We model the vacuum as a discrete face-centered-cubic (K=12) tensor network with Bell-pair bonds and use it to predict a two-step quantum-to-classical threshold for macroscopic center-of-mass superpositions. A reversible dispersive deformation of the center-of-mass mode sets in at msoft≈13.1μg, and coherence becomes geometrically unsustainable at mhard≈22.6μg. The two scales are separated by the exact, parameter-free ratio 3, fixed by the edge-to-circumradius ratio of the cuboctahedral triangular face. Gravitational-collapse models predict a single scale of the same order, so the distinctive, falsifiable content is the two-step structure and the exact 3 separation, testable by a mass scan across the window; the recent 16.2μg cat-state oscillator of Bild et al. falls between the thresholds, where coherence is not ruled out. The absolute window depends on the bond length L=4ln2ℓP≈1.665ℓP, fixed by one calibration against the Bekenstein–Hawking area law. This calibration and the Compton representability hypothesis—that a mass excitation remains coherent only while its reduced Compton wavelength is resolvable by the lattice—are stated model inputs rather than derivations, motivated by the Compton frequency internal clock of massive excitations, the mass cutoff generic to lattice-regularized field theories, and the total-mass dependence observed in composite-object interferometry. Open problems are stated explicitly.
We model the vacuum as a discrete face-centered-cubic (K=12) tensor network with Bell-pair bonds and use it to predict a two-step quantum-to-classical threshold for macroscopic center-of-mass superpositions. A reversible dispersive deformation of the center-of-mass mode sets in at msoft≈13.1μg, and coherence becomes geometrically unsustainable at mhard≈22.6μg. The two scales are separated by the exact, parameter-free ratio 3, fixed by the edge-to-circumradius ratio of the cuboctahedral triangular face. Gravitational-collapse models predict a single scale of the same order, so the distinctive, falsifiable content is the two-step structure and the exact 3 separation, testable by a mass scan across the window; the recent 16.2μg cat-state oscillator of Bild et al. falls between the thresholds, where coherence is not ruled out. The absolute window depends on the bond length L=4ln2ℓP≈1.665ℓP, fixed by one calibration against the Bekenstein–Hawking area law. This calibration and the Compton representability hypothesis—that a mass excitation remains coherent only while its reduced Compton wavelength is resolvable by the lattice—are stated model inputs rather than derivations, motivated by the Compton frequency internal clock of massive excitations, the mass cutoff generic to lattice-regularized field theories, and the total-mass dependence observed in composite-object interferometry. Open problems are stated explicitly.
A model of the vacuum as a face-centered-cubic lattice predicts a two-step quantum–classical threshold, at 13.1 and 22.6 µg, from the hypothesis that a center-of-mass excitation stays coherent only while its reduced Compton wavelength is resolvable by the lattice. Collapse models also limit macroscopic coherence, so the two must be told apart by more than a scale. We derive three discriminators from the model's postulates and compute the counterpart in Diósi–Penrose collapse and in continuous spontaneous localization (CSL). The thresholds depend on total mass alone, while both collapse models depend on density. Below 13.1 µg the model predicts no intrinsic decoherence, where collapse takes 1 s for Diósi–Penrose and about a microsecond for CSL at its experimental bound, for 10⁻¹⁵ kg over 1 µm. The model predicts no measurable heating; read as position localization, its own rate scale would exceed the LISA Pathfinder bound by 66 orders of magnitude, so coherence loss above the threshold must be dephasing in the energy basis. If its effective mode mass is the relevant mass, a 16.2 µg mechanical cat state then bounds the irreversible coupling at 38 orders below its natural scale. A worked levitated-particle example and a public script complete the analysis.
For decades, theoretical physics has struggled to discretize spacetime without inadvertently breaking Lorentz invariance [1,2]. Building upon the Selection-Stitch Model (SSM) [3], we model the vacuum as an emergent Face-Centered Cubic (FCC, K = 12) tensor network. In this unified framework, we demonstrate that the foun- dational scales of both relativity and quantum mechanics emerge naturally from the strict geometric limits of this saturated lattice. First, we show that the macroscopic speed of light (c) is simply a geometric renormalization of the underlying lattice hopping speed (c = 4vlattice). Second, rather than treating the Planck scale as an arbitrary mathematical cutoff, we derive the fundamental lattice spacing a≈0.77lP as the exact limit where the vacuum’s elastic energy density strikes the absolute a/√3 kinematic exclusion limit (the metric wall) [4]. Third, by treating the vacuum as a Chiral Cosserat continuum, we explicitly derive the complex unit i and the Schr¨odinger equation from lattice gyroscopics. Finally, by intersecting this wave mechanics with the metric wall, we predict a strictly falsifiable, two-step decoher- ence limit for macroscopic superposition: a soft onset of Schr¨odinger breakdown at msoft ≈28µg, and an absolute structural hard cutoff at mhard = √3msoft ≈49µg.
A companion paper predicted a two-step quantum–classical threshold at 13.1–22.6 μg from a close-packed vacuum lattice, resting on a stated hypothesis (P3): the lattice sustains a coherent mass excitation only while it can resolve the excitation's Compton wavelength. Here we derive as much of that structure as the lattice's own error-correcting code permits, working exactly on the [[3L_s^3, 2L_s^3+2, 3]] CSS family. Results: (1) an exact dephasing law — the vacuum code's own syndrome extraction dephases center-of-mass superpositions of edge-supported excitations at a rate set by the weight variance of the stabilizer group on the excitation's support; (2) a revival dichotomy theorem — at clock phase π per cycle, coherence is exactly 1 or exactly 0, decided by a one-line kernel criterion; (3) exact locality and composite laws — the composite clock runs at total mass because rest energies add, and dephasing is exactly additive beyond contact range, with a subadditive co-monitoring correction at contact; (4) a tracking band, conditional on one isolated dynamical assumption: if passive verification gives way to active checking at phase aliasing, the crossover spans m_alias = h/(8Lc) = 10.3 μg to m_wrap = h/(4Lc) = 20.5 μg — a cadence-derived band that the geometric window 13.1–22.6 μg overlaps without coinciding, so two independently constructed mechanisms select the same narrow microgram regime; and (5) the calibration foundation — the vacuum's entanglement obeys an exact area law on flat cuts, and for ball regions the exactly derived staircase factor of 3/2 is numerically compensated by inter-facet correlations to 10–15% at the tested sizes, with exactness of the compensation conjectured. What is not derived is stated with equal care: the existence of the passive-to-active transition is postulated, not derived, and the precise geometric endpoints and their √3 ratio remain inputs. Every claim carries a status tag.
Levitated optomechanical systems are approaching the regime where macroscopic quantum superpositions become experimentally accessible. A central question is whether gravity itself, through its unavoidable coupling to material quantum fluctuations, imposes a fundamental decoherence channel on such superpositions. Starting from two independently well-tested physical elements—the quantum vacuum fluctuations of the material energy-momentum tensor, and the weak-field linear response kernel of classical general relativity—we derive a structurally rigid scaling law for the gravitational decoherence rate: \Gamma \propto G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L). The exponents and dependence on mass M, superposition separation d, and object size L are fixed entirely by dimensional analysis and the semiclassical field equations, without tunable parameters. The overall amplitude is set by a single phenomenological input—the ultraviolet cutoff scale l_* of the effective geometric noise. Identifying l_* with the Planck length yields \Phi \sim \mathcal{O}(1) and a decoherence rate of order 1\,\text{Hz} for nanoparticles with M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, and L \sim 10^{-6}\,\text{m}, placing the prediction within the foreseeable sensitivity window of next-generation levitated optomechanical setups. We provide explicit falsification conditions, a three-path staged verification strategy that does not require simultaneous optimisation of all parameters, and operational signatures—including a distinctive pure-dephasing channel without energy relaxation—that distinguish this mechanism from environmental noise, zero-temperature electromagnetic vacuum fluctuations, and the Diósi-Penrose model.
The generalized uncertainty principle (GUP) modifies the Heisenberg relation by a term β₀(ℓ_P Δp/ħ)² and implies a minimal length Δx_min = √β₀ ℓ_P. Theory expects β₀ ~ 1 but does not fix its value; experiments bound it from above. Here we report a closed-form value, β₀ = (4/3) ln 2 ≈ 0.9242, obtained from two published inputs of the Selection–Stitch Model (SSM): a minimal approach distance r_min = L/√3 set by lattice geometry, and a bond length L = 2√(ln 2) ℓ_P set by an exact, codeword-independent entanglement calibration of the model's [[3L_s³, 2L_s³+2, 3]] vacuum code. The same inputs fix the model's macroscopic decoherence threshold m_soft = ħ/(Lc), which yields a bridge identity, β₀ = (1/3)(m_P/m_soft)². The identity ties two separate experimental programs — deformed-commutator tests and microgram-scale superposition tests — to one quantity, and it can be tested without adopting the model: a measured decoherence threshold predicts β₀, and conversely. All assumptions are tagged.
The primary objective of the experiment is to reliably identify the critical threshold at which quantum coherence collapses. Detecting this threshold is fundamental: it marks the birth of the arrow of time and the transition from unitary quantum dynamics to irreversible dissipation. In the proposed protocol, the threshold is determined by measuring the interference fringe contrast V while systematically varying the microsphere mass; its value (Dcrit = 2,863 µm, Mcrit = 27,04 pg) provides a clear boundary between the “quiet zone” (coherence preserved) and the regime of plastic flow of the vacuum (irreversible coherence loss). Without a robust determination of this threshold, any tests for irreversibility or control of the arrow of time are physically meaningless. An experimental protocol is proposed for direct laboratory testing of the hypothesis of a fundamental yield limit of the physical vacuum — a critical value of gravitational self-energy E_max ≈ 2.05 × 10⁻³² J at which the reversible elastic deformation of the vacuum (GR metric) transitions to irreversible plastic flow. The protocol is based on measurements of the free oscillation ringdown of the center of mass of levitated fused silica (SiO₂) microspheres in a diamagnetic trap at cryogenic temperatures. A precision scanning grid of eight steps is constructed in the diameter range 1.0–5.0 µm with a critical point D_crit = 2.863 µm and critical mass M_crit = 27.04 pg. The key prediction is a slope kink in the contrast function V(M) at the threshold point, experimentally distinguishable from the smooth monotonic decay predicted by the Penrose– Diósi and GRW/CSL models. Below the threshold — a flat zone of silence (V = 1); above — decay of V according to the law exp(−x(x − 1)), where x = E_G/E_max. At the threshold point V = 1 (flow is just beginning), while Penrose gives V = 1/e ≈ 0.37. Distinguishable. The exponent 1/3 in the formula for E_max is not a fitting parameter. It is uniquely determined by the dimensionality of space and does not yield a macroscopic, experimentally accessible threshold for any other value of d. The central goal of the protocol is to investigate the birth of the arrow of time at the transition point. The protocol consists of two parts: a bottom-up pass (birth of the arrow) and a top-down pass (test of irreversibility). An additional test — rotation of the sphere at the moment of threshold crossing — examines the connection between parity and the direction of the arrow (TP-invariance). The window for controlling the direction is the interval from M_crit to 1.4 × M_crit, where dissipation is already underway but the flux is weak and the direction has not yet frozen. The model is falsifiable by three independent criteria: • A flat zone of silence at small D. • V ≈ 1 at the threshold point. • Quadratic decay above the threshold. The use of diamagnetic levitation instead of an optical tweezer eliminates the dominant decoherence channel — photon scattering from the trap. At pressure P = 10⁻¹³ mbar and trap frequency f₀ = 1 Hz, the background decoherence is ~1% of the threshold (signal-to-background ratio ~100). At f₀ = 100 Hz — 0.01% (signal-to-background ratio ~10,000).