A home rerun of the GRB 090510 light-speed test, and sound waves that keep their own limit

Some ideas about quantum gravity predict that light in vacuum travels at a speed that depends slightly on photon energy. A short, distant gamma-ray burst tests this well, because high-energy and low-energy photons leave together and travel for billions of years. We reran the test on the public Fermi Large Area Telescope photons from GRB 090510 with a simple method, fixed in advance. Our rerun bounds any linear energy-dependent change in light speed to less than 7.6e-18 of c at 29.9 GeV, a linear energy scale above 0.32 Planck energies, about 24 times weaker than the published limit of 7.6 Planck energies from the same burst.c1 The value of the rerun is as a reproduction of the method, and the published limits stand. Planted delays from 1 to 10 times our bound were recovered within 0.9 percent, and the fitted slope of zero sat inside the range that shuffled photon energies gave.c2 In the same study we simulated sound, which has a speed limit of its own. Sound in a uniform flow moved at the flow speed plus or minus the sound speed to within 1e-6, and in a simulated condensate the wave frequencies followed the Bogoliubov law within 2 percent, with a short-wavelength packet moving at 2.89 times the sound speed.c3 Twelve of the 15 preregistered verdicts passed; the three that failed were two forecasts of our own bound's strength and one test of a packet near a simulated horizon.c4

Special relativity says every observer measures the same speed of light. Several approaches to quantum gravity allow a small Lorentz invariance violationDefinition: Lorentz invariance violation particle physics and quantum gravity phenomenology Any departure from the rule of special relativity that every observer measures the same speed of light. The form tested here is a speed of light in vacuum that changes with photon energy. Excludes the slowing of light in a medium such as glass or plasma, which is ordinary optics. full definition in which that speed depends on photon energy. The size of such an effect is usually stated as a linear energy scale (E_QG,1)Definition: linear energy scale (E_QG,1) quantum gravity phenomenology The photon energy at which a speed change that grows in proportion to energy would reach the full speed of light. A lower limit on it is the usual way to state a time-of-flight bound. Excludes the quadratic scale, for a speed change that grows with the square of energy, which this paper does not bound. full definition, and the natural reference is the Planck energyDefinition: Planck energy physics The energy built from the constant of gravitation, Planck's constant and the speed of light, about 1.22e19 GeV. Many quantum-gravity models expect new effects near it. Excludes any energy reached by a particle accelerator, which is about fifteen powers of ten lower. full definition. A photon of 30 GeV is about 2.5e-18 of the Planck energy, so the expected effect on its speed is tiny, and only a very long flight can make it visible.

Gamma-ray bursts give that flight. Jacob and Piran [5] derived how an energy-dependent speed turns into an arrival-time delay over a path through an expanding universe; that relation is the one used here. GRB 090510 is a short burst at redshift 0.903, measured from the spectrum of its host galaxy [6]. Abdo and colleagues [2] used the Fermi observation of this burst, with emission up to about 31 GeV, and set a lower limit of 1.2 Planck energies on the linear scale under conservative assumptions about when the photons were emitted. Vasileiou and colleagues [3] analysed four bright Fermi bursts with three complementary methods; their strongest limit, from GRB 090510, is above 7.6 Planck energies at 95 percent confidence for the case where higher energies travel slower. The LHAASO collaboration [4] used the TeV photons of GRB 221009A and reported a linear limit above 10 Planck energies.

We had a narrower aim. A published limit rests on a pipeline most readers cannot run. We asked how close a short, plain analysis of the public photon file comes, with its forecasts and kill rules fixed before the run. The same study asked the companion question for sound: sound in a fluid has its own speed limit, and that limit is known to bend at short wavelength. Trachenko and colleagues [7] proposed an upper bound on the speed of sound in condensed matter, about 36 km per second, built from fundamental constants; it entered our study as one table check.

The preregistrationDefinition: preregistration research method (metascience) A dated written plan for a study, fixed and hash-locked before any result is seen: the question, the data, the statistic, the controls, the forecasts and the kill conditions. Excludes a plan revised after looking at the outcome, and a protocol written only for the record after the run. full definition and three forecast files were written and hash-locked on 31 October 2026, each before any run or data opening for its item. The hypothesis under test was that some sound and light waves travel faster or slower than c and follow different laws. The decision it informed: if the vacuum form fails, the published limits are quoted and our rerun is used only as a reproduction of method.

The lock records a debug run made before it. That run showed 84 photons in the analysis window and a bootstrap limit weaker than our forecast, so two forecast rows were known to fail. The rows were kept unchanged and are reported as failures. A one-photon bound was added after the debug run, and it is labelled as added wherever it appears. Two simulation settings were retuned in debug: the horizon packet was moved to start near the horizon, and the grid for the frame test was doubled.

Kill conditions, fixed in advance:

Each kill conditionDefinition: kill condition research method (our usage, after Popper's falsification) A rule written in the preregistration that, when met, decides against the claim with no room for judgement after the run. Excludes reasons found after the run for setting a result aside. full definition and forecast became a rule set whose pass or fail is a verdictDefinition: verdict research method (our usage) The pass or fail of one preregistered rule set against the run's numbers, read off by code. Excludes an interpretation written after reading the numbers. full definition read off by code.

The photons are from the Fermi Large Area Telescope public archive at the NASA High Energy Astrophysics Science Archive Research Center [1]: the weekly photon file for mission week 49 (processing P305, Source event class), which holds 1,214,533 photons, together with the trigger folder for bn090510016, all fetched on 31 October 2026. Fermi data are public with no restriction on use. The trigger time was read from the trigger file header. The burst position and the redshift of 0.903 were entered from memory before the run; the trigger header gives the same position to one decimal place, and the redshift matches the published value [6].

Photons were kept if they arrived between 1 s before and 3 s after the trigger, had energy above 100 MeV and zenith angle below 105 degrees, and fell within an energy-dependent radius of the burst, up to 12 degrees at low energy. That radius was set from memory of the telescope's point-spread function; the published response tables were not used. This gave 119 photons. The analysis window, 0.5 to 1.45 s after the trigger, holds 84 of them, with energies from 0.1 to 29.9 GeV. The highest-energy photon carried 29.9 GeV and arrived 0.828 s after the trigger.

The sound part uses no external data. The sound-speed table for the Trachenko check lists 14 materials with values entered from memory.

If the speed of light changes in proportion to photon energy, a photon of energy $E$ arrives later or earlier than a low-energy photon emitted with it by a time proportional to $E$:

where $\tau$ is the delay per GeV. This is dispersionDefinition: dispersion wave physics The dependence of a wave's speed on its frequency or energy, written as a relation between frequency and wavenumber. Excludes a delay that is the same at every energy, such as a fixed travel time. full definition in vacuum. Following Jacob and Piran [5], the slope sets the linear energy scale through a cosmological distance factor $K$:

with the integral taken from 0 to the redshift 0.903, $H_0$ = 67.4 km/s/Mpc and matter density $M$ = 0.315. The factor came out at 4.58e17 s. A bound ${\tau }_{\lim }$ on the slope gives

and the fractional speed change at the top energy $E_{\mathrm{top}}$ is

For a trial slope $\tau$, each photon's time is shifted back to $x_i=t_i-\tau E_i$. If the trial slope is right, the shifted times bunch most tightly. The fit maximises a sharpness score

over all photon pairs, where $G$ is a Gaussian of width 30 ms. The slope was searched on a grid from -250 to +250 ms per GeV in steps of 2 ms per GeV. This is a simple version of the methods in the published analyses, without the instrument response and without a model of the burst's own spectral lag.

The 84 photons were resampled with replacement 300 times, a bootstrapDefinition: bootstrap statistics Resampling the data with replacement many times and recomputing the estimate each time, so that the spread of the recomputed values gives an interval for it. Excludes an interval taken from a formula that assumes a distribution. full definition, and the slope refitted each time. The 95% intervalDefinition: 95% interval statistics The range that holds the middle 95 percent of the bootstrap or control draws for a number. We report it beside the number. Excludes a statement that the true value lies inside with 95 percent probability. full definition of the refitted slopes runs from its 2.5th to its 97.5th percentile, and ${\tau }_{\lim }$ is the larger of its two ends in size. The added one-photon bound assumes the top photon was emitted no earlier than the trigger, so its delay cannot exceed its arrival time:

This form follows the conservative argument of Abdo and colleagues [2] in outline only.

Three simulations solved the linear wave equation for sound in a moving fluid, in units where the sound speed $c_s$ is 1. In a uniform flow of speed $u$ = 0.5, rays should move at

A frame test checked that a solution transforms between frames under the sound speed and fails under a wrong one. A horizon flow $u\left(x\right)=-1+0.5\tanh \left(2\lambda x\right)$, with $\lambda$ = 0.4, makes an acoustic horizonDefinition: acoustic horizon analogue gravity The place in a moving fluid where the flow speed equals the sound speed, so that sound travelling against the flow cannot get out. It mimics the horizon of a black hole. Excludes a gravitational horizon, and any place where the flow is slower than sound. full definition at $x$ = 0 with surface gravityDefinition: surface gravity (of a horizon) analogue gravity, after black-hole physics The slope of the flow speed at the acoustic horizon. It sets how fast a trapped wave's wavelength is stretched. Excludes the pull of gravity at a planet's surface. full definition $\lambda$; a wave packet was released near it and its position and wavenumber compared with ray predictions.

The fourth simulation solved the one-dimensional Gross-Pitaevskii equation for a uniform condensate and measured the frequency of small plane waves at six wavenumbers. The known answer is the Bogoliubov dispersionDefinition: Bogoliubov dispersion condensed-matter physics (Bose-Einstein condensates) The frequency of small waves in a uniform condensate: equal to the sound speed times the wavenumber at long wavelength and rising faster, towards the free-particle law, at wavelengths near the healing length. Excludes sound in an ordinary gas or solid, whose dispersion is set by other physics. full definition

where $h$ is the healing lengthDefinition: healing length condensed-matter physics The length below which a condensate's density cannot change smoothly. Waves shorter than it stop behaving like sound. Excludes the wavelength of any particular wave. full definition. Its slope, the group velocityDefinition: group velocity wave physics The speed at which a packet of waves, and the energy it carries, moves. It equals the slope of frequency against wavenumber. Excludes the phase velocity, the speed of a single crest, which can differ from it. full definition, rises above $c_s$ once $kh$ nears 1.

Two checks were run on the photon fit.

The first controlDefinition: control statistics and experimental design A version of the data with the structure under test removed (for example shuffled or pooled), scored the same way as the real data, so the real score has something to beat. Excludes a comparison with a different dataset or with a published number. full definition shuffled the photon energies among the 84 photons, which breaks any link between energy and arrival time, and refitted the slope 300 times. The shuffled slopes ran from -44 to +76 ms per GeV (2.5th to 97.5th percentile). The real fitted slope, 0, sits inside that range, as forecast.

The planted checkDefinition: planted check research method; called a positive control in experimental science Data built so that the right answer is known, run through the same analysis before the real data, to show that the analysis can see the effect when it is there. Excludes any check made on the real data, which cannot show what the analysis misses. full definition added a known delay, $\tau E$, to every photon at 1, 3, 5 and 10 times our bound, with both signs, and refitted. Table 1 gives the result: every planted delay came back within 0.9 percent, so the fit sees a delay of the size of our bound when one is there. The result file stores one recovered value for each planted size, a positive delay, and none for the opposite sign. Three of the four planted delays lie outside the search grid of -250 to +250 ms per GeV stated in the methods, so the planted refits searched a wider range than that sentence gives; the file does not record the range.

For sound, the frame test is its own control: under the true sound speed the residual was 4.5e-4, and under a wrong speed 0.78.

Table 2 gives the photon results. The fitted slope is 0, on a 2 ms per GeV grid. The bootstrap interval runs from -117 to +46 ms per GeV, so the bound is 117 ms per GeV. Through eq. 3 that is a linear energy scale of 3.9e18 GeV, or 0.32 Planck energies. Our rerun bounds any linear energy-dependent change in light speed to less than 7.6e-18 of c at 29.9 GeV, a linear energy scale above 0.32 Planck energies, about 24 times weaker than the published limit of 7.6 Planck energies from the same burst.c1 The speed change is below the preregistered 1e-15, so the vacuum form of the hypothesis is killed in the band tested, 0.1 to 30 GeV.

Figure 2 sets our two bounds beside the published ones. The bootstrap bound is weak because resampling often leaves out the single 29.9 GeV photon, which sets most of the fit. The one-photon bound uses that photon directly and reaches 1.36 Planck energies, still a factor of about 5.6 below the published 7.6.

Table 3 gives the simulation results. Sound in a uniform flow moved at the flow speed plus or minus the sound speed to within 1e-6, and in a simulated condensate the wave frequencies followed the Bogoliubov law within 2 percent, with a short-wavelength packet moving at 2.89 times the sound speed.c3 Figure 3 shows the measured frequencies leaving the sound line as the wavelength nears the healing length.

The horizon packet stayed trapped, and its wavenumber followed the ray prediction within 3.3 percent. Its position lagged the ray by 0.16 in scaled units against a limit of 0.01, which failed. The packet is about as wide as the distance it travels, so a ray, which has no width, is a poor description of it; we did not refine the test after the run.

The Trachenko value computed from constants was 36.10 km per second, inside the forecast band of 36.0 to 36.2, and none of the 14 materials in our remembered table exceeded it; the fastest was diamond at 18 km per second.

Table 4 sets the forecasts written before the run against the outcomes.

Twelve of the 15 preregistered verdicts passed; the three that failed were two forecasts of our own bound's strength and one test of a packet near a simulated horizon.c4 Appendix A lists every rule.

The rerun did what a reproduction of method should do. On the same burst, with a plain fit, it finds no energy-dependent delay, and its controls behave: shuffled energies give a range that holds the real slope, and planted delays of the bound's size come back almost exactly. The number it produces is weaker than the published limits, by a factor of about 24 for the bootstrap bound and about 5.6 for the one-photon bound.

The gap has visible causes. Our bootstrap is dominated by whether the single 29.9 GeV photon is drawn, which makes the interval wide. The published analyses used the instrument response, careful event selection and several estimators, and they modelled or bounded the burst's own spectral lag [3]. We did none of that. The top energy also differs: the published abstract reports emission up to about 31 GeV [2], and our selection's top photon has 29.9 GeV in the weekly file's reconstruction; we did not trace the difference.

So the vacuum result is a check that the method can be run from public data and lands in the right place. It sets no new limit. The published limits of 7.6 Planck energies from this burst [3] and 10 from GRB 221009A [4] are the numbers to quote.

The sound results confirm known theory. Sound in a moving fluid obeys its own cone, flow speed plus or minus sound speed, at long wavelength, and it leaves that cone at short wavelength by the Bogoliubov law. A wave can then move faster than the sound speed of its medium by an ordinary mechanism, and it remains far below c. The hypothesis that some waves follow different laws holds only in that ordinary sense.