1.7 seconds: the photo finish of a 130-million-year race between gravity and light

Part IOne speed limit, or several?

Chapter 1What the speed of light really is

The speed of light, c, is badly named. In relativity it is not really a property of light. It is the exchange rate between space and time: how many metres of space are worth one second of time. It sets the top speed for any cause and its effect. Light travels at c only because photons, as far as anyone can tell, have no mass. Anything massless must move at exactly that speed, and anything with mass must move slower.

Since 1983 the metre has been defined by fixing c at exactly 299,792,458 metres per second. So in SI units you can no longer "measure the speed of light"; any experiment that tried would be measuring the length of its own metre stick. (Nº 1 made the same point about lengths: only ratios can be measured.) What you can measure is whether different things share the same top speed. That is the question of this page.

It is a real question. Neutrinos have mass: oscillation experiments have shown it since 1998,¹ and KATRIN's direct measurement caps it below 0.45 electronvolts.² So they move very slightly slower than light, and their speed depends on their energy. That is expected. (The heaviest of the Big Bang's own neutrinos should now be down to a few thousand kilometres a second: Nº 4.) The deeper question is whether every kind of particle approaches the same limit as its energy grows. Sidney Coleman and Sheldon Glashow made this precise in 1997–99. They gave each species of particle its own maximum speed and asked how different those speeds could be without anyone noticing.³ Different limits would have odd consequences. A particle moving faster than another species' top speed could shed that species, the way a boat sheds a bow wave ("vacuum Cherenkov radiation"). A photon moving faster than the electron's limit could split into an electron and a positron. Simply seeing cosmic-ray protons at 10²⁰ electronvolts tells us, in their framework, that the proton's top speed can exceed light's by at most one part in 10²³.

Draw the history of the universe on a spacetime diagram, with time upwards and space sideways, and a flash of light from any event spreads out along a cone: the light cone. In Einstein's theory, every massless messenger rides the same cone. Many theories that go beyond Einstein predict several cones instead:

A cone for gravity. Many theories of dark energy give gravitational waves their own effective spacetime, with its own speed.⁴ Ezquiaga and Zumalacárregui call it the "GW cone".
A cone that depends on energy. If space has a grain at the smallest scales, with a preferred rest frame, high-energy light might travel slightly slower (or faster) than low-energy light.
A cone that depends on polarisation. In the simplest version of that idea, left- and right-handed light travel at different speeds.

This page follows two races that put the single cone to the test. In Race one, gravity runs against light. In Race two, light runs against light. Before either, though, there is a story about how wrong a great physicist could be about the speed of gravity, and why.

Chapter 2A hundred million times the speed of light

In 1805, Pierre-Simon Laplace asked how fast gravity travels. In the fourth volume of his Traité de mécanique céleste, he pictured gravity as the push of a fluid streaming in towards each attracting body at some finite speed.⁵ A planet moving through that stream would meet it slightly from the front, the way rain seems to slant towards you when you run. Light from the stars shows exactly this effect, called aberration: Earth's motion tilts the apparent direction of every star by up to about 20 seconds of arc.

For gravity, the tilt would have a consequence. A stream that meets a moving body slightly from the front also pushes it slightly backwards, so a small part of the force would act as a brake. Oddly, braking a moon makes it sink into a smaller orbit, which it then goes round faster. Laplace worked out what this would do to the Moon. To explain the Moon's observed slow speeding-up entirely this way, gravity would have to travel about seven million times faster than light. But he believed he had already explained that speeding-up another way, through the slow change in the shape of Earth's orbit. So the gravitational effect had to be much smaller, and gravity had to be at least a hundred million times faster than light. Geometers, he concluded, could treat it as instantaneous.

There is a twist. Laplace's explanation of the Moon was itself only half right. In 1853 John Couch Adams found terms Laplace had dropped: the change in Earth's orbit explains only about half of the Moon's acceleration. In 1865 Charles-Eugène Delaunay, and independently the American William Ferrel, proposed that the rest comes from tides, which slowly brake Earth's spin, and that turned out to be correct.⁶ So the famous bound rested on a lunar theory that was incomplete. The same braking of Earth's spin is the long-term reason for leap seconds, which the CGPM voted on 15 October 2026 to end from 20 May 2027 (Nº 9).

But the deeper error was elsewhere. In relativity, gravity's changes travel at the speed of light, and yet Laplace's tilt almost entirely disappears. Arthur Eddington pointed this out in 1920 with an electrical analogy.⁷ Electric influences also travel at the speed of light, yet the pull between two charges moving steadily past each other points very nearly towards each other's present positions, not where they were when the influence set out.

Steven Carlip spelled out why in 2000.⁸ For a charge moving at constant velocity, the electric field at a distance points at where the charge is now. The field "knows" where the charge was when the influence set out, and how fast it was moving, and in effect extrapolates in a straight line. If the charge suddenly stopped, distant fields would keep pointing at the extrapolated position until news of the stop, travelling at light speed, arrived. Gravity does even better. In general relativity the pull is aimed at where the source would be if you extrapolated not just its velocity but its acceleration too. The aberration is cancelled by velocity-dependent parts of the force almost exactly. What is left over is tiny, and it is real: it is the radiation reaction that makes orbiting pulsars slowly spiral together as they emit gravitational waves.

The simplest way to see it uses relativity itself. In the Sun's own rest frame its gravitational field is static. Nothing is changing, so there is nothing for the field to lag behind. The laws of physics cannot depend on which steadily moving observer is describing them. So from Earth's point of view too, where the Sun is the thing that moves, the pull must point (very nearly) at where the Sun is now.

The numbers make the difference vivid. Seen from Earth, the Sun moves at about 30 km/s. Its light takes 499 seconds to reach us, and in that time the Sun moves about 14,900 km. That is why we see the Sun about 20.5 seconds of arc away from its true direction. Gravity has no such offset. Suppose it did, with the pull aimed at the Sun's old position: in the modern form of the worry, Newton's law with a light-speed delay added, reckoned from Earth's point of view so that the pull is aberrated just as sunlight is. The pull would then push Earth forwards along its orbit with a force about 1/10,000 of the Sun's pull (the ratio of Earth's speed to the speed of light). Earth would spiral outwards at about 6 metres per second, and its distance from the Sun would double in about 1,200 years. That figure was published by Tom Van Flandern in 1998,⁹ and this page's own integration gives 1,201 years. Mercury would double its distance in 180 years. Reckoned from the Sun's point of view instead, the same recipe gives almost no tilt; an answer that depends on the viewpoint is exactly what relativity forbids. (In Laplace's own stream picture, with gravity at the same speed, the sideways force would instead be a brake of the same size: the orbits would shrink, and Earth would fall into the Sun in about 400 years. Figure 1 shows both, with this page's arithmetic.) Carlip, citing a textbook exercise, says Solar System orbits would shift substantially "on the order of a hundred years".⁸ Planets have kept their orbits for billions of years.

Figure 1🌞 Try it

If gravity pointed at the past

Real numbers

Years after the switch

Speed of gravity

Earth to Sun

A year lasts

The pull is tilted by

Three answers to "where does the Sun's pull point?", applied to the real planets. Einstein: at the Sun's present position (very nearly), so the orbits stay put. Delayed: Newton's law with a delay added, aimed at where the Sun was, as seen from each planet, when the pull set out (499 seconds earlier for Earth, if gravity travels at light speed), with no relativistic cancellation. Each planet then feels a forward push equal to v/c_g times the Sun's pull (v its orbital speed, c_g the speed of gravity), and its distance grows as r² = r₀² + 4GMt/c_g: the same added amount for every planet (about 1/400 of a square astronomical unit per year at light speed), so the inner planets crowd together as they move out. Laplace's stream: gravity as a fluid streaming in towards the Sun meets each planet slightly from the front, so the sideways part is a brake of the same size, and r² = r₀² − 4GMt/c_g. Year length follows Kepler's third law, P ∝ r^3/2. Today's orbits are dashed. The shift of the point the pull aims at, and the sideways arrow, are exaggerated (the real tilt for Earth at light speed is 20.5 seconds of arc in today's orbit; it goes as 1/√r, with Earth's orbital speed, as the card shows); the orbiting is speeded up, and each turn of Earth's trail stands for 400 orbits. This page's arithmetic; the 1,200-year doubling time agrees with Van Flandern (1998). In general relativity the aberration cancels and the orbits stay put.What if the Sun's pull aimed at where the Sun was 8 minutes ago? Pick "Delayed", press Run, and watch Earth drift out past where Mars orbits today. Turn the dial to make gravity faster, and the drift slows to a crawl. Laplace's own stream of gravity would act as a brake instead, and the planets would fall in. In reality, Einstein's gravity points at where the Sun is now, and the planets stay put. Drag the picture to turn it.

Van Flandern drew the opposite lesson: that gravity must act almost instantly. Mainstream physics rejects that conclusion. Carlip's paper was in part a reply: stable orbits need the cancellation, not infinite speed. The real test of gravity's speed had to wait for something that changes suddenly enough to send news: a gravitational wave.

Chapter 3Two hundred years of indirect evidence

On 5 June 1905, a hundred years after Laplace's bound, Henri Poincaré proposed that gravitation spreads at the speed of light, through what he called ondes gravifiques, gravitational waves.¹⁰ Einstein's general relativity (1915) made the idea precise, and his papers of 1916 and 1918 showed that weak gravitational waves travel at c. For the next century, the evidence was indirect.

Binary pulsars. Two neutron stars in orbit lose energy to gravitational waves and slowly spiral together. In the Hulse–Taylor pulsar, discovered in 1974, the measured decay of the orbit matches general relativity's prediction to 0.9983 ± 0.0016.¹¹ In the Double Pulsar the agreement is 0.999963 ± 0.000063.¹² Within general relativity, the radiation reaction depends on the speed of gravity, so these numbers say that speed equals c to about 1% or better.⁸ But that conclusion holds only inside the theory being tested.

Jupiter, 2002. On 8 September 2002, Jupiter passed 3.7 arcminutes from a distant quasar. Its gravity bent the quasar's radio waves by 1,190 microarcseconds, and Sergei Kopeikin and Ed Fomalont measured a small extra part of the bending, 51 microarcseconds, caused by Jupiter's motion. They reported the speed of gravity as 1.06 ± 0.21 times c.¹³ Several theorists replied that, at the precision reached, the effect depends on the speed of light, not of gravity.¹⁴ Most later analyses agreed with that reading; Kopeikin and Fomalont still disagree. It makes a neat bookend, though: in 1676 Ole Rømer used delays in the eclipses of Jupiter's moon Io to show that light has a finite speed.

Gravitational Cherenkov radiation. If gravity were even slightly slower than light, the fastest cosmic-ray protons would outrun it, and they would shed gravitational waves as they flew, like a boat's bow wave. They would lose energy before reaching us. Guy Moore and Ann Nelson used the cosmic rays we do see to show that gravity can be slower than light by at most 2 parts in 10¹⁵ if the cosmic rays come from our own galaxy, or 2 parts in 10¹⁹ if they come from beyond it.¹⁵ This argument works only in one direction: it says nothing about gravity being faster. (The same rain of cosmic rays, at its far commoner low-energy end, makes the carbon-14 in the air: Nº 12.)

A template from 1987. On 23 February 1987, about two dozen neutrinos from supernova SN 1987A, in the Large Magellanic Cloud 168,000 light-years away, arrived about three hours before its light. The light was late because it escapes only when the shock wave reaches the star's surface. Allowing for that, the neutrinos and the light shared a top speed to about 2 parts in a billion.¹⁶ Both messengers had also been slowed by the Milky Way's gravity, by about 4.8 months in Michael Longo's estimate, and they were slowed equally to within about 0.2–0.5%.¹⁷ Thirty years later, this would be the template for Race one, with gravitational waves in place of neutrinos.

By the 2010s, theorists were waiting for exactly that. In 2014, Atsushi Nishizawa and Takashi Nakamura proposed timing gravitational waves against light from the same event, and projected a precision of about 10⁻¹⁶.¹⁸ In 2016 Lucas Lombriser and Andy Taylor showed that a popular class of dark-energy models, tuned to mimic the observed expansion, needs gravitational waves to travel below 95% of the speed of light today.¹⁹ If such a model were right, a gravitational wave from 130 million light-years away would arrive millions of years after its light.

Part IIRace one: gravity against light

Chapter 417 August 2017

At 12:41:04 UTC on 17 August 2017, the two LIGO detectors in Hanford, Washington and Livingston, Louisiana recorded a gravitational wave that had been rising in pitch for about 100 seconds.²⁰ Over some 3,000 cycles it swept up from about 24 hertz, the "chirp" of two neutron stars, with a combined mass of 2.74 times the Sun's, spiralling together and merging. The European detector Virgo, which had joined the run only sixteen days earlier, saw almost nothing. That near-silence was useful: it meant the source sat in one of Virgo's weak directions, and it shrank the patch of sky to search from 190 square degrees (two detectors) to 31, and finally to 28.

It was nearly missed in real time. A brief glitch hit the Livingston detector 1.1 seconds before the merger. Such glitches happen every few hours, and this one blocked the automatic check for a signal in both detectors at once. The first automatic trigger came from Hanford alone. What made people look closely was a second, independent alert from space.^20,21

NASA's Fermi satellite carries a Gamma-ray Burst Monitor that watches most of the sky at once. It recorded a short, faint burst of gamma rays, GRB 170817A, and sent out an automatic notice 15.6 seconds after the merger. The ESA satellite INTEGRAL saw the same burst. Corrected to Earth's centre, the gamma rays began 1.74 ± 0.05 seconds after the merger.²²

The gravitational waves alone put the source at 40 (+8, −14) megaparsecs, about 130 million light-years.²⁰ Its host turned out to be the galaxy NGC 4993, at 41.0 ± 3.1 Mpc.²³ The signals set out in the Early Cretaceous, when dinosaurs ruled and flowering plants were just getting started.

Then the rest of astronomy joined in. The paper describing the follow-up has more than 3,500 authors from about 950 institutions, in 61 teams.²¹ The press releases spoke of some 70 observatories on all seven continents and in space.

Figure 2🏁 Try it

The photo finish, and everything after

Press play

The finish, second by second

Everything after, from seconds to years

Top: the last seconds on an ordinary time axis. The gravitational-wave chirp is drawn with far fewer cycles than the real one (about 3,000 from 24 Hz), and the gamma-ray light curve is schematic: a main pulse of about half a second and a softer tail, about 2 seconds in all, beginning 1.74 ± 0.05 s after the merger. Bottom: the first signals of each kind on a time axis that is logarithmic in both directions from the merger (so seconds, hours and years all fit). Times are measured from the merger at 12:41:04 UTC on 17 August 2017. Drag along either axis, or press Play. Sources: LIGO–Virgo (PRL 119, 161101), the joint gamma-ray paper (ApJL 848, L13), the multi-messenger paper (ApJL 848, L12), Goldstein et al. (ApJL 848, L14), Coulter et al., Troja et al., Hallinan et al., Mooley et al. and Katira et al.Press Play to watch the finish in real time: the ripple in space rises to the crash, and the flash of gamma rays crosses the line 1.74 seconds later. Then time speeds up through everything that arrived over the next seven years. (The ripple is drawn with far fewer wiggles than the real one.) Drag along the lines to look around.

Light kept arriving for years. The visible glow of the explosion, a kilonova, was found 10.9 hours after the merger by the small Swope telescope in Chile, as soon as the sky was dark there.²⁴ Ultraviolet followed after about 15 hours, X-rays after 9 days,²⁵ and radio waves after about 16 days.²⁶ About seven years later the afterglow could still be detected.²⁷ But the race that matters here was decided in the first two seconds.

Chapter 5Fifteen decimal places

Here is the arithmetic of the race. Two signals leave the same place, the gamma rays a time Δt_launch after the gravitational waves. They cross the same distance D. If gravity is faster than light by a fraction Δv/c, it gains a lead of (D/c)(Δv/c) on the way. So the gap we see at Earth is

Δt_arrive ≈ Δt_launch + (D/c) × (Δv/c)Δv = v_gravity − v_light; the formula holds for small Δv.

The trip took about D/c ≈ 4.1 × 10¹⁵ seconds (130 million years). If all 1.74 seconds of the gap came from a speed difference, that difference would be 1.74 / 4.1 × 10¹⁵ ≈ 4 × 10⁻¹⁶. But we don't know when each signal left, and that is the whole difficulty. The LIGO, Virgo, Fermi and INTEGRAL teams handled it by bracketing the launch gap instead of modelling it:²²

How much faster could gravity be? Assume both signals left at the same instant. Then the whole gap, up to 1.79 seconds at the edge of its error bar, is gravity's lead. Use the smallest plausible distance, 26 Mpc, the low end of the gravitational-wave range, because a shorter track makes a given lead mean a bigger speed difference. The result: Δv/c ≤ 7 × 10⁻¹⁶.
How much slower could gravity be? Assume the gamma rays left as late as 10 seconds after the merger, which is generous for this kind of burst. Then gravity must have lost about 8.3 seconds on the way. The result: Δv/c ≥ −3 × 10⁻¹⁵.

−3 × 10⁻¹⁵ ≤ (v_gravity − c) / c ≤ +7 × 10⁻¹⁶GW170817 and GRB 170817A. Assumes the gamma rays left between 0 and 10 seconds after the merger.

That is about fifteen decimal places. The paper also notes that more exotic models allow launch gaps from −100 to +1,000 seconds; with those, the bounds loosen to roughly −4 × 10⁻¹³ and +4 × 10⁻¹⁴ (this page's arithmetic).²² The same 1.74 seconds also improved one standard measure of how gravity might break relativity's symmetry by more than ten orders of magnitude.

Figure 3⏱️ Try it

Fix the race

Can you match 1.74 s?

The gamma rays set off this long after the merger

Gravity is faster than light by (parts in a million billion)

Show me

Distance to the merger

Gap you'd see

Gap we saw1.74 ± 0.05 s

Verdict

Arrival gap Δt = Δt_launch + (D/c)(Δv/c), for luminosity distances of 26, 40 and 48 Mpc (the GW range, 40 +8 −14). Top: the finish line at Earth, at the moment the first signal arrives; the gap is shown as a distance in light-seconds, with the Moon's distance (1.28 light-seconds) for scale. "Race" zooms in from the whole 85–157 million light-year track to the last few light-seconds, then plays the finish in real time. Bottom: the band of launch delays and speed differences that reproduce the observed 1.74 ± 0.05 s at the chosen distance. The dashed box is the astrophysical assumption of the 2017 analysis, a launch delay between 0 and 10 seconds; where it cuts the band gives the bounds on the speed difference. At 26 Mpc they are −3.1 × 10⁻¹⁵ and +6.7 × 10⁻¹⁶, rounded in the paper to −3 × 10⁻¹⁵ and +7 × 10⁻¹⁶. Click, or drag the dot, on the plot to choose a point. (Over 130 million light-years, expansion corrections are below the precision shown.)The flash of light arrived 1.74 seconds after the ripple in space: about 520,000 km behind it, farther than the Moon. Two things could cause a gap: the light setting off late, or gravity being faster. Play with both and see how much speed difference the 1.74 seconds allows. Hint: not much. The thin band (almost a line) on the chart shows every combination that works. Press Race to zoom in from the whole track. It starts at the cautious low-end distance the scientists used, 26 Mpc (85 million light-years); pick 40 Mpc for the best estimate, the 130 million light-years of our story.

Some ways to picture fifteen decimal places (this page's arithmetic):

A speed difference of 7 × 10⁻¹⁶ would separate two racers by about 0.1 mm, a hair's width, over the distance from Earth to the Sun.
Kept up for the whole age of the universe, 13.8 billion years, it would add up to about five minutes.
The 1.74-second gap itself is about 522,000 km of light travel: 1.36 times the distance to the Moon. After 130 million years, that was the margin.

And the two racers could hardly have been more different. The gravitational waves near the merger had frequencies of hundreds of hertz and wavelengths of about 3,000 km at 100 hertz. The gamma rays had wavelengths of a few trillionths of a metre. That is a difference of almost eighteen orders of magnitude in frequency, with the same speed.

Chapter 6Why the light was late

Nobody thinks the 1.74 seconds measures a difference in speed. If it did, gravity would be faster than light by about 4 × 10⁻¹⁶, and that bound above would be a detection. The gap is about how the light was made.

The gravitational waves peak at the moment of merger. The gamma rays come later, through a chain of steps, each of which takes time:²⁸

Building the engine. The merger leaves a hot, rapidly spinning remnant. A jet may need it to collapse into a black hole first, which could take around a second.
Breaking out. In the last milliseconds, the merger had already thrown out a cloud of neutron-rich debris. The jet, and the hot "cocoon" of material it inflates, had to punch through it.
Getting transparent. The outflow must travel far enough out to become transparent and release its gamma rays.

One popular model says the gamma rays we saw came from the cocoon breaking out of the debris, not from the jet's core. It reproduces both the burst's weak energy and the 1.7-second delay.²⁹ Ehud Nakar stresses that the jet itself could have been launched at any time between the merger and the gamma rays.

We also saw it off-axis. Radio and optical tracking of the jet put our line of sight about 20° from its axis (19° to 25° in a 2022 analysis that added Hubble data), with a narrow jet core only a few degrees wide.^30,31,32 That is why the burst was so weak: its energy, if radiated equally in all directions, would have been 2 to 6 orders of magnitude below that of other short bursts with known distances.²² Seen head-on, it would have looked like an ordinary bright short gamma-ray burst.

Here is a strange detail. Radio telescopes spread across continents tracked the jet's position 75 and 230 days after the merger. Its image moved across the sky at an apparent 4.1 ± 0.5 times the speed of light.³¹ A 2022 measurement combining Hubble images with radio data gave 7.6 ± 1.3 times.³² The same event that tied gravity to light's speed also showed something apparently moving four to eight times faster than light.

It's an illusion of geometry, known since the 1970s from quasar jets. A jet moving towards us at nearly light speed almost keeps pace with its own light. Light it emits later has a shorter trip to make, so its image seems to move across the sky faster than it really does. For a jet moving at speed βc at an angle θ to our line of sight,

β_apparent = β sin θ / (1 − β cos θ)The largest possible value is βΓ, where Γ = 1/√(1 − β²); so an apparent speed of 7.6c needs Γ ≥ 7.7.

An apparent speed of 4.1c needs the jet to move at 97% of the speed of light or more, and 7.6c needs 99.1% or more (this page's arithmetic). Nothing outran light. The race between the gravitational waves and the gamma rays was a dead heat; the gamma rays were simply late off the starting line.

Figure 4🔦 Try it

Faster than light? A trick of the angle

Can it beat light?

What we see on the skysame scale for both rows

The blob's image, one dot per flash

How far light moves sideways in that time

Real speed of the blob

Direction it moves (angle from our line of sight)

Real speed

Looks like (sideways)

Flashes arrive

Verdict

A blob moving at speed βc at angle θ to our line of sight sends out a flash at equal intervals. Earth is far off to the right, so all the light that reaches us travels horizontally. Each flash starts closer to us than the last, so the flashes arrive (1 − β cos θ) times as far apart as they were sent, and the image moves across the sky at β_app = β sin θ / (1 − β cos θ). For a given speed the fastest-looking angle is cos θ = β, where β_app = βΓ; for any speed below light's, β_app can be at most cot(θ/2), so 7.6c needs a direction within 15° of our line of sight and 4.1c within 27° (this page's arithmetic). The tiles show both ceilings live. Chips: 4.1 ± 0.5c from radio interferometry (Mooley et al. 2018) and 7.6 ± 1.3c from Hubble and radio data (Mooley et al. 2022), each at the lowest real speed that can produce it. The angle here is the moving spot's direction: the jet's axis was 19° to 25° from our line of sight (Mooley et al. 2022), and in a structured jet the bright part that moves need not lie on the axis. The rings are each flash's light spreading out; the sky rows are rescaled to fit, the same for both. The arrivals are shown in slow motion when they come close together.Each flash starts closer to us than the last, so the flashes arrive bunched up. The blob's real speed stays below light's. Drag the arrow to aim the blob, or pick a case, then send the flashes. The "Looks like" card also shows the most this real speed could ever look like. Real jets are messier: the bright spot that moved may have pointed closer to us than the jet's centre line, which was about 20° away.

Chapter 7Falling together

There was a second test hidden in the same 1.74 seconds. Anything that travels past a mass is slowed slightly by its gravity, compared with a trip through empty space. This is the Shapiro delay, first measured with radar echoes from Mercury and Venus in the 1960s and most precisely with radio signals to the Cassini spacecraft in 2002. Cassini found that light behaves as general relativity predicts to a few parts in 100,000.³³

On their way here, both signals from GW170817 passed through the Milky Way's gravity. In the usual "parametrised" form of the delay,

Δt_Shapiro = (1 + γ) / c³ × ∫ |U| dlU is the Newtonian gravitational potential along the path; γ = 1 in general relativity.

Einstein's equivalence principle says that everything falls the same way in a gravitational field, so gravitational waves and light should share the same γ. If they didn't, the Milky Way would delay them by different amounts. The 2017 paper made a deliberately cautious estimate. It counted only the part of the path more than 100 kiloparsecs (about 330,000 light-years) from the Milky Way's centre, and treated the galaxy as a point of 2.5 × 10¹¹ solar masses, the low end of estimates for the mass inside that radius. The result:²²

−2.6 × 10⁻⁷ ≤ γ_GW − γ_EM ≤ 1.2 × 10⁻⁶

How large was the delay itself? In that cautious model, this page's arithmetic gives about 160 days for each messenger. Including the Milky Way's full dark-matter halo and the host galaxy, Sibel Boran and colleagues estimated about 400 ± 90 days.³⁴ So, by the usual reckoning, both signals were held back by somewhere between five months and more than a year, and they still arrived within two seconds of each other. Gravitational waves fall under gravity just as light does, to about a part in a million in this model.

There is an honest caveat. Olivier Minazzoli and colleagues showed in 2019 that this absolute delay is not something general relativity actually defines on cosmic scales. It is measured against an imaginary empty universe, and the answer depends on choices of coordinates.³⁵ Adding up the pull of every galaxy with the usual formula gives a "delay" for GW170817 of 23,000 to 190,000 years; a corrected formula gives tens of years, and in one galaxy catalogue the sign even flips. So counting only the Milky Way is not guaranteed to be cautious. The γ bounds are best read as an illustration, less robust than the speed bound. The equal treatment is the point: SN 1987A had shown it for neutrinos and light, to a fraction of a per cent;¹⁷ GW170817 showed it for gravitational waves, with seconds instead of hours to spare.

Chapter 8The same-day graveyard

Why did dark-energy theorists care so much? The universe's expansion is speeding up. The simplest explanation is a cosmological constant, a fixed energy of empty space. Many physicists hoped instead for something dynamic: a new field, spread through space, whose slow evolution drives the acceleration, perhaps by changing gravity itself on cosmic scales.

In 1974 Gregory Horndeski wrote down the most general theory of gravity plus one such field (a scalar field φ) whose equations stay well-behaved.³⁶ It has four free functions, G₂ to G₅, of the field and of its kinetic term X (on a cosmological background, half the square of its rate of change). On the expanding universe, gravitational waves in Horndeski theory travel at a speed c_T given by

c_T² = F_T / G_T
F_T = 2[G₄ − X(φ̈ G_5,X + G_5,φ)]
G_T = 2[G₄ − 2X G_4,X − X(Hφ̇ G_5,X − G_5,φ)]In units with c = 1. Commas denote derivatives, dots denote time derivatives, and H is the Hubble rate.

If G₄ depends on X, or G₅ is not constant, then c_T differs from c whenever the field is changing, and a dark-energy field has to change to do its job. Natural versions of these theories therefore predicted differences of order one, like the "below 95%" of Chapter 3. After GW170817 the difference had to be below about 10⁻¹⁵. Either the troublesome terms are absent, or they are tuned to cancel to fifteen decimal places.

The announcement came on Monday 16 October 2017. That same day, three theory papers appeared on the arXiv preprint server working out the consequences,^37,38,4 and a fourth followed the next day.³⁹ All four were published side by side in one issue of Physical Review Letters. The test had been anticipated for years, and rumours of an optical counterpart had circulated since August, so the calculations were ready. Jose María Ezquiaga and Miguel Zumalacárregui titled theirs "Dark energy after GW170817: dead ends and the road ahead".

Theory or family	After GW170817
Quartic and quintic Horndeski (G₄ depending on X, G₅ not constant)	Ruled out unless finely tuned^4,37
Quartic and quintic covariant Galileons, as dark energy	Ruled out^4,38
Most "beyond Horndeski" and DHOST theories	Cornered; with a later argument (gravitational waves decaying into dark energy), all quartic and quintic beyond-Horndeski (GLPV) theories ruled out⁴⁰
"Fab Four" self-tuning models; many vector-field theories	Mostly ruled out^4,39
Einstein-aether (a theory with a preferred frame)	One combination of its parameters pinned below about 10⁻¹⁵⁴¹
Hořava gravity	Its favoured parameter range squeezed to a strip less than 10⁻¹⁵ wide⁴²
TeVeS and similar relativistic MOND theories, as "dark-matter emulators"	Ruled out: gravity and light would have arrived more than a year apart³⁴
Quintessence, k-essence, "kinetic braiding" (cubic Horndeski), Brans–Dicke, f(R)	Survive

The terms that died were the main way a field could accelerate the universe "by itself", the hope of several research programmes. (The simplest survivor that could still do it, the cubic Galileon, had already failed a different test: its predicted imprint on the cosmic microwave background, found by matching CMB maps against galaxy maps, came out with the wrong sign.⁹⁶) MOND, the idea that gravity changes at very low accelerations, survived by adapting: in 2021 Constantinos Skordis and Tom Złośnik built a relativistic version whose gravitational waves move at c by design, and which fits the cosmic microwave background.⁴³ GW170817 became a design rule.

The loophole: gravitational rainbows. These dark-energy theories are "effective" theories: approximations valid only below some energy, beyond which unknown physics takes over. For many of them the breakdown energy is a little under 2 × 10⁻¹³ electronvolts. In this page's arithmetic that corresponds to a frequency of about 40 hertz (a wavelength of about 7,000 km), right in LIGO's band. Claudia de Rham and Scott Melville pointed out in 2018 that the unknown physics there could restore c_T = c at LIGO's frequencies even if gravity's speed differs for the very long waves that matter for cosmology.⁴⁴ They called it a "gravitational rainbow": a speed that depends on frequency. It is a little like testing a bridge with a bicycle and concluding it will hold a lorry. The way to close the loophole is to time gravitational waves at much lower frequencies. The space detector LISA, due to launch in the 2030s, could do it with a source seen by both LISA and ground detectors.⁴⁵

Gravity against gravity. LIGO's own data test part of the rainbow. If the graviton, the particle of gravity, had a mass, the low notes of a chirp would travel slightly slower than the high notes, and a signal that had crossed billions of light-years would arrive distorted. No such distortion has been seen. Using 83 signals, the LIGO–Virgo–KAGRA team puts the graviton's mass below 1.9 × 10⁻²³ electronvolts (a 2026 preprint).⁴⁶ In that model, waves of 20 and 300 hertz share one speed to about 3 parts in 10²⁰ (this page's arithmetic). So across LIGO's band, from tens to hundreds of hertz, there is no sign of a rainbow of this kind. The very long waves that matter for dark energy remain untested.

Why the graveyard matters again. Analyses of the DESI galaxy survey from 2025 and 2026 hint, at about three standard deviations, that dark energy may be weakening; that is short of the five-sigma discovery standard (Nº 1 has the details).⁴⁷ If it holds up, whatever drives the change has to respect GW170817's verdict, or slip through the rainbow loophole. Some proposals do it with a field coupled to gravity itself, in one of the ways that leave gravitational waves at exactly c.⁴⁸ Such theories can leave another fingerprint: gravitational waves that fade with distance at a slightly different rate from light. The GWTC-4.0 catalogue analysis (published 2026) measures this with a number Ξ₀, which is 1 in general relativity, and finds 1.4 (+1.0, −0.4), consistent with general relativity so far.⁴⁹ The GWTC-5.0 analysis (May 2026) again finds no departure.⁵⁸ The speed test has mostly done its work; the test of loudness is now under way.

Chapter 9Gold, a Hubble constant, and a long wait

The kilonova. The glow found by Swope was first blue and then, over days, red. The blue light came from debris poor in heavy elements called lanthanides, and the red from debris rich in them, because lanthanides trap light and redden it. Models put the total mass of freshly made heavy elements at a few hundredths of a Sun's mass.⁵⁰ These elements are built by the rapid neutron-capture process, or r-process, when nuclei swallow neutrons faster than they can decay. In 2019 Darach Watson's team identified strontium in the spectrum: the first single element identified in a kilonova.⁵¹ In 2023 the James Webb Space Telescope found signs of tellurium, another such element, in the glow of a different merger, GRB 230307A, seen in light alone; its gamma rays lasted about 35 seconds, far longer than a "short" burst should.⁵²

The gold. A famous press release said the merger made about 200 Earth masses of gold and 500 of platinum. That figure is not in the peer-reviewed paper, and gold was never actually detected; a later search found no prominent signs of platinum or gold in the spectra.⁵³ One peer-reviewed estimate is 3 to 13 Earth masses of gold, from models.⁵⁴ How much of the universe's gold comes from neutron-star mergers, compared with rare collapsing stars or giant flares from magnetars, is still argued over.⁵⁵ Wherever it was made, gold's yellow colour is an effect of relativity (Nº 11).

A Hubble constant. The gravitational waves gave the distance directly, with no cosmic distance ladder, and the host galaxy gave the speed at which it recedes. Together they gave the expansion rate of the universe: H₀ = 70 (+12, −8) km/s per megaparsec.⁵⁶ Adding the jet's viewing angle from radio data narrowed it to 70.3 (+5.3, −5.0).⁵⁷ Later analyses of this one event range from about 65 to 75. In a 2026 paper the LIGO–Virgo–KAGRA team combined it with about 140 mergers seen without light, whose redshifts can only be inferred statistically, and found 75 (+13, −9).⁴⁹ The next catalogue, GWTC-5.0 (May 2026, a preprint), used 236 signals and found 71.7 (+9.4, −7.5).⁵⁸ That is not yet precise enough to settle the "Hubble tension" between the early-universe value of about 67 and local values of about 70 to 73 (Nº 1 tells that story).

The long wait. GW170817 is still the only gravitational-wave event with a confirmed counterpart in light. The fourth observing run of LIGO, Virgo and KAGRA ran from May 2023 to 18 November 2025 and produced roughly 250 significant candidates. The catalogue of its second part, released in May 2026, brought the catalogue's total to 390 events and found no new events containing a neutron star in that stretch.⁵⁸ Neutron stars have been heard since 2017, in a probable second merger of two neutron stars in 2019 and in several mergers of a neutron star with a black hole, but each was too far away or too poorly located for any light to be found, or (when a black hole swallows its neutron star whole) not expected to shine.⁵⁹ A 2025 candidate was announced as a possible "superkilonova", but its gravitational signal was a weak, sub-threshold alert, and most teams classify the light as a Type IIb supernova, probably unrelated. Two 2026 studies did not settle it: a radio study found a faint counterpart consistent with either picture, and the European ENGRAVE team concluded the supernova is unrelated. The claim is disputed.⁶⁰ The 2017 paper had expected 0.1 to 1.4 joint detections with Fermi per year in the following run.²² Nature has been less generous. The next stretch of observing, a six-month run called IR1, is planned to start in mid-January 2027; dates for the fifth full run, O5, are still under discussion.⁶¹

Part IIIRace two: light against light

Chapter 10Does space have pixels?

The Planck length, √(ħG/c³) ≈ 1.6 × 10⁻³⁵ m, is fantastically small. A proton is about 10²⁰ Planck lengths across. Blow a proton up to 175 km across and a Planck length becomes the size of a proton (this page's arithmetic). (Nº 0 places it on a ladder of sizes: the bubbles a spontaneous decay of the vacuum would most likely make are only about a hundred times larger.) It is often called "the pixel size of the universe". It isn't, or at least no accepted theory says so. It is simply the scale at which, by dimensional analysis, quantum effects and gravity become equally important, so that our current theories stop being reliable.⁶²

Still, suppose space really were a fine grid. Waves on a grid don't all travel at the same speed. On a lattice of spacing a, a wave's frequency grows more slowly than its wavenumber once its wavelength gets close to a, so short waves lag. Light of high energy, meaning short wavelength, would arrive later than light of low energy. And a grid has a rest frame: someone moving past it sees its rows tilted and squashed, so they can tell they are moving. Relativity says no such frame exists. A grid breaks Lorentz invariance, the symmetry between all steadily moving observers.

In 1998 Giovanni Amelino-Camelia, John Ellis and colleagues pointed out that a speed difference of order E/E_QG, where E_QG is some quantum-gravity energy scale near the Planck energy, could be measured.⁶³ The difference for a single photon is absurdly small. But gamma-ray bursts make ideal racetracks: they are billions of light-years away (a long track), they flicker on millisecond time scales (a sharp starting gun), and they shine across a vast range of energies (very different runners).

The standard way to write this is as a change to the relation between a photon's energy E and momentum p:

E² ≈ p²c² [1 − s (pc / E_QG,n)ⁿ]
v ≈ c [1 − s (n+1)/2 × (E/E_QG,n)ⁿ]s = +1: high-energy light is slower ("subluminal"); s = −1: faster ("superluminal"). n = 1: linear; n = 2: quadratic.

Across an expanding universe the delay builds up in a particular way. A photon had more energy earlier in its trip (it has since been redshifted), so the speed difference was larger then; and delays picked up far away are stretched by the expansion. Uri Jacob and Tsvi Piran worked out the formula in 2008:⁶⁴

Δt = s (1+n)/(2H₀) × (E_hⁿ − E_lⁿ)/E_QG,nⁿ × K_n
K_n = ∫₀^z (1+z′)ⁿ dz′ / √(Ω_m(1+z′)³ + Ω_Λ)E_h and E_l are the photon energies measured at Earth; z is the source's redshift.

For the two bursts in this race, the integral K_n is 1.00 (linear) and 1.46 (quadratic) at z = 0.903, and 0.156 and 0.168 at z = 0.151, with Planck 2018 parameters⁶⁵ (this page's arithmetic). This standard form assumes a preferred cosmic frame; in "deformed relativity" models, which keep every steadily moving observer equivalent, the travel time can depend on distance differently.⁶⁶ One more thing to notice in the formula: the delay grows with the photon's energy and with distance, but a source's own quirks (high-energy light being emitted a little earlier or later) do not grow with distance. Separating the two is the main difficulty of every such test.

Chapter 11A photon older than the Sun

The first decade of tests used flaring galaxies and gamma-ray bursts and stayed below the Planck energy. One result looked like a hint. In 2005 the MAGIC telescope caught a flare from the galaxy Markarian 501 in which the highest-energy gamma rays peaked about four minutes after the lower-energy ones.⁶⁷ Its authors noted that a quirk of the source, such as particles being accelerated gradually inside the emitting region, could explain it. Later tests pushed the scale far above what the hint would have needed.

Year	Instrument and source	Linear E_QG above
1999	Whipple, flare of Markarian 421⁶⁸	4 × 10¹⁶ GeV
1999	BATSE and EGRET, GRB 930131⁶⁹	8.3 × 10¹⁶ GeV
2008	MAGIC, flare of Markarian 501⁶⁷	2.1 × 10¹⁷ GeV
2009	Fermi, GRB 090510⁷⁰	1.5 × 10¹⁹ GeV = 1.2 E_Pl
2011	H.E.S.S., flare of PKS 2155−304⁷¹	2.1 × 10¹⁸ GeV
2013	Fermi, GRB 090510 re-analysed⁷²	7.6 E_Pl
2024	LHAASO, GRB 221009A⁷³	1.0 × 10²⁰ GeV ≈ 8 E_Pl

The burst that crossed the Planck line went off on 10 May 2009. GRB 090510 was a short burst, the kind now known to come (at least sometimes) from merging neutron stars, at redshift 0.903. Its light travelled for about 7.5 billion years, so it set out about 3 billion years before the Sun formed (this page's arithmetic). Fermi's two instruments caught it, and among the photons was one of about 31 GeV, tens of thousands of times more energetic than the burst's typical photons. It arrived 0.829 seconds after the burst triggered the detector. The faintest first emission had started 30 milliseconds before the trigger. So, setting aside a faint precursor about 13 seconds earlier that a later search turned up (Troja, Rosswog and Gehrels, 2010), the 31 GeV photon finished within 0.86 seconds of the first light from the burst.⁷⁰

Run the formula. If E_QG,1 were equal to the Planck energy, the photon (30.5 GeV at the measured central value) from z = 0.903 would arrive about 1.15 seconds late (this page's arithmetic). It wasn't that late. Using cautious choices (the photon's energy at the low end of its 1σ range, 28 GeV, and the earliest possible start), the Fermi team found E_QG,1 > 1.2 E_Pl: the first time-of-flight limit beyond the Planck energy. Less cautious choices of the starting line give 3.4, 5.1, 10 or even 102 times the Planck energy. The paper is explicit that quadratic effects are not significantly constrained. A 2013 re-analysis using all the photons, not just one, raised the linear limit to 7.6 E_Pl.⁷²

As a fraction of the trip, 0.86 seconds in 7.5 billion years is 3.6 × 10⁻¹⁸ (this page's arithmetic). That is about a hundred times finer than Race one's gap of 1.74 seconds in 130 million years, and its bounds are correspondingly tighter, though for a different pair of runners.

Figure 5🔬 Try it

How big can the pixels be?

Pixel size (quantum-gravity energy E_QG)Pixel size

Predicted lag

Allowed by the data

Pixel size, roughly

Verdict

Top: when the light arrives, measured from the burst's first light (schematic light curves). The solid high-energy marks are what was observed; the hollow ones are where they would have to be if the effect had the chosen size. Bottom: predicted arrival delay of a photon of energy E relative to very low-energy light, from the Jacob–Piran formula with Planck 2018 parameters (this page's arithmetic), for subluminal effects that grow linearly (n = 1) or quadratically (n = 2) with energy; drag the dot up or down to change E_QG. GRB 090510 (z = 0.903): the 31 GeV photon arrived within 0.859 s of the burst's first emission; the verdict uses 28 GeV, its 1σ lower energy, as Abdo et al. did, which gives a linear limit of 1.22 E_Pl here (1.19 in the paper). The quadratic "Fermi 2013" chip (1.3 × 10¹¹ GeV) comes from a re-analysis using all the burst's photons, so it sits well inside the "allowed" region of this one-photon model. GRB 221009A (z = 0.151): the box marks LHAASO's analysis band; the allowed lag between 0.35 and 1.6 TeV is this page's conversion of LHAASO's published limits (1.0 × 10²⁰ GeV linear, 6.9 × 10¹¹ GeV quadratic), about 0.9 s and 0.6 s. The 13 TeV and the disputed 300 TeV photons are marked for scale. "Pixel size" is the length ħc/E_QG, only a rough translation: the formula assumes a preferred cosmic frame, and no accepted theory says space has pixels.If space were a fine grid, high-energy light would trail behind low-energy light. Bigger "pixels" mean a bigger lag. Slide towards bigger pixels and watch the high-energy light fall behind, until it would have arrived later than the real photons did. Then the photons say no.

Chapter 12The brightest of all time

On 9 October 2022 a burst so bright that astronomers nicknamed it "the BOAT", the brightest of all time, swept across the Solar System. GRB 221009A came from a collapsing massive star at redshift 0.151, about 2 billion light-years of travel away (this page's arithmetic). One team estimated a burst this bright should be seen about once in 10,000 years;⁷⁴ others argue it is less rare.

China's LHAASO observatory, a field of detectors 4,400 metres up on the Tibetan Plateau, happened to have it in view from the start. It recorded more than 64,000 gamma rays between 0.2 and 7 TeV in the first 3,000 seconds, and photons up to 13 TeV, the most energetic ever seen from a gamma-ray burst at the time.^73,75 A TeV is a thousand GeV, about the energy of a flying mosquito packed into one photon.

LHAASO's test did not rely on one photon. It compared the shape of the afterglow's rise and fall in ten energy bands. If higher-energy light travelled slower, the high-energy curves would be shifted later and smeared out. They weren't. If the linear scale were the Planck energy, light around 1.6 TeV would trail light around 0.35 TeV by about 7.3 seconds (this page's arithmetic); the published limit allows no more than about a second (this page's conversion, at 95% confidence). The published limits are E_QG,1 > 1.0 × 10²⁰ GeV, about 8 times the Planck energy (the abstract rounds this to "10 times"), and E_QG,2 > 6.9 × 10¹¹ GeV, among the best quadratic time-of-flight limits (about five times Fermi's), though still only about 6 × 10⁻⁸ of the Planck energy.⁷³ An independent analysis of public data found a linear limit of about 6 E_Pl and a similar quadratic one.⁷⁶

Did the BOAT break relativity? For a while, it looked as if it might. At this distance, photons above about 10 TeV should mostly be absorbed on the way, by colliding with the faint infrared light that fills intergalactic space. Early reports of 18 TeV photons, and a detection by the Carpet experiment in Russia of an air shower of about 300 TeV, about 75 minutes after the burst, prompted papers proposing Lorentz violation or new particles. Since then, LHAASO's highest energy has been revised down to 13 TeV. LHAASO's own paper says even that hints at a more transparent intergalactic space than expected. A slightly dimmer infrared background would explain it, though the authors also list Lorentz violation and axion-like particles as alternatives.⁷⁵ The Carpet team puts the chance that an unrelated shower would line up this well with the burst, in direction and time, at about 1% (9 × 10⁻³).⁷⁷ No collaboration claims a violation. One group has argued for years for a signal at about 3 × 10¹⁷ GeV, but it rests on assumptions about when different energies left the source, and is a minority view.⁷⁸

The other side of the bet. If high-energy light were faster than c, there would be an even stronger test. A superluminal photon could decay on its own, into an electron and a positron or into three photons, so above some energy the gamma-ray sky would go dark. In 2021 LHAASO reported photons up to about 1.4 PeV (1,400 TeV) from sources in our own galaxy (it has since seen one of about 2.5 PeV⁷⁹). They survive the trip, which puts the superluminal linear scale above about 10⁵ times the Planck energy.⁸⁰

The twist test. The simplest way to add a linear effect to the theory of light, worked out by Robert Myers and Maxim Pospelov in 2003, makes the two circular polarisations of light travel at slightly different speeds.⁸¹ The plane of polarised light would then rotate by an amount that grows with energy and distance. Across a detector's energy range the rotations would differ so much that the light would arrive unpolarised. Some gamma-ray bursts are seen to be polarised, which pushes this effect at least 10¹⁶ times below its natural size (the parameter ξ < 10⁻¹⁶).⁸² The polarisation detections themselves are only modestly significant, and some models of quantum-gravity foam are built to avoid this effect, so time-of-flight tests still matter.

Chapter 13Pixels that don't pick a side

"We looked for the pixels and found none" would overclaim. What these races rule out, at the Planck scale and a few times beyond it, is one specific kind of graininess: one that slows (or speeds) light in proportion to its energy, whether through a preferred rest frame or through the "deformed" versions of relativity that some researchers propose. Space could still be grainy in a way that keeps relativity intact.

The clearest example is the causal set programme. Instead of a grid, imagine spacetime as a random scattering of points, "sprinkled" with a fixed average density, like raindrops on a pavement. A regular grid looks different to a moving observer. A random sprinkle doesn't: after a change of viewpoint, its points are still scattered at random with the same density. Fay Dowker, Joe Henson and Rafael Sorkin argued in 2004 that discreteness of this kind need not conflict with Lorentz invariance,⁸³ and in 2009 Luca Bombelli, Henson and Sorkin proved that no rule can extract a preferred direction from such a sprinkling.⁸⁴ Theories like this predict no systematic energy-dependent delay, so the races can't see them; their possible signatures are of a different kind, such as tiny random "swerves" in a particle's momentum.⁸³

Figure 6🎛️ Try it

A grid has a rest frame. A sprinkle doesn't.

Drag the pictures

A grid

A random sprinkle

Under each picture: which way each point's nearest neighbour lies

Your speed past the points

Two discrete spacetimes in one space dimension, drawn with space across and time up, and the diagonal light cone through the centre. Left: a square lattice (one cell shaded). Right: a Poisson sprinkling at the same average density. Dragging either picture, or the slider, applies a Lorentz boost, x′ = γ(x − βt), t′ = γ(t − βx). The lattice's rows and columns tilt and stretch, revealing the frame in which it is at rest; the sprinkling looks statistically unchanged, because a Poisson process in Minkowski space is Lorentz invariant (Bombelli, Henson and Sorkin 2009). The small dials show the directions from each point to its nearest neighbour as drawn: four spikes for the lattice at rest, which swing towards the light cone as you move; a ragged circle for the sprinkling at every speed (a boost preserves area, so the boosted sprinkling is again a Poisson process of the same density). The light cone is the same in every frame.Two pictures of grainy spacetime: space goes across, time goes up. Drag either picture sideways to fly past it. The grid tilts and squashes, so you could tell you're moving. The random sprinkle still looks like a random sprinkle. Try the 🎯 game: someone has set you moving, and you have to find where the grid looks square again. With the sprinkle, there's nothing to find.

Other approaches are less clear-cut. In loop quantum gravity, areas and volumes come in discrete steps. Early calculations suggested light of different handedness might travel at different speeds, but later work argued that discrete steps are compatible with relativity, because a moving observer sees the same possible values with different probabilities.⁸⁵ There is no agreed prediction. String theory is Lorentz invariant in its standard formulations, although some string-inspired scenarios break the symmetry spontaneously or predict photon delays of just the kind these races look for.

There is also a theoretical reason to have expected a null result. John Collins and colleagues showed in 2004 that a preferred frame at the Planck scale does not stay politely at the Planck scale. Quantum effects carry it down to everyday energies, where it would produce violations of relativity of order a per cent, unless its parameters are tuned extraordinarily finely.⁸⁶ Laboratory tests see nothing remotely like that. So many theorists already doubted that simple E/E_QG effects exist. Experiments that looked for Planck-scale "jitter" in other ways, like Fermilab's Holometer, also ruled out only the specific model they were built for.⁸⁷

Kind of graininess	Status (October 2026)
Linear, high-energy light slower	Above about 8 E_Pl (time of flight)⁷³
Linear, high-energy light faster	Above about 10⁵ E_Pl (PeV photons don't decay)⁸⁰
Linear, depending on polarisation	Suppressed by at least 10¹⁶⁸²
Quadratic, (E/E_QG)²	Slower: above about 6 × 10⁻⁸ E_Pl; faster: above about 10⁻³ E_Pl. Wide open at the Planck scale either way^73,80
Random, frame-free graininess (causal sets)	No delay predicted; not tested by these races⁸⁴

Part IVOne cone

Chapter 14The speed-limit ladder

Put the main tests side by side and the result is a ladder. Each rung asks how different the top speeds of two things can be, written as a fraction |δv/c|. The rungs are not all alike. Some apply only at a particular energy, some only in one direction (only slower, or only faster), and some depend on a model to convert into a speed. But they all point the same way: so far, everything tested shares one top speed.

Figure 7📏 Try it

The speed-limit ladder

Tap a rung

Upper limits on the fractional difference between the top speeds of two things, |δv/c|, on a logarithmic scale; farther right means a tighter test. The rungs are not like-for-like: some hold only at the stated energy, some only in one direction (marked "one way"), and some need a model to turn into a speed (marked "model", with a hollow end). The 2011 OPERA value was a claimed signal, later traced to an equipment fault. "Decimal places" is −log₁₀|δv/c|, rounded. Values: OPERA 2011 and 2013; Longo 1987; Hohensee et al. 2009; GW170817 (ApJL 848, L13); Moore and Nelson 2001; LIGO–Virgo–KAGRA 2026 (graviton mass, a preprint; converted here); LHAASO 2024 at 1 TeV and LHAASO 2022 at 1.4 PeV (converted here); GRB 090510 (0.86 s in 7.5 billion years, this page's arithmetic); Nagel et al. 2015; Li and Ma 2022; KM3NeT 2025, with Satunin 2025 and Yang et al. 2025 (converted here); Coleman and Glashow 1999; IceCube 2018 (a limit on a term mixing muon and tau neutrinos); GRB polarisation (Götz et al. 2014, converted here). "Chain the races" links Race one, Fermi and LHAASO, this page's synthesis (below).The main tests of "does everything share one speed limit?", lined up. The longer the bar, the more decimal places the speeds agree to. The coloured rungs are this page's two races. Tap any rung for the story, or press "Chain the races".

A few rungs deserve a word:

The rung that fell. In 2011 the OPERA experiment reported neutrinos arriving from CERN 60 nanoseconds early over 730 km, faster than light by 2.5 parts in 100,000. The cause turned out to be a badly connected optical fibre; a second fault, in a clock oscillator, pulled slightly the other way. The corrected result agrees with c.⁸⁸ Theory had objected first. Within a week of the claim, Andrew Cohen and Sheldon Glashow (the Glashow of Chapter 1) showed that neutrinos that fast would shed electron–positron pairs on the way, a bow wave like those in Chapter 1, and arrive drained of energy; the ICARUS detector, in the same laboratory, saw no such loss.⁸⁹ In 2025 the KM3NeT telescope in the Mediterranean reported a neutrino of about 220 PeV, the most energetic yet seen. That it survived its journey limits any faster-than-light excess for neutrinos to roughly 10⁻²², in the models used.⁹⁰
Neutrinos from SN 1987A matched light to about 2 parts in a billion over 168,000 light-years.¹⁶
Electrons and photons in accelerators share a limit to about 10⁻¹¹: if they didn't, fast electrons at CERN's LEP collider would have shed light, or high-energy photons at Fermilab's Tevatron would have decayed.⁹¹
Electrons of about 2 PeV, revealed by the Crab Nebula's gamma rays, can exceed light's top speed by at most about 5 × 10⁻²⁰; otherwise they would radiate themselves away.⁹²
Light in different directions, a modern Michelson–Morley experiment with rotating resonators, agrees to about 10⁻¹⁸.⁹³
Gravity on its own. If gravity were slower than the fastest cosmic rays by more than about 2 parts in 10¹⁵, they would shed gravitational waves and lose their energy before reaching us (Chapter 3).¹⁵ And if gravitons had a mass, the low notes of each chirp would lag the high notes; they don't, which keeps waves of 20 and 300 hertz within about 3 × 10⁻²⁰ of one speed (Chapter 8; this page's conversion).⁴⁶
Muon and tau neutrinos: any Lorentz-violating speed term that would mix them is below about 4 × 10⁻²⁸ (in the Standard-Model Extension, a standard framework for such tests), from the way atmospheric neutrinos change type while crossing Earth in IceCube.⁹⁴
Left- and right-handed gamma rays, from the polarisation of bursts, agree to about 10⁻³⁸ at a few hundred keV, in the model used to interpret them (a conversion made for this page).⁸²

The two races sit in the middle of the ladder. But chained together, they span an extraordinary range. Gravity at about 100 hertz matches gamma rays of tens to hundreds of keV to about 10⁻¹⁵ (Race one). Gamma rays of that kind match a 31 GeV gamma ray to better than 10⁻¹⁷ (Fermi). And if any speed difference grows in step with energy, LHAASO's limit means even a 13 TeV gamma ray lags by at most about 1.3 × 10⁻¹⁶ (about 5 × 10⁻¹⁶ if it grows with the square of the energy). So a gravitational wave of 100 hertz and a gamma ray of 13 TeV share one top speed to about fifteen decimal places, across about twenty-five orders of magnitude in frequency. (That chain is this page's synthesis; no single experiment compares them directly.)

That is why physicists treat the light cone as one of the best-tested structures in nature. Laplace's question, "how fast is gravity?", turned out to be part of a bigger one: "is there one cone, or several?" Every test so far says one.

What would change the story:

A second merger seen in both gravity and light. It would re-run Race one, and might close the last finely tuned windows in dark-energy theories.⁴ The next run, IR1, is planned to start in mid-January 2027.⁶¹
Gravity at other frequencies. LISA, in the 2030s, could test the "gravitational rainbow" at frequencies a hundred thousand times lower than LIGO's.^44,45
Quadratic effects. Still unconstrained at the Planck scale; they need brighter, higher-energy, more distant bursts, from instruments like the Cherenkov Telescope Array Observatory and LHAASO.
The 300 TeV photon. Real or coincidence? Only another extreme burst can tell.⁷⁷

Chapter 15Glossary and sources

c: The speed of light in a vacuum: exactly 299,792,458 m/s, by the definition of the metre. In relativity, the top speed for cause and effect.
Light cone: The set of all places a flash from one event can reach, drawn in a diagram of space against time.
Lorentz invariance: The symmetry of relativity: the laws of physics are the same for every steadily moving observer, so no rest frame is special.
Gravitational wave: A ripple in the shape of spacetime, made by accelerating masses, which in general relativity travels at c.
Gamma-ray burst (GRB): A brief flash of gamma rays from a jet. Short bursts usually come from mergers of neutron stars, and long bursts usually from collapsing massive stars, but there are exceptions both ways.
Kilonova: The glow of radioactive heavy elements made in a neutron-star merger.
Shapiro delay: The extra travel time of a signal passing through a gravitational field.
Aberration: The tilt in the apparent direction of something because the observer is moving, like rain slanting towards a runner.
Horndeski theory: The most general theory of gravity plus one scalar field with well-behaved equations; the home of many dark-energy models.
Planck energy, E_Pl: About 1.22 × 10¹⁹ GeV, the energy scale at which quantum gravity is expected to matter.
E_QG: The energy scale of a hypothetical quantum-gravity effect on the speed of light; linear (n = 1) or quadratic (n = 2).
Causal set: An approach to quantum gravity in which spacetime is a random scattering of points ordered by cause and effect.

Sources

Super-Kamiokande Collaboration (Y. Fukuda et al.), "Evidence for oscillation of atmospheric neutrinos," Phys. Rev. Lett. 81, 1562 (1998), hep-ex/9807003.
KATRIN Collaboration, "Direct neutrino-mass measurement based on 259 days of KATRIN data," Science 388, 180 (2025).
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1.7 seconds

The universe's speed limit

100 million times faster than light

200 years of clues

The call from the sky

A dead heat

Why the light was late

Falling together

A graveyard in a day

Gold, and a long wait

Does space have pixels?

A photon older than the Sun

The brightest burst of all time

Pixels that don't pick a side

One speed limit

One point seven seconds

Chapter 1What the speed of light really is

Chapter 2A hundred million times the speed of light

Chapter 3Two hundred years of indirect evidence

Chapter 417 August 2017

Chapter 5Fifteen decimal places

Chapter 6Why the light was late

Chapter 7Falling together

Chapter 8The same-day graveyard

Chapter 9Gold, a Hubble constant, and a long wait

Chapter 10Does space have pixels?

Chapter 11A photon older than the Sun

Chapter 12The brightest of all time

Chapter 13Pixels that don't pick a side

Chapter 14The speed-limit ladder

Chapter 15Glossary and sources

Sources