When studying a complex system, scientists identify smaller pieces called subsystems that they can make sense of. By studying subsystems and the correlations between them, they reconstruct an understanding of the whole.

This approach has been used with great success to explain phenomena and develop applications in computing, cryptography and sensing based on quantum mechanics—the physics of matter and energy at the scale of the atom or smaller. But this approach is limited to systems that operate in a world where time is absolute.

This description of subsystems falls short when describing scenarios that involve Einstein’s theory of general relativity, where time is relative to an observer’s motion and tightly interwoven with space into a four-dimensional “spacetime.”

Now, a theoretical study co-authored by Alexander Smith, assistant professor of physics at Saint Anselm College and adjunct assistant professor at Dartmouth, and Shadi Ali Ahmad ’22, proposes a new way to identify subsystems and correlations compatible with general relativity.

Theoretical physicists have long been striving to combine quantum mechanics and general relativity into a unified theory of quantum gravity. It is hoped that this work may be applied in developing a quantum description of spacetime, says Smith.

The results, published in April in Physical Review Letters, build on previous work on a generalized notion of subsystems by the James Frank Family Professor of Physics Lorenza Viola and her collaborators. “Instead of having composite building parts that are glued together into a larger system, subsystems should be thought of as directly arising from the observable properties one can measure,” says Viola.

“Quantum mechanics allows for correlations that are not consistent with our classical understanding of the world,” says Smith, “Viola and her collaborators gave us a new way to think about these unintuitive quantum correlations.”

Smith, Ali Ahmad and their collaborators apply this idea to build a framework for identifying subsystems, which is consistent with relativity, and find that the notion of the subsystem is no longer rigid.

“The way we partition a system is also relative. It depends on who is looking at it,” says Smith. While their method currently applies to simple systems of several particles, the authors are working to generalize the framework to quantum field theory, which constitutes our most fundamental description of nature.

Several theoretical concepts that are driving the emerging understanding of quantum gravity have their origin in quantum information theory—a relatively new field that studies how information in a quantum system can be analyzed and manipulated. “Quantum information science has given us this whole new way to think about quantum mechanics itself,” says Smith.

Working with Smith and other researchers, Ali Ahmad, a physics and mathematics major from Beirut, has used quantum information theory to study a number of different theoretical problems. In previous work, they were the first to examine how gravitational waves—ripples in spacetime produced when massive astronomical objects (e.g. black holes) speed up to extreme levels—affect entanglement between systems. Another project tackled the question of how work—the measure of how much energy is transferred when a force acts on an object—can be defined operationally at the quantum scale.

Smith says Ali Ahmad is one of the most driven to learn, hardworking and productive students he has encountered. “Seeing Shadi develop his ability in theoretical physics over the past four years has been very rewarding,” he says.

Ali Ahmad won the 2022 Gazzaniga Family Science Award, which recognizes scientific accomplishment of a graduating senior in the sciences. He is also the recipient of the Physics and Astronomy Chair’s Prize.

“Quantum information theory is a toolbox that I like to borrow from and use broadly,” says Ali Ahmad. The promise of access to undergraduate research opportunities and funding was what drew him to Dartmouth, he says. Now a research fellow at Dartmouth, Ali Ahmad is wrapping up ongoing projects as he prepares to apply to graduate programs.

With classes as a springboard, he sought out research mentors in the physics and mathematics departments, collaborating with them on a wide range of research topics. “Talking about science with people shapes the way you think,” says Ali Ahmad, who already has three publications under his belt. “I think it really sharpens your interests.”