Substrate framework's energy-eigenstate decoherence formula γeff = (ΔE/MPc2)2 × νP [1] depends on the energy gap between superposed states, not on cosmological distance directly. But typical ΔE values for thermal modes, particle physics processes, and inflaton field fluctuations are functions of cosmic energy density, which evolves dramatically over cosmic history. This paper develops the cosmological evolution of substrate intrinsic decoherence across the principal epochs: • Planck era (t ~ 10−44 s): Substrate framework breaks down; γ formula not applicable. • Inflation era (ΔE ~ 1016 GeV): γ ~ 1037 Hz. Catastrophically fast decoherence drives primordial perturbation classicalization — providing the microscopic mechanism for the well-known but mechanistically unexplained quantum-to-classical transition of cosmological perturbations. • EW epoch (ΔE ~ 100 GeV): γ ~ 109 Hz. Coherence time τ ~ ns; particle physics processes decohere rapidly. • QCD epoch (ΔE ~ 100 MeV): γ ~ 103 Hz. τ ~ ms. • Nucleosynthesis (ΔE ~ MeV): γ ~ 0.1 Hz. τ ~ 10 s. • Recombination (ΔE ~ 0.3 eV): γ ~ 10−15 Hz. τ ~ 30 Myr, longer than the age of the universe at that time — the threshold at which the universe becomes capable of sustaining cosmologically long quantum coherence. • Present era (ΔE ~ kBTCMB ~ 0.2 meV): γ ~ 10−21 Hz. τ ~ 30 Gyr, longer than the current age of the universe. Coherent quantum systems can persist for cosmological timescales. • de Sitter future: Floor of γ set by dark energy; in the limit, decoherence approaches a constant minimum tied to the cosmological constant. Three principal results: (i) The decoherence rate has dropped by ~58 orders of magnitude over cosmic history, from γ ~ 1037 Hz at inflation to γ ~ 10−21 Hz today. The universe has become exponentially more capable of sustaining coherent quantum behavior as it has cooled. (ii) Coherent quantum behavior is a late-universe phenomenon. Modern quantum-mechanical experiments (atom interferometry, molecular interferometry, atomic clocks, B-meson oscillations) require a low-energy-density universe to operate. They could not have been performed in the radiation-dominated era because thermal energies were too high. (iii) Substrate framework provides a microscopic mechanism for primordial perturbation classicalization. Inflaton field quantum fluctuations decohered at γ ~ 1037 Hz during inflation, becoming classical perturbations that seeded the large-scale structure observed today. This resolves a long-standing puzzle in cosmology, where the quantum-to-classical transition is traditionally treated as a black box. Additionally, the cosmological floor on momentum uncertainty Δpmin ≥ ℏH(t)/c evolved from Δpmin ~ MPc at Planck era to Δpmin ~ 10−61 kg·m/s today — a quantum bound that has weakened by ~60 orders of magnitude. In the early universe, quantum uncertainty operated at vastly different scales than today. These results imply that the substrate framework's intrinsic decoherence sector is fundamentally a cosmological history sector: the framework's quantum-mechanical behavior changes character with cosmic epoch. Quantum coherence is not a universal property but rather a feature of low-energy-density universes. The framework's testable predictions in the modern era (thermal molecular interferometry, atomic clocks) are made possible by the universe having sufficiently cooled. Section II clarifies what does and doesn't depend on cosmic time. Section III develops the cosmological floor evolution. Section IV develops the decoherence rate across cosmic history with a master table. Section V addresses the early universe's rapid classicalization. Section VI addresses the inflation era specifically and primordial perturbations. Section VII addresses the present era. Section VIII addresses the de Sitter future. Section IX synthesizes the cross-epoch comparison of quantum properties. Section X concludes. Keywords: substrate theory; cosmological decoherence; primordial perturbations; inflation; quantum-to-classical transition; cosmological floor; energy-eigenstate formula; cosmic evolution of quantum capacity.
Substrate framework's energy-eigenstate decoherence formula γeff = (ΔE/MPc2)2 × νP [1] depends on the energy gap between superposed states, not on cosmological distance directly. But typical ΔE values for thermal modes, particle physics processes, and inflaton field fluctuations are functions of cosmic energy density, which evolves dramatically over cosmic history. This paper develops the cosmological evolution of substrate intrinsic decoherence across the principal epochs: • Planck era (t ~ 10−44 s): Substrate framework breaks down; γ formula not applicable. • Inflation era (ΔE ~ 1016 GeV): γ ~ 1037 Hz. Catastrophically fast decoherence drives primordial perturbation classicalization — providing the microscopic mechanism for the well-known but mechanistically unexplained quantum-to-classical transition of cosmological perturbations. • EW epoch (ΔE ~ 100 GeV): γ ~ 109 Hz. Coherence time τ ~ ns; particle physics processes decohere rapidly. • QCD epoch (ΔE ~ 100 MeV): γ ~ 103 Hz. τ ~ ms. • Nucleosynthesis (ΔE ~ MeV): γ ~ 0.1 Hz. τ ~ 10 s. • Recombination (ΔE ~ 0.3 eV): γ ~ 10−15 Hz. τ ~ 30 Myr, longer than the age of the universe at that time — the threshold at which the universe becomes capable of sustaining cosmologically long quantum coherence. • Present era (ΔE ~ kBTCMB ~ 0.2 meV): γ ~ 10−21 Hz. τ ~ 30 Gyr, longer than the current age of the universe. Coherent quantum systems can persist for cosmological timescales. • de Sitter future: Floor of γ set by dark energy; in the limit, decoherence approaches a constant minimum tied to the cosmological constant. Three principal results: (i) The decoherence rate has dropped by ~58 orders of magnitude over cosmic history, from γ ~ 1037 Hz at inflation to γ ~ 10−21 Hz today. The universe has become exponentially more capable of sustaining coherent quantum behavior as it has cooled. (ii) Coherent quantum behavior is a late-universe phenomenon. Modern quantum-mechanical experiments (atom interferometry, molecular interferometry, atomic clocks, B-meson oscillations) require a low-energy-density universe to operate. They could not have been performed in the radiation-dominated era because thermal energies were too high. (iii) Substrate framework provides a microscopic mechanism for primordial perturbation classicalization. Inflaton field quantum fluctuations decohered at γ ~ 1037 Hz during inflation, becoming classical perturbations that seeded the large-scale structure observed today. This resolves a long-standing puzzle in cosmology, where the quantum-to-classical transition is traditionally treated as a black box. Additionally, the cosmological floor on momentum uncertainty Δpmin ≥ ℏH(t)/c evolved from Δpmin ~ MPc at Planck era to Δpmin ~ 10−61 kg·m/s today — a quantum bound that has weakened by ~60 orders of magnitude. In the early universe, quantum uncertainty operated at vastly different scales than today. These results imply that the substrate framework's intrinsic decoherence sector is fundamentally a cosmological history sector: the framework's quantum-mechanical behavior changes character with cosmic epoch. Quantum coherence is not a universal property but rather a feature of low-energy-density universes. The framework's testable predictions in the modern era (thermal molecular interferometry, atomic clocks) are made possible by the universe having sufficiently cooled. Section II clarifies what does and doesn't depend on cosmic time. Section III develops the cosmological floor evolution. Section IV develops the decoherence rate across cosmic history with a master table. Section V addresses the early universe's rapid classicalization. Section VI addresses the inflation era specifically and primordial perturbations. Section VII addresses the present era. Section VIII addresses the de Sitter future. Section IX synthesizes the cross-epoch comparison of quantum properties. Section X concludes. Keywords: substrate theory; cosmological decoherence; primordial perturbations; inflation; quantum-to-classical transition; cosmological floor; energy-eigenstate formula; cosmic evolution of quantum capacity.
Earlier substrate-theory papers [1-3] used the intrinsic decoherence formula γ = (m/MP)2 × νP, motivated by F1/F2 sampling at a per-mass rate. This formula gives reasonable BMV-scale predictions but over-predicts decoherence for composite quantum systems by orders of magnitude. The most severe tension is with C60 molecular interferometry [4]: the per-mass formula predicts decoherence at 108 Hz for a C60 molecule (m ≈ 720 amu), whereas observed coherence times in Talbot-Lau interferometers extend to milliseconds. The 5-order-of-magnitude tension is real and unresolvable within the per-mass framework. This paper formally introduces the energy-eigenstate decoherence formula: γeff = (ΔE / MP c2)2 × νP (1) where ΔE is the energy difference between superposed states. This formula: (i) Reduces to the per-mass formula in the special case of particle creation/annihilation (ΔE = mc2). (ii) Gives ΔE = 0 → γeff = 0 for translation-symmetric position superpositions (same kinetic energy in both branches). Resolves the C60 tension. (iii) Predicts γeff = (kBT / MPc2)2 × νP for thermal molecular beams, giving ~100 Hz at T = 300 K. Testable in current molecular interferometry. (iv) Predicts γeff ≈ 1.4 × 10−20 Hz for B0-B̄0 oscillations — essentially perfect coherence, consistent with all observations but not a discovery target. (v) Gives γeff ≈ 1037 Hz at inflationary energy scales — cosmologically relevant. The formula is derived from substrate's F1/F2 ontology [5]: F2 events sample between substrate-mode energy eigenstates with rate proportional to (ΔE/MPc2)2, representing the rate at which the F1 wavefunction's off-diagonal coherence between energy eigenstates is sampled. Position-basis decoherence is not intrinsic to substrate framework; it emerges from environmental decoherence as in standard QM. This paper audits the existing substrate corpus for predictions affected by the formula change: • B-meson anomalies paper [v3, ref. 6]: B-B̄ decoherence prediction (5.4 × 10−4 amplitude suppression) replaced by essentially zero. The decoherence prediction is withdrawn; substrate consistent with observations. • Heisenberg uncertainty paper [ref. 1]: BMV-scale predictions revised. Old: γ ~ 10−8 Hz at m = 10−14 kg from per-mass formula. New: γ depends on gravitational interaction energy ΔE = Gm2/r, giving γ ~ 10−24 Hz at BMV scales. Far below BMV sensitivity; prediction effectively withdrawn at lab scales. • F1/F2 paper [ref. 5]: Framework presentation updated to specify energy-eigenstate sampling. • Inflation paper [ref. 7], MOND paper [ref. 8], dark energy paper [ref. 9], cluster mass paper [ref. 10]: no decoherence content affected. The energy-eigenstate formula opens new testable predictions in experimental programs that the per-mass formula did not access cleanly: thermal molecular interferometry (γ ∝ T2), trapped-ion motional-eigenstate superpositions (γ ∝ ΔE2), and atomic clock internal-state superpositions. The substrate decoherence sector thus becomes richer and more falsifiable under the new formula, even as some previous predictions (B-B̄, BMV) are no longer accessible signatures. Section VII presents a specific falsification test: thermal molecular interferometry with varying beam temperature, measuring whether the coherence time scales as τ ∝ 1/T2 (substrate prediction) or τ ∝ 1/m2 (CSL/GRW prediction) or shows no intrinsic decoherence (standard QM with only environmental decoherence). The same apparatus can test all three competing intrinsic-decoherence proposals. Keywords: substrate theory; intrinsic decoherence; energy-eigenstate sampling; F1/F2 ontology; molecular interferometry; CSL; GRW; BMV protocol; corpus audit.
This paper develops the substrate-theoretic mechanism of intrinsic decoherence in three connected directions: (i) the description of the double slit experiment for electrons vs photons under the energy-eigenstate formula [1, 2]; (ii) the microscopic mechanism by which substrate time-quantum F2 events interact with matter (radial-mode displacements per postulate P6); and (iii) the role of the 5D cascade structure (which makes matter stable [3]) in shaping the decoherence process. Three principal results: (i) Electrons and photons both show full interference in the standard symmetric double slit under the energy-eigenstate formula. ΔE = 0 between branches → γeff = 0 for both. But substrate framework distinguishes them at the field level: electrons are localized radial-mode displacements of the substrate (per P6, mass IS substrate displacement); photons are excitations of the substrate gauge sector with no radial displacement. Both yield identical observable interference patterns despite different substrate-level identities. (ii) The decoherence mechanism is F2 sampling between substrate-mode energy eigenstates, with rate γ = (ΔE/MPc2)2 × νP. F2 events occur uniformly throughout substrate at the Planck clock rate νP; they detect substrate field configurations including matter (radial-mode displacements). The ΔE2 scaling emerges because pairs of F2 events are needed to consistently distinguish two energy eigenstates — analogous to how Born-rule probabilities scale as amplitude squared. Mass-as-displacement gives matter substrate presence that F2 events sample, but mass alone does not drive decoherence — the energy gap between superposed states does. (iii) The 5D cascade structure prevents matter decay but does not directly suppress decoherence. Matter at the IR brane (cascade site 15) has wavefunction overlap with the bulk radial mode suppressed by q15 ≈ 10−15, giving decay-rate suppression q30 ≈ 10−30 — necessary for matter stability. But F2 sampling is a global substrate process occurring at νP throughout the substrate, not localized to specific 5D positions. The 5D structure determines what energy spectrum matter has access to (which sets the available ΔE values), but does not suppress the decoherence rate for a given ΔE. Decoherence and decay are therefore distinct processes: decay is energy transfer from matter (IR brane) to bulk radial mode (throughout 5D), requiring wavefunction overlap, suppressed by 5D localization; decoherence is information transfer between superposed energy eigenstates via local F2 sampling, not requiring bulk overlap, not suppressed by 5D localization. Implications for experimental tests: • Standard double slit (electrons or photons): substrate predicts full interference, ΔE = 0 in symmetric setups. Consistent with all observations. • Asymmetric interferometers (potential difference, frequency shift): substrate predicts γ ∝ (ΔE)2, but for lab-scale ΔE ~ eV, γ ~ 10−13 Hz, undetectable. • Thermal molecular interferometry: substrate predicts γ ∝ T2, mass-independent — uniquely substrate among intrinsic-decoherence frameworks [2]. Principal near-term test. • Cosmological-scale superpositions (inflaton fields, primordial perturbations): substrate predicts γ ~ 1037 Hz at inflation, providing microscopic mechanism for quantum-to-classical transition. Keywords: substrate theory; double slit; electrons; photons; F2 sampling; mass-as-displacement; 5D cascade; matter stability; decoherence mechanism; energy-eigenstate formula.
Description : This work introduces a novel, model-independent diagnostic framework for quantifying quantum decoherence in primordial inflationary perturbations. The study addresses the fundamental problem of the quantum-to-classical transition in cosmology by defining a normalized persistence functional that captures the suppression of quantum coherence over time. Within an open quantum system approach, each perturbation mode is treated as an effective quantum degree of freedom interacting with an environment, leading to Gaussian suppression of off-diagonal density matrix elements. The proposed functional provides a direct and scalable measure of decoherence efficiency without relying on detailed microscopic modeling. A key feature of the framework is the introduction of a residual coherence parameter, which accounts for possible late-time deviations from complete classicalization. The work further establishes a monotonicity property for the decoherence functional and connects the persistence measure to entropy growth, offering an information-theoretic interpretation of the decoherence process. Importantly, the framework suggests a phenomenological link between residual coherence and observable non-Gaussianity in the cosmic microwave background, opening a pathway for potential observational constraints. The proposed diagnostic functional is broadly applicable across inflationary models and provides a unified tool for comparing decoherence efficiency under different environmental interactions. This work lays the foundation for future studies on quantum signatures in cosmological observables and the persistence of quantum features in the early universe. Keywords : Quantum Decoherence Inflationary Cosmology Primordial Perturbations Open Quantum Systems Quantum-to-Classical Transition Non-Gaussianity Cosmological Perturbation Theory Density Matrix Quantum Cosmology Early Universe Physics Decoherence Functional Entropy and Information Theory
Description: This work explores the conditions under which quantum superposition may emerge or persist at cosmological scales, challenging the common assumption that the early universe was the most favorable environment for quantum coherence. While the universe is widely believed to have originated from a quantum regime, the extreme interaction density, thermal noise, and intense field couplings of the early universe are argued to have caused rapid decoherence, effectively suppressing sustained quantum superposition beyond minimal scales. In this sense, the early universe is interpreted as a decoherence-dominated environment rather than a coherent quantum domain. The paper proposes an alternative perspective in which the late universe, characterized by cosmic expansion, reduced interaction density, and lower environmental noise, may offer more favorable conditions for partial isolation and the re-emergence of quantum superposition under specific circumstances. This conceptual framework reframes the quantum–classical transition as an environmentally driven process rather than a purely temporal or scale-dependent one, contributing to ongoing discussions in quantum cosmology, decoherence theory, and the foundations of physics. 🔹 Keywords: Quantum cosmology; Quantum superposition; Decoherence; Early universe; Late universe; Environmental noise; Quantum–classical transition; Interaction density; Foundations of physics; Conceptual physics
This research introduces a novel quantitative framework for understanding one of the most fundamental questions in theoretical physics: How and when do quantum systems become classical? By developing a normalized Quantum Persistence Function (QPF) , we provide a continuous measure of residual quantum coherence in open systems interacting with their environment. The framework is rigorously derived from the spin-boson model—a paradigm for studying decoherence—and distinguishes between Markovian (memoryless) and non-Markovian environments based on spectral density structure (Keywords) Quantum decoherence Inflationary cosmology Open quantum systems Quantum–classical transition Primordial perturbations Cosmic Microwave Background Non-Gaussianity Spin-boson model Environmental entanglement Planck mission
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.