What CERN Actually Measures About Spacetime

The Large Hadron Collider has no instrument pointed at spacetime. It has magnets that bend beams, a pipe emptied to ultra-high vacuum, and detectors that record where particles went and how much energy they carried. Everything CERN learns about spacetime, it learns sideways. Spacetime is defined by a handful of symmetries, those symmetries dictate how particles behave, and the experiments check the behaviour to absurd precision. Every check that comes back clean is a statement about geometry.

First in a series on spacetime, light and information: CERN, wormholes, gravitational lensing, entanglement, and ER=EPR.

A collider is not a telescope

It is tempting to read a collider as a telescope aimed at the fabric of space, with more energy buying a sharper picture. Half of that is right: higher energy means shorter wavelength, and shorter wavelength means finer resolution. But the thing under the lens is never spacetime. It is a proton, a muon, an antihydrogen atom, and spacetime enters as the rulebook those objects obey.

The rulebook is mostly a list of things that do not matter — changes you can make to an experiment without the physics noticing. That is what a physicist means by a symmetry, and the full list of moves the laws ignore is a symmetry group. Relativity’s list holds three kinds of move.

Translations: doing the experiment here or a metre to the left, today or next Tuesday.
Rotations: turning the whole apparatus to face north instead of east.
Boosts: repeating it aboard something already coasting at a constant velocity.

Physics is unchanged by all three. That package has a name: Lorentz invariance.

The three mirrors behind CPT

Put quantum fields on that geometry and one more symmetry joins the list, assembled from three operations.

Charge conjugation, C: swap every particle for its antiparticle.
Parity inversion, P: reflect space the way a mirror does, so left becomes right.
Time reversal, T: run the film backwards.

Apply all three at once and the physics must come out the same. That combined symmetry is CPT, and the claim is about the combination: the three go together, not one at a time.

CPT is what turns antimatter into a measuring device. Build the antimatter version of an experiment and compare: any difference between a particle and its antiparticle is a crack in the symmetry. That is why two of the sharpest results below use antiprotons and antihydrogen.

These symmetries are not decorations. They are what “flat spacetime” means, operationally. A preferred direction would mean laws that changed with which way you faced; a preferred frame, a state of motion that counted as truly at rest. Either would leave fingerprints on particles.

CERN does not observe spacetime. It tries, and fails, to break its symmetries.

Why c belongs to spacetime, not to light

Take two events: two things that happen, each at a place and a time. Relativity asks for one number describing how far apart they are — not a distance plus a separate duration, but one combined number, the interval.

Writing it down runs into a problem. The gap in time is in seconds, the gaps in space in metres, and you cannot add seconds to metres. You need an exchange rate between the two, and there is exactly one on offer.

ds^2 = -(c dt)^2 + dx^2 + dy^2 + dz^2

dt is the time between the two events, in seconds. Multiplied by c it becomes a length in metres.
dx, dy and dz are the separations along the three directions of space, already in metres; squared and added, ordinary Pythagoras.
The minus sign on the time term has no counterpart in ordinary geometry. Time enters the sum with the opposite sign to space.

So c is not fundamentally a speed limit. It is the exchange rate between the time and space axes. The nearest everyday analogy is converting feet to metres before summing two lengths — with one caveat: feet and metres are human bookkeeping, and that minus sign is not.

Since the 1983 redefinition of the metre, c is a definition rather than a measurement: c = 299 792 458 m/s exactly, zero uncertainty. The metre follows from it, and nobody measures c any more.

A worldline is the track an object traces through space and time, and a massless particle has no choice about its worldline. Zero mass forces ds^2 = 0: the time term and the space terms cancel exactly, which forces |dx/dt| = c. There is no second solution to pick.

Photons travel at c not because light is special, but because nothing without mass can do anything else. Light is a passenger on the structure, not its author.

Plot time as c t and both axes carry metres, which puts a massless worldline at exactly 45 degrees. The cone belongs to the geometry, not to photons, and anything with mass stays inside it. c is exact by SI definition (NIST CODATA 2022).

Time dilation is engineering, not a curiosity

In Run 3 the LHC collides protons at 13.6 TeV — 6.8 TeV in each of the two beams. A proton sitting still has a rest energy of 938.272 MeV. Divide the one by the other and you get the Lorentz factor: 6.8 x 10^12 eV over 9.383 x 10^8 eV, about 7250.

A clock riding one of those protons ticks 7250 times slower than a clock bolted to the tunnel wall. The proton’s speed sits roughly 9.5 parts per billion below c. Nobody at CERN finds this remarkable. It is a design parameter.

The cleanest direct test is older than the LHC. A muon is unstable: left alone it survives a couple of microseconds, then decays. Bailey and colleagues held muons in the CERN Muon Storage Ring at a Lorentz factor of 29.33, timed in the laboratory frame.

μ+, positive muons: 64.419 ± 0.058 µs
μ−, negative muons: 64.368 ± 0.029 µs
the same particle at rest, its proper lifetime: 2.1948 ± 0.0010 µs

Divide a stored lifetime by the at-rest lifetime and out comes the dilation factor. It agreed with Einstein to a fractional error of 2 x 10^-3, at 95% confidence.

Without dilation a muon covers about 660 m in one mean lifetime, even at nearly c. These flew some 19 km of orbit, under enormous centripetal acceleration the whole way, and the dilation still depended only on their speed. Established, and replicated many times since.

What a broken symmetry would look like

Everything so far assumes spacetime is smooth — that you can keep zooming in and nothing changes. Several approaches to quantum gravity suggest it stops being smooth near the Planck length, 10^-35 m. If so, Lorentz invariance is an approximation, and approximations leak: a symmetry only nearly true leaves traces of its failure in things you can measure today.

So how do you hunt for a leak when nobody knows what it looks like? You enumerate. The Standard-Model Extension is a catalogue of every way Lorentz invariance and CPT could break, each written into the Standard Model’s equations as an extra term — an effective field theory whose job is to name every possible violation.

Each term carries a coefficient: a knob that reads exactly zero if the symmetry is exact. Experiments work through the knobs one at a time, each measurement squeezing one coefficient into a narrower band around zero. Kostelecký and Russell keep the tables.

Be clear about the status. The framework is speculative: no coefficient has ever been measured non-zero. The bounds are not speculative. Each is a hard measurement, and together they say how little room a violation has left to hide in.

Three places people have looked

Some of the sharpest bounds come from CERN’s Antiproton Decelerator. BASE compared the charge-to-mass ratios of the proton and the antiproton, held in a cryogenic Penning trap — a cage of electric and magnetic fields that pins charged particles in place. Over more than 24 000 comparisons of their cyclotron frequencies — the rate at which a trapped particle circles in the field — the two ratios came out equal to within 16 parts per trillion: the most precise CPT test on baryons, the family the proton belongs to. For scale, that is a kilometre measured to the last 16 nanometres.

Next door, ALPHA asked a blunter question: which way does antimatter fall? It released roughly 100 trapped antihydrogen atoms from a magnetic bottle and recorded where they annihilated. The measured acceleration was a_g = [0.75 ± 0.13 (stat. + syst.) ± 0.16 (sim.)] g. Antihydrogen falls down.

Read that status carefully, it is easy to overstate. It is a first direct observation. It is one experiment. Its precision is about 20% of g. What it rules out is repulsive antigravity — antimatter falling upwards. Whether antihydrogen falls at exactly g, to better than 20%, is untested.

For photons the sharpest constraint is astrophysical, not laboratory. Fermi detected a 31 GeV photon from gamma-ray burst GRB 090510, at redshift 0.903, a long way off. It arrived with no measurable energy-dependent delay. Had the speed of light depended on photon energy, the burst’s photons would have straggled in.

That excludes a propagation speed varying linearly with photon energy, up to a quantum-gravity mass scale above 1.2 Planck masses. One caveat rides with it: the bound assumes when photons of different energies left the source, so the exact factor is model-dependent. The conclusion — no linear-in-energy dispersion at the Planck scale — holds.

Every one of these is a null result: the experiment looked for a difference and found none. In this field the absence is the measurement.

The gap the LHC cannot cross

There is a hard limit on all of this. The Planck energy — the scale where spacetime is expected to stop being smooth — is 1.220890(14) x 10^19 GeV. The LHC’s collision energy is 1.36 x 10^4 GeV. The ratio is about 9 x 10^14, a hair under fifteen orders of magnitude.

An exponent flattens a gap like that, so unpack it. Going from a proton sitting still, at 0.938 GeV, to an LHC collision is a factor of roughly 15 000 — the jump the whole machine buys you. To reach the Planck energy you would have to repeat it three and a half more times, each starting where the last finished: a shortfall of nine hundred million million.

Nature’s own accelerators do not close it. The most energetic cosmic ray on record, the 244 EeV Telescope Array event of 2021, carried 2.4 x 10^11 GeV — seven orders of magnitude beyond the LHC, and still roughly eight orders short of the Planck energy.

So the LHC does not probe quantum gravity. It probes the symmetries any quantum theory of gravity must reproduce at low energy — a real constraint, but not the same thing.

Every marker is a measured or defined value: LHC Run 3 at 13.6 TeV (CERN), the 244 EeV Telescope Array event (Science, 2023), the Planck energy 1.220890(14) x 10^19 GeV (NIST CODATA 2022). The axis is log10 of E in GeV, so equal distances are equal factors.

What to take away

Work on spacetime at CERN is a load test on a bridge. You are not looking at the structure, you are pushing on it and confirming that nothing moves.

Three results carry the weight. c is the conversion factor between the time and space axes, not a fact about light, and massless particles are locked to it because a zero interval leaves no alternative. Time dilation is not a paradox but a number accelerator physicists design around. And the tests that would expose a grainy spacetime keep coming back null — fifteen orders of magnitude short of the energy where graininess should appear.

Spacetime looks smooth everywhere we can push on it. We cannot yet push where it matters most.