Could You Pull a Quark Out of a Proton?
You Can Grab It. You Cannot Keep It.
Everything is made of smaller things, and every smaller thing has been taken out and put in a box. Molecules out of crystals, atoms out of molecules, electrons out of atoms, nuclei out of atoms, protons out of nuclei. Give me the next one. A proton is three quarks. Take hold of one and pull. I do not care how hard.
The request is taken exactly as stated and physics answers it one wall at a time, each wall marked by how firmly it stands. The Quark page explains what quarks are and why they come in threes. This page assumes that and asks only whether one can be got out.
What Physics Says, Wall by Wall
The request is not naive, and the first wall is not a wall. Quarks carry electric charge, two thirds and minus one third of an electron’s, so an electric field takes hold of them exactly as it takes hold of anything charged. That is how they were found. In 1968 electrons fired into protons at Stanford bounced off hard points inside, three of them, the way alpha particles had bounced off nuclei sixty years before. There are parts in there, and each part has a handle.
So take the handle. Put a strong enough field across the proton and one of the three moves toward the edge. For the first fraction of a femtometre nothing unusual happens: the force between quarks at close range even weakens as they separate, which is the strange fact the Quark page calls asymptotic freedom. Then the quark reaches the edge of the proton, about 0.8 femtometres from the centre, and the second wall begins.
Every force you have ever pulled against gets weaker with distance. Gravity and electricity both fall as the square of the separation, which is why taking things apart works at all: get the parts far enough away and they are on their own. The force between quarks does the opposite. Past about a third of a femtometre the field between them stops spreading out and gathers into a tube, and a tube of field has a fixed energy per unit length. The force is that energy per length, and it is constant. Pull the quark to twice the distance and the pull is the same. Ten times, the same.
The number is large. The tension of the tube is about 0.9 GeV per femtometre, which in ordinary units is 1.5 × 10⁵ newtons: the weight of fifteen tonnes, hanging from a thread thinner than a proton, and never getting lighter. It is three thousand times the electric attraction between the same two quarks at that distance, and 10⁴⁰ times their gravity. Pull the quark outward at walking pace and you are delivering a hundred and fifty kilowatts to a string.
Because the force is constant, the energy you store grows in a straight line with distance: nearly a billion electron volts for every femtometre. That is the trap. By the time the quark is one proton-width away from the others, the string holds about the mass-energy of a whole proton, and a string with that much energy has a cheaper option than getting longer.
A quark and an antiquark together weigh a few hundred million electron volts once dressed in their field. When the string holds more energy than that, the vacuum can pay for a new pair out of the string itself, and it does: the tube breaks, a new quark appears at one end of the break and a new antiquark at the other. The energy you put in did not buy distance. It bought particles.
Be exact about the instant of the break, because that is where the request would like to find its lone quark. The pair is not created beside the string and then attached to it. It is created in the string, by the string. The break is a quantum tunnelling event of the same kind by which a strong enough electric field makes pairs out of empty space, and the new quark and antiquark appear as the two new ends of the two pieces of tube. The stretch of tube between them, about 0.7 femtometres, is what paid for their mass. Tunnelling has no duration. Asking how long the new quark went unattached is like asking how long an electron spends inside a barrier. What does take time is the field settling around the break, and it settles at the speed of light: 3 × 10⁻²⁴ seconds across a femtometre, and during that time each half is already vibrating as a meson.
Nor is there a bare charge anywhere in this story. A charge without its field is a bookkeeping device of the calculation, not a state of the world. An electron is never without its electric field, and a quark is never without its colour field. The new quarks are born dressed, because the dressing is what gave birth to them.
Follow the bookkeeping, because the outcome is stranger than a refusal. The proton was two up quarks and a down. You pulled an up. At the break the new quark stays with the proton and the new antiquark leaves with yours. Behind you is now up, down, down: a neutron. In your hand is an up and an anti-down: a positive pion. Charge checks out, one on each side. You reached for a third of a proton and came away with a whole particle of a different kind, and the proton you left is no longer a proton.
Neither survives your afternoon. The pion decays in 26 nanoseconds into a muon and a neutrino, and the muon into an electron and two more neutrinos two microseconds after that. The neutron, on its own, decays in about fifteen minutes back into a proton, an electron and an antineutrino. Half an hour after your pull, nothing you did remains except the energy you paid, scattered across a few light particles leaving at nearly the speed of light. There was never a moment, not even an instant, when a quark was alone. The pair was born already tied.
The picture below is the tug-of-war with two gauges. Drag the quark out. The force gauge climbs to fifteen tonnes and stays there. The energy gauge climbs in a straight line toward the mark where a new pair becomes affordable. Cross it, and the string does what strings do.
The request said it did not care how hard. Colliders take that literally a billion times a second. Strike a quark with hundreds of billions of electron volts and it flies out of the proton at nearly the speed of light, alone for about 10⁻²⁴ seconds. Then the string behind it breaks, and breaks again, and again, as fast as the energy allows, and what arrives at the detector is a spray of dozens of pions, kaons and protons all travelling in the quark’s direction. Physicists call it a jet, and the jet is the quark’s only public appearance. The harder the pull, the more particles in the spray. None of the energy ever buys freedom. All of it buys company.
There is one way to get quarks loose, and it is not pulling. Heat matter past about 155 million electron volts per particle, which is 1.8 × 10¹² K, and the strings dissolve. Quarks and gluons then move freely through one another in a liquid with no protons in it at all. Universe was that liquid for its first twenty microseconds, and gold and lead nuclei slammed together at nearly the speed of light make a droplet of it again: about ten femtometres across, lasting 3 × 10⁻²³ seconds.
Inside the droplet, the request is granted. A quark there is nobody’s. But you cannot take one out, and the reason is the sharpest version of the whole page: the thing that confines quarks is not the proton, it is the vacuum. Empty space itself is the medium in which colour field gathers into strings. The droplet is a patch where the vacuum has been changed, and the moment a quark reaches its edge it is back in ordinary vacuum, dressed and confined before it has travelled a femtometre. A free quark is possible. A free quark outside a furnace is not.
Here is an odd ending for a wall. The theory of the strong force is written down completely, in one line, and it has been checked to high precision wherever it can be calculated. Everyone is sure it confines quarks. Computers that solve it numerically on a grid find confinement every time and reproduce the string tension. And no one has been able to show, from the equation itself, with pencil and proof, that a free quark cannot exist. The Clay Mathematics Institute has offered a million dollars for it since 2000, and the prize is unclaimed.
So the request is refused by a fact whose reason is not understood in full. That is worth pausing on. It is not that the wall might have a hole in it; the numerical solutions are the equation, worked out the slow way, and they leave no room. It is that the shortest explanation of why a proton cannot be taken apart is still, after fifty years, the computer’s.
Where the Request Was Right
There are parts, and they have handles. The picture of a proton as three things you could take hold of is the picture the Stanford experiment confirmed, and for a while physicists themselves had resisted it. One correction: the three quarks account for about one percent of the proton’s mass. The other ninety-nine percent is the field between them, the same string you were pulling on. The proton is mostly the thing that stops you taking it apart.
Enough energy does free them. The request’s stubborn clause, I do not care how hard, is right in a way the request did not intend: put enough energy into enough quarks at once and they are free, in a plasma, as they were in the first twenty microseconds of universe. The mistake was only about where the energy has to go: not into one string, but into the vacuum of a whole region.
One quark never gets a hadron. The top quark, the heaviest of the six, decays in 5 × 10⁻²⁵ seconds, about seven times faster than a string can form around it. It has its colour field, as every quark must, but never the hadron that would normally enclose it, and its mass is measured as a free particle’s would be. The request asked for a lone quark and one exists, for less time than light takes to cross a proton, and never for the taking.
Is There a Bigger Bag?
Heat is one way to change the vacuum; pressure may be another. In the core of a heavy neutron star, matter is squeezed to several times the density of an atomic nucleus. The neutrons there may be pressed so close that their quarks stop belonging to any one of them. If so, the centre of such a star is a single body of free quarks a few kilometres across: the largest bag of loose quarks anywhere, held shut by gravity instead of by the vacuum. Two kinds of measurement bear on it. The NICER telescope on the space station measures the radii of neutron stars, and the 2017 gravitational-wave merger showed how two of them deform each other. Both are consistent with quark cores in the heaviest stars, and neither yet demands them.
Even there, the request fails the same way. Pull a quark out of the core and it crosses back into ordinary vacuum somewhere in the star’s crust, and there it is dressed. The free quarks in universe, if they exist, are all inside something: a droplet, a star, the first twenty microseconds. None has ever been in a box.
An Opinion, Dated
The walls above are physics. This box is the drafting model’s own bets, and they are scoreable.
Two in five that the heaviest known neutron stars have cores of deconfined quark matter, settled by 2040 by the combination of radius measurements and the tidal signatures of mergers.
One in six that confinement is proved from the equations, at the standard the Clay prize demands, by 2050. The problem has resisted the best people for half a century, and nothing about the recent decades suggests the tools are close.
Ninety-nine in a hundred that no isolated fractional electric charge is ever found in ordinary matter. The remaining one is not for a loophole in the argument above. It is for the possibility that the vacuum has an exception nobody has imagined.
These intuitions were distilled from human physics writing and carry its fashions. Weigh them accordingly.
The Updated Map
Taking things apart has always worked because the forces between parts fade with distance, so that past some separation each part is on its own. That is the picture to give up. This force does not fade. Its energy lives in a string, and beyond a proton’s width the string finds it cheaper to become new matter than to grow. So the parts are real, and the isolation is impossible, and the two facts do not conflict: a thing can be made of pieces that cannot exist alone. The proton is the first object on the way down that will not come apart, and it is mostly made of the reason why.
