Last update: February 24, 2026

At the Heart of Matter: The Proton's Well-Kept Secrets

Artistic visualization of the chaotic internal structure of a proton, with its quarks and gluons interacting

The Proton: A Particle We Thought We Understood

Since its discovery in 1919 by Ernest Rutherford (1871-1937), the proton seems familiar to us. Together with the neutron, it forms the nucleus of atoms, and thus 99.9% of visible matter. Yet, more than a century later, this particle continues to defy physicists' understanding. Its exact size, the origin of its mass, the stability of its internal composition: so many mysteries that remain unsolved. Since then, generations of physicists have probed this particle with increasingly powerful instruments. Despite this, the proton jealously guards several of its fundamental secrets.

The answer lies in two words: quantum chromodynamics (QCD).

The Mental Challenge of the Quantum World

If quantum physics is so counterintuitive, it is because our brain, shaped by millions of years of evolution in a world of stones and trees, is not equipped to visualize the quantum world. We instinctively seek an image: a small hard ball, a compact nucleus surrounded by electron(s) in orbit, like a miniature solar system. This image, popularized by textbooks, is fundamentally erroneous.

At the heart of matter, reality does not exist. A particle in the quantum world (electron, quark, etc.) is an entity governed by probabilities. Visualizing an atom is therefore "seeing" a probability map, a fuzzy cloud where the density of the cloud represents the chance of finding the particle. For the proton, one must imagine a trembling ball of energy, where pairs of virtual particles constantly spring up and annihilate, a chaos ordered by the laws of quantum chromodynamics.

1st Mystery: The Mass of the Proton

The proton has a mass of about \(938.3\) MeV/c². Yet, if we add up the masses of the three constituent quarks, we only get a few MeV, less than 1% of the total mass. Where does the rest come from? The answer is one word: energy.

According to Albert Einstein's (1879-1955) famous equivalence, \(E = mc^2\), mass is just a condensed form of energy. Inside the proton, quarks are in perpetual motion and the gluon fields that connect them interact constantly, generating virtual quark-antiquark pairs all the time. It is this quantum bubbling, this energy confined in an infinitesimal volume, that constitutes most of the proton's mass. It is therefore not an intrinsic property of the quarks that compose it, but of pure energy trapped by the strong nuclear force. But the real mystery is not there.

The mystery is that gluons are massless particles. How does the strong interaction manage to trap such colossal energy in such a tiny volume? And above all, why do direct calculations from QCD remain so difficult, to the point that supercomputers still struggle to reproduce the exact value of this mass?

The mass of the proton is the visible manifestation of hidden physics, that of the quantum vacuum and the most powerful force in the Universe. Understanding its origin is understanding how the invisible becomes matter.

2nd Mystery: The Proton Spin Enigma

Spin is a quantum property of particles, often (wrongly) compared to a rotation on themselves. In the 1980s, deep inelastic scattering experiments revealed an anomaly. The sum of the spins of the valence quarks represented only a small fraction of the proton's total spin.

Where did the spin go? The answer probably lies in two contributions: the spin of the gluons, which can contribute via their own angular momentum, and the orbital motion of the quarks and gluons inside the proton.

Experiments such as those at the RHIC are attempting to unravel these contributions, but the puzzle remains unsolved.

3rd Mystery: Quark Confinement

Quarks have never been observed in a free state. They are always imprisoned inside hadrons, bound together by gluons. This phenomenon, called confinement, is one of the most baffling features of QCD.

Its mechanism is counterintuitive: the more one tries to pull two quarks apart, the more the force that binds them increases, unlike what is observed in electromagnetism. The energy stored in the gluon field tube grows linearly with distance. When this energy exceeds the threshold for creating a quark-antiquark pair, the string breaks and gives rise to new hadrons. A free quark never appears: nature seems to forbid any isolated color charge.

Simulations of lattice QCD, whose foundations were laid by Kenneth Wilson (1936-2013), allow the confinement to be reproduced numerically with good precision. But a simulation is not proof. Understanding why nature confines quarks remains one of the deepest questions in all of theoretical physics.

Summary Table of the Proton's Mysteries

The Three Great Unsolved Mysteries of the Proton
Mystery	Observation	What Theory Predicts	What Remains Unexplained
Origin of Mass	The proton weighs \(938.3\) MeV/c², about 100 times the combined mass of its quarks	QCD attributes mass to the kinetic energy of quarks and gluon fields (\(E = mc^2\))	No rigorous analytical calculation from first principles; only lattice QCD simulations approach the result
Origin of Spin	The proton has a spin of \(\frac{1}{2}\) (in units of \(\hbar\))	The three valence quarks should be the main source	Quarks contribute only ~30% of the total spin; gluons and orbital moments fill the rest in an still imprecise way
Quark Confinement	No free quark has ever been observed in nature	QCD predicts that the force between quarks increases with distance, making their separation impossible	No formal mathematical demonstration of confinement

N.B.: These three mysteries are intimately linked: confinement conditions the internal structure of the proton, which determines both the mass distribution and the spin distribution. The future EIC (Electron-Ion Collider), scheduled to start operating around 2030-2035, is specifically designed to provide quantitative answers to these open questions.