The quantum–classical boundary is one of the deepest unsolved problems in physics. The Information Bottleneck Theorem of the Order Parameter Spacetime Theory provides a precise criterion: when the total information dissipation coefficient Υ=0, the system resides in the quantum sector (unitary evolution, entanglement conservation); when Υ>0, irreversible classicality emerges. How can this binary criterion be tested experimentally? This paper reveals that the binary nature of the Information Bottleneck Theorem—the transition of entanglement from "strict conservation" to "onset of decay"—does not manifest as a discontinuous jump of entanglement, but rather as a nonlinear signature in the decoherence rate. This nonlinearity originates from complex metric back-reaction: information dissipation alters the spacetime geometry, and the geometry in turn modifies the dissipation rate, forming an information–geometry closed loop. Specifically, for a two-qubit entangled state evolving under a pure dephasing channel, the standard Lindblad theory predicts that log C(t) is a straight line; the complex metric back-reaction predicts that log C(t) bends upward—the decay rate slows down as entanglement decreases, i.e., entanglement is protected. At the critical coupling α=1/r₀², the theory predicts exact protection of entanglement (C(t)=constant); in the strong-coupling regime α>1/r₀², the theory predicts that in the initial stage entanglement exceeds its maximum value (C>1). This paper provides a complete theoretical prediction and data analysis scheme to test these predictions using existing experimental data. The decision logic is binary: either log C(t) is a straight line (α=0, complex metric back-reaction falsified), or it is not (α>0, information–geometry closed loop verified).
The quantum–classical boundary is one of the deepest unsolved problems in physics. The Information Bottleneck Theorem of the Order Parameter Spacetime Theory provides a precise criterion: when the total information dissipation coefficient Υ=0, the system resides in the quantum sector (unitary evolution, entanglement conservation); when Υ>0, irreversible classicality emerges. How can this binary criterion be tested experimentally? This paper reveals that the binary nature of the Information Bottleneck Theorem—the transition of entanglement from "strict conservation" to "onset of decay"—does not manifest as a discontinuous jump of entanglement, but rather as a nonlinear signature in the decoherence rate. This nonlinearity originates from complex metric back-reaction: information dissipation alters the spacetime geometry, and the geometry in turn modifies the dissipation rate, forming an information–geometry closed loop. Specifically, for a two-qubit entangled state evolving under a pure dephasing channel, the standard Lindblad theory predicts that log C(t) is a straight line; the complex metric back-reaction predicts that log C(t) bends upward—the decay rate slows down as entanglement decreases, i.e., entanglement is protected. At the critical coupling α=1/r₀², the theory predicts exact protection of entanglement (C(t)=constant); in the strong-coupling regime α>1/r₀², the theory predicts that in the initial stage entanglement exceeds its maximum value (C>1). This paper provides a complete theoretical prediction and data analysis scheme to test these predictions using existing experimental data. The decision logic is binary: either log C(t) is a straight line (α=0, complex metric back-reaction falsified), or it is not (α>0, information–geometry closed loop verified).
We derive testable consequences of the hypothesis that quantum decoherence is subject to a global compression bound. Starting from the bounded compression condition, we show that simultaneous decoherence across multiple channels of a quantum system must satisfy a trade-off relation. We formulate this bound in terms of three representation-invariant measures—the purity loss rate, the dissipative entropy production rate, and the Kossakowski eigenvalue sum—ensuring that all predictions are independent of the non-unique Lindblad decomposition. We derive the bound from two independent physical principles: the finite quantum channel capacity of the environment as an information sink, and the thermodynamic cost of irreversible decoherence via the Landauer principle. For multi-qubit systems, we predict that the decoherence rate of maximally entangled (GHZ) states saturates for sufficiently large qubit number N, deviating from the linear scaling predicted by standard Lindblad theory. We identify the transition regime between weak and strong system–environment coupling as the natural domain where the bound becomes experimentally accessible, and propose concrete protocols using superconducting qubits, trapped ions, and mesoscopic systems. The predictions are falsifiable and independent of any specific interpretive framework for quantum mechanics.
Entropy geometry of a two-level open quantum system predicts a specific ratio between cubic and quintic nonlinear coefficients in the Markovian limit. Two candidate values currently have theoretical support: α/β=6 ("Route B") and α/β=5/3 ("Route A," currently the better-supported of the two). We propose a circuit QED experiment using a superconducting transmon qubit under continuous measurement to test this prediction directly. Phase evolution data are fit to αL−βL² with α and β as independent free parameters; their ratio is the experimental output, discriminating between Route A, Route B, and neither. The experiment is feasible with existing hardware at 3σ significance with 10⁴ experimental runs. v2 correction (Aug 2026): the original Falsification Condition treated α/β=6 as the framework's default/expected prediction. This is corrected throughout: five separate attempted derivations of α/β=6 find no independent theoretical support, while a genuine variational derivation gives α/β=5/3, confirmed four separate times. This strengthens rather than weakens the experimental design — the three-hypothesis structure (H1: α/β=6; H2: α/β=5/3; H3: neither) is exactly the right experiment, now presented evenhandedly. All three figures have been regenerated to show both hypotheses with equal visual weight (the original figures visually singled out α/β=6 as "the prediction"). No change to the experimental protocol, run-count requirements, or feasibility analysis.
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.
We derive a testable consequence of the hypothesis that quantum decoherence is subject to a global compression bound. Starting from the bounded compression condition, we show that simultaneous decoherence across multiple channels of a quantum system must satisfy a trade-off relation: the weighted sum of individual decoherence rates is bounded by a maximum determined by the system's energy scale and the quantum channel capacity of the system-environment coupling. We derive this bound from two independent physical principles: the finite quantum channel capacity of the environment as an information sink, and the thermodynamic cost of irreversible decoherence via the Landauer principle. For multi-qubit systems, we predict that the decoherence rate of maximally entangled (GHZ) states saturates for sufficiently large qubit number N, deviating from the linear scaling predicted by standard Lindblad theory. We identify the transition regime between weak and strong system-environment coupling as the natural domain where the bound becomes experimentally accessible, and propose concrete protocols using superconducting qubits, trapped ions, and mesoscopic systems. The predictions are falsifiable and independent of any specific interpretive framework for quantum mechanics.
This repository presents a theoretical and experimental proposal for a non-conservative source of quantum decoherence linked to irreversible logical erasure in a physically coupled classical system. The work introduces a minimal model in which a quantum system is weakly coupled to a classical predictor performing real-time inference. When the predictor irreversibly erases internal counterfactual states, the model predicts an additional decoherence channel that scales with the rate of logical erasure, independently of energy dissipation or measurement strength. The manuscript derives the expected scaling, defines strict null tests excluding standard decoherence mechanisms, and outlines a concrete experimental protocol designed to be decisively falsifiable. No experimental data are included. This deposit establishes theoretical priority and experimental criteria for testing the proposed effect.
Preprint: This paper derives quantitative bounds on measurement windows for finite-capacity observers extracting information from decohering quantum systems, extending standard decoherence theory to realistic experimental constraints. Main Result: For Gaussian-Markovian decoherence with exponential information decay I(t) = I₀ exp(-2Γt), bounded-capacity observers lose access to system distinctions when mutual information drops below detection threshold ε, yielding measurement window: τ_c = (1/2Γ) log(α C_A / ε) where Γ is decoherence rate [s⁻¹], C_A is observer capacity [bits] defined via Shannon formula (bandwidth × log₂(SNR) × integration time), ε is detection threshold [bits], and α ~ 0.1-1 is a model-dependent constant from spectral decomposition of environmental information. This establishes logarithmic capacity-scaling: doubling detector quality extends measurement windows by only ~0.35/Γ seconds, implying diminishing returns from capacity improvements. Experimental Predictions: For state-of-the-art circuit QED (superconducting transmon qubits, T₁ = 100 μs, bandwidth Δf = 10 MHz, SNR = 10), the framework predicts τ_c ~ 4-10 μs. Varying bandwidth from 1-30 MHz (capacity C_A ∈ [3, 90] bits) produces measurable Δτ_c ≈ 1.7 μs variation (5-10% of coherence time). Five experimental tests discriminate capacity-scaling from standard decoherence: ∙ Tests 1-3: Verify logarithmic capacity-scaling, inverse rate-dependence, threshold-dependence ∙ Test 4: Multi-observer non-redundancy (at most one narrowband detector succeeds) ∙ Test 5: Capacity-dependent redundancy buildup (primary discriminating signature) Key Contributions: ∙ First quantitative analysis of Zurek's pre-objective phase under explicit finite-resource constraints ∙ Capacity-scaling law connecting Shannon information theory to quantum measurement dynamics ∙ Operational definitions ensuring falsifiability (capacity, threshold, mutual information defined via measurement protocols) ∙ Concrete numerical predictions for three platforms (circuit QED, spin qubits, optomechanics) with resource estimates ∙ Design principle: environmental shielding (linear benefit in τ_c) outperforms detector improvement (logarithmic benefit) when both options available Technical Approach: The bound follows from threshold-crossing analysis of exponential decay with capacity-limited initial information I₀ = α C_A, justified via spectral decomposition of environmental information under flat-spectrum approximation for narrowband observation. All parameters (Γ, C_A, ε) are operationally defined and independently measurable, avoiding circularity. Extensions to non-Markovian dynamics (memory kernels), scrambling systems (black holes, many-body chaos), and non-Gaussian noise (Lévy flights, 1/f noise) are discussed with conjectured scaling laws. Scope: The bound applies specifically to Gaussian-Markovian systems (harmonic oscillators, qubits in dispersive limit, weak continuous measurement with memoryless baths). Circuit QED provides optimal testbed due to tunable Purcell filters (bandwidth control), high coherence times (T₁ > 300 μs achieved), and multiplexed readout infrastructure (5+ independent detectors demonstrated). Validity requires α C_A > ε (initial information exceeds threshold); domain violations occur when capacity too small, threshold too high, or coupling too weak. Relation to Prior Work: Zurek's Quantum Darwinism (2003-2009) explains asymptotic objectivity emergence through environmental redundancy but assumes unbounded observers (C_A → ∞, t → ∞). This work analyzes the complementary finite-resource regime (C_A < ∞, t ~ τ_c), providing first capacity-parameterized bound on pre-objective phase duration. Framework is interpretation-neutral—compatible with Copenhagen, Many-Worlds, Bohmian mechanics, and relational quantum mechanics. Philosophical implications (process ontology, observer-dependent reality, impermanence) are explored but clearly separated from testable predictions. Methods: Open quantum systems theory, Shannon information theory, operational quantum measurement, circuit QED experimental physics, numerical prediction for realistic parameters. Content: Complete 90-page manuscript with axiomatic framework (§2), narrowband observation model (§3), main theorem with proof (§4), numerical predictions (§5), five experimental falsification tests (§6), detailed Quantum Darwinism comparison (§7), extensions and limitations (§8), interpretive options (§9), and honest assessment (§10). Includes 77 references and operational definitions for all information-theoretic quantities. Target Audience: Quantum foundations researchers, experimental quantum physicists (circuit QED, trapped ions, quantum dots), quantum information theorists, philosophers of physics interested in measurement and objectivity.