Quantum foundations of the PhaseGeometry Z₂ phase medium: observers, decoherence and Quantum Darwinism This record presents the quantum foundations of the PhaseGeometry Z₂ programme, uniting the ontology of observers and branching histories (Foundations IV) with their concrete physical realisation via decoherence and Quantum Darwinism (Foundations V). The PhaseGeometry Z₂ framework proposes that a single binary phase field can account for dark energy, dark matter and the emergence of the classical world. The central insight is that the homogeneous broken phase acts as a universal phase medium — a physical substrate that simultaneously sources the cosmological background and supports quantum observers, measurements and branching histories. Part IV – Phase medium, observer and branching historiesDevelops the ontological layer of the framework. The homogeneous Z₂ vacuum is reinterpreted as a physical phase medium, and clocks, observers and classical branches are defined as inherent structures within this medium, without appealing to external agents. Part V – Decoherence and Quantum Darwinism in a binary phase mediumProvides a quantitative proof of concept. Using finite Z₂ chains as toy universes, it demonstrates: rapid decoherence of a binary event; saturation of subsystem entropy; the emergence of Quantum Darwinism and redundant classical records. These results show how an effectively objective classical reality can arise from the unitary dynamics of the phase medium itself. The toy models used here are short 1D Ising chains; they are intended as minimal demonstrations of the mechanisms, not as direct quantitative predictions for cosmological scales. Taken together, Foundations IV and V show how the same Z₂ field that underlies dark-energy- and dark-matter–like phenomena also provides a complete observer medium, in which systems, apparatus and classical branches all emerge as patterns and correlations of a single physical substrate. This record is part of the PhaseGeometry Z₂ Core Package v1.0: “Binary Phase, Dark Energy and Dark Matter” (series DOI: 10.5281/zenodo.17652957).A unified journal-style preprint version of this material is available as “PhaseGeometry Z₂: Decoherence, Quantum Darwinism and Branching in a Binary Phase Medium” (DOI: 10.5281/zenodo.17773135). Contents PDF of Foundations IV (phase medium, observers, branching histories); PDF of Foundations V (decoherence and Quantum Darwinism). All materials are released under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.
Quantum foundations of the PhaseGeometry Z₂ phase medium: observers, decoherence and Quantum Darwinism This record presents the quantum foundations of the PhaseGeometry Z₂ programme, uniting the ontology of observers and branching histories (Foundations IV) with their concrete physical realisation via decoherence and Quantum Darwinism (Foundations V). The PhaseGeometry Z₂ framework proposes that a single binary phase field can account for dark energy, dark matter and the emergence of the classical world. The central insight is that the homogeneous broken phase acts as a universal phase medium — a physical substrate that simultaneously sources the cosmological background and supports quantum observers, measurements and branching histories. Part IV – Phase medium, observer and branching historiesDevelops the ontological layer of the framework. The homogeneous Z₂ vacuum is reinterpreted as a physical phase medium, and clocks, observers and classical branches are defined as inherent structures within this medium, without appealing to external agents. Part V – Decoherence and Quantum Darwinism in a binary phase mediumProvides a quantitative proof of concept. Using finite Z₂ chains as toy universes, it demonstrates: rapid decoherence of a binary event; saturation of subsystem entropy; the emergence of Quantum Darwinism and redundant classical records. These results show how an effectively objective classical reality can arise from the unitary dynamics of the phase medium itself. The toy models used here are short 1D Ising chains; they are intended as minimal demonstrations of the mechanisms, not as direct quantitative predictions for cosmological scales. Taken together, Foundations IV and V show how the same Z₂ field that underlies dark-energy- and dark-matter–like phenomena also provides a complete observer medium, in which systems, apparatus and classical branches all emerge as patterns and correlations of a single physical substrate. This record is part of the PhaseGeometry Z₂ Core Package v1.0: “Binary Phase, Dark Energy and Dark Matter” (series DOI: 10.5281/zenodo.17652957).A unified journal-style preprint version of this material is available as “PhaseGeometry Z₂: Decoherence, Quantum Darwinism and Branching in a Binary Phase Medium” (DOI: 10.5281/zenodo.17773135). Contents PDF of Foundations IV (phase medium, observers, branching histories); PDF of Foundations V (decoherence and Quantum Darwinism). All materials are released under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.
This record contains the preprint version of the article “PhaseGeometry Z₂: Decoherence, Quantum Darwinism and Branching in a Binary Phase Medium”, submitted to a peer-reviewed journal. The work develops a unified quantum–foundational layer of the PhaseGeometry Z₂ programme, in which a single real scalar field with a Z₂-symmetric double-well potential plays a dual role:– as a cosmological substrate, whose homogeneous broken phase sources dark-energy–like expansion and whose inhomogeneities generate dark-matter–like halo profiles and static black holes with binary phase hair;– as a quantum phase medium, within which systems, apparatuses, observers and classical branches are all realised as patterns of the same underlying field. On the physical side, the article introduces a finite Z₂ chain evolving under a transverse-field Ising Hamiltonian as a fully explicit “toy Universe” of the phase medium. Within this model it demonstrates, under strictly unitary dynamics:– rapid decoherence of macroscopically distinct binary events;– saturation of the subsystem entropy at classical values;– the emergence of a clear Quantum Darwinism plateau in the mutual information between the system and environment fragments, signalling redundant objective records. On the conceptual side, the work formulates an ontology in which:– observers are stable, information-rich patterns in the phase medium;– branches are identified with disjoint amplitude humps in Z₂ configuration space;– delayed-choice and quantum-eraser scenarios are reinterpreted in a purely unitary, medium-based language. Taken together, these results show that the PhaseGeometry Z₂ phase medium can simultaneously underpin dark-sector phenomenology and the emergence of classical observers and histories, providing a concrete Everett–Zurek–style measurement framework in a closed Universe. A related two-part foundations set (“PhaseGeometry Z₂ Foundations IV–V: Phase medium, observers, decoherence and Quantum Darwinism”, DOI: 10.5281/zenodo.17772072) presents a more modular split between ontology (IV) and numerical implementation (V). This preprint is part of the PhaseGeometry Z₂ Core Package v1.0: “Binary Phase, Dark Energy and Dark Matter” (series DOI: 10.5281/zenodo.17652957). All materials are released under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.
Quantum Darwinism is a leading framework for explaining how classical reality emerges from a quantum universe—the environment redundantly encodes the pointer state information of quantum systems, enabling multiple independent observers to reach consensus about reality. However, a fundamental question has remained unanswered: Why does the environment possess this capacity for redundant recording? This paper proposes, within the information-potential conversion framework, that the redundant recording mechanism of quantum Darwinism is the physical realization of the information-potential conversion consensus protocol—the environment, acting as the physical medium for information-potential conversion, redundantly encodes system information, providing consistent conversion records for independent information processing units, from which classical reality emerges. Based on this interpretation, three testable quantitative predictions are proposed: (1) In superconducting quantum circuits, when system complexity exceeds a critical threshold, the efficiency of redundant recording should exhibit an abrupt transition—a signal of the information-potential conversion phase transition of the consensus protocol from “quantum critical” to “classically locked”; (2) There should exist a precise linear relationship between functional information and information-potential conversion energy consumption: each additional bit of functional information doubles the minimum heat dissipation required for record stabilization; (3) Consensus strength—the stability of classical reality—should be positively correlated with the number of information processing units participating in the consensus protocol, and a critical number exists at which the consensus phase transition occurs. quantum Darwinism, information-potential conversion, consensus protocol, classical emergence, redundant recording, functional information
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.
Modern physics faces a constellation of foundational puzzles: the Big Bang singularity, time's arrow, dark matter and dark energy, the cosmological constant problem, fine-tuning, quantum measurement, and quantum gravity unification. This Perspective proposes a unified resolution grounded in complexity-driven selection from diverse quantum paths. Prior to the Big Bang, reality comprises a pre-temporal quantum substrate (lacking classical time coordinate but governed by unitary quantum evolution), evolving reversibly across multiple trajectories—including opposing time arrows. The Big Bang marks an emergence threshold (λ) where decoherence locks spacetime parameters, yielding our classical universe as a "survivor" of local emergence rather than a closed totality. Dark matter and dark energy represent unevolved quantum paths—residuals exerting gravitational influence without full manifestation. This framework reframes cosmology as the study of layered emergence, dissolving "why" questions into "when/how" selection dynamics, with testable predictions in CMB perturbations, quantum decoherence experiments, and gravitational wave observations. By shifting from reductionism to emergentism, it suggests a universal pattern: threshold-gated emergence from diverse substrates, applicable from the cosmos to consciousness.
The substrate field theory, developed in the first three papers of this series, posits a universal physical medium whose rigidity K and effective density ρ₀ determine the speed of light and whose dissipation governs cosmological redshift and orbital decay. In this paper, we show that the same substrate field naturally gives rise to all quantum phenomena as emergent properties of its microscopic structure. The substrate is assumed to possess a discrete granularity at a fundamental scale l₀, leading to quantization of energy and momentum. Linear excitations of the substrate—wave packets—exhibit wave–particle duality. The linearity of the wave equation allows coherent superpositions, giving rise to superposition and entanglement. The substrate's inherent dissipation provides a physical mechanism for decoherence, resolving the measurement problem without invoking a conscious observer. The Heisenberg uncertainty relation emerges as a Fourier property of wave packets in the substrate. Thus quantum mechanics is not a fundamental theory but an effective description of substrate dynamics at microscopic scales. This framework unifies quantum phenomena with classical physics, cosmology, and thermodynamics, eliminating the need for quantum postulates and explaining the apparent "weirdness" of the quantum world as natural consequences of a physical medium.Part IV of the Substrate Field Theory series
Quantum mechanics does not require parallel universes — only phase-relative structure within a shared spacetime manifold. This preprint presents an interpretive framework for quantum multiplicity that avoids spatial “parallel universe” metaphors. Building on standard quantum field theory, Everettian quantum mechanics, and decoherence theory, it argues that apparent multiplicity can be understood as phase-relative branch structure within a single shared spacetime manifold, rather than as spatially separate worlds. The work introduces no new dynamics, equations, or empirical predictions. Its contribution is conceptual: clarifying how mutually exclusive classical outcomes arise through branch-relative accessibility and loss of correlation, while preserving all governing invariants, including conservation laws and universal gravitational coupling in the semiclassical regime. A companion supplementary document presents the standard mathematical formalism—Hilbert space structure, density matrices, decoherence, and expectation-value stress–energy—to demonstrate that the interpretation remains fully consistent with established physics. In approaches to quantum gravity where spacetime is emergent—such as loop quantum gravity or holographic dualities—the framework would naturally reformulate in relational or entanglement-theoretic terms. In that context, branch-relative multiplicity corresponds not to multiple times or geometries, but to multiple decohered relational histories or bulk reconstructions supported by a single underlying quantum state. This paper is intended as a foundations-level reinterpretation for physicists and philosophers of physics interested in quantum ontology, decoherence, and the conceptual structure of spacetime.