Time Cosmology in the laboratory: irreversible selection as gravitational threshold collapse, its non-radiative survival of the Diósi–Penrose bound, and a matter-wave test
Time Cosmology (TC) reads the dark sectors as tenses and identifies the present with an irreversible selection performed by the fundamental forces. At the background and recent-universe level TC is observationally degenerate with quintessence. This paper exhibits the program's first non-cosmological discriminant. Carried to the laboratory, the irreversible recording of an outcome into the gravitational ledger is governed by the Penrose energy-time criterion tau ~ hbar/E_G, a parameter-free collapse time for spatial superpositions; TC supplies the ontological reason Penrose left open (collapse = writing to the past) and attaches a Landauer cost. Because TC selection is a quantum non-demolition (QND) measurement by the existing forces, not a stochastic noise field, it carries no continuous momentum diffusion and hence no spontaneous radiation; it therefore survives the 2021 Gran Sasso experiment that excluded the parameter-free Diosi-Penrose model. The prediction is falsifiable: a spatial superposition of ~1e-17 to 1e-15 kg held beyond tau must collapse; the gap to capability is ~6 orders of magnitude for second-scale experiments, shrinking to ~1-2 orders for long-hold MAQRO-class proposals. Scope is stated explicitly: the collapse time reproduces Penrose's (the novelty is the grounding and the non-radiative survival); the non-radiativity rests on strict non-stochasticity, with a residual-diffusion bound left as the central open calculation; the test is not within current reach. All numerical claims are reproduced by the archived code included in this record. Companion records: Indispensable Present (10.5281/zenodo.20707004), N3 (10.5281/zenodo.20564003), N5 calorimeter (10.5281/zenodo.20617808).
Time Cosmology (TC) reads the dark sectors as tenses and identifies the present with an irreversible selection performed by the fundamental forces. At the background and recent-universe level TC is observationally degenerate with quintessence. This paper exhibits the program's first non-cosmological discriminant. Carried to the laboratory, the irreversible recording of an outcome into the gravitational ledger is governed by the Penrose energy-time criterion tau ~ hbar/E_G, a parameter-free collapse time for spatial superpositions; TC supplies the ontological reason Penrose left open (collapse = writing to the past) and attaches a Landauer cost. Because TC selection is a quantum non-demolition (QND) measurement by the existing forces, not a stochastic noise field, it carries no continuous momentum diffusion and hence no spontaneous radiation; it therefore survives the 2021 Gran Sasso experiment that excluded the parameter-free Diosi-Penrose model. The prediction is falsifiable: a spatial superposition of ~1e-17 to 1e-15 kg held beyond tau must collapse; the gap to capability is ~6 orders of magnitude for second-scale experiments, shrinking to ~1-2 orders for long-hold MAQRO-class proposals. Scope is stated explicitly: the collapse time reproduces Penrose's (the novelty is the grounding and the non-radiative survival); the non-radiativity rests on strict non-stochasticity, with a residual-diffusion bound left as the central open calculation; the test is not within current reach. All numerical claims are reproduced by the archived code included in this record. Companion records: Indispensable Present (10.5281/zenodo.20707004), N3 (10.5281/zenodo.20564003), N5 calorimeter (10.5281/zenodo.20617808).
VERSION NOTE (v2, 2026-07-02): This version supersedes v1 (April 2026). The central empirical-viability claims of v1 — a thermodynamically viable collapse kernel and a favorable DESI DR1 cosmological signature — were falsified by the author's own subsequent analysis. Fixing the smearing length to its holographically mandated value forces confrontation with the full hierarchy of collapse bounds, where spontaneous-heating measurements exclude it by ~9 orders of magnitude. The work has been rewritten as a parameter-free no-go constraint. v1 is retained below for the version record but should not be cited as a viability result. ABSTRACT (v2): The Diósi–Penrose (DP) model of gravity-induced wavefunction collapse requires an ad hoc mass-smearing length, set phenomenologically at the nucleon scale, R0 ~ 1e-15 m. We show that this scale is fixed by holographic cosmological geometry: evaluating the Károlyházy metric variance over the cosmological apparent horizon, as mandated by the Bousso covariant entropy bound, yields R0 = (lP^2 RH)^(1/3) = 3.3 fm from measured constants alone — a parameter-free reproduction of the historical choice. The decoherence-time kinematics survive every current test: a quantum–classical partition at m_crit ≈ 120 m_e protects atomic chemistry (electron tau ~ 1e21 s) and matter-wave interferometry (C60: ~115 yr) while imposing definiteness on macroscopic bodies, with the ambiguous mesoscopic window falling in the macromolecular regime accessible to near-term interferometry. The standard dynamical realization does not survive. The Einstein Equivalence Principle suppresses single-nucleus dipole bremsstrahlung by a derived factor (k_X R0)^2 ≈ 3e-8, and any noise cutoff below 1e18 Hz evades the underground X-ray bound; but neither defense touches spontaneous heating, which with the standard prefactor predicts ~28 mW/kg — nine orders of magnitude above cryogenic heat-leak ceilings. The heating is charge-independent and probes THz phonons via the relative momentum diffusion of atoms separated by 1e5 correlation lengths, so it is immune to the equivalence principle and robust to any high-frequency cutoff. The framework derives exactly two temporal scales (the pixel light-crossing rate ~1e22 Hz and the horizon refresh rate ~1e-19 Hz); neither lands in the fifteen-decade escape window, and inserting one by hand reinjects the free parameter the construction eliminates. We conclude that if objective collapse is sourced by cosmological holographic geometry, it cannot be mediated by continuous stochastic momentum diffusion: a parameter-free no-go constraint forcing gravity-induced reduction toward non-dissipative or purely kinematic mechanisms.
Version 2.8 — submission manuscript. Preprint prepared for submission to Foundations of Physics. Supersedes v2.6, v2.5, v2.3, v2.2 and v1. A gravitational collapse model in which spacetime geometry is postulated to be irreducibly classical and superpositions of massive systems decay under a stochastic dynamics driven by a physical temporal medium: one stationary noise field combining the Diósi–Penrose spatial kernel with a coloured temporal kernel of finite universal bandwidth ω_u — the single new parameter of the primary model. The decoherence envelope is derived exactly (Gaussian onset, DP exponential tail), and two universality propositions are proved: the DP tail is fixed by the kernel's zero-frequency weight alone, and a Gaussian onset is generic for any finite-bandwidth medium — making the crossover, not any particular kernel, the experimental signature. A selectivity theorem shows each configuration draws its collapse dominantly from noise modes near its own gravitational frequency ΔE_g/ℏ. The parameter-free tuning of earlier versions is retained as named Conjecture C1, with a proof that no single stationary spectrum realises it for all configurations at once. The coloured kernel suppresses collapse-induced spontaneous radiation, reconciling the model with underground null results; heating bounds survive at full strength. Predictions include a closed-form optimal measurement window (separation 0.330 at t = 0.837 τ_dec under C1) and a mass-and-time ceiling on Bell violations, with five falsification conditions. The BMV/GIE treatment is current with the 2024–2026 literature. Changes in v2.8 (Appendix B, B11–B13): universal-bandwidth primary model with derived (ω_u, R_0) window; C1 demoted to conjecture with proved obstruction; no-signalling corrected and branch-conditioned; non-Markovian trajectory literature engaged, Born-rule theorem declared open; one prediction and the "present moment" identification withdrawn with reasons; GIE dispute disentangled; references verified. This paper builds on v1 of the companion collapse-model work (10.5281/zenodo.19960071). The lowest-energy principle assumed here was withdrawn in v2.2 of that paper and does not appear in the current version (v2.8); the framework presented here has not been revised accordingly. Retained as a record of the earlier line of enquiry All revisions, withdrawn claims, and corrected errors are documented in Appendix B; open problems in Section 8. AI tools (Claude, Anthropic) assisted with formalisation and editing; the conceptual framework originated with the author, who takes full responsibility. Full declaration in the manuscript.
We develop a gravitational collapse model in which spacetime geometry is postulated to beirreducibly classical and quantum superpositions of massive systems decay under a stochasticdynamics driven by a physical temporal medium. The model combines the Diósi–Penrosespatial kernel with a coloured temporal kernel of finite correlation time _c; the hypothesis _c τ τ= / E_g renders it parameter-free. The decoherence envelope is derived exactly: Gaussian at ℏ Δearly times, crossing to exponential Diósi–Penrose decay — a signature distinguishing themodel from thermal decoherence and from all Markovian collapse models. The coloured kernelsuppresses collapse-induced spontaneous radiation by ( _c) ², reconciling gravitational ωτ ⁻collapse with the underground null results that exclude the parameter-free Markovian model.We give quantitative predictions for levitated nanospheres and matter-wave interferometry, sixfalsification conditions, and outline interpretive consequences: a classicality wavefrontdefining the present moment, a selective arrow of time, and dark energy as the unimodularaccumulation of collapse-injected energy.
Version 4 (October 2026), interim correction: an independent review found that the main result is a reformulation rather than a recovery. Both inputs to the budget-saturation condition, the superposition cost and the budget B = ħ/τ, are posited, so its agreement with the Penrose–Diósi criterion holds by construction. The uniform-sphere coefficient in the testable prediction is off by a factor of 6/5, and the tabulated collapse times use a small-displacement formula outside its range. These results should not be cited until the revised version is posted. Details are in the Revision History of the PDF.We show that the Penrose–Diósi gravitational collapse criterion — which predicts that quantum superpositions decay on a timescale τ = ℏ/E_G, where E_G is the gravitational self-energy of the difference mass distribution — arises as the budget-saturation condition of the selective reconstruction framework (Russell 2026a). When the reconstruction budget B is identified with ℏ/τ_local via the Margolus–Levitin theorem, the Russell constraint C_super ≤ B becomes the Penrose–Diósi inequality E_G ≤ ℏ/τ. "Observation" is thereby reframed not as a primitive physical event but as the condition under which the gravitational self-energy of a superposition exhausts the geometric reconstruction budget of the boundary observer. The result is observer-dependent and recovers relational quantum mechanics as a consequence of resource constraints. A falsifiable, mass-scaling prediction (τ ∝ M⁻² d⁻² R³) is derived for levitated-nanosphere experiments. A structural isomorphism with Nanite's LOD scheduling algorithm is noted as a conceptual heuristic. Epistemic status: The budget identification is motivated by the Margolus–Levitin theorem but is not formally derived from AdS/CFT. This is a working paper inviting scrutiny, not an established result.v3 (2026-05-27): Format converted from HTML to LaTeX. §5 collapse-time table recomputed under the stated d=R, ρ=2200 kg/m³ convention (prior values were inconsistent with the formula by ~30 orders of magnitude). Reference 8 updated per consolidation of Virtualized Geometry into Spacetime as Optimal Allocation. Minor text corrections: sub-femtokelvin → sub-microkelvin, Verlinde (2010) → (2011), Stanford → ETH Zurich. Figures regenerated with layout fixes (no content changes). ORCID, email, and concept DOI added to front matter.
We derive an objective-collapse prediction for massive spatial superpositions from a singlepremise — that physical distinguishability is finite and discrete — and show that it evades thespontaneous-radiation bounds that exclude the parameter-free Di´osi–Penrose model. The mechanism is conservative: a superposition of a massive body in two locations is a superposition oftwo gravitational configurations, and when the gravitational self-energy difference ∆E betweenthem reaches the capacity of one distinguishability cell, coherence commits, on the timescaleτ ∼ℏ/∆E. This reproduces the Di´osi–Penrose collapse time, here derived rather than posited,with a regularisation length fixed without tuning as the nucleon Compton wavelength, giving acollapse mass ceiling of order 1012–1014 amu. The prediction is consistent with every matterwave interference experiment performed — at the current record (∼ 105 amu) the predictedcoherence time exceeds the experimental one by ten orders of magnitude — and lies withinreach of next-generation nanoparticle interferometry. Crucially, we derive the collapse masterequation and show that the momentum-diffusion coefficient, which controls spontaneous electromagnetic radiation and by which white-noise collapse models are experimentally excluded,vanishes exactly. The reason is structural: because the distinguishability ledger is discrete,the collapse rate as a function of branch separation is identically zero below a threshold — ahard step, not a smooth rise — so its curvature at zero separation, which sets the momentumdiffusion, is exactly zero. Localised charges therefore radiate nothing, and the undergroundradiation bounds do not apply. The result rests on one stated assumption, strict discreteness ofthe distinguishability count, which is the premise itself; granting it, the evasion of the radiationbounds is a theorem rather than a tuning.
The Penrose-Diósi gravitational objective reduction criterion predicts wavefunction collapse at τ_PD = ħ/E_G where E_G = Gm²/r. Entropy-Response Gravity (ERG) modifies this criterion with zero free parameters via G_eff(r,m) = G/μ(Gm/r²a₀), where μ(x) = x/√(1+x²) and a₀ = cH₀/√(4π²−1) is derived from the Bekenstein-Hawking entropy S=A/4G. The collapse time is τ_ERG = τ_PD × μ(Gm/r²a₀) ≤ τ_PD: ERG always predicts faster collapse. At the crossover r_trans = √(Gm/a₀), where μ(1) = 1/√2 exactly: τ_ERG = τ_PD/√2. For m = 10⁻¹⁴ kg: r_trans = 74.6–79.2 nm. Current levitated nanosphere experiments have achieved ~50 nm, placing them within a factor of 1.5 of the ERG crossover. The diagnostic is the shape of τ(r): standard Penrose-Diósi gives τ∝r (linear); ERG develops a kink at r_trans with subsequent r^(3/2) steepening. The kink position is predicted from H₀ alone — not fitted. This is the first modification of the Penrose-Diósi criterion with zero free parameters, and the most concrete near-term laboratory test of quantum gravity yet proposed. ERG Preprint Letter II. Full programme: Zenodo records 19077317, 19161618, 19318665, 19415023, 19424980, 19484181, 19512503, 19537805. PRL Letter I: 10.5281/zenodo.19547151.