We present a quantitative emergence framework in which a complexity-dependent scalar λ governs the transition from microscopic quantum reversibility to macroscopic classical spacetime. Empirical inputs from many-body localization, Krylov-complexity measurements, and entanglement-based gravity programs identify two robust thresholds that explain staged irreversibility in laboratory systems. The formalism λ (ρ, C, S) = ραCβ exp(−S/Scrit) combines energy density, organizational complexity, and symmetry-resolved entropy; calibrated exponents (α ≈ 0.41, β ≈ 0.70, Scrit ≈ 50 nats) reproduce experimental dual thresholds and export directly to cosmology. Big Bang regularization, the arrow of time, dark-sector phenomena, and the quantum measurement problem become calculable threshold crossings, while seventeen falsifiable predictions anchored in laboratory and astrophysical observables ensure Popperian accountability. The same bookkeeping extends cautiously to higher organizational layers, offering a disciplined template for cross-scale emergence studies.
We present a quantitative emergence framework in which a complexity-dependent scalar λ governs the transition from microscopic quantum reversibility to macroscopic classical spacetime. Empirical inputs from many-body localization, Krylov-complexity measurements, and entanglement-based gravity programs identify two robust thresholds that explain staged irreversibility in laboratory systems. The formalism λ (ρ, C, S) = ραCβ exp(−S/Scrit) combines energy density, organizational complexity, and symmetry-resolved entropy; calibrated exponents (α ≈ 0.41, β ≈ 0.70, Scrit ≈ 50 nats) reproduce experimental dual thresholds and export directly to cosmology. Big Bang regularization, the arrow of time, dark-sector phenomena, and the quantum measurement problem become calculable threshold crossings, while seventeen falsifiable predictions anchored in laboratory and astrophysical observables ensure Popperian accountability. The same bookkeeping extends cautiously to higher organizational layers, offering a disciplined template for cross-scale emergence studies.
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.
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.
Abstract The ontological status of time remains unresolved in fundamental physics. In quantum mechanics, time appears as an external classical parameter, whereas in general relativity it is dynamical and intertwined with spacetime geometry. Canonical approaches to quantum gravity, most notably the Wheeler–DeWitt formulation, eliminate time altogether, leading to the well-known “problem of time.” These tensions motivate frameworks in which time is not fundamental but emergent. In this work, we propose a discrete, update-based framework in which the universe evolves through a sequence of global quantum states indexed by an abstract update parameter rather than by a physical time coordinate. Evolution is formulated as a completely positive, trace-preserving (CPTP) quantum channel acting on the universal density operator, ensuring exact conservation of probability and global quantum information at every update. The framework is deliberately conservative: it preserves the formal structure of quantum mechanics and quantum field theory, enforces vacuum stability, and supports global conservation laws without introducing new dynamical postulates. Within this setting, time emerges relationally at the level of subsystems. As subsystems become increasingly entangled with their environments, entropy gradients arise that define an effective arrow of time, closely aligned with the thermodynamic arrow. The resulting temporal flow is relative, statistical, and observer-dependent, while the global evolution remains information-preserving and, in the closed-system limit, reversible. We explore the implications of this framework for cosmology and black hole physics. The Big Bang is reinterpreted as an initial quantum state rather than a singular beginning of time, avoiding temporal singularities. Black hole evaporation is shown to be compatible with unitary evolution when the full quantum state is considered, naturally reproducing the expected Page curve and resolving the apparent information paradox. Overall, the framework provides a coherent, minimal setting in which time, irreversibility, and cosmological history emerge from quantum correlations rather than from a fundamental temporal background.
This paper presents a unified theoretical framework and an experimental protocol for detecting the precise boundary between the reversible quantum world and the irreversible classical macroworld. We propose that the quantum-to-classical transition is not a gradual process governed by environmental decoherence, but a discrete, threshold-driven phase transition of the physical vacuum itself. Based on the concept of induced gravity and the metric elasticity of the vacuum (A. D. Sakharov) [1], we demonstrate that the Fine-Structure Constant (α ≈ 1/137) emerges naturally as the invariant modulus of elasticity of the quantum vacuum condensate. The value of α is not a free parameter but a direct consequence of the ultimate strength (yield point) of the vacuum, E_max ≈ 2.05 × 10⁻³² J, derived as the geometric mean between the Planck energy scale and the dark energy density. For a test object of fused silica (ρ = 2200 kg/m³), the threshold is reached at a critical mass of M_crit = 27.04 pg, corresponding to a critical diameter of D_crit = 2.863 µm. Below this threshold, the vacuum undergoes purely elastic deformation, preserving time-reversal symmetry (t → -t). Above the threshold, the vacuum enters a plastic flow regime, triggering a dissipative cascade (I. Prigogine) [3] that breaks time symmetry and induces objective wavefunction collapse. We detail an optomechanical cryogenic levitation protocol to detect this transition via a sharp jump in energy dissipation with a predicted damping ratio of Γ7 / Γ6 ≈ 3.90 and the emergence of Fibonacci-ordered vortex structures in phase space, transforming the problem of the origin of α and the arrow of time from abstract speculation into a precise, tabletop experiment.
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
The quantum measurement problem remains one of the most profound unresolved issues in fundamental physics. While quantum mechanics delivers extraordinarily precise statistical predictions, it does not specify a physical mechanism by which definite classical outcomes arise from quantum superpositions. Decoherence theory accounts for the suppression of interference but does not explain outcome selection or the stability of classical reality. This paper investigates quantum measurement within the framework of Relativistic Coherent Vacuum Gravity Theory (rCVGT). In rCVGT, the vacuum is modeled as a structured relativistic medium characterized by a coherence order parameter ψ(x), a coherence magnitude Q(x) = |ψ(x)|², a vacuum-flow four-field u^μ(x), and a physical time-rate field τ(x). We propose that quantum measurement corresponds to a dynamical instability of vacuum coherence induced by macroscopic coupling to matter and radiation. Classical outcomes emerge when local vacuum coherence is driven below a critical stability threshold, resulting in an irreversible reconfiguration of the vacuum state. The collapse timescale is determined by the vacuum-coherence self-energy defined within rCVGT. This mechanism simultaneously provides a physical foundation for classicality, irreversibility, and the arrow of time. The framework preserves the formal structure and empirical predictions of quantum mechanics while offering a unified physical explanation of measurement grounded in relativistic vacuum dynamics.