UC professor brings novel approach to quantum mechanics
Quantum mechanics is one of the most effective approaches for understanding the workings of atoms and subatomic particles.
But it’s also one of the most abstract.
Marc Cahay, professor and department head at the University of Cincinnati, is using a number system called quaternions to deepen our understanding of quantum mechanics. Cahay, with colleagues Dennis Morris from England and George Purdy from UC, published the results of the work in Physica Scripta.
The work reflects the university’s innovation agenda, a platform of UC’s strategic direction, Next Lives Here.
Cahay’s quaternion approach focuses on one of quantum mechanics’ most fundamental concepts: the spin of an electron. The spin of an electron tells us not only about the workings of atoms and subatomic particles but also of chemical bonds, the periodic table and other physical phenomena.
UC professor Marc Cahay stands next to a portrait of renowned mathematician, Paul Erdős. Cahay recently published a paper with the late George Purdy, who published several papers with Erdős. Photo/Corrie Stookey/CEAS Marketing
Traditionally, to calculate the spin of an electron, people use equations with complex numbers. Cahay, however, is using quaternions. While complex numbers are expressed by two components, quaternions are expressed by four. This quaternion number matches the dimensions of space-time, with its three spatial and one time-based dimensions.
“As engineers and physicists, we are used to complex numbers to analyze and model a lot of fundamental and practical systems,” said Cahay. “You have to back up a little bit and do the math properly when you deal with quaternions. It’s a rather tricky business.”
But quaternions aren’t completely perplexing. Aerospace engineers often use quaternions to track the orientation and rotation of an object, like a rocket or a satellite. The paper’s novelty is in the application of this approach to study the spin of subatomic particles in quantum mechanics.
This work teaches the students a very versatile way of attacking widely different problems in quantum mechanics.
Marc Cahay, UC professor and department head
UC professor Marc Cahay holds a plaque that honors the late George Purdy. Purdy, known for the Purdy polynomials in math and computer science circles, first introduced Cahay to applying quaternions to quantum mechanics. Photo/Corrie Stookey/CEAS Marketing
Cahay’s publication only deals with the spin of the electron, but Cahay hopes to eventually use the quaternion approach as a universal tool for solving quantum mechanics problems.
“This work teaches the students a very versatile way of attacking widely different problems in quantum mechanics,” said Cahay. “Many different phenomena can be analyzed using quaternions and their associated algebra”
Cahay dedicated the work to friend and colleague, the late UC professor George Purdy, who first introduced Cahay to applying quaternions to quantum mechanics. Purdy, known for the Purdy polynomials in cryptography, was an expert in fundamental quantum mechanics and a co-author of several papers with renowned mathematician Paul Erdős.
“I cannot tell you how many times I wish George would still be around to shine light on the many questions about quaternions I have come across since he left us,” said Cahay. “But what is most important for me with this paper is that I am able to honor George’s memory.”
Featured image at top: Marc Cahay sits at a table in his office. Cahay is using a number system called quaternions to deepen our understanding of quantum mechanics. Photo/Corrie Stookey/CEAS Marketing
Bending the Future
The University of Cincinnati is the region's destination for thinking, making, doing, discovery and delivery. Next Lives Here.
Related Stories
UC student inspired by other women in tech
November 22, 2024
As a high school student, Minha Raza was determined to pursue a degree in the medical field after graduation. However, after taking the introductory Engineering Design Thinking course her first year at the University of Cincinnati, she found an untapped passion for engineering and problem solving. She switched her major to computer science and is now leading a student group and attending conferences in her field.
Beyond the classroom: perspectives on long-term study abroad
November 21, 2024
More than 1,300 UC students studied abroad in 2023-24. Most students tend to sway towards the most popular option of faculty-led programs, because of its shorter duration and high level of faculty support. But some UC students strike out on their own, choosing to fly solo for a semester to a year with long-term study abroad programs.
Telling how keen your date is with an app
November 18, 2024
The UK Daily Mail highlights UC engineering technology that can track conversational synchrony to determine if your date is into you.