What Would Count as Quantum-Gravity Evidence?

A credible quantum-gravity observation must do more than occur near a compact object or involve a very small length. Its prediction must differ from a specified alternative and survive calibration, selection, nuisance-parameter, and trials checks. There are two distinct targets: evidence for nonclassical gravitational dynamics, which low-energy quantum GR can already predict, and evidence distinguishing a microscopic completion from that same EFT. As of the 2026-08-20 evidence cutoff, no observation establishes a particular microscopic completion. Existing measurements constrain parametrizations or test ingredients of candidate theories.

Required background. Einstein Equations supplies the classical null hypothesis. Quantum Mechanics supplies states and statistical predictions.

Helpful background. Flat-Spacetime Quantum Field Theory supplies particle propagation and detector amplitudes, while Quantum Information supplies operational tests of nonclassical correlations.

Observational examples and inference targets

The examples distinguish a dataset from an interpretation. GRB 090510 and GWTC-3 are historical published analyses used to teach the inference method; they are not a claim to reproduce their event files here or to list the latest available catalogs. A proposal is not a detection.

Case and pinned record	Discriminator and current result	Calibration and selection	Scope and principal limitation
Fermi GRB 090510; 2009 published analysis, with LAT/GBM products available from NASA HEASARC	Energy-dependent photon arrival time; lower bounds on a linear dispersion scale under emission-time assumptions	Spacecraft clock, reconstructed photon energy, effective area, event class; burst time window and association probability	Source-intrinsic emission time is unknown; constrains a propagation ansatz, not quantum spacetime generally
GWTC-3; 2023 published tests with GWOSC strain and catalog products	Residuals and parameterized propagation or waveform deformations; consistency with general relativity in those tests	Strain response, data-quality vetoes, power spectrum, waveform and calibration nuisance parameters; detected-event selection	Historical worked example; waveform degeneracies and population selection limit interpretation
Proposed gravity-mediated entanglement experiments	Entanglement witness between two masses; proposal-only in these examples	Would require phase, force, displacement, electromagnetic, thermal, vibration, and clock calibration; predeclared witness window	Entanglement can exclude a specified classical local mediation model under its assumptions; it does not reconstruct ultraviolet gravity

The Fermi analysis associated a roughly $31\,\mathrm{GeV}$ photon with GRB 090510 and used several conservative emission-time hypotheses to bound linear and quadratic energy-dependent propagation Abdo et al. 2009, Methods and Table 2. The public archive supplies event and response products, but the inference also needs event-class definitions, clock provenance, response functions, and a source-lag model. The GWTC-3 tests likewise combine strain with calibration and waveform uncertainties rather than treating a catalog point estimate as raw evidence LIGO Scientific, Virgo, and KAGRA Collaborations 2023, §§II–VI.

The tabletop proposal occupies a different logical category. Starting from uncorrelated masses, entanglement generated solely by locally mediated dynamics can exclude a mediator with only commuting observables under the proposal’s composition and dynamical assumptions Bose et al. 2017, pp. 1–5. Allowing a direct nonlocal interaction or changing the classical–quantum dynamical framework changes the inference. The tabletop comparison examines these alternatives. A positive witness would test the interaction channel without by itself measuring gravitons, Planck-scale discreteness, or a microscopic geometry.

From a theory to a discriminator

For a propagation test, a commonly used phenomenological ansatz is

$$E^2=p^2\left[1+s_n\left(\frac{E}{M_{\mathrm{QG},n}}\right)^n+\cdots\right],$$

where $s_n=\pm1$ and $n$ is declared. In an expanding universe this produces, to leading order, an observed lag

$$\Delta t_{\mathrm{prop}}\equiv t_h-t_l =-s_n\frac{n+1}{2}\frac{E_h^n-E_l^n}{M_{\mathrm{QG},n}^n} \int_0^z\frac{(1+z')^n}{H(z')}\,dz'.$$

The sign follows from the displayed dispersion relation: positive $s_n$ makes the high-energy group velocity larger at this order, so $t_h-t_l$ is negative. Here $E_h,E_l$ are detector-frame energies. Specify their response, a cosmology, and whether the intrinsic emission lag is source-frame or observer-frame: a source-frame lag contributes $(1+z)\Delta t_{\mathrm{src}}$ to the observed lag, together with propagation and timing error. A large $M_{\mathrm{QG},n}$ therefore bounds this ansatz rather than measuring “the Planck scale.” Models with exact Lorentz symmetry are untouched.

A stronger quantum-spacetime discriminator would compare normalized likelihoods

$$p(d\mid H_i)=\int p(d\mid\theta_i,\eta,H_i)\, p(\theta_i,\eta\mid H_i)\,d\eta\,d\theta_i,$$

where $d$ denotes calibrated data, $\theta_i$ theory parameters, and $\eta$ astrophysical and instrumental nuisances. The joint prior need not factorize if these parameters are correlated. The hypotheses must be fixed before inspecting the anomaly: $H_0$ includes conventional source physics, propagation, detector backgrounds, and calibration uncertainty; $H_1$ changes a controlled spacetime observable. A likelihood ratio or Bayes factor has meaning only with declared priors or sampling distribution, a trials family, and a decision threshold.

Selection, systematics, and adverse checks

An analysis record must state why an event entered the sample; energy, time, channel, and quality cuts; the searched sky or source population; and how many related tests were tried. Post-selecting an energetic photon because its delay looks suggestive invalidates a single-trial probability. For gravitational waves, selecting only confidently detected events creates a population-dependent observation process that must enter the likelihood.

The adverse checks should deliberately enlarge the null. For photons, allow source-intrinsic spectral evolution, propagation through ordinary media, energy dispersion, clock offsets, and event misclassification. For gravitational waves, vary calibration splines, power-spectrum estimates, waveform families, eccentricity or precession assumptions, and population hyperparameters. For a tabletop witness, inject electromagnetic and vibrational couplings at their measured uncertainties, reverse controllable phases, use null masses or separations, and keep the witness definition blinded.

A null result constrains only the intersection of the reported energy or curvature regime, operator ansatz, source population, and instrument response. It cannot exclude approaches that predict no effect in that domain. Conversely, an unexplained residual is not positive evidence until ordinary alternatives have been quantitatively disfavored and the quantum model predicts more than the residual used to fit it.

Reproduction path and present boundary

For GRB 090510, the reproducible path is: pin the HEASARC LAT and GBM event files and instrument-response version; reproduce the event selection; verify the high-energy photon’s probability, energy posterior, and timing; implement each published source-emission hypothesis; integrate the displayed cosmological kernel; and recover the corresponding row of the published limit table. This page independently checks only the dimensional sufficient statistic $M_{\mathrm{QG},1}\sim E\,H_0^{-1}/\Delta t$ from the published energy, redshift, and lag scales. It gives an order-$M_{\mathrm{Pl}}$ sensitivity, consistent with the reported bound, but it is not an event-level numerical reproduction because the pinned event files and response calculation are not retained with this page.

For GWTC-3, a reproduction must pin a GWOSC release, analysis segment, calibration version, power-spectrum procedure, waveform code, priors, and sampler settings. A plot read from the paper is not a reproduction. No synthetic strain or inferred event values are substituted here for that missing computational record.

Presently, the scientifically defensible claims are asymmetric: observation has tightly tested particular Lorentz-violating propagation terms and many strong-field waveform deformations, while no dataset discriminates a controlled microscopic quantum theory of spacetime from a complete conventional null. Analog and tabletop experiments can validate mechanisms or witness nonclassical mediation, but their mapping to gravity must be stated rather than assumed.

Exercises

Exercise. Suppose two photons from a source at low redshift $z$ differ in energy by $\Delta E$, their measured arrival-time difference is $\Delta t$, and a linear subluminal ansatz is used. Neglect source lag and take $H(z)\simeq H_0$. Derive the lower scale inferred when no lag larger than $\lvert\Delta t\rvert$ is allowed. Then name two reasons it is not a model-independent quantum-gravity bound.

Solution

For $n=1$ and $z\ll1$, the integral is $\int_0^z(1+z')H(z')^{-1}dz'\simeq z/H_0$. The predicted magnitude is therefore $\lvert\Delta t_{\mathrm{prop}}\rvert\simeq \Delta E\,z/(M_{\mathrm{QG},1}H_0)$. Requiring it not to exceed the observed allowance gives

$$M_{\mathrm{QG},1}\gtrsim\frac{\Delta E\,z}{H_0\lvert\Delta t\rvert}.$$

The result assumes the photons were emitted simultaneously; an intrinsic energy-dependent source lag is degenerate with propagation. It also constrains only the chosen linear dispersion term: a Lorentz-invariant theory, a quadratic correction, or a theory whose leading observable is not photon propagation can satisfy the bound without approaching its ultraviolet scale.

References

• Abdo, Aous A., et al. “A Limit on the Variation of the Speed of Light Arising from Quantum Gravity Effects.” Nature 462 (2009): 331–334. DOI.
• Bose, Sougato, et al. “Spin Entanglement Witness for Quantum Gravity.” Physical Review Letters 119 (2017): 240401. DOI.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “Tests of General Relativity with GWTC-3.” Physical Review D 107 (2023): 022005. DOI.