Swirling Forces, Crushing Pressures Measured in the Proton
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Welcome to the Quanta Science Podcast. Each episode, we bring you stories about developments in science and mathematics. I am Susan Vallett. Physicists have begun to explore the proton as if it were a subatomic planet. How are they doing it and what have they found? That's next. ♪

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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.

Latifa Elo-Adriri is a physicist at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia. She wasn't involved in the effort. We really see it as opening up a completely new direction that will change our way of looking at the fundamental structure of matter. 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 spacetime 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. That's 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.

Cédric Lorce is a physicist at the École Polytechnique in France who wasn't involved in the work. Physicists have learned a tremendous amount about the proton over the last 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 that buzz about inside it. Just a refresher, quarks are elementary particles with fractions of charge.

Physicists 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.

Peter Schweitzer is a theoretical physicist at the University of Connecticut. This is extremely exciting. So, for instance, what do we know about the particle? We know the total mass.

So right now we have, for instance, the information from the electromagnetic form factors how the electric charge is distributed. But how is really matter and energy distributed inside the proton? 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. So the energy-momentum tensor knows like everything

there is to be known about the particle. Albert Einstein's theory of general relativity casts gravitational attraction as objects following curves in spacetime.

In that theory, the energy-momentum tensor tells spacetime how to bend. For instance, it describes the arrangement of energy, the source of the lion's share of spacetime 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 spacetime.

Russian and American physicists independently worked out in the 1960s that if we could learn the shape of spacetime surrounding a proton, 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. That's a collective property physicists refer to as the "druck" term, after the word for "pressure" in German. One global property is just the mass, another is just the spin, and there is a third one as important as mass and spin. That's the "druck" term. And nobody knows what it is. Because so far we had no way of measuring it.

Though that's starting to change. In the 60s, it seemed as if measuring the energy-momentum tensor and calculating the droop 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 proton.

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.

Volker Burkert is a member of the Jefferson Lab team. I remember reading this when I was a student. A summary that he put into his paper says, unfortunately, because the gravity is so extremely weak, we will probably never be able to learn anything about mechanical properties of particles.

He was talking about particles like the proton. Gravitational experiments are still unimaginable today, but research in the late 1990s and early 2000s by physicist Shin Dong-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.

Gies 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. How could two photons know anything about gravity?

The answer involves gnarly mathematics, but physicists have two ways of thinking about why the trick works. Photons are ripples in the electromagnetic field. They can be described by a single arrow, a vector, at each location in space indicating the field's value and direction.

Gravitons would be ripples in the geometry of spacetime. There's 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. But here's an alternative interpretation of the math.

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. Here's physicist Cedric Lorce. We are not doing gravitational experiments. We can extract part of the information that you will attribute to the energy momentum tensor.

And from the initial momentum tensor, since it is essentially the source of the gravitational fields according to Einstein relativity, we say we should learn how a proton should interact with a graviton. 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, an experiment

And in 2007, they smashed electrons into protons enough times to amass roughly a half million graviton-mimicking collisions. Analyzing the experimental data took another decade. From their Index of Space-Time Bending Properties, the team extracted the elusive Druk term, publishing their estimate of the protons' 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 of the heart of a neutron star. Farther out from the center, the pressure falls and eventually turns inward.

Here's Burckert again. This is exactly how it should be in principle. There has to be positive pressure inside. If the pressure were negative, it would collapse. And the outer part being the opposite case, if it were positive, it would explode. So this proton would not be stable at all. So this comes out of the experiment. It shows, yes, the proton is actually stable. The Jefferson Lab group continued to analyze the Druk term.

As part of a review published in December of 2023, they released an estimate of the shear forces. Those are the internal forces pushing parallel to the proton surface. 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. 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's the area where its constituent quarks buzz around.

but that charge radius has some quirks. For instance, in the neutron, the proton's neutral counterpart, two negatively charged quarks tend to hang out deep inside the particle, while one positively charged quark spends more time near the surface.

In that case, the charge radius comes out as a negative number. Here's Schweitzer again. It doesn't mean the size is negative. It's just not a faithful measure for the size of the system. The new approach measures the region of spacetime that's significantly curved by the proton. In a preprint, the Jefferson lab team calculated that this radius may be about 25 percent smaller than the charge radius, or just 0.6 femtometers.

Conceptually, this kind of analysis smooths out the blurry dance of quarks into a solid planet-like object, with pressures and forces acting on each speck of volume.

That frozen planet doesn't fully reflect the proton in all its quantum glory, but it's a useful model. Or as Schweitzer says: "This is like an interpretation. And then you can wonder, 'Hmm, does it bring us something?'" 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.

Plus, the proton is more than its quarks. It also contains gluons, which slosh around with their own pressures and forces. The two-photon trick can't detect gluon's 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 that was also based on limited low-energy data.

Yoshitaka Hata is a physicist at Brookhaven National Laboratory. He was inspired to start studying the gravitational proton after the Jefferson Lab Group's 2018 work. It's a fast step, right? They did the best based on what they have. Sharper gravitational maps of both the proton's quarks and its gluons may come in the 2030s.

That's 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. Fiala Shanahan, a nuclear and particle physicist at MIT, 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 of last year, they estimated the radius, among other properties. So far, their digital findings have broadly aligned with Jefferson Lab's physical ones. Shanahan says she's quite excited by the consistency between recent experimental results and their data.

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.

Francois-Xavier Giraud is a Jefferson Lab physicist who worked on the experiments. By taking into account what we learn here, the physics we investigate here, already models that are used at CERN have been updated. 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 only 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.

Giroux says it's not a definite answer, but it points toward the fact that these simple images with elastic bands are not relevant for light quarks. Arlene Santana helped with this episode. I'm Susan Vallett. For more on this story, read Charlie Wood's full article, Swirling Forces, Crushing Pressures Measured in the Proton, on our website, quantummagazine.org.

Quantum Magazine is an editorially independent online publication supported by the Simons Foundation to enhance public understanding of science.