MIT scientists use classical physics tools to explain quantum behavior of particles

A new study by researchers at the Massachusetts Institute of Technology (MIT) has bridged the gap between quantum and classical physics. This study shows that mathematical ideas from classical physics can be used to explain the strange and “spooky” behavior attributed to quantum particles.

Despite the development of applications such as quantum computing and sensing, there are many aspects of the quantum realm that are unknown to scientists. At the subatomic scale, particles behave very differently than they do in the real world, so scientists often need to develop new theories to explain this behavior.

But Winfried Lohmiller and Jean-Jacques Slotine of the Massachusetts Institute of Technology’s Nonlinear Systems Laboratory have come up with a new formula that helps scientists reach the same solution as the Schrödinger equation commonly used in quantum mechanics, while still using principles from classical physics. The researchers demonstrated this in multiple quantum mechanical scenarios, including double-slit experiments and quantum tunneling.

What is the double slit experiment?

One of the most commonly referenced examples of nonclassical behavior at the quantum scale is the double-slit experiment, in which two slits are cut from a metal wall. When a single photon is sent through a wall, classical physics assumes that the photon will pass through either slit and reach the other side.

However, during experiments, scientists observed alternating light and dark stripes. This is caused by a quantum phenomenon in which a photon takes multiple paths at the same time, passing through both holes along two paths and eventually interfering with each other.

The fringes indicate that the photon’s two interference paths are wavy, and also suggest that the quantum particle behaves like a wave. Even the famous physicist Richard Feynman found this behavior difficult to explain. Feynman said that to explain this you would have to consider and average all the theoretical paths a photon could take, whether straight or zigzag, but this contradicted everything about classical smooth paths.

What did the MIT researchers do differently?

Researchers Slotine and Lohmiller wondered if classical physics could make this possible by quantum superposition, which allows photons to take multiple paths. Instead of computing an infinite number of passes, the researchers proposed computing a “minimum action” classical pass that would yield the same result.

They used the Hamilton-Jacobi equation. This suggests that when an object is thrown from A to B, it follows a real path whose motion is minimized at every point along the path. If a ball is thrown, the minimized action is the sum of the difference between its kinetic energy and potential energy over time.

By adding density, an element 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 slit, as opposed to Feynman’s infinity proposal.

The researchers’ calculations produced a wavefunction that describes the distribution of possible paths for photons, matching the predictions of the Schrödinger equation.

“We have shown that the Schrödinger equation of quantum mechanics and the Hamilton-Jacobi equation of classical physics are actually identical if you calculate the density properly,” Slotine said in a press release.

“This is a purely mathematical result. We are not saying that quantum phenomena occur on classical scales. We are saying that this quantum behavior can be calculated with very simple classical tools.”