The Quest to Map the Inside of the Proton

Long-anticipated experiments that use light to mimic gravity are revealing the distribution of energies, forces, and pressures inside a subatomic particle for the first time.

Physicists have begun to explore the proton as if it were a subatomic planet. Cutaway maps display newfound details of the particle’s interior. The proton’s core features pressures more intense than in any other known form of matter. Halfway to the surface, clashing vortices of force push against each other. And the “planet” as a whole is smaller than previous experiments had suggested.

The experimental investigations mark the next stage in the quest to understand the particle that anchors every atom and makes up the bulk of our world.

“We really see it as opening up a completely new direction that will change our way of looking at the fundamental structure of matter,” said Latifa Elouadrhiri, a physicist at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia, who is involved in the effort.

The experiments literally shine a new light on the proton. Over decades, researchers have meticulously mapped out the electromagnetic influence of the positively charged particle. But in the new research, the Jefferson Lab physicists are instead mapping the proton’s gravitational influence—namely, the distribution of energies, pressures, and shear stresses throughout, which bend the space-time fabric in and around the particle. The researchers do so by exploiting a peculiar way in which pairs of photons, particles of light, can imitate a graviton, the hypothesized particle that conveys the force of gravity. By pinging the proton with photons, they indirectly infer how gravity would interact with it, realizing a decades-old dream of interrogating the proton in this alternative way.

“It’s a tour de force,” said Cédric Lorcé, a physicist at the École Polytechnique in France who was not involved in the work. “Experimentally, it’s extremely complicated.”

From Photons to Gravitons

Physicists have learned a tremendous amount about the proton over the past 70 years by repeatedly hitting it with electrons. They know that its electric charge extends roughly 0.8 femtometers, or quadrillionths of a meter, from its center. They know that incoming electrons tend to glance off one of three quarks—elementary particles with fractions of charge—that buzz about inside it. They have also observed the deeply strange consequence of quantum theory where, in more forceful collisions, electrons appear to encounter a frothy sea made up of far more quarks as well as gluons, the carriers of the so-called strong force, which glues the quarks together.

All this information comes from a single setup: You fire an electron at a proton, and the particles exchange a single photon—the carrier of the electromagnetic force—and push each other away. This electromagnetic interaction tells physicists how quarks, as charged objects, tend to arrange themselves. But there is a lot more to the proton than its electric charge.

Latifa Elouadrhiri, a senior staff scientist at Jefferson Laboratory, led the collecting of data from which

she and her collaborators are now calculating mechanical properties of the proton.

 Courtesy of Latifa Elouadrhiri

“How are matter and energy distributed?” asked Peter Schweitzer, a theoretical physicist at the University of Connecticut. “We don’t know.”

Schweitzer has spent most of his career thinking about the gravitational side of the proton. Specifically, he’s interested in a matrix of properties of the proton called the energy-momentum tensor. “The energy-momentum tensor knows everything there is to be known about the particle,” he said.

In Albert Einstein’s theory of general relativity, which casts gravitational attraction as objects following curves in space-time, the energy-momentum tensor tells space-time how to bend. It describes, for instance, the arrangement of energy (or, equivalently, mass)—the source of the lion’s share of space-time twisting. It also tracks information about how momentum is distributed, as well as where there will be compression or expansion, which can also lightly curve space-time.

If we could learn the shape of space-time surrounding a proton, Russian and American physicists independently worked out in the 1960s, we could infer all the properties indexed in its energy-momentum tensor. Those include the proton’s mass and spin, which are already known, along with the arrangement of the proton’s pressures and forces, a collective property physicists refer to as the “Druck term,” after the word for pressure in German. This term is “as important as mass and spin, and nobody knows what it is,” Schweitzer said—though that’s starting to change.

In the ’60s, it seemed as if measuring the energy-momentum tensor and calculating the Druck term would require a gravitational version of the usual scattering experiment: You fire a massive particle at a proton and let the two exchange a graviton—the hypothetical particle that makes up gravitational waves—rather than a photon. But due to the extreme weakness of gravity, physicists expect graviton scattering to occur 39 orders of magnitude more rarely than photon scattering. Experiments can’t possibly detect such a weak effect.

“I remember reading about this when I was a student,” said Volker Burkert, a member of the Jefferson Lab team. The takeaway was that “we probably will never be able to learn anything about mechanical properties of particles.”

Gravity Without Gravity

Gravitational experiments are still unimaginable today. But research in the late 1990s and early 2000s by the physicists Xiangdong Ji and, working separately, the late Maxim Polyakov revealed a workaround.

The general scheme is the following. When you fire an electron lightly at a proton, it usually delivers a photon to one of the quarks and glances off. But in fewer than one in a billion events, something special happens. The incoming electron sends in a photon. A quark absorbs it and then emits another photon a heartbeat later. The key difference is that this rare event involves two photons instead of one—both incoming and outgoing photons. Ji’s and Polyakov’s calculations showed that if experimentalists could collect the resulting electron, proton and photon, they could infer from the energies and momentums of these particles what happened with the two photons. And that two-photon experiment would be essentially as informative as the impossible graviton-scattering experiment.

Courtesy of Merrill Sherman/Quanta Magazine

How could two photons know anything about gravity? The answer involves gnarly mathematics. But physicists offer two ways of thinking about why the trick works.

Photons are ripples in the electromagnetic field, which can be described by a single arrow, or vector, at each location in space indicating the field’s value and direction. Gravitons would be ripples in the geometry of space-time, a more complicated field represented by a combination of two vectors at every point. Capturing a graviton would give physicists two vectors of information. Short of that, two photons can stand in for a graviton, since they also collectively carry two vectors of information.

An alternative interpretation of the math goes as follows. During the moment that elapses between when a quark absorbs the first photon and when it emits the second, the quark follows a path through space. By probing this path, we can learn about properties like the pressures and forces that surround the path.

“We are not doing a gravitational experiment,” Lorcé said. But “we should obtain indirect access to how a proton should interact with a graviton.”

Probing Planet Proton

The Jefferson Lab physicists scraped together a few two-photon scattering events in 2000. That proof of concept motivated them to build a new experiment, and in 2007, they smashed electrons into protons enough times to amass roughly 500,000 graviton-mimicking collisions. Analyzing the experimental data took another decade.

From their index of space-time-bending properties, the team extracted the elusive Druck term, publishing their estimate of the proton’s internal pressures in Nature in 2018.

They found that in the heart of the proton, the strong force generates pressures of unimaginable intensity—100 billion trillion trillion pascals, or about 10 times the pressure at the heart of a neutron star. Farther out from the center, the pressure falls and eventually turns inward, as it must for the proton not to blow itself apart. “This comes out of the experiment,” Burkert said. “Yes, a proton is actually stable.” (This finding has no bearing on whether protons decay, however, which involves a different type of instability predicted by some speculative theories.)

Courtesy of Merrill Sherman/Quanta Magazine

The Jefferson Lab group continued to analyze the Druck term. They released an estimate of the shear forces—internal forces pushing parallel to the proton’s surface—as part of a review published in December. The physicists found that close to its core, the proton experiences a twisting force that gets neutralized by a twisting in the other direction nearer the surface. These measurements also underscore the particle’s stability. The twists had been expected based on theoretical work from Schweitzer and Polyakov. “Nonetheless, witnessing it emerging from the experiment for the first time is truly astounding,” Elouadrhiri said.

Now they’re using these tools to calculate the proton’s size in a new way. In traditional scattering experiments, physicists had observed that the particle’s electric charge extends about 0.8 femtometers from its center (that is, its constituent quarks buzz about in that region). But that “charge radius” has some quirks. In the case of the neutron, for instance—the proton’s neutral counterpart, in which two negatively charged quarks tend to hang out deep inside the particle while one positively charged quark spends more time near the surface—the charge radius comes out as a negative number. “It doesn’t mean the size is negative; it’s just not a faithful measure,” Schweitzer said.

The new approach measures the region of space-time that’s significantly curved by the proton. In a preprint that has not yet been peer reviewed, the Jefferson Lab team calculated that this radius may be about 25 percent smaller than the charge radius, just 0.6 femtometers.

Planet Proton’s Limits

Conceptually, this kind of analysis smooths out the blurry dance of quarks into a solid, planetlike object, with pressures and forces acting on each speck of volume. That frozen planet does not fully reflect the raucous proton in all its quantum glory, but it’s a useful model. “It’s an interpretation,” Schweitzer said.

And physicists stress that the initial maps are rough, for a few reasons.

First, precisely measuring the energy-momentum tensor would require much higher collision energies than Jefferson Lab can produce. The team has worked hard to carefully extrapolate trends from the relatively low energies they can access, but physicists remain unsure how accurate these extrapolations are.

Moreover, the proton is more than its quarks; it also contains gluons, which slosh around with their own pressures and forces. The two-photon trick cannot detect gluons’ effects. A separate team at Jefferson Lab used an analogous trick (involving a double-gluon interaction) to publish a preliminary gravitational map of these gluon effects in Nature last year, but it too was based on limited, low-energy data.

“It’s a first step,” said Yoshitaka Hatta, a physicist at Brookhaven National Laboratory who was inspired to start studying the gravitational proton after the Jefferson Lab group’s 2018 work.

Sharper gravitational maps of both the proton’s quarks and its gluons may come in the 2030s when the Electron-Ion Collider, an experiment currently under construction at Brookhaven, will begin operations.

In the meantime, physicists are pushing ahead with digital experiments. Phiala Shanahan, a nuclear and particle physicist at the Massachusetts Institute of Technology, leads a team that computes the behavior of quarks and gluons starting from the equations of the strong force. In 2019, she and her collaborators estimated the pressures and shear forces, and in October, they estimated the radius, among other properties. So far, their digital findings have broadly aligned with Jefferson Lab’s physical ones. “I am certainly quite excited by the consistency between recent experimental results and our data,” Shanahan said.

Even the blurry glimpses of the proton attained so far have gently reshaped researchers’ understanding of the particle.

Some consequences are practical. At CERN, the European organization that runs the Large Hadron Collider, the world’s largest proton smasher, physicists had previously assumed that in certain rare collisions, quarks could be anywhere within the colliding protons. But the gravitationally inspired maps suggest that quarks tend to hang out near the center in such cases.

“Already the models they use at CERN have been updated,” said Francois-Xavier Girod, a Jefferson Lab physicist who worked on the experiments.

The new maps may also offer guidance toward resolving one of the deepest mysteries of the proton: why quarks bind themselves into protons at all. There’s an intuitive argument that because the strong force between each pair of quarks intensifies as they get further apart, like an elastic band, quarks can never escape from their comrades.

But protons are made from the lightest members of the quark family. And lightweight quarks can also be thought of as lengthy waves extending beyond the proton’s surface. This picture suggests that the binding of the proton may come about not through the internal pulling of elastic bands but through some external interaction between these wavy, drawn-out quarks. The pressure map shows the attraction of the strong force extending all the way out to 1.4 femtometers and beyond, bolstering the argument for such alternative theories.

“It’s not a definite answer,” Girod said, “but it points toward the fact that these simple images with elastic bands are not relevant for light quarks.”

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