“How are matter and energy distributed?” asks Peter Schweitzer, a theoretical physicist at the University of Connecticut. “we do not know.”
Schweitzer spent much of his career thinking about the gravitational aspects of the proton. Specifically, he was interested in a matrix of proton properties called the energy-momentum tensor. “The energy-momentum tensor knows everything about a particle,” he said.
In Albert Einstein’s general theory of relativity, which treats gravity as an object following the curve of space-time, the energy-momentum tensor tells how space-time curves. For example, it describes the arrangement of energy (or, equivalently, mass)—the source of most distortions in space-time. It also tracks information about how momentum is distributed and where compression or expansion occurs, which can also bend spacetime slightly.
Russian and American physicists independently studied the shape of spacetime around the proton in the 1960s. If we can understand the shape of spacetime around the proton, we can infer all the properties indexed in its energy-momentum tensor. These include the known mass and spin of the proton, as well as the proton’s pressure and arrangement of forces, which physicists call the “Drucker term,” after the German word for pressure. The term is “as important as mass and spin, but no one knows what it is,” Schweitzer said—though that’s starting to change.
In the 1960s, measuring the energy-momentum tensor and calculating the Drucker term seemed to require a gravitational version of the usual scattering experiment: shoot a massive particle at a proton and let the two exchange a graviton—the hypothetical particle that constitutes gravitational waves, rather than photons. But because gravity is extremely weak, physicists expect graviton scattering to be 39 orders of magnitude less likely to occur than photon scattering. It would be impossible to detect such a weak effect experimentally.
“I remember reading this when I was a student,” said Volker Burkert, a member of the Jefferson Lab team. The conclusion is that “we may never learn anything about the mechanical properties of the particles.”
Gravity without gravity
Gravity experiments are still unthinkable today. But research in the late 1990s and early 2000s by physicists Ji Xiangdong and the late Maxim Polyakov revealed a solution.
The overall plan is as follows. When you gently fire an electron at a proton, it usually passes a photon to one of the quarks, which flashes off. But in less than one in a billion events, something special happens. Incoming electrons send photons. The quark absorbs it, then emits another photon one heartbeat later. The key difference is that this rare event involves two photons instead of one – an incoming photon and an outgoing photon. Gee and Polyakov’s calculations showed that if experimentalists could collect the resulting electrons, protons and photons, they could infer what happened to the two photons based on the energy and momentum of those particles. This two-photon experiment is essentially as informative as the impossible graviton scattering experiment.