麻豆淫院

Stress is a very real factor in the structure of our universe. Not the kind of stress that students experience when taking a test, but rather the physical stresses that affect everyday objects. Consider the stress that heavy vehicles exert on a bridge as they cross over it鈥攊t's essential that engineers understand and consider this factor when designing new trestles. Or consider the stresses that a star experiences鈥攖his internal factor influences everything from its shine to its lifetime.

But in the quantum world, what stresses do protons face?

That's a question that nuclear physicists at the U.S. Department of Energy's Thomas Jefferson National Accelerator Facility are looking to answer. Now, Adam Freese, a postdoctoral fellow, has applied a new approach to factoring in the effects of stress in the quantum world, from atoms to their nuclei to the nucleus's building blocks.

In the world of atoms and their nuclei, stress describes the internal forces present in a system as it is deformed. At Jefferson Lab, researchers have measured the stress in a proton as it is pushed and pulled from different directions. Investigating stress in the proton and how it affects the proton's constituent particles, quarks and gluons, may reveal more about these particles' complicated interactions. This information could give nuclear physicists a better view of how these particles build our universe.

Conceptual stress

The concept of stress comes from continuum classical mechanics, the branch of mechanics that studies the behavior of systems from a zoomed-out, macroscopic perspective. To use stress to understand subatomic particles, it needs to be dealt with from a quantum mechanical perspective, which allows for a more zoomed-in view.

Freese's work mathematically connects the dots between classical and quantum mechanics to properly calculate stress for this more zoomed-in view.

In theory work in 麻豆淫院ical Review D, he used a quantum theory to calculate the stresses present in an atom of hydrogen. His results show how precise measurements of proton stress could be used to probe the forces acting on quarks and gluons.

"Since the proton is such a complicated system that we don't understand that well, the point of my paper was to try to use the hydrogen atom, which is a really well-understood system and a very iconic system in quantum mechanics as well, to understand how stresses work when you look at quantum mechanical as opposed to classical systems," Freese said.

Building on first forays into quantum stress management

The seeds of this work were first planted in 2021, when Freese gave a talk over Zoom about studying stresses in quantum mechanical systems for the Center for Nuclear Femtography. Freese said that when Xiangdong Ji, a theoretical physicist hosting the meeting, expressed skepticism about this endeavor, Freese proposed starting with a simple system, like hydrogen.

Ji and his collaborators considered Freese's proposal and then made the calculations. This step was an important proof of principle, showing that this line of research could be seriously pursued. However, these first calculations used the standard theory of quantum mechanics, which poses a major drawback.

"One shortcoming of standard quantum mechanics is that it doesn't provide a sharp image of what's happening in a system," Freese said. "It's basically a recipe for calculating things, like the rate at which electrons scatter at various angles when you shoot them at a proton target. What exactly is going on, it doesn't really tell you."

So, using this standard approach, it was unclear where the stresses were coming from.

Looking to uncover this information, Freese took the next step and calculated the stresses in a hydrogen atom using pilot wave theory, a specific interpretation of quantum mechanics that gives all the particles in a system well-defined positions and trajectories. Their motions are guided by a theoretical wave known as the pilot wave. Pilot wave theory permits a quantum perspective supplemented with a sharp image, allowing Freese to figure out where the stresses are originating on a subatomic level.

He is the first to use pilot wave theory for this purpose.

"I found by talking to a lot of other physicists over the past year that it's not popular," said Freese. "But it's not popular because of a misconception that it's incompatible with quantum mechanics."

Many scientists believe that John Stewart Bell, a prominent physicist of the 20th century, ruled out the use of the pilot wave theory in quantum contexts. But Freese dug deeper into Bell's published journal articles.

While reading Bell's works, he was surprised to learn that Bell was a staunch advocate of this theory. This finding inspired him to apply pilot wave theory to stresses in the hydrogen atom, a project he began in October 2024.

Using stress to learn about force

Freese found that, in the pilot wave interpretation, the electron and proton in hydrogen are standing still relative to each other. This is due to the stress the pilot wave exerts on the electron. He likens their relationship to a stone arch. The stress of adjacent stones pushing against the keystone at the apex prevents it from falling despite there being nothing underneath.

"You have something similar happening in the hydrogen atom, where the pilot wave is exerting these oblique forces on the electron that largely cancel in the sideways directions and then cancel out the electrostatic force that's pulling the electron toward the proton," Freese said. "So, it remains static, and the hydrogen atom is stable for that reason."

With this picture of hydrogen, Freese also demonstrated how measurements of stress can be used to learn about the fundamental forces present in a system. He found that if you can measure the stress felt by a part of hydrogen, such as the electron, you can figure out the force exerted by the pilot wave. Since the system is stable, the pilot wave's force must be balanced by the electrostatic force between the electron and proton, which offers quantitative information about this force.

Though physicists have known how the electrostatic force operates since the 18th century and have understood its role in atomic structure for nearly 100 years, Freese's work signals a way to gain additional insight into force by measuring stress. This new calculation then lays the groundwork to extend the idea to the proton.

"In principle, if we get more precision measurements of these stresses in the proton, we could potentially use that to deduce what the average force acting on each quark in the proton is," Freese said. "And I find that possibility really exciting."

With the preliminary work done, Freese next plans to calculate stress from a quantum perspective in more complicated systems. With colleagues, he has started looking at the nucleus of deuterium, an isotope of hydrogen. He hopes that calculating the stresses in this system will allow him to access the force that binds together the proton and neutron in this nucleus.