On Quantum Gravity Tests with Composite Particles

Martin B. Plenio; Shreya P. Kumar

REVIEW 2 major objections 6 minor 1 cited by

On Quantum Gravity Tests with Composite Particles

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper derives the first positive experimental lower bound on the particle-number suppression of quantum-gravity corrections, α > 0.07 at β0 = 1, from a macroscopic pendulum's period-versus-amplitude data.

desk verdict First positive bound on the particle-number suppression exponent alpha, but the headline value rests on unmodeled systematics in a 1964 pendulum dataset. read the letter →

arxiv 1908.11164 v2 pith:4NVV64K7 submitted 2019-08-29 quant-ph gr-qc

Shreya P. Kumar , Martin B. Plenio This is my paper · ORCID

classification quant-phgr-qc

keywords deformedcommutationrelationsgeneralizeduncertaintyprincipleparticle-numbersuppressioncompositetestmassespendulumperiodmeasurementsoccer-ballproblemquantumgravityboundsdiamagneticlevitation

topics Quantum Gravity

open problems Quantum Gravity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quantum-gravity models that deform the position–momentum commutator predict corrections of order $\beta_0$, but when the test object is a composite mass the correction is expected to be suppressed by an unknown power $\alpha$ of the number of constituent particles $N$. The paper introduces the two-parameter description $[x,p] = i\hbar(1+\beta_0 p^2/(N^\alpha (M_p c)^2))$ and argues that no table-top test using composite masses is interpretable without bounding both parameters together. Reanalyzing the period-versus-amplitude data of a macroscopic pendulum from a 1964 precision experiment, it derives the first positive bound on the suppression exponent, $\alpha > 0.07$ for $\beta_0 = 1$ (indeed for any $\beta_0 > 10^{-2}$). It further shows that the same analysis of recent quantum-regime oscillator experiments yields only negative bounds on $\alpha$, so entering the deep quantum regime is not the decisive advantage. If the claim holds, the commonly assumed point $\beta_0 = 1$, $\alpha = 0$ is excluded, and composite-mass quantum-gravity tests must explicitly account for particle-number suppression.

What carries the argument

The load-bearing object is the two-parameter deformed commutator $[x,p] = i\hbar(1 + \beta_0 p^2/(N^\alpha (M_p c)^2))$, in which $N$ is the number of constituent particles and $\alpha$ the unknown suppression exponent. The identity that carries the argument is the pendulum period formula $T_{2\pi} \approx 2\pi\sqrt{L/g}(1 + A^2/(16L^2) - \beta_0 m^2 g A^2/(2 N^\alpha (M_p c)^2 L))$: the classical anharmonic term and the quantum-gravity term have opposite signs and both scale with $A^2$, so the measured slope of $T$ versus $A^2$ isolates the combination $\beta_0/N^\alpha$. The classical derivation deforms the Poisson bracket as $\{x,p\} = 1 + \beta p^2$ and restores the standard bracket with the redefined momentum $\tilde p = \tan^{-1}(\sqrt{\beta}p)/\sqrt{\beta}$; a fully quantum treatment using the deformed-commutator eigenfunctions, a generalized Heisenberg algebra, and Gazeau–Klauder coherent states reproduces the same period formula. The exclusion regions in the $(\alpha,\beta_0)$ plane are the organizing device that lets the pendulum, the oscillator, and the optomechanical experiments be compared on equal footing.

What would settle it

A re-measurement of the pendulum's period versus amplitude squared in a vacuum chamber at several pressures, with drag independently characterized, would settle it: if the slope residual below the classical $0.0242$ s/m² shrinks as pressure drops and extrapolates to zero at zero damping, the quantum-gravity attribution is wrong and the $\alpha > 0.07$ bound collapses. A complementary check is to repeat the measurement with bobs of different mass and different suspensions; a consistent derived $\beta_0 N^{-\alpha}$ across masses would support the claim, while a mass-dependent residual would point to a systematic effect.

Watch

Extended reading notes

Core claim

The central claim is that particle-number suppression of quantum-gravity corrections can be bounded from below by the period of a classical pendulum, and that the first positive bound obtained this way is $\alpha > 0.07$ for $\beta_0 = 1$. The argument runs through the slope of the pendulum's time-period versus amplitude-squared curve. For the deformed commutator $[x,p] = i\hbar(1+\beta p^2)$ with $\beta = \beta_0/(N^\alpha (M_p c)^2)$, the paper computes the period to first order in $\beta$ as $T_{2\pi} \approx 2\pi\sqrt{L/g}(1 + A^2/(16L^2) - \beta_0 m^2 g A^2/(2 N^\alpha (M_p c)^2 L))$: the classical anharmonic term raises the period with amplitude while the quantum-gravity term lowers it, so a precise slope measurement isolates the combination $\beta_0/N^\alpha$. Fitting the extracted data of the 1964 conventional-suspension pendulum, with the 1.22 kg iron bob counted as $N = 7.32 \times 10^{26}$ nucleons, gives a measured slope of $0.0232 \pm 0.0012$ s/m² against the theoretical $0.0242 - 0.197\,\beta_0/N^\alpha$ s/m²; consistency requires $\beta_0 N^{-\alpha} < 10^{-2}$, hence $\alpha > 0.07$ when $\beta_0 = 1$. The paper also shows that two recent micro- and nano-oscillator experiments give only negative bounds on $\alpha$ at $\beta_0 = 1$, that an optomechanical phase measurement likewise gives a negative bound unless the resonator is prepared with large momentum, and that the classical calculation agrees with a fully quantum treatment using Gazeau–Klauder coherent states, generalized coherent states that stay coherent under the deformed Hamiltonian.

Load-bearing premise

The entire bound rests on attributing the small residual between the measured period-versus-amplitude slope ($0.0232$ s/m²) and the classical anharmonic prediction ($0.0242$ s/m²) to the quantum-gravity correction, without a measured model of other amplitude-dependent effects such as air drag and suspension nonlinearity; the paper itself notes that dissipation should be measured and included in future experiments.

Editorial extensions

If this is right

The point $(\beta_0 = 1, \alpha = 0)$ is excluded by data, so any quantum-gravity test using a composite mass must quote bounds on both $\beta_0$ and $\alpha$; the common working assumption $\alpha = 0$ can no longer be justified at the theoretically expected $\beta_0 \sim 1$.
Micro- and nano-scale quantum harmonic oscillators, often proposed as the most sensitive probes, yield only negative bounds on $\alpha$ for $\beta_0 = 1$; a macroscopic pendulum with a precisely calculable nonlinearity outperforms them, so entering the deep quantum regime is not required for this type of test.
A diamagnetically levitated test mass with low damping is projected to reach $\alpha > 0.24$ (conservative) or $\alpha > 0.35$ (optimistic) for $\beta_0 = 1$, with further improvement expected in space where pressure is about 2000 times lower, approaching the $\alpha > 1$ regime the paper associates with several models.
The optomechanical phase-acquisition scheme analysed in the paper can produce a positive bound on $\alpha$ if the resonator starts in a coherent state with large momentum and a larger mass, because the extra momentum-dependent phase term scales with mass while the leading term scales inversely.
The classical (deformed Poisson bracket) and quantum (deformed commutator with Gazeau–Klauder coherent states) derivations give identical period corrections, connecting two approaches previously regarded as independent.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the bound follows from $\beta_0 N^{-\alpha} < 10^{-2}$, it grows only logarithmically with particle number ($\alpha \gtrsim \log(10^2\beta_0)/\log N$): heavier pendulums barely move the bound, so the steepest gains should come from reducing slope uncertainty by controlling dissipation, which the paper itself flags as the necessary next step.
The same slope-versus-$A^2$ analysis could be rerun on other archival precision pendulum and balance data, and on vacuum repeats of the 1964-style experiment, turning historical metrology into a reusable resource for bounding $\beta_0/N^\alpha$ without new infrastructure.
The proposed diamagnetically levitated experiment doubles as a discriminating check on whether the $\alpha > 0.07$ signal is real: measuring the period-frequency slope at several pressures separates a dissipation-driven residual from a pressure-independent quantum-gravity residual, and only the latter would reproduce the bound at higher precision.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper to know about: Kumar and Plenio introduce a particle-number suppression exponent α for GUP-type commutator deformations and report the first positive experimental bound, α > 0.07 for β0 = 1, from a 1964 pendulum experiment. The specific number is real but shakier than it looks, because the slope difference the bound is built on is only about 5% of the measured slope, and no systematics are modeled. That said, the qualitative exclusion of β0 = 1, α = 0 is robust: it would take a slope shift of almost 0.2 s/m² to wash out, so the central message survives.

What is genuinely new: the α parameter is a useful axis for reporting constraints, and the pendulum period derivation via a deformed Poisson bracket extends earlier harmonic-oscillator treatments. The corroborating quantum calculation with Gazeau–Klauder coherent states is a solid cross-check and connects two approaches that are usually treated separately. The bound itself is not in the cited literature; previous oscillator experiments give negative α bounds, so this is a genuine step, not a restatement.

The soft spot is exactly where the reader's report puts it: all of the α > 0.07 weight sits on a slope difference of 0.0012 s/m² (the 95% uncertainty) between the measured 0.0232 and the classical anharmonic 0.0242. The paper does not model air drag, amplitude decay during timing, or suspension anelasticity. The authors are honest about this—they explicitly say future experiments should measure dissipation—but as written the headline number is conditional on these effects being below roughly 10⁻³ s/m². A 0.001 s/m² systematic would lower α to about 0.06–0.07, which is not a disaster but does change the reported value. The factor-of-four inconsistency flagged in the internal report is a non-issue; substituting A = φL in Eq. (26) gives Eq. (27) exactly.

This paper deserves a serious referee. It is clearly written, the calculations are traceable, the extracted data are in a table, and the diamagnetic levitation proposal is a sensible next step. The main request should be a systematic-error analysis of the pendulum data and a presentation of the constraint as β0 N^(−α) < 10⁻² rather than overemphasizing the specific α > 0.07 at β0 = 1. If you work on quantum gravity phenomenology, read this and cite the α parameter—just don't quote the number without the caveat. My recommendation: send it to peer review; it will come back with revision requests, and it should.

Referee Report

2 major / 6 minor

Summary. This paper introduces a phenomenological parameter α to describe the suppression of quantum-gravity corrections to the canonical commutation relations with the number N of constituent particles, and analyzes what can be learned from a macroscopic pendulum. The authors derive the leading correction to the pendulum period as a function of amplitude (Eq. (10)), fit the 1964 Smith data for a conventional-suspension pendulum, obtain the 95% bound β0 N^{-α} < 0.011 and hence α > 0.07 for β0 = 1, compare this with bounds from Bawaj et al., Bushev et al., and optomechanical proposals, and propose improved levitated and optomechanical experiments. A Methods section reports the classical calculation and a quantum harmonic-oscillator calculation with Gazeau-Klauder coherent states, which is used to argue for agreement between deformed-Poisson and deformed-commutator approaches.

Significance. If the quantitative bound survives a systematic-error analysis, this is the first positive lower bound on α, and it demonstrates that the particle-number suppression cannot be neglected when interpreting composite-body tests of deformed commutators. The paper's principal strengths are its transparent two-parameter framework, the explicit extraction and tabulation of the 1964 data, the self-contained classical derivation of the period correction, the nontrivial quantum harmonic-oscillator calculation with Gazeau-Klauder states, and the concrete proposals for future experiments. The paper is also careful to frame the result as a bound rather than a detection, although the robustness of the headline number is conditional on unmodeled classical slope corrections.

major comments (2)

[Bounds on QG parameters from experimental data, Eqs. (13)-(14)] The numerical bound α>0.07 is not protected against unmodeled amplitude-dependent classical effects. The measured slope 0.0232±0.0012 is within the quoted 95% confidence interval of the anharmonic slope 0.0242, so the positive bound arises from the one-sided upper confidence limit on X=β0N^{-α}, and the entire slope deficit of about 0.001 s/m^2 is attributed to the quantum-gravity term in Eq. (10). The paper does not model or bound air drag, amplitude decay during timing, or suspension anelasticity for the 1964 conventional-suspension pendulum; the text itself states that dissipation should be measured in future experiments. A classical slope systematic of magnitude 0.001 s/m^2 changes the inferred X by about 0.005 and shifts the α bound by about 0.01, which is the same order as the claimed precision. The manuscript should either supply a quantitative systematic-error budget for the 1964 data or explicitly present the bound as conditional on the absence of such effects.
[Results, 'Correction to time period of pendulum' and Methods, 'Rigorous calculations using deformed commutators'] The paper's quantum-mechanical corroboration is performed for a harmonic oscillator, not for the pendulum. Eq. (57) in the Methods describes the time-dependent position of an oscillator in a harmonic potential, whereas the central claim concerns the anharmonic pendulum. The classical deformed-Poisson calculation is therefore the actual basis for Eq. (10), and the quantum calculation only establishes consistency between the two deformation schemes in the harmonic limit. This limitation should be stated where the corroboration is claimed, because the present wording that the quantum calculation 'shows that the results hold' is stronger than what the calculation supports.

minor comments (6)

[Methods, Eq. (26)] The rendering of the coefficient as '− β 2m2gLφ2' is ambiguous: it should be made explicit whether this is −(β/2)m²gLφ² or −β·2m²gLφ². On the natural reading β/2, it is consistent with Eq. (27), but the typesetting should be unambiguous.
[Bounds on QG parameters from experimental data] The sentence 'This data is reported and the method of extraction of the data is detailed in Sec .' contains an empty cross-reference; add the section number or delete the sentence.
[Fig. 1 caption] The caption states that shaded regions are 'excluded' without specifying that the bounds are one-sided 95% confidence limits; adding this to the caption would prevent over-interpretation of the boundary lines.
[Bounds on QG parameters from experimental data] The reduced chi-squared of the linear fit is reported as 0.07, far below 1; this indicates that the marker-size extraction errors are conservative and that the 95% slope interval is likely wider than the statistical scatter. A short comment to this effect would help readers interpret the quoted uncertainty.
[Correction to time period of pendulum] The model treats the pendulum bob as a point mass, while the experiment uses an iron cylinder of finite size and a conventional suspension; the possible small correction to the coefficient in Eq. (13) is not discussed and should be noted.
[Diamagnetic levitation for enhanced tests of QG] The optimistic and conservative bounds α>0.35 and α>0.24 for β0=1 are quoted without showing the full calculation or an error budget for the magnetic-field gradient stability; please provide the derivation or state the simplifying assumptions.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the pendulum bound is a parameter constraint derived from an independent 1964 dataset, not a prediction built from fitted inputs.

full rationale

The paper's central claim is a lower bound on the particle-number suppression exponent alpha, obtained by comparing a derived time-period formula with external pendulum data from Smith (1964). No step in this chain reduces to its own input. The suppression parameter alpha is introduced as an unknown in Eq. (2), and the time-period correction in Eq. (27) is derived from deformed Poisson brackets and then independently cross-checked by a deformed-commutator quantum calculation; neither step assumes the experimental slope. The experimental slope (0.0232 +/- 0.0012) is fitted from the extracted data and then used to constrain the combination beta0 N^(-alpha), which is ordinary parameter estimation, not a 'prediction' made from a fitted parameter. The bound alpha > 0.07 for beta0 = 1 is an inference from that constraint, and the paper explicitly presents it as a bound rather than a prediction. The only self-citations are methodological or contextual: [4] and [37] list related work by co-author Plenio, and [7] is the authors' prior error analysis for an optomechanical comparison that is not the main pendulum result. These citations are not load-bearing for the central derivation, and the central pendulum analysis rests on external data [26] and external theoretical results [13, 19, 20, 31, 32]. No equation is defined in terms of the quantity it is said to predict, no fitted parameter is renamed as a prediction, and no uniqueness claim is imported from the authors' own prior work. The unmodeled amplitude-dependent systematics in the 1964 data are a legitimate scientific limitation, but a limitation of systematics is not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

All quantitative results rest on the deformed-commutator model in Eq. (2), the choice of nucleon counting, and the assumption that the 1964 slope is free of unmodeled systematics. beta0 and alpha are the target parameters, while N is an input assumption.

free parameters (3)

beta0 = assumed 1 for the headline bound; varied in Fig. 1
Dimensionless GUP parameter expected to be order unity but not fixed by theory. The paper quotes alpha > 0.07 at beta0 = 1.
alpha = constrained as alpha > 0.07 for beta0 = 1
Unknown particle-number suppression exponent introduced in Eq. (2). It is bounded from the pendulum slope, not independently measured.
N = 7.32e26 nucleons
Number of elementary constituents chosen by assuming nucleons are the elementary particles. The paper notes the bound is insensitive to factor-of-few changes.

assumptions (5)

domain assumption For a composite test mass, the deformed commutator takes the form [x,p] = i hbar (1 + beta0 / (N^alpha (Mp c)^2) p^2).
Invoked in Eq. (2). The polynomial N^-alpha scaling is motivated by quasi-rigid bodies from Ref. [19] but is not derived from a full quantum gravity theory.
domain assumption The classical limit of the deformed commutator is a deformed Poisson bracket {x,p} = 1 + beta p^2, with dynamics generated by the modified Hamiltonian Eq. (8).
Alternative prescriptions exist in the literature. The paper connects this prescription to the quantum derivation for a harmonic oscillator, not for a pendulum.
standard math First-order expansions in beta and in the square of the angular amplitude are sufficient for the data range.
Used in Eqs. (25) to (27). The data have phi <= 0.16 rad and beta is assumed small, so the expansion is justified.
domain assumption N is the number of nucleons in the test mass.
The paper assumes nucleons are the fundamental constituents. It acknowledges that the definition of a fundamental particle remains open.
domain assumption The 1964 pendulum's amplitude-period slope is determined by the standard anharmonic term plus the quantum-gravity term to within the stated uncertainty.
Dissipation and suspension effects are noted but not modeled. A violation of this assumption changes the extracted value of beta0 / N^alpha.

how reviews work

0 comments

Cite this review

Pith. "Pith review of On Quantum Gravity Tests with Composite Particles." pith.science (2026). https://pith.science/paper/4NVV64K7

@misc{pith2026190811164,
  author       = {Pith},
  title        = {Pith review of: On Quantum Gravity Tests with Composite Particles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4NVV64K7}},
  note         = {Machine review of arXiv:1908.11164}
}

read the original abstract

Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on concrete experiments involving macroscopic pendula and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds thus bringing rigorous and well-controlled tests of quantum gravity closer to reality.

Figures

Figures reproduced from arXiv: 1908.11164 by the authors.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Spectra for Reactions in Astrophysical Electromagnetic Cascades with Lorentz Invariance Violation: The Vacuum Cherenkov Effect
astro-ph.HE 2024-12 conditional novelty 4.0 of 10

The authors provide closed-form total rates and simulated photon and electron spectra for vacuum Cherenkov radiation under second-order Lorentz invariance violation.

Reference graph

Works this paper leans on

42 extracted references · 39 canonical work pages · cited by 1 Pith paper

[1]

L. J. Garay, Quantum gravity and minimum length, Int. J. Mod. Phys. A 10, 145 (1995)

work page 1995
[2]

Amelino-Camelia, J

G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Tests of quantum gravity from observations of γ-ray bursts, Nature 393, 763 (1998). 10

work page 1998
[3]

Pikovski, M

I. Pikovski, M. R. Vanner, M. Aspelmeyer, and M. S. Kim, Probing Planck-scale physics with quantum optics, Nat. Phys. 8, 393 (2012)

work page 2012
[4]

Albrecht, A

A. Albrecht, A. Retzker, and M. B. Plenio, Testing quantum gravity by nanodiamond interferometry with nitrogen-vacancy centers, Phys. Rev. A 90, 033834 (2014)

work page 2014
[5]

Bawaj, C

M. Bawaj, C. Biancoﬁore, M. Bonaldi, F. Bonﬁgli, A. Bor- rielli, G. Di Giuseppe, L. Marconi, F. Marino, R. Natali, A. Pontin, G. A. Prodi, E. Serra, D. Vitali, and F. Marin, Probing deformed commutators with macroscopic har- monic oscillators, Nat. Commun. 6, 1 (2015)

work page 2015
[6]

Bosso, S

P. Bosso, S. Das, I. Pikovski, and M. R. Vanner, Ampliﬁed transduction of Planck-scale eﬀects using quantum optics, Phys. Rev. A 96, 23849 (2017)

work page 2017
[7]

S. P. Kumar and M. B. Plenio, Quantum-optical tests of Planck-scale physics, Phys. Rev. A 97, 63855 (2018)

work page 2018
[8]

P. A. Bushev, J. Bourhill, M. Goryachev, N. Kukharchyk, E. Ivanov, S. Galliou, M. E. Tobar, and S. Danilishin, Testing the generalized uncertainty principle with macro- scopic mechanical oscillators and pendulums, Phys. Rev. D 100, 066020 (2019)

2019

Show all 42 references

[9]

Maggiore, A generalized uncertainty principle in quan- tum gravity, Phys

M. Maggiore, A generalized uncertainty principle in quan- tum gravity, Phys. Lett. B 304, 65 (1993)

1993
[10]

Scardigli, Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment, Phys

F. Scardigli, Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment, Phys. Lett. B 452, 39 (1999)

1999
[11]

R. J. Adler and D. I. Santiago, On gravity and the uncer- tainty principle, Mod. Phys. Lett. A 14, 1371 (1999)

1999
[12]

D. V. Ahluwalia, Wave-Particle duality at the Planck scale: Freezing of neutrino oscillations, Phys. Lett. A 275, 31 (2000)

2000
[13]

Kempf, G

A. Kempf, G. Mangano, and R. B. Mann, Hilbert space representation of the minimal length uncertainty relation, Phys. Rev. D 52, 1108 (1995)

1995
[14]

Maggiore, The algebraic structure of the generalized uncertainty principle, Phys

M. Maggiore, The algebraic structure of the generalized uncertainty principle, Phys. Lett. B 319, 83 (1993)

1993
[15]

A. F. Ali, S. Das, and E. C. Vagenas, Discreteness of space from the generalized uncertainty principle, Phys. Lett. B 678, 497 (2009)

2009
[16]

Das and E

S. Das and E. C. Vagenas, Universality of quantum gravity corrections, Phys. Rev. Lett. 101, 221301 (2008)

2008
[17]

Marin, F

F. Marin, F. Marino, M. Bonaldi, M. Cerdonio, L. Conti, P. Falferi, R. Mezzena, A. Ortolan, G. A. Prodi, L. Taf- farello, G. Vedovato, A. Vinante, and J.-P. Zendri, Gravi- tational bar detectors set limits to Planck-scale physics on macroscopic variables, Nat. Phys. 9, 71 (2012)

2012
[18]

Villalpando and S

C. Villalpando and S. K. Modak, Probing Quantum Grav- ity with Large Molecular Wave-packets, arXiv e-prints (2019), arXiv:1901.09696 [gr-qc]

2019 arXiv
[19]

Amelino-Camelia, Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geome- try, Phys

G. Amelino-Camelia, Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geome- try, Phys. Rev. Lett. 111, 101301 (2013)

2013
[20]

Magueijo and L

J. Magueijo and L. Smolin, Generalized Lorentz invariance with an invariant energy scale, Phys. Rev. D 67, 44017 (2003)

2003
[21]

Amelino-Camelia, L

G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman, and L. Smolin, Relative locality and the soccer ball prob- lem, Phys. Rev. D 84, 87702 (2011)

2011
[22]

Hossenfelder, The Soccer-Ball Problem, Symmetry, Integr

S. Hossenfelder, The Soccer-Ball Problem, Symmetry, Integr. Geom. Methods Appl. 10, 1 (2014)

2014
[23]

Amelino-Camelia, Planck-Scale Soccer-Ball Problem: A Case of Mistaken Identity, Entropy 19, 400 (2017)

G. Amelino-Camelia, Planck-Scale Soccer-Ball Problem: A Case of Mistaken Identity, Entropy 19, 400 (2017)

2017
[24]

Bhattacharya, A

M. Bhattacharya, A. N. Vamivakas, and P. Barker, Levi- tated optomechanics: introduction, J. Opt. Soc. Am. B 34, LO1 (2017)

2017
[25]

Zheng, Y

D. Zheng, Y. Leng, X. Kong, R. Li, Z. Wang, X. Luo, J. Zhao, C.-K. Duan, P. Huang, J. Du, M. Carlesso, and A. Bassi, Room temperature test of the continuous spontaneous localization model using a levitated micro- oscillator, Phys. Rev. Research 2, 013057 (2020)

2020
[26]

M. K. Smith, Precision Measurement of Period vs Ampli- tude for a Pendulum, Am. J. Phys. 32, 632 (1964)

1964
[27]

Nozari and T

K. Nozari and T. Azizi, Coherent States of Harmonic Oscillator and Generalized Uncertainty Principle, arXiv e-prints (2005), arXiv:gr-qc/0504090 [gr-qc]

2005 arXiv
[28]

Benczik, L

S. Benczik, L. N. Chang, D. Minic, N. Okamura, S. Rayyan, and T. Takeuchi, Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation, Phys. Rev. D 66, 26003 (2002)

2002
[29]

Nozari and S

K. Nozari and S. Akhshabi, Noncommutative geometry and the stability of circular orbits in a central force po- tential, Chaos Soliton. Fract. 37, 324 (2008)

2008
[30]

Pedram, A higher order GUP with minimal length uncertainty and maximal momentum II: Applications, Phys

P. Pedram, A higher order GUP with minimal length uncertainty and maximal momentum II: Applications, Phys. Lett. B 718, 638 (2012)

2012
[31]

Pedram, Coherent States in Gravitational Quantum Mechanics, Int

P. Pedram, Coherent States in Gravitational Quantum Mechanics, Int. J. Mod. Phys. D 22, 1350004 (2013)

2013
[32]

J. P. Gazeau and J. R. Klauder, Coherent states for systems with discrete and continuous spectrum, J. Phys. A. Math. Gen. 32, 123 (1999)

1999
[33]

A. F. Ali, S. Das, and E. C. Vagenas, Proposal for testing quantum gravity in the lab, Phys. Rev. D 84, 44013 (2011)

2011
[34]

Brau, Minimal length uncertainty relation and the hydrogen atom, J

F. Brau, Minimal length uncertainty relation and the hydrogen atom, J. Phys. A. Math. Gen. 32, 7691 (1999)

1999
[35]

Scardigli and R

F. Scardigli and R. Casadio, Gravitational tests of the generalized uncertainty principle, Eur. Phys. J. C 75, 425 (2015)

2015
[36]

P. T. Boggs, R. H. Byrd, J. E. Rogers, and R. B. Schnabel, User’s reference guide for odrpack version 2.01: Software for weighted orthogonal distance regression, US Depart- ment of Commerce, National Institute of Standards and Technology (1992)

1992
[37]

J. S. Pedernales, G. W. Morley, and M. B. Plenio, Motional dynamical decoupling for interferometry with macroscopic particles, Phys. Rev. Lett. 125, 023602 (2020)

2020
[38]

P. S. Epstein, On the resistance experienced by spheres in their motion through gases, Phys. Rev. 23, 710 (1924)

1924
[39]

B. R. Slezak, C. W. Lewandowski, J.-F. Hsu, and B. D’Urso, Cooling the motion of a silica microsphere in a magneto-gravitational trap in ultra-high vacuum, New Journal of Physics 20, 063028 (2018)

2018
[40]

Dupree and C

R. Dupree and C. J. Ford, Magnetic susceptibility of the noble metals around their melting points, Phys. Rev. B 8, 1780 (1973)

1973
[41]

L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations, Phys. Rev. D 65, 125027 (2002)

2002
[42]

Bosso, S

P. Bosso, S. Das, and R. B. Mann, Planck scale corrections to the harmonic oscillator, coherent, and squeezed states, Phys. Rev. D 96, 1 (2017)

2017

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

L. J. Garay, Quantum gravity and minimum length, Int. J. Mod. Phys. A 10, 145 (1995)

work page 1995

[2] [2]

Amelino-Camelia, J

G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Tests of quantum gravity from observations of γ-ray bursts, Nature 393, 763 (1998). 10

work page 1998

[3] [3]

Pikovski, M

I. Pikovski, M. R. Vanner, M. Aspelmeyer, and M. S. Kim, Probing Planck-scale physics with quantum optics, Nat. Phys. 8, 393 (2012)

work page 2012

[4] [4]

Albrecht, A

A. Albrecht, A. Retzker, and M. B. Plenio, Testing quantum gravity by nanodiamond interferometry with nitrogen-vacancy centers, Phys. Rev. A 90, 033834 (2014)

work page 2014

[5] [5]

Bawaj, C

M. Bawaj, C. Biancoﬁore, M. Bonaldi, F. Bonﬁgli, A. Bor- rielli, G. Di Giuseppe, L. Marconi, F. Marino, R. Natali, A. Pontin, G. A. Prodi, E. Serra, D. Vitali, and F. Marin, Probing deformed commutators with macroscopic har- monic oscillators, Nat. Commun. 6, 1 (2015)

work page 2015

[6] [6]

Bosso, S

P. Bosso, S. Das, I. Pikovski, and M. R. Vanner, Ampliﬁed transduction of Planck-scale eﬀects using quantum optics, Phys. Rev. A 96, 23849 (2017)

work page 2017

[7] [7]

S. P. Kumar and M. B. Plenio, Quantum-optical tests of Planck-scale physics, Phys. Rev. A 97, 63855 (2018)

work page 2018

[8] [8]

P. A. Bushev, J. Bourhill, M. Goryachev, N. Kukharchyk, E. Ivanov, S. Galliou, M. E. Tobar, and S. Danilishin, Testing the generalized uncertainty principle with macro- scopic mechanical oscillators and pendulums, Phys. Rev. D 100, 066020 (2019)

2019