A 350-Year-Old Theorem Can Explain The Quantum Properties Of Light

Physicists have applied classical mechanical rules to light – with success.

Light can behave both as a wave and a particle, a head-scratcher that confused scientists for centuries before the fact became obvious. This duality is a cornerstone of quantum mechanics, and the peculiar behavior of the quantum world has mostly left classical mechanics theorems behind in the realm of things our own size. 

A research team has now used classical mechanics to explain two particular properties of light: polarization and entanglement. The first is the ability of light waves to have an orientation – a fact that is used in sunglasses to filter out some light. The second is the ability of entangled photons to form a quantum system whose parts remain connected even if separated by vast distances. Changes to one would mean instantaneous changes to the other. 

These don’t sound like classical mechanics at all, but the team considered whether there could be an analog to the behavior of polarization in the Huygens–Steiner theorem. That 350-year-old theorem is about how a solid body rotates with respect to an axis that doesn’t go through its center of mass, and it is useful in both technical applications and studying celestial objects. 

 

 

"This is a well-established mechanical theorem that explains the workings of physical systems like clocks or prosthetic limbs," lead author Xiaofeng Qian, from the Stevens Institute of Technology, said in a statement. "But we were able to show that it can offer new insights into how light works, too."

 The researchers used the intensity of light as an analog for the mass of a physical object, and the rest of the properties were able to be mapped out following the structure of the theorem, even though light is not a classical body. 

"Essentially, we found a way to translate an optical system so we could visualize it as a mechanical system, then describe it using well-established physical equations," explained Qian. "This was something that hadn't been shown before, but that becomes very clear once you map light's properties onto a mechanical system. What was once abstract becomes concrete: using mechanical equations, you can literally measure the distance between 'center of mass' and other mechanical points to show how different properties of light relate to one another." 

 

The reason why these relationships exist and why the mapping works so well is currently not clear. Understanding this connection might have important implications for our understanding of quantum properties, as well as how we use them in applications. 

 

The study is published in Physical Review Research.