R̂_k at Hubble horizon exit (2N_freeze ≥ C_UPTC) with oscillatory power spectrum cutoff; (4) Unified Dark-Sector Effective Action S_dark[g, φ_dec] where kinetic transition condensates and potential floors simultaneously yield the cosmic dark-to-baryonic matter ratio Ω_DM,0 / Ω_b,0 = C_UPTC / (12 c_𝒯 (1 + ε_SHID)) ≈ 5.33 and a thawing dynamic dark-energy equation of state w_eff(z) = −1 + (ε_SHID² / (3 C_UPTC)) (1 + z)^(c_𝒯 / (1 + c_𝒯)) > −1; (5) Primordial Quantum Discord and Scale-Dependent Non-Gaussian Bispectrum Bounds |f_NL^trans(k)| ≤ (5/12) ε_SHID c_𝒯 < 1; and (6) Anytime-Valid Martingale e-Value Model Selection (E_N ≥ 1/α) separating Unified Dark Physics from ΛCDM. Complete Python numerical verification is provided in Appendix A.
The four axioms of Modular Entropic Gravity (MEG) implicitly contain the Doplicher–Haag–Roberts (DHR) superselection structure of algebraic quantum field theory. This paper establishes the result through a four-link chain: Axiom 1 (modular Hamiltonians of local regions) commits the theory to the Haag–Kastler framework; Axiom 3 (Bisognano–Wichmann and the PLES functional) provides a mass gap with exponential clustering; Axiom 2 (JLMS) restricts physical states to a class satisfying the Buchholz–Fredenhagen exponential localisation criterion, as proved for an explicitly defined admissible state class with bounded modular energy; and the DHR theorem then implies superselection sectors labelled by representations of a compact group, with block decomposition of regional operator algebras and block-diagonal admissible states. The paper demonstrates that this result has consequences beyond the gauge theory application for which it was first identified in the MEG programme (Zenodo DOI: 10.5281/zenodo.19635025). Specifically, it completes the Born rule dissolution established in the companion paper on convex field representations (Zenodo DOI: 10.5281/zenodo.19600153). That paper showed that within a single superselection sector, the Born rule is not a separate measurement postulate but a structural feature of the convex entropy field representation. What it could not address was the origin of the sector structure itself. The DHR superselection structure answers three questions left open by the Born rule paper, all from the axioms alone. First, why do sectors exist? — because the DHR theorem reconstructs them from the Haag–Kastler framework with mass gap and exponential localisation. Second, why are cross-sector superpositions forbidden? — because JLMS-admissible states are block-diagonal, a theorem of the DHR framework rather than a postulate. Third, why are cross-sector branches distinguishable? — because states in distinct sectors carry different quantum numbers under the DHR group, forcing their entropy field configurations to differ. The synthesis gives the Born rule and superselection structure from the MEG axioms: the sector decomposition from DHR (this paper), the Born rule within each sector from the convex dissolution (companion paper), and the absence of cross-sector interference from the block-diagonal constraint. No independent probability postulate is required.x
We propose a conceptual framework in which the pilot wave of de Broglie-Bohm quantum mechanics has a concrete physical substrate: dark matter existing in a fourth spatial dimension. Quantum superposition is reinterpreted as rapid physical oscillation — consistent with the Zitterbewegung predicted by the Dirac equation — rather than simultaneous existence in multiple classical states. Wave function collapse is correspondingly reinterpreted as physical interruption of this oscillation by detector interaction, rather than observation-dependent state reduction. The framework advances a coherence argument against the Many Worlds interpretation: real superposition, as evidenced by the ordered interference pattern in the double slit experiment, produces coherent identical behavior across superposed states rather than divergent branching. Divergent branches would produce detectable decoherence signatures inconsistent with observed interference; their absence constitutes evidence against branching interpretations by the same evidential standard used to establish superposition itself. The Born rule is proposed to be a relational property of the detector-system interaction rather than an intrinsic quantum axiom. Since detector physical constants — mass, charge, interaction energy — are fixed across measurements, probability distributions are determined by the interaction geometry rather than by unexplained features of the wave function alone. The squared amplitude relationship is identified as a universal property of wave energy mechanics appearing at quantum scale. The nonlocality problem of pilot wave theory is resolved by proposing that dark matter exists in a fourth spatial dimension. Particles entangled across cosmological distances in three-dimensional space may be geometrically adjacent in four-dimensional space, making instantaneous correlation a short-range 4D connection rather than superluminal 3D signaling. This is consistent with Kaluza-Klein dark matter proposals and brane cosmology. The inaccessibility of the wave medium to electromagnetic instruments follows naturally from the confinement of standard model forces to the three-dimensional brane. The framework makes several testable predictions: correlation between dark matter density and quantum coherence times; systematic shifts in Born rule probability distributions under varying detector parameters; and potential gravitational wave signatures of large-scale quantum collapse events. Mathematical formalization and experimental testing are identified as open problems.