Physicists use a 350-year-old theorem to reveal new properties of light waves

When scientists originally disagreed on the nature of light in the 17th century, between Christiaan Huygens and Isaac Newton, they couldn't agree on whether light should be seen as a particle or a wave, or maybe both at once at the quantum level. Using a 350-year-old mechanical theorem—typically applied to explain the motion of massive, physical objects like planets and pendulums—researchers at Stevens Institute of Technology have now unveiled a new relationship between the two viewpoints. This theorem explains some of the most intricate behaviors of light waves.

The research, led by Stevens assistant professor of physics Xiaofeng Qian, and published in the August 17 online edition of Physical Review Research, also establishes for the first time a direct and complementary relationship between the degree of polarization and non-quantum entanglement of a light wave. The amount of polarization may be used to immediately determine the level of entanglement, and vice versa, when one rises and the other lowers. This implies that much easier-to-measure variables, like light intensity, may be used to infer difficult-to-measure optical properties, such amplitudes, phases, and correlations—possibly even those of quantum wave systems.

It has been known for more than a century that light may act as a particle or a wave, but bringing those two frames into harmony has proven to be quite challenging, according to Qian. "Our work demonstrates that there are significant connections between wave and particle concepts not only at the quantum level but also at the level of classical light-waves and point-mass systems, even though it doesn't solve that particular problem."

Qian's group employed a mechanical theory that describes how the energy needed to spin an item increases with its mass and the axis it rotates. Huygens first proposed this theorem in a 1673 book on pendulums. Qian said, "This is a well-known mechanical theory that describes how physical devices like clocks or prosthetic limbs operate. However, we were also able to demonstrate that it can provide fresh perspectives on the nature of light.

Since there is no mass to detect in light, how could this 350-year-old theorem—which details correlations between masses and their rotating momentum—be applied to light? Qian's group translated measurements of light intensity into a coordinate system that could be understood by using Huygens' mechanical theory, interpreting light intensity as the mass of a physical object. "Basically, we figured out how to convert an optical system into a mechanical system that we could see and then describe with standard physical equations," said Qian.

New relationships between the wave's features, such as the obvious relationship between polarization and entanglement, were evident as soon as the researchers envisioned a light wave as a component of a mechanical system.

"This had never been demonstrated before, but it becomes evident as soon as you transfer the characteristics of light onto a mechanical system," Qian added. What was previously abstract becomes concrete: you can practically measure the distance between the "center of mass" and other mechanical sites to illustrate the relationships between various aspects of light using mechanical equations.

It might be possible to infer complex and difficult-to-measure features of optical systems—or even quantum systems—from more straightforward and reliable measurements of light intensity if these correlations are clarified, according to Qian. More broadly, the results of the team's research raise the prospect of simulating and comprehending the peculiar and intricate behaviour of quantum wave systems through the use of mechanical systems.

"We've demonstrated with this first study that it is possible to understand optical systems in a completely new way by applying mechanical concepts, but that still lies ahead of us," Qian added. "Ultimately, by enabling us to identify the intrinsic underlying connections between seemingly unrelated physical laws, this research is helping to simplify our understanding of the world."