We investigate a candidate, scale-free coherence invariantΠ ≡ℏ τmd2 ,built from an inertial (or effective modal) mass m, a characteristic coherence or separationlength d, and a coherence or correlation time τ . The original motivation was the possibilitythat a single dimensionless parameter might organize coherence behaviour across a widerange of physical regimes. In this work we take a more modest and technically explicitposition.First, P we present the theoretical framework that motivates Π: a phase–ledger C(t) =i Φi(t) whose conservation, ˙C = 0, leads to local quadratic invariant manifolds in native,dimensionless coordinates. We show, via Buckingham–Π analysis, that for systems whoserelevant variables are (m, d, τ ; ℏ) there is a unique dimensionless combination of this form.Second, we test the coherence invariant hypothesis on a set of heterogeneous butconcrete examples drawn from nine “rungs”: quantum decoherence and matter-waveinterferometry, nonlocal/Bell-type experiments, near- and far-field electromagnetism,astrophysical lines, condensates, cosmic expansion, and dynamic “poke-and-return” motionin atom interferometers and Bose–Einstein condensates. The goal is not to claim a fullyestablished universal law, but to examine where the proposed invariant is (and is not)consistent with data under clearly stated choices of (m, d, τ ).Third, we confront a key limitation: in many platforms there are multiple, physicallyplausible definitions of d and τ . Different choices can shift Π by many orders of magnitude.We therefore emphasize the risk of post-hoc scale selection (“curve fitting”) and propose acanonical scale protocol for future tests: (i) state all plausible definitions of (m, d, τ ) for agiven dataset, (ii) compute Π for each, and (iii) treat the choice that minimizes deviationfrom a hypothesized invariant surface as an empirical question, not a built-in assumption.With these caveats, we find that:• Near-field matter-wave interferometers analysed using the Talbot time as the native τadmit a natural mapping in which an onset band in Π near O(10−1) appears plausible.• Cold-atom and BEC transport experiments, when expressed in terms of their trapscales and transport times, yield very large Π (deep coherence), consistent with theintuitive classification of strongly regulated motion.• In other domains (Bell tests, far-field EM, astrophysical lines, cosmology) the presentevidence is mixed or inconclusive: sensible alternative choices of (m, d, τ ) cannot yetbe ruled out, and the existence of a single cross-domain onset constant is thereforeunproven.iThe main contribution of this paper is thus not a final claim of universality but aclearly defined hypothesis, a normalization and falsifiability protocol, and a set of workedexamples illustrating both the promise and the pitfalls of coherence invariants acrossphysical scales. We highlight specific experiments and re-analyses—especially in matterwaveinterferometry, collisional decoherence, condensates, and atom interferometer/BECdynamics—that could rapidly confirm or falsify key aspects of the framework.Contents
We investigate a candidate, scale-free coherence invariantΠ ≡ℏ τmd2 ,built from an inertial (or effective modal) mass m, a characteristic coherence or separationlength d, and a coherence or correlation time τ . The original motivation was the possibilitythat a single dimensionless parameter might organize coherence behaviour across a widerange of physical regimes. In this work we take a more modest and technically explicitposition.First, P we present the theoretical framework that motivates Π: a phase–ledger C(t) =i Φi(t) whose conservation, ˙C = 0, leads to local quadratic invariant manifolds in native,dimensionless coordinates. We show, via Buckingham–Π analysis, that for systems whoserelevant variables are (m, d, τ ; ℏ) there is a unique dimensionless combination of this form.Second, we test the coherence invariant hypothesis on a set of heterogeneous butconcrete examples drawn from nine “rungs”: quantum decoherence and matter-waveinterferometry, nonlocal/Bell-type experiments, near- and far-field electromagnetism,astrophysical lines, condensates, cosmic expansion, and dynamic “poke-and-return” motionin atom interferometers and Bose–Einstein condensates. The goal is not to claim a fullyestablished universal law, but to examine where the proposed invariant is (and is not)consistent with data under clearly stated choices of (m, d, τ ).Third, we confront a key limitation: in many platforms there are multiple, physicallyplausible definitions of d and τ . Different choices can shift Π by many orders of magnitude.We therefore emphasize the risk of post-hoc scale selection (“curve fitting”) and propose acanonical scale protocol for future tests: (i) state all plausible definitions of (m, d, τ ) for agiven dataset, (ii) compute Π for each, and (iii) treat the choice that minimizes deviationfrom a hypothesized invariant surface as an empirical question, not a built-in assumption.With these caveats, we find that:• Near-field matter-wave interferometers analysed using the Talbot time as the native τadmit a natural mapping in which an onset band in Π near O(10−1) appears plausible.• Cold-atom and BEC transport experiments, when expressed in terms of their trapscales and transport times, yield very large Π (deep coherence), consistent with theintuitive classification of strongly regulated motion.• In other domains (Bell tests, far-field EM, astrophysical lines, cosmology) the presentevidence is mixed or inconclusive: sensible alternative choices of (m, d, τ ) cannot yetbe ruled out, and the existence of a single cross-domain onset constant is thereforeunproven.iThe main contribution of this paper is thus not a final claim of universality but aclearly defined hypothesis, a normalization and falsifiability protocol, and a set of workedexamples illustrating both the promise and the pitfalls of coherence invariants acrossphysical scales. We highlight specific experiments and re-analyses—especially in matterwaveinterferometry, collisional decoherence, condensates, and atom interferometer/BECdynamics—that could rapidly confirm or falsify key aspects of the framework.Contents
This manuscript develops three concrete, falsifiable predictions based on a framework in which time and space are operationally equivalent, and classical reality is understood as the record. In this scalar-clock / awareness-tensor / Trinity picture, an observation is any physical process that stabilizes correlations into durable, revisitable records, and gravity is interpreted as time decoherence: clock-locking and time selection into dominant mass time-zones. The paper introduces three phenomenological parameters that are exactly zero in standard GR+QM: (i) ϵ\epsilonϵ, the sensitivity of co-located clock rates to engineered decoherence and monitoring strength; (ii) η\etaη, the sensitivity of effective gravitational acceleration to record-export structure at fixed mass distribution; and (iii) a scalar time-mismatch scale ΔT∗\Delta T_\astΔT∗, beyond which interference visibility near a mass exhibits a protocol-dependent threshold. These parameters are tied to operational proxies: clock-locking depth, time mismatch, and coupling gradients. From this framework, three testable predictions follow: Entanglement-dependent time dilation: Two identical, co-located precision clocks in the same gravitational potential but in different record-coupling regimes (high vs. low monitoring and decoherence) should exhibit a small, persistent differential drift that tracks clock-locking depth, not altitude or velocity. Gravity modulation by engineered decoherence: In a torsion balance, atom interferometer, or precision gravimeter, the measured acceleration toward a test mass should differ slightly between “decoherence OFF” and “decoherence ON” conditions, even when the mass distribution and EM fields are unchanged. The key signature is a protocol-locked Δg\Delta gΔg that appears only when scattered quanta are recorded, not when the same fields are present but their outputs are dumped locally. Entanglement horizon near mass: In a matter-wave interferometer, as one arm approaches a mass (or as the mass is increased), interference visibility should drop at a characteristic threshold set by scalar-clock mismatch and record structure. This defines an “entanglement horizon” in time-mismatch space, distinct from smooth environmental decoherence. For each effect, the paper defines explicit null hypotheses, identifies leading systematics, and sketches minimal experimental protocols compatible with current or near-term optical clocks, gravimetry, and matter-wave interferometry platforms. A brief CPT-compatibility analysis clarifies that microscopic dynamics remain CPT-symmetric in the usual QFT sense; any asymmetries arise only at the coarse-grained level of record formation and clock-locking. The proposals can therefore be read either as parameterized extensions of GR+QM using measurement architecture as an additional knob, or as an operational test of a broader “gravity as time decoherence” interpretation in which geometry becomes explicitly record-sensitive. This Version 2 is a revised and expanded update of the original upload, adding a phenomenology-first summary, clarifying the roles of the parameters (ϵ,η,ΔT∗)(\epsilon,\eta,\Delta T_\ast)(ϵ,η,ΔT∗), and situating the framework more explicitly relative to existing work on gravity-related decoherence, hybrid classical–quantum gravity, and clock/interferometry proposals (Diósi–Penrose, Bassi, Anastopoulos–Hu, Oppenheim, Zych–Costa–Pikovski–Brukner, Bose et al.). The updated version explicitly restricts the criterion to record-sensitive effects, rather than any effect. It explicitly spells out what “record formation on/off” means in practice: detectors and logging are turned on/off while the physical fields are held fixed, i.e., outputs are either stored or not stored. This version tightens falsifiability and lab usability. It (i) commits to explicit benchmark model families for the three predictions, each reducing to standard physics when ϵ=η=κ=0\epsilon=\eta=\kappa=0ϵ=η=κ=0; (ii) defines an unambiguous export-axis variable via the exported mutual-information rate I˙XR\dot I_{XR}I˙XR and export depth E\mathcal{E}E, enabling cross-platform comparisons; (iii) adds a fully worked, platform-specific optical lattice clock pilot (C1 vs C2 export-only toggle) including invariance audits, confound/error budgeting, preregistered power/discriminability analysis, and an end-to-end analysis pipeline; and (iv) upgrades mandatory reporting/preregistration templates so null results produce publishable bounds on (ϵ,η,κ)(\epsilon,\eta,\kappa)(ϵ,η,κ).
When a quantum system couples to a scale-invariant environment, what form must its decoherence take? We prove that the answer is unique: under locality, Lorentz invariance, unitarity, and continuous scale invariance, the effect of any such environment is mathematically equivalent to that of an \emph{unparticle bath} -- a scale-invariant continuum of states -- characterized entirely by the scaling dimension dU of the coupled operator. This is not a modelling choice but a consequence of conformal symmetry. All decoherence and dissipation exponents are fixed by dU through exact consistency relations, providing falsifiable predictions independent of microscopic details. We validate the framework using multi-channel transport data from the unitary Fermi gas, where two genuinely independent observables yield a consistent dU=7/4. We further show that quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos -- spanning more than 25 orders of magnitude in energy -- are unified as specific realizations of the same structure. A decoherence phase transition at dU=5/2, where quantum coherence is \emph{protected} rather thandestroyed at long times, is a qualitative prediction inaccessible to any memoryless dynamical description.
We propose an explicitly testable unified framework in which (i) the emergence of definite measurement outcomes from quantum superposition and (ii) the emergence of conscious, unified experience are treated as two manifestations of the same metastability-to-stability transition in a structured pattern space. The theory is grounded in two primitives: distinction acts Ξ (elementary differentiation) and a structuring operator | (composition into persistent organization). Any realizable pattern P is characterized by an integrity functional I(P) ∈ [0,1] (internal coherence and resistance to fragmentation) and an effective coherence radius Rc(P) (correlation length in physical, neural, or semantic space). Metastable patterns are postulated to satisfy a balance law, I(P)Rc(P) = ξ0, defining a slow manifold whose deviations quantify instability and foreshadow transition events.To encode collapse-like transitions and outcome/contents selection with minimal topological complexity, states are represented on a toroidal manifold T 2 with angles (θ, φ), where φ is a collapse (stability) order parameter (wave-like at φ = π, particle-like at φ = 0) and θ labels branch phase. A harmonic closure postulate 2R = 2πr yields R/r = π without inserting π as a fit parameter, motivating a universal residual fraction 1/π and a complementary critical integrity threshold C2 = 1 − 1/π ≈ 0.682 for robust self-referential Patterns of Experience. Dynamics are formulated as noisy relaxation of balance-mismatch, predicting critical slowing down and a universal critical angle φc ≈ 2π/3 (under the closure hypothesis). Apparent randomness is attributed to phase sensitivity and noise, with outcome probabilities expressed as basin measures in θ, providing a concrete route to Born-like statistics under contextual constraints.The empirical program specifies operational proxies for I and Rc (with explicit calibration to [0,1]) and proposes falsifiable tests in neuroscience (EEG/MEG/ECoG; invariance of C2, early-warning signals, phase “freezing”) and quantum platforms (context engineering, weak/continuous measurement, complexity scaling of collapse times). Clear failure modes include systematic deviation from C2, absence of critical slowing down, and non-clustering of inferred φc near 2π/3.
We propose that the quantum measurement problem is a frame problem, resolved by recognizing that coherence is relative to a choice of coherence frame—analogous to the relativity of simultaneity in special relativity. We introduce coherence relativity, a geometric framework in which physical reality is described on a joint manifold M×Σ, where M is emergent spacetime and Σ is a coherence manifold whose points represent distinct observational perspectives. In this framework, wave function collapse is not a dynamical process but a transformation between coherence frames induced by measurement interactions. We present a derivation of the Born rule—that measurement probabilities equal squared amplitudes—as the unique probability measure invariant under coherence-frame relabelings and splittings, given additivity and continuity. This derivation unifies insights from Gleason's theorem, Zurek's envariance, and operational reconstruction programs within a single geometric structure. We demonstrate the framework with the double-slit experiment in two coherence frames and identify six experimentally testable signatures distinguishing Coherence Relativity from standard quantum mechanics: non-linear visibility scaling, frame-transformation hysteresis, coherence-space curvature effects, modified gravitational decoherence, measurable transformation timescales, and coherence revival. The most accessible predictions—erasure hysteresis and transformation timescales—are testable with current superconducting qubit and trapped ion platforms. v4 (April 2026): Adds three new paradox resolutions (Quantum Zeno with D_f completion interpretation, Sleeping Beauty via CR-internal derivation from axioms A1+A3, and a unifying meta-theorem characterizing all quantum paradoxes as non-Born-compliant frame transport). Introduces Prediction 7 (Zeno/anti-Zeno crossover at τ_meas ≈ τ_transform with pointer-basis dependence). Total experimentally testable signatures increased from six to seven. 21 pages.
We report systematic validation of the Davis Law of Critical Velocity governing vortex nucleation in two-dimensional Gross-Pitaevskii dynamics: C=Kτ⇒β=csvc=f(Keff)(species-independent, geometry-indexed) Through GPU-accelerated Gross-Pitaevskii simulations across three atomic species (⁸⁷Rb, ²³Na, ⁷Li) spanning a 12:1 mass ratio, we demonstrate that the dimensionless critical velocity β = v_c/c_s is species-independent—a universal geometric invariant within each curvature regime, determined solely by obstacle geometry. Key Results Universal Critical Velocity: Hard obstacles (tanh-wall): β_hard = 0.425 ± 0.000 across all three species Semi-hard obstacles (Gaussian, V₀ = 50μ): β_soft = 0.486 ± 0.000 across all species Excellent agreement with Frisch-Pomeau-Rica result (β ≈ 0.4) Perfect Species Independence: The coefficient of variation is 0.0% for both obstacle types across a 12:1 mass ratio, definitively proving that β depends only on obstacle geometry, not atomic properties. Davis Law Support: The relation C = τ/K from the Davis Field Equations correctly predicts that obstacle curvature controls the critical velocity. High-curvature (hard) obstacles nucleate vortices at lower β than low-curvature (soft) obstacles. Quantum vs Classical Wake Dynamics: In the post-critical wake, coherent oscillations occur with phase φ ≈ 0° (symmetric breathing) rather than φ ≈ π (alternating von Kármán), implying suppression of the classical anti-phase shedding mode. The Geometric Trichotomy Regime Obstacle Type K_eff Mechanism β = v_c/c_s Sonic Hard (tanh-wall) High Local Mach = 1 at obstacle rim 0.42–0.49 Sonic Semi-hard (Gaussian) Medium Same mechanism, different K_eff ~0.486 Quantum Truly soft (V₀ ≪ μ) Low Holonomy budget τ = 2π exhausted ~0.95–√2 The functional relationship β = f(K_eff) is universal—independent of atomic mass, scattering length, and density—with distinct numerical values corresponding to distinct geometric classes. Unifying Principle The various measured thresholds are unified by a single principle: Geometry selects the regime (soft vs hard) Compressibility selects the prefactor (local c_s and amplification A) Barrier physics selects the delay (sonic onset vs nucleation threshold) This validates the Davis Law prediction that coherence thresholds are determined by constraint geometry (C = τ/K), not microscopic physics. Evidence Status Claim Status Evidence β is species-independent Proven 0.0% CV across 12:1 mass ratio β_hard = 0.425 ± 0.000 Proven Identical value across Rb-87, Na-23, Li-7 β_soft = 0.486 ± 0.000 Proven Identical value across Rb-87, Na-23, Li-7 K_eff controls regime Proven Curvature scaling law shows monotonic β(K_eff) C = τ/K governs transition Supported Qualitative agreement; mechanism confirmed Wake mode is symmetric Proven Phase φ ≈ 0° measured (not 180° classical VK) Frisch-Pomeau-Rica agreement Proven β_hard = 0.425 matches FPR β ≈ 0.4 Included Files Simulation Code multi_species_trichotomy.py — Main simulation testing β across Rb-87, Na-23, Li-7 curvature_scaling_law.py — Tests C = τ/K scaling, K_eff operational definition Figure Generation plot_davis_landau_law.py — Publication figures (universal β, v_c vs c_s) mach_summary_for_paper.py — M_rim vs v/c_s showing sonic onset mechanism phase_comparison_figure.py — VK vs GP symmetric modes diagnostic stability_islands_extended.py — Stability islands analysis Data trichotomy_data.json — Pre-computed multi-species results superfluid_test_results_corrected.json — Validation data Relation to Prior Work This paper extends the Davis Framework for geometric physics: The Incompressibility of Topological Charge (Yang-Mills Mass Gap) — DOI: 10.5281/zenodo.17846521 Holonomy-First Navier-Stokes Regularity — DOI: 10.5281/zenodo.18216597 Field Equations of Semantic Coherence — DOI: 10.5281/zenodo.14784553 The critical velocity emerges as the threshold where topological defect creation (vortex nucleation) becomes energetically favorable—the "cost of distinguishability" in the information-geometric framework. Keywords Bose-Einstein condensate, critical velocity, superfluidity, Gross-Pitaevskii equation, vortex nucleation, Landau criterion, sonic onset, geometric trichotomy, Davis Law, quantum hydrodynamics, obstacle geometry, Mach number, effective curvature, species independence, universal constant License Creative Commons Attribution 4.0 International (CC BY 4.0) Related Identifiers References: DOI 10.5281/zenodo.17846521 (Yang-Mills Mass Gap) References: DOI 10.5281/zenodo.18216597 (Navier-Stokes Regularity) References: DOI 10.5281/zenodo.14784553 (Field Equations of Semantic Coherence)
UST vΩ — Rung 15: Universal Coherence Damping Across Physical Systems UST vΩ (Unified Structural Theory, vOmega) is an exploratory theoretical framework aimed at identifying structural regularities that persist across otherwise disparate physical systems. Rather than proposing new particles, forces, or modifications to established theories, UST vΩ seeks to understand whether certain physical behaviors can be organized and compared through shared structural and topological features that emerge at the level of observable quantities. Rung 15 of UST vΩ focuses specifically on coherence loss, damping, and degradation across a wide range of systems, including superconducting microwave resonators, classical electromagnetic cavities, magnons, and electrochemical batteries. These systems span many orders of magnitude in frequency, timescale, and underlying microscopic physics, yet they all admit experimentally measurable quantities related to coherence, dissipation, or decay. This work does not seek to replace quantum mechanics, the Standard Model, or condensed-matter theory. All existing frameworks remain fully valid within their established domains. Instead, Rung 15 offers a complementary, higher-level perspective: that coherence loss may admit a universal structural description when viewed through appropriate dimensionless observables and scaling relationships. Across all systems examined, coherence degradation can be expressed through an effective rate Empirical analysis of large datasets—most notably superconducting microwave devices—reveals the existence of a stiffness-limited coherence ceiling. For superconductors, this ceiling is controlled by the imaginary (superfluid) conductivity, leading to an empirical envelope Real systems fall below this ceiling by varying amounts. To quantify this deviation in a system-independent way, UST vΩ introduces a dimensionless defect participation coordinate, Within UST vΩ, is interpreted as a measure of topological defect participation rather than a catalog of microscopic defects such as two-level systems, quasiparticles, or chemical degradation pathways. This interpretation is motivated by analogies to coherence-driven topological annealing observed in tessellated systems, where dissipation localizes on structural defects and relaxes under coherent driving. In this view, coherence loss represents a structural tax imposed by defect participation within a constrained manifold. Combining stiffness limitation and defect participation yields the closed Rung-15 law: Importantly, this framework does not contradict existing microscopic models. Standard loss mechanisms remain valid and necessary for detailed local understanding. UST vΩ instead operates at a structural level, organizing the observable consequences of those mechanisms into a compact, comparative description. In this sense, Rung 15 is best viewed as a synthesis layer rather than a replacement theory. Rung 15 is considered mathematically closed within the UST vΩ program. All quantities introduced are dimensionless or directly measurable, no free parameters are added beyond empirical constants, and all datasets used are explicitly documented. Predictions arising from this rung are framed as guidance in parameter space—identifying regions where higher coherence may be structurally favored—rather than claims of undiscovered physics. This document freezes Rung 15 as a stable reference layer. It is intended to serve as a portable backbone for future work, including higher rungs that explore nonlinear coherence coupling, collective effects, and structural scaling. The value of Rung 15 lies not in overturning existing theories, but in offering a different lens through which coherence across physical systems can be compared, organized, and explored.