“How are matter and energy distributed?” asked Peter Schweitzer, a theoretical physicist at the University of Connecticut. “We do not know it.”
Schweitzer has spent most of his career thinking about the gravitational side of the proton. In particular, he is interested in a matrix of properties of the proton, the so-called energy-momentum tensor. “The energy-momentum tensor knows everything there is to know about the particle,” he said.
In Albert Einstein’s general theory of relativity, which depicts gravitational attraction as objects following curves in spacetime, the energy-momentum tensor tells spacetime how to bend. For example, it describes the arrangement of energy (or, equivalently, mass) – the source of the lion’s share of space-time distortion. It also tracks information about how momentum is distributed and where compression or expansion occurs, which can also result in a slight curvature of spacetime.
If we could learn the shape of spacetime around a proton, which Russian and American physicists worked out independently in the 1960s, we could infer all the properties indexed in its energy-momentum tensor. These include the proton’s mass and spin, which are already known, as well as the arrangement of the proton’s pressures and forces, a collective property that physicists call the “pressure term” after the German word for pressure. This term is “as important as mass and spin, and no one knows what it is,” said Schweitzer – although that is gradually changing.
In the 1960s, it seemed as if measuring the energy-momentum tensor and calculating the pressure term would require a gravitational version of the usual scattering experiment: fire a massive particle at a proton and let the two exchange a graviton – the hypothetical one Particles that make up gravitational waves – and not a photon. However, due to the extreme weakness of gravity, physicists believe that the scattering of gravitons occurs 39 orders of magnitude less frequently than the scattering of photons. Experiments cannot possibly detect such a weak effect.
“I remember reading about it as an undergraduate,” said Volker Burkert, a member of the Jefferson Lab team. The conclusion was: “We will probably never be able to learn anything about the mechanical properties of particles.”
Gravity without gravity
Gravity experiments are still unimaginable today. But research by physicists Xiangdong Ji and the late Maxim Polyakov in the late 1990s and early 2000s found a workaround.
The general scheme is the following. Typically, when you lightly fire an electron at a proton, it sends a photon to one of the quarks, knocking it off. But in fewer than one in a billion events something special happens. The incident electron emits a photon. A quark absorbs it and emits another photon a heartbeat later. The main difference is that this rare event involves two photons instead of one – both incoming and outgoing photons. Ji and Polyakov’s calculations showed that if experimenters could collect the resulting electrons, protons, and photons, they could infer what happened to the two photons from the energies and momenta of these particles. And this two-photon experiment would be essentially as informative as the impossible graviton scattering experiment.