A new study by researchers at the Massachusetts Institute of Technology (MIT) now bridges the gap between quantum and classical physics. The work demonstrates that mathematical ideas from classical physics can be used to describe weird and ‘spooky’ behavior that is often attributed to quantum particles. 

Even as applications such as quantum computing and sensing are being developed, much about the quantum realm remains unknown to scientists. At subatomic scales, particles behave very differently from those in the real world, and scientists often have to develop new theories to explain this behavior. 

However, Winfried Lohmiller and Jean-Jacques Slotine at the Nonlinear Systems Laboratory at MIT have derived a new formulation that can help scientists arrive at the same solution as the Schrödinger equation, commonly used in quantum mechanics, while using principles of classical physics. The researchers demonstrated this for multiple quantum-mechanical scenarios, including the double-slit experiment and quantum tunneling. 

What is the double slit experiment? 

One of the most commonly referred to examples of nonclassical behavior at a quantum scale is the double slit experiment, where two slits are cut out of a metal wall. When a single photon is sent through the wall, classical physics assumes that the photon will travel through either of the slits and reach the other side. 

However, during experiments, scientists have observed alternating bright and dark stripes. This is caused by a quantum phenomenon where a photon takes more than one path simultaneously and passes through both the holes, along two paths and then end up interfering with each other. 

The pattern of stripes shows that the photon’s two interfering paths are wave-like, also suggesting that a quantum particle behaves much like a wave. Even noted physicist Richard Feynman found it difficult to explain this behavior. Feynman had said that to explain this, one would have to consider and average every single theoretical path that a photon could take whether straight line or zig-zag, which contradicts every classical smooth path. 

What did MIT researchers do differently? 

Researchers Slotine and Lohmiller realized that quantum superposition allows the photon to take multiple paths and if classical physics could entertain this. Instead of calculating an infinite number of paths, the researchers suggested calculating ‘least action’ classical paths that could produce the same result. 

They used the Hamilton-Jacobi equation, which suggests that an object, when thrown from A to B follows an actual path where its action is minimized at every single point in the path. In case of a ball thrown, minimized action is the sum over time of the difference between its kinetic and potential energy. 

By adding density, an ingredient of classical physics, to the double slit experiment, the researchers tweaked the Hamilton-Jacobi experiment and found that they only needed to consider two classical paths through the slits, as opposed to Feynman’s suggestion of infinite. 

The researchers’ calculations produced a wave function that showed the distribution of possible paths the photon could take and matched the prediction of the Schrodinger equation. 

“We show that Schrödinger’s equation of quantum mechanics and the Hamilton-Jacobi equation of classical physics are actually identical given a suitable computation of density,” said Slotine in a press release.

“That’s a purely mathematical result. We’re not saying that quantum phenomena happen at classical scales. We’re saying you can compute this quantum behavior with very simple classical tools.”