The antiatom that had to be weighed anyway

The fall that does not depend on what is falling followed three hundred years of dropping two different things and finding that they fall together: wood and gold, aluminium and platinum, beryllium and titanium, now to a part in 10¹⁵. The binding energy that has to fall too asked the same of gravitational self-energy and used the Moon to answer it. The pull that has to equal the pull back turned the question round and asked whether things pull as they are pulled. Every one of those tests compared one sample of ordinary matter with another.

The test masses were never antimatter, and the essay on the fall noted the gap without filling it. That might seem a mere omission. Antimatter is matter with its charges reversed, and gravity does not care about charge. But that is the claim to be tested, not a reason to skip the test, and for most of the twentieth century there was a respectable minority opinion, revived every decade or so, that antimatter might fall upwards. The case against it was built from arguments of startling indirectness, and the direct measurement, when it came in 2023, took one of the most elaborate pieces of apparatus in low-energy physics to make.

Why nobody simply dropped a positron #

The obvious experiment is to release an antiparticle in a vacuum and time its fall over a metre. It fails because antiparticles are charged and gravity is weak.

An antiproton weighs 1.6 × 10⁻²⁶ newtons. An electric field of a ten-millionth of a volt per metre pushes on it just as hard, and no laboratory can promise fields that small. Metal surfaces are not equipotentials at the level that matters: the crystal grains of any real surface present different faces with different work functions, and the patch fields they make reach millivolts per metre at a few centimetres — ten thousand times the antiproton’s weight. Its own image in the nearest wall pulls on it with thirty-five times its weight from a centimetre away. Even a neutral beam has to be made from charged particles and decelerated by fields.

An attempt was made with electrons in the 1960s, as a calibration for a positron experiment that was to follow. William Fairbank and Fred Witteborn let electrons drift up a vertical copper tube nearly a metre long, carefully shielded, and timed them. The electrons behaved as though gravity were absent, which turned out to be what should have been expected. Inside a metal tube, the conduction electrons sag under their own weight until the electric field they produce, $E = m_e g/e$, holds them up. That field, which the inside of a conductor treats as exactly zero, is fifty-six picovolts per metre, and it acts on a free electron inside the tube just as it acts on the conduction electrons, cancelling its weight. A positron in the same tube would have felt the field push it down as gravity did, and fallen at 2g if it fell normally or not at all if it fell upwards. Whether the field inside a tube really is the electrons’ sag or something larger, involving the metal’s lattice compressed by its own weight, was argued over for years. The positron experiment was never done.

So the question waited for antimatter that is neutral, and for a way to hold neutral antimatter still.

An engine that would run for ever #

Before any measurement, the question had already been argued to a conclusion, and the oldest argument needs nothing but conservation of energy. Philip Morrison set it out in 1958.

At the foot of a tower of height h, two gamma rays make an electron and a positron. The pair is lifted to the top. There they annihilate into two gamma rays, which are sent back down. Light falling in a gravitational field gains energy — the effect the clock that runs slow lower down measures, a fractional gain of gh/c² — so the gamma rays arrive at the foot with their original energy plus 2mgh, where m is the electron’s mass, and make the next pair with that much to spare.

If the positron falls like the electron, the lift costs exactly 2mgh, and the cycle returns what was spent. If the positron falls upwards, it is pushed up by gravity as hard as the electron is pulled down; the lift costs nothing, and each turn of the cycle produces 2mgh from nowhere. The machine runs for ever.

There is one escape and it closes immediately. The gain of falling light could be different from what the electron alone would suggest — if light fell like antimatter, say, and lost energy on the way down. But a photon is its own antiparticle. It cannot fall like matter and like antimatter at once, and the gravitational redshift of light has been measured, in a tower at Harvard and then in clocks a few centimetres apart. Light falls like matter. So, if energy is conserved, does the positron.

The positrons inside every nucleus #

The second argument is subtler, and it turns the whole history of torsion-balance experiments into a test of antimatter. Leonard Schiff made it in 1958.

A nucleus contains protons, which repel one another, and some of its mass is that electrostatic energy, divided by $c^2$. In quantum electrodynamics the field round a charge is not empty space: it is filled with virtual electron–positron pairs that appear, polarise in the field and vanish, and part of the electrostatic energy of the nucleus is carried by them. If positrons fell upwards, that part of every nucleus’s mass would be pulled up while the rest was pulled down.

The share of electrostatic energy grows roughly as $Z^2/A^{4/3}$, so it is very different from one element to another: half a part in a thousand of beryllium’s mass, four parts in a thousand of platinum’s. An element with more of it would fall at a slightly different rate from one with less, by an amount proportional to the part carried by virtual pairs. Schiff calculated that part and found that an upward fall of positrons would make aluminium and platinum fall at rates differing by far more than the Eötvös experiments of his day allowed. Those experiments had been reaching for a part in 10⁸; the torsion balances and satellites that followed reached a part in 10¹⁵, with MICROSCOPE comparing titanium and platinum, whose electrostatic shares differ by two parts in a thousand. If virtual positrons fell upwards, those masses would be in disagreement at a level many orders of magnitude above anything seen.

This is the same move the binding energy that has to fall too made with gravitational self-energy: when an exotic form of energy cannot be isolated, find bodies that contain different amounts of it and compare their falls. Here the exotic form is antimatter itself, present in every nucleus as a fleeting cloud, and the comparison was already in the record before anyone thought to read it that way.

The argument depends on virtual pairs gravitating like real ones, which is not something an experiment on real antimatter can check, and that is the honest objection to it. A theory could be built in which the vacuum’s contribution was treated differently. It would have to be built on purpose, and none has survived.

What CPT does and does not say #

A third argument is often offered and is weaker than it looks. The combined symmetry of charge conjugation, parity and time reversal — CPT — holds in every quantum field theory consistent with relativity, and it implies that antimatter is an exact mirror of matter. From that it is sometimes concluded that antimatter must fall like matter.

What CPT actually relates is a whole situation to its mirror. An antiapple falling towards an anti-Earth must behave exactly as an apple falls towards the Earth. CPT says nothing about an antiapple falling towards the Earth, which is a mixed situation with no mirror in the theorem, and that is the only situation any laboratory on this planet can set up. The symmetry rules out some exotic possibilities, such as antimatter having a negative inertial mass, but the cross-term — how matter’s gravity acts on antimatter — is exactly the term in question, and CPT leaves it free.

The same is true of general relativity. In it every form of energy, positive and negative charges alike, couples to the same curvature, and antimatter falls down. But that is the theory’s assumption about the cross-term, built in through the equivalence principle, and the point of an experiment is to stop relying on it.

Why anyone still wanted it to fall up #

With energy conservation and the torsion balances against it, an upward fall survived for a reason that had nothing to do with laboratory physics. A universe in which matter and antimatter repelled each other would behave very differently on the largest scales. If equal amounts of each had separated early on, their mutual repulsion could drive the expansion apart in a way that mimics an accelerating universe without any vacuum energy, and in some versions the question of why the observed universe is made of matter at all would dissolve, because the antimatter would simply be elsewhere. Models of that kind were published as recently as the 2010s, as alternatives to a cosmological constant whose size the estimate that misses by a hundred and twenty shows nobody can explain.

They were never popular, and the arguments above are each strong reasons to doubt them. But their authors could point out, correctly, that none of those reasons was a measurement of real antimatter falling, and each rested on an assumption — virtual pairs gravitating like real ones, the redshift of light being what it is for the same reason — that the models were free to reject. A question that matters to cosmology and can be settled by an experiment on a bench should be settled on the bench.

Neutral, cold and held still #

The way round the charge was to make antihydrogen: a positron bound to an antiproton, neutral overall. Antiprotons from CERN’s decelerator and positrons from a radioactive sodium source are cooled in separate electromagnetic traps and merged, and a fraction of the encounters form atoms. Most of them are too hot to keep. The few that are slow enough, below half a kelvin, can be caught in a magnetic bottle, because antihydrogen in the right spin state is a low-field seeker: its energy rises with the magnitude of the magnetic field, so it is pushed towards a minimum of the field’s strength.

That is allowed, though nothing can be held still by a static field when what is trapped is a charge. Earnshaw’s argument forbids a minimum of a potential obeying Laplace’s equation; the magnitude of a magnetic field does not obey it and can have a minimum in empty space. ALPHA, the collaboration that first trapped antihydrogen in 2010, built its bottle from a set of coils making a field that rises in every direction from the centre, about half a kelvin deep in temperature units.

The ALPHA-g apparatus stood the bottle on end. Its two mirror coils, a quarter of a metre apart, close the ends of the trap, and gravity adds a slope along it.

The slope is a third of a millikelvin from bottom to top, a thousandth of the trap’s depth. To read it, the experiment lowers both mirrors together over about twenty seconds, and the atoms, which have a spread of energies, leak out as the barriers fall below them. An atom leaves through whichever barrier is lower. If antihydrogen falls down, more atoms leave through the bottom. The escaping atoms annihilate on the walls, and a detector round the trap records where each annihilation happened: above or below.

A count of ups and downs alone would be hostage to every imperfection of the magnets, since a tilt of a third of a millikelvin is a field difference of less than five gauss. So the experiment adds a deliberate tilt of its own, a magnetic gradient along the axis that can be set to any strength and reversed. Repeating the release at many settings of that bias gives a curve, and the setting at which the atoms split evenly is the one at which the magnetic bias exactly cancels gravity’s.

The balance point #

The model behind the figure is far simpler than the real experiment. Each atom bounces along the axis between the mirrors with a fixed energy and a random starting phase and leaves through the first mirror it reaches that has dropped below its energy. Even so it shows why the result is read from the crossing rather than from any one count. The curves are smooth rather than stepped because the mirrors go on falling during the few milliseconds an atom takes to cross the trap, so an atom that reaches the upper mirror just after it has opened leaves that way; and they would be shifted by any unknown magnetic tilt. But the crossing point of the curve, the bias that gives an even split, is fixed by the balance of forces, and a stray tilt shifts it by an amount that can be calibrated with the magnets alone.

ALPHA-g reported in 2023 that antihydrogen falls with an acceleration of 0.75 g, with a combined uncertainty of about a fifth of a g. The upward fall that had been argued over since the 1950s was excluded, and so was the possibility that antimatter feels no gravity at all. The uncertainty is large by the standards of the equivalence principle — a part in five, against MICROSCOPE’s part in 10¹⁵ — but it is the first time the fall of antimatter was seen rather than inferred.

What the arguments and the measurement each establish #

The two kinds of evidence are not interchangeable, and it is worth being exact about what each one covers. Morrison’s engine shows that antimatter falling upwards would violate energy conservation, if light gains energy as it falls; it says nothing about whether antimatter might fall a few per cent faster or slower than matter. Schiff’s argument limits the gravitational behaviour of virtual positrons to the precision of the best torsion balances, provided virtual and real positrons gravitate alike. The SN 1987A neutrinos — antineutrinos, as it happens, caught by their reaction with protons in water — arrived after a journey of 168,000 years within hours of when light from the same collapse would have been expected, which bounds how differently an antiparticle and a photon are delayed by the galaxy’s gravity to a part in a few hundred.

None of these is a measurement of the gravitational acceleration of real antimatter atoms near the Earth, and that is what ALPHA-g supplied, at a precision far below the indirect bounds. The value of the measurement is not that it changed anyone’s expectation. It is that the equivalence principle is a claim about everything, and a claim about everything has to be tested on the things it would be easiest to be wrong about.

Where the toy model stops #

The release model is one-dimensional and treats the barriers as falling at a steady rate with the gravitational slope drawn on top; the real trap is three-dimensional, atoms move between the axial and radial motions, the mirror fields fall non-linearly and the magnetic field must be mapped to a fraction of a gauss along the whole axis. The experiment’s quoted uncertainty is dominated by exactly those things: how well the field is known and how well the atoms’ energies are simulated. The figure shows the logic of reading a balance point from a curve; it does not reproduce the measured curve, which is broader. The electrostatic shares are computed for a uniformly charged sphere of the standard nuclear radius, adequate to show the trend with atomic number, and the virtual-pair part of them is not drawn because computing it needs the full theory of vacuum polarisation in a nucleus’s field. The Morrison cycle assumes the gravitational redshift of light, measured in towers and with clocks.

The domain, then, is low-energy, neutral antimatter near the Earth, at the level of a fifth of g.

Still open: whether antimatter falls at exactly g #

The measurement says that antimatter falls down. It does not yet say how close to g, and experiments now under construction aim to say it to a per cent and beyond. ALPHA-g itself is being refined, with colder atoms and better-mapped magnets. Two other CERN experiments take different routes: AEgIS forms a beam of antihydrogen and measures its deflection with a fine grating, and GBAR makes positive antihydrogen ions, cools them to microkelvin, strips off the extra positron and times the neutral atom’s fall over a few centimetres — and eventually measures the quantum levels of antihydrogen bouncing on a surface, the staircase that the bounce that comes in fixed heights drew for neutrons. Whether antimatter falls at g to a part in a hundred, or in a million, is what those experiments will decide, and no theory now taken seriously predicts a difference.

The habit worth carrying away is to ask of a symmetry exactly which situations it relates. CPT maps an antiapple on an anti-Earth onto an apple on the Earth, and says nothing about an antiapple on the Earth; the arguments that do — a pair-lifting engine that would gain 2mgh a turn, and the virtual positrons in every nucleus — had to be made separately, and the measurement, 0.75 g with a fifth of a g of uncertainty, needed an atom with no charge at all. When a principle claims to cover everything, the parts of everything that are hardest to test are the ones it has to be tested on.