{"id":"9651cc88-9cca-47e6-886c-0fa613c5ee1e","arxiv_id":"2411.13523","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Random spacetime fluctuations would decohere quantum systems in momentum space, and a superconducting-qubit-controlled 16 µg mechanical resonator places weak upper bounds on the fluctuation parameters.","lead":"The authors derived how random spacetime jitters would erase quantum coherence, and used a 16 microgram vibrating crystal to bound the jitter's strength. The bounds are weak, but the analysis shows how quantum mechanical devices can test spacetime fluctuation models.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The β and l_k bounds rest entirely on attributing the measured 2% ground-state Wigner ellipticity to GUP squeezing; no calibration/systematics analysis is given, so a 2% quadrature-gain anisotropy would invalidate both bounds.","rationale":"The paper's central deliverable is two experimental constraints: κ from T1/T2 and β (plus l_k) from ground-state ellipticity. The κ constraint is a genuine upper bound: if additional technical dephasing is present, the extracted κ is overestimated, so κ ≤ 4×10^46 s remains conservative (the paper mislabels the τ_G direction, but the κ bound direction is right). The β constraint, however, has no such robustness. It relies on a single point estimate ϵ = 0.020(5) from a published Wigner function, with no calibration check. A 2% ellipticity is a small effect; detector gain asymmetry at the percent level is common in homodyne/tomography setups, and the paper does not report any control measurement. The same data also support the l_k bound, so both headline bounds are contingent on the same unvalidated attribution. This is exactly the reader's weakest assumption. The theoretical derivation of the variance formula and the master equation appears internally consistent, and the κ bound is conservative, so the correct response is to keep the CONDITIONAL verdict pending a calibration check.","tokens_in":21256,"tokens_out":34474,"duration_ms":337276,"concrete_test":"Reanalyze the raw Wigner-function data of Ref. [39] with an independent quadrature-gain calibration: reconstruct the covariance matrix for a calibration state known to be circular (e.g., a coherent state or the vacuum/thermal state acquired in the same run) using the same tomography pipeline. If the calibration state's variance ratio deviates from unity by more than ~0.5%, the extracted ϵ = 0.020(5) cannot be attributed to GUP; equivalently, check whether the measured ellipse minor axis matches the quadrature predicted by the corrected first-order variance calculation for H_β = 4a_P β K².","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing step is in the 'Ground state deformation' section: the entire β bound (and the l_k bound built on the same measurement) follows from writing Δx_θ² = 1/2 − (1/4)ϵ cos(2θ) and extracting ϵ = 0.020(5) from a two-dimensional Gaussian fit to the Wigner function of Ref. [39]. The paper offers no independent calibration of the two quadrature gains, no check that a known circular state yields a circular Wigner function with the same reconstruction pipeline, and no discussion of how a 2% detection asymmetry would be separated from a 2% physical ellipticity. Since the ideal ground state is circular, any small anisotropic systematic in the tomography/heterodyne calibration appears directly as a spurious ϵ; the reported uncertainty 0.005 is only statistical. The T1/T2-derived κ bound is less fragile because extra technical noise only strengthens the upper bound on κ, but the β and l_k bounds have no such safety net.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies decoherence induced by a fluctuating spacetime at low energies. In the first model, the deformation parameter β in the GUP-type commutator [X,P]=iℏ(1+βℓ_P²P²/ℏ²) is promoted to a stochastic process with mean β and covariance κf(t−t′). The authors derive a non-Markovian master equation for the momentum-basis decoherence, recover a Markovian limit, and compute the decay of Fock-state coherences and populations for a harmonic oscillator, including amplitude damping. In a second model, isotropic metric fluctuations à la Breuer et al. lead to a K-covariance master equation with amplitude τ_c. Using published T1 and T2 data from a 16 µg HBAR oscillator, they extract τ_G and γ and claim κ≤(4.0±0.9)×10^46 s; using the ground-state Wigner function ellipticity (ϵ=0.020(5)) they claim β<2.2(6)×10^30 and l_k≤5.9(8)×10^-20 m, and from the same T1/T2 data they claim τ_c≤(3.7±0.8)×10^-18 s.","tokens_in":21519,"tokens_out":51447,"duration_ms":490680,"significance":"The master-equation derivation is careful and self-contained: it generalizes the white-noise model of Ref. [12] to non-Markovian noise, corrects a factor-2 error in the Markovian Lindblad coefficient, and correctly separates the mean-deformation unitary term from the fluctuation-induced decoherence. The use of genuinely quantum mechanical oscillator data (T1, T2, and Wigner tomography) rather than classical measurements is a real step forward for constraining GUP-type models without the deformed Poisson-bracket assumption. The κ and τ_c bounds, if properly one-sided, are useful, and the metric-fluctuation bound is significantly tighter than the GUP one. However, the β and l_k bounds are not yet secure: they rest on a single 2% ellipticity extracted from a Wigner function with no quadrature-gain calibration or systematics budget, and the derivation of the variance formula is not shown. The paper also contains a concrete factor-4 error in the RWA Hamiltonian and a misstated bound direction for τ_G. These issues affect central claims and require correction.","major_comments":[{"comment":"The derivation of β<2.2(6)×10^30 from the ground-state Wigner function ellipticity rests entirely on identifying the measured Δx²_max/Δx²_min=(2+ϵ)/(2−ϵ) with the GUP-induced squeezing of the mechanical mode. No calibration of the two quadrature gains is reported, no control measurement of a known circular state is described, and no systematic uncertainty budget is given; a 2% detection anisotropy in the tomography pipeline would produce exactly the same signal as the claimed physical ellipticity. The stated uncertainty 0.005 on ϵ is therefore not sufficient to support a one-sided bound. In addition, the variance formula Δx_θ²=1/2−1/4ϵ cos(2θ) is asserted without derivation. A standard first-order perturbative treatment of H_β=4a_PβK² in the canonical quadratures yields Δx_θ²=1/2+(1/4)ϵ cos(2θ) with ϵ=6βa_Pℏω, i.e. the opposite sign of the ellipticity; the paper should justify its sign and specify whether the measured quadratures are canonical or physical momentum operators. Because the l_k bound in the following paragraph is built on the same ϵ measurement, it inherits the same fragility.","section":"Ground state deformation"},{"comment":"The text states that the fitted values γ^{-1}=169.9±47.5 µs and τ_G=975.2±237.4 µs 'should be considered as upper bounds' because T2 has additional technical-noise contributions. If the only unmodelled noise is extra dephasing in T2, then the solved 1/τ_G is overestimated, so τ_G is underestimated, not overestimated; the quoted τ_G is then a lower bound, and the quoted γ^{-1} is also a lower bound. The claimed bound κ≤(4.0±0.9)×10^46 s is conservative in that particular scenario, but only if the unmodelled noise is absent from the T1 (population) channel. If the T1 channel also contains additional relaxation/heating, the solved 1/τ_G can move in the opposite direction and the one-sided κ bound is not guaranteed. The authors need to state this assumption explicitly and provide a sensitivity analysis. Furthermore, the uncertainty ±0.9×10^46 s is not obtained from a visible propagation of the quoted T1 and T2 fit errors; since κ∝1/τ_G, the propagated error is asymmetric.","section":"Experimental tests"},{"comment":"Equation (10) and the corresponding SM Eq. (28) contain a factor-4 error in the RWA of the modified Hamiltonian. With K=p²/2m and the oscillator expression p²=(mℏω/2)(2N+1−a†²−a²), the number-conserving part of K² is (3ℏ²ω²/8)(N²+N+1/2). Multiplying by 4a_Pβ from Eq. (5) gives a correction (3/2)a_Pβℏ²ω²(N²+N+1/2), not (3/8)a_Pβℏ²ω²(N²+N+1/2). A consistency check is that ⟨0|H_RWA|0⟩ would be (3/16)a_Pβℏ²ω², whereas the exact ground-state expectation of H_β is (3/4)a_Pβℏ²ω². This error affects the unitary evolution and the non-Markovian results, even though the white-noise decoherence rates in Eqs. (12,13) are independent of the RWA coefficient.","section":"Eq. (10) and SM Eq. (28)"},{"comment":"The bound l_k≤5.9(8)×10^-20 m is presented without any derivation of the mapping between the measured ground-state ellipticity and l_k. The text only says that the quartic x^4 term in the nonlocal Hamiltonian 'plays a similar role' to the p^4 term in H_β. Since this bound is quoted as on par with LHC constraints, the explicit relation between the measured ϵ and l_k must be shown. As written, the l_k result cannot be checked, and it also inherits the calibration uncertainty of the same ϵ measurement.","section":"Ground state deformation, l_k paragraph"}],"minor_comments":[{"comment":"The phrase 'upper bounds for the corresponding parameters' is ambiguous because the quoted numbers are inverse rates; please restate in terms of γ and 1/τ_G or correct the direction as discussed in the major comments.","section":"Experimental tests"},{"comment":"The paper presents κ≤(4.0±0.9)×10^46 s and τ_c≤(3.7±0.8)×10^-18 s as one-sided bounds with symmetric errors; since the conversion from measured times to these parameters is nonlinear, a one-sided confidence interval at a stated confidence level would be more appropriate.","section":"Experimental tests / Metric fluctuations model"},{"comment":"The value ϵ=0.020(5) is quoted without stating whether 0.005 is statistical, systematic, or total; please clarify what is included in this uncertainty.","section":"Ground state deformation"},{"comment":"The definition of a_P contains a typo: 'e−1 P' should read 'e_P^{-1}'. Please also give the dimensions of a_P explicitly, since several later formulas depend on its units.","section":"Modified dynamics, after Eq. (5)"},{"comment":"The note says the measurements in Fig. 2 are taken for t/τ_G<0.2; because τ_G is itself extracted from the same data, this is a post-fit consistency condition rather than an a priori validity check. Stating t/T1 and t/T2 would make the short-time assumption transparent.","section":"Experimental tests, note [41]"},{"comment":"The quantities ∆E_k used in Eq. (9) are defined only in the Supplementary Material; please define them in the main text at first use.","section":"Eq. (9)"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the journal's scope. The strongest part is the master-equation derivation; the weakest is the interpretation of the 2% Wigner ellipticity. If the authors can either obtain a calibration statement from the experimental group or restrict the claims to an upper bound with a clear systematic caveat, the paper could be publishable after revision. The factor-4 error in Eq. (10) and the bound-direction issue should be corrected before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe core of this paper is a careful derivation of a non-Markovian master equation for a harmonic oscillator with a GUP whose deformation parameter β(t) fluctuates. That part is genuinely good: the factor-2 correction to the Petruzziello–Illuminati Lindblad coefficient and the extra unitary β-dependent term are right, and the supplementary-materials derivation is internally consistent. The application to a 16 μg HBAR oscillator and the κ bound from T1/T2 data is a legitimate step, albeit numerically weak.\n\nThe soft spots are in the experimental interpretation. The β bound (and the l_k bound built on it) rests entirely on attributing the measured ϵ = 0.020(5) ellipticity of the ground-state Wigner function to GUP squeezing. There is no calibration check that the tomography pipeline maps a known circular state to a circular Wigner function, and a 2% quadrature-gain anisotropy would mimic the signal. The reported uncertainty is statistical only. This is load-bearing: without the ellipticity attribution, the β bound collapses. The κ bound from T1/T2 is safer because extra technical noise only moves the inference in one direction, but even there the direction is misstated. Since τ_G is inversely proportional to κ, if the inferred τ_G is an upper bound, the bound on κ should be a lower bound, not the κ ≤ ... written in the text. The same issue affects the τ_c bound for the metric-fluctuation model.\n\nThat said, the theory portion deserves a serious referee. The master-equation derivation and the perturbative oscillator solutions are clearly presented and checkable. The experimental bounds are weak and partly fragile, but the authors are honest about the weakness and about their assumptions. This is a solid extension of earlier work, not a paradigm shift.\n\nI would send it to peer review, ask for a corrected bound direction and a calibration discussion for the ellipticity extraction, and then accept it as a decent phenomenological contribution.\n\nRegards.","headline":"Solid master-equation derivation, but the β bound rests on an uncalibrated 2% ellipticity and the κ bound direction is flipped.","tokens_in":21966,"tokens_out":4248,"would_cite":false,"duration_ms":43496,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Yz","04.60.-m"],"model":"deepseek-v4-flash","headline":"A fluctuating Planck-scale deformation parameter makes quantum superpositions decohere in momentum space, and a 16 µg oscillator bounds the effect.","keywords":["generalized uncertainty principle","deformed commutator","momentum decoherence","mechanical oscillator","spacetime fluctuations","HBAR resonator","quantum gravity phenomenology","nonlocal dynamics"],"falsifier":"Measure the T2 excess and ground-state ellipticity of the same HBAR mode after an independent calibration of the readout chain, and repeat on a second oscillator with a different effective mass: the model predicts a GUP decoherence rate proportional to $m^2\\omega^4$ and a squeezing $\\varepsilon\\propto m$, so observed scalings that disagree would falsify the $\\kappa$ and $\\bar\\beta$ bounds.","tokens_in":21070,"feed_emoji":"⚛️","tokens_out":10090,"duration_ms":96556,"temperature":0.7,"pith_summary":"This paper claims that a stochastic component in the Planck-scale deformation of the position–momentum commutator turns spacetime into a source of momentum-basis decoherence for any quantum system. Starting from $[\\hat X,\\hat P]=i\\hbar(1+\\beta\\ell_P^2\\hat P^2/\\hbar^2)$ with $\\beta(t)$ fluctuating around a mean $\\bar\\beta$, the authors derive a master equation whose non-unitary term is a double commutator with $\\hat K^2$, so superpositions of different momenta decay. They apply the model to a $16\\,\\mu\\mathrm g$ high-frequency mechanical oscillator prepared in quantum states and use measured energy relaxation and Ramsey dephasing times to bound the fluctuation amplitude $\\kappa\\le 4.0\\times10^{46}\\,\\mathrm s$ and the mean deformation $\\bar\\beta<2.2\\times10^{30}$; the same ground-state data also bound the nonlocality length scale $\\ell_k\\le5.9\\times10^{-20}\\,\\mathrm m$. A sympathetic reader would care because these are quantum-regime bounds, which do not require the contested assumption that a deformed commutator also deforms classical Poisson brackets.","feed_headline":"Fluctuating spacetime scale decoheres quantum oscillators","feed_subtitle":"A 16 µg quantum resonator bounds spacetime-fluctuation amplitude to κ ≤ 4.0×10^46 s.","key_machinery":"The load-bearing object is the fluctuating deformation parameter $\\beta(t)$ inside the deformed commutator $[\\hat X,\\hat P]=i\\hbar(1+\\beta(t)\\ell_P^2\\hat P^2/\\hbar^2)$, characterized by its mean and by an autocorrelation $\\kappa f(t-t')$. The calculation works through the transformation $\\hat X=\\hat x$, $\\hat P=(1+\\beta\\ell_P^2\\hat p^2/\\hbar^2)\\hat p$, which maps the modified algebra to the canonical one plus a perturbation $\\hat H_\\beta=4a_P\\bar\\beta\\hat K^2$; a Born–Markov average over the noise then produces the double-commutator master equation. For the oscillator, the rotating-wave approximation reduces the unitary part to a Kerr-like number-squared term, and the collapse operator $\\hat K^2$ is evaluated in the Fock basis to give the short-time decay rates used in the data analysis.","core_discovery":"The central discovery is that allowing the deformation parameter in the generalized uncertainty principle to fluctuate turns the GUP correction into a genuine open-quantum-system effect: after averaging over the noise, the reduced dynamics contains a Lindblad term proportional to $[\\hat K^2,[\\hat K^2,\\hat\\rho]]$, which damps coherences between momentum eigenstates while leaving energy eigenstates of a free particle decohered only if their kinetic energies differ. For a harmonic oscillator in the white-noise limit, a superposition $(|0\\rangle+|1\\rangle)/\\sqrt2$ loses coherence as $1-\\frac{30}{8}t/\\tau_G$ with $1/\\tau_G\\equiv 8a_P^2\\kappa\\hbar^2\\omega^4$, and the ground state itself acquires a slow heating term $1-\\frac{6}{8}t/\\tau_G$. Applying these formulas to $T_1$ and $T_2$ data from a $16.2\\,\\mu\\mathrm g$ sapphire HBAR mode yields the upper bound $\\kappa\\le4.0\\times10^{46}\\,\\mathrm s$ and, from the measured ground-state Wigner-function ellipticity $\\varepsilon=0.020(5)$, the bound $\\bar\\beta<2.2\\times10^{30}$. The paper also corrects a factor of two and an omitted unitary term in the earlier white-noise master equation, and re-derives bounds for the metric-fluctuation model, giving $\\tau_c\\le3.7\\times10^{-18}\\,\\mathrm s$.","pith_inferences":["If the GUP-squeezing interpretation is right, the ground-state ellipticity of the same oscillator should change linearly with its effective mass at fixed frequency; measuring that scaling would separate genuine spacetime squeezing from readout calibration artifacts.","The predicted leakage out of the ground state is a distinctive signature of this model, and a long-time population measurement of a deeply cooled oscillator could test it because ordinary thermalization acts in the opposite direction.","The master-equation derivation is not tied to white noise, so a non-Markovian spectrum $f(t-t')$ would imprint a frequency dependence on the decoherence rate that could distinguish this mechanism from ordinary environmental dephasing.","Because the quantum-regime $\\bar\\beta$ bound is much weaker than classical-oscillator bounds, combining the two types of measurement could test whether a deformed commutator must also deform classical dynamics."],"forward_implications":["If the model is right, any massive quantum superposition decoheres in momentum space at a rate set by $\\kappa$, so the $T_1$ and $T_2$ data already exclude spacetime fluctuations of this type as the dominant decoherence source for a $16\\,\\mu\\mathrm g$ oscillator.","The ground-state ellipticity gives a quantum-regime bound $\\bar\\beta<2.2\\times10^{30}$ that does not assume deformed Poisson brackets, and a heavier oscillator should tighten it because the predicted squeezing grows with mass.","The same variance measurement bounds the quantum-gravity nonlocality scale to $\\ell_k\\le5.9\\times10^{-20}\\,\\mathrm m$, comparable to the LHC-derived bound but obtained on a tabletop quantum device.","For the independent metric-fluctuation model, the same data give $\\tau_c\\le3.7\\times10^{-18}\\,\\mathrm s$, and probing $\\tau_c\\sim t_P$ would demand the very large product $\\omega^2/\\gamma\\sim10^{43}\\,\\mathrm s^{-1}$."],"supporting_citations":[{"why":"Supplies the earlier fluctuating-β model whose master equation this paper corrects and extends to non-Markovian noise.","marker":"[12]"},{"why":"Supplies the metric-fluctuation model whose amplitude τ_c is bounded with the same experimental data.","marker":"[26]"},{"why":"Defines the nonlocal-dynamics length scale l_k that the ground-state variance measurement bounds.","marker":"[25]"},{"why":"Provides the HBAR Fock-state preparation and energy-relaxation measurements used for the T_1 data.","marker":"[37]"},{"why":"Provides the HBAR Ramsey and cat-state measurements used for the T_2 data.","marker":"[38]"},{"why":"Provides the ground-state Wigner function from which the ellipticity ε is extracted.","marker":"[39]"},{"why":"Supplies the Jaynes–Cummings swap used to prepare superpositions (|0⟩+|1⟩)/√2.","marker":"[40]"},{"why":"Provides the hydrogen 1S-2S β bound that the quantum-oscillator result improves.","marker":"[45]"}],"fun_headline_variants":["16-µg oscillator bounds quantum spacetime fluctuations","Spacetime fluctuation noise decoheres momentum states","Quantum gravity noise constrained by mechanical resonator","Quantum oscillator sets limit on spacetime fluctuations"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The β bound rests on attributing the measured ground-state Wigner-function ellipticity entirely to GUP-induced squeezing; any part of that ellipticity coming from calibration or other systematics would invalidate the bound.","fun_headline_variants_meta":{"raw":{"variants":["16-µg oscillator bounds quantum spacetime fluctuations","Spacetime fluctuation noise decoheres momentum states","Quantum gravity noise constrained by mechanical resonator","Quantum oscillator sets limit on spacetime fluctuations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000261,"raw_usage":{"total_tokens":1599,"prompt_tokens":958,"completion_tokens":641,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":574,"completion_tokens_details":{"reasoning_tokens":585}},"tokens_in":574,"tokens_out":641,"duration_ms":8448,"temperature":1.0,"reasoning_tokens":585,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T16:19:08.255417+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the T2 excess and ground-state ellipticity of the same HBAR mode after an independent calibration of the readout chain, and repeat on a second oscillator with a different effective mass: the model predicts a GUP decoherence rate proportional to $m^2\\omega^4$ and a squeezing $\\varepsilon\\propto m$, so observed scalings that disagree would falsify the $\\kappa$ and $\\bar\\beta$ bounds.","supporting_citations":[{"cited_title":"Kempf, Journal of Physics A: Mathematical and General 30, 2093 (1997)","cited_arxiv_id":null,"evidence_quote":"Supplies the earlier fluctuating-β model whose master equation this paper corrects and extends to non-Markovian noise."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the metric-fluctuation model whose amplitude τ_c is bounded with the same experimental data."},{"cited_title":"Scardigli, G","cited_arxiv_id":null,"evidence_quote":"Defines the nonlocal-dynamics length scale l_k that the ground-state variance measurement bounds."},{"cited_title":"Asprea, G","cited_arxiv_id":null,"evidence_quote":"Provides the HBAR Fock-state preparation and energy-relaxation measurements used for the T_1 data."},{"cited_title":"Donadi and A","cited_arxiv_id":null,"evidence_quote":"Provides the HBAR Ramsey and cat-state measurements used for the T_2 data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the hydrogen 1S-2S β bound that the quantum-oscillator result improves."}],"review_version":1}