August 28, 2023

Mechanics (the study of the motion of physical bodies) and optics (the study of light) are among the oldest branches of physics, reflecting centuries of investigation into how our world works. They’ve always been viewed as two distinct fields – that is, until now. 

Xiaofeng Qian, assistant professor in the Department of Physics at Stevens Institute of Technology, has made a surprising discovery, offering a tantalizing glimpse not only into how mechanics and optics could be connected, but also into how these standards of classical physics could significantly advance the modern study of quantum physics.

“It’s difficult to imagine that the wave behavior of light could be quantitatively related to any particle-based mechanical concepts,” Qian said, “but this is exactly what our work has found! It opens a novel avenue of exploring and understanding wave optics and classical mechanics.”

Qian’s research builds upon the trailblazing 17th- and 18th-century work of leading physicists such as Isaac Newton and Christiaan Huygens. In fact, it connects two seemingly unrelated theories proposed by Huygens. This Dutch scientist’s mechanical studies included exploring rotational energy, which led to his inventing the pendulum clock. Through his optic investigations, he also suggested that light is a wave, in direct contrast to Newton’s theory that light behaves like particles. 

Huygens likely never considered any connection between his mechanics and optics theories – but Qian did. 

His initial focus was on the behavior of light waves. Two areas of consideration were entanglement, which describes how systems remain connected despite their distance or any barriers, and polarization, which involves the direction of vibration of the waves. 

“We found that we could represent entanglement in a geometric structure,” he said.”While systematically studying that geometric representation, I noticed that some of the symmetries of this geometry were similar to what I had learned when studying mechanics as an undergraduate student.”

That observation led to the surprising discovery of a quantitative relationship between wave optics and particle mechanics. That is, the entanglement and polarization of a light beam can be expressed by the moments of inertia of a point-mass system.  Although still theoretical, this breakthrough discovery fundamentally connects light wave features with mechanical mass concepts for the first time and deepens the fundamental understanding of both optics and mechanics. 

In particular, it provides a visual mechanical interpretation of the intriguingly abstract concept of entanglement, which in turn shows exciting promise for impact in quantum information, computation and simulation.

“Measuring entanglement or polarization usually takes a complex procedure and requires several expensive, fine-tuned devices and complicated experiment designs,” Qian said. “But if these concepts have exact correspondence in the mechanical systems, then we can also do measurements in mechanical systems, which tend to be much easier, more economical, more efficient and more robust. Using new methods to explore scientific concepts can generate powerful outcomes, but this is using classical ways to explore new areas with unexpected and still powerful outcomes.” 

This integration of two apparently unrelated theories from Huygens has paved the way for a fresh view of wave optics and mechanics. The potential impact reaches across and beyond these diverse disciplines, offering new avenues for research, exploration and education in both classical and quantum physics. The  Physics Review Research journal has published Qian’s findings.

“Optics and mechanics are among the oldest branches of physics, and they serve as fundamental basics of physics and core curriculum for most undergraduate physics and engineering majors,” Qian said. “Even so, we can still find something completely new. This teaches me to never take anything for granted, even if it seems normal and intuitive to our everyday life experience. When we dig deeper, even those familiar things could offer a surprisingly fresh perspective.”