A team at the Massachusetts Institute of Technology (MIT) has found a new way to explain the strange behavior of quantum particles using simple classical physics ideas.
Their study suggests the quantum world may be far less mysterious than scientists once believed.
For decades, physics has stood on two pillars. Classical physics explains everyday motion, such as a ball thrown into the air. Quantum physics, on the other hand, deals with tiny particles that behave in strange and unpredictable ways.
These two systems have long seemed disconnected. But the new study builds a direct mathematical link between them.
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The research appears in the journal Proceedings of the Royal Society. It shows that a classical idea called ‘least action’ can describe quantum motion just as accurately as the famous Schrödinger equation.
This equation is one of the core tools for understanding quantum systems. Matching its results using classical ideas is a major shift in thinking.
“We built a strong bridge between classical and quantum physics,” says Winfried Lohmiller. He explains that earlier links only worked for larger quantum systems, not the smallest scales. Now, he says, the connection works across all scales.
His co-author, Jean-Jacques Slotine, makes the goal clear. “We are not replacing quantum mechanics,” he says. “We are showing a simpler way to compute it using familiar ideas.”
The story begins with a basic concept from classical physics. When an object moves, it follows a path that minimizes something called action. This idea comes from the Hamilton-Jacobi equation, a key mathematical tool in classical mechanics. It describes motion in terms of energy and time.
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In simple terms, action is the change in kinetic energy minus the change in potential energy over time. Objects naturally follow the path where this value is minimized. For example, a thrown ball could take many paths from one point to another. But in reality, it follows the one that minimizes action.
Slotine and Lohmiller were using this idea to solve engineering problems. Their work involved robotics, aircraft control, and machine learning systems.
While doing this, they noticed something unusual. With a few changes, the same equation could describe quantum systems. This realization led them to test one of the most famous experiments in physics: the double-slit experiment.
In this experiment, light particles called photons pass through two tiny slits. Classical physics predicts that each photon should go through one slit and form a simple pattern.
But in reality, the result is very different. The photons create a pattern of bright and dark stripes, as if they behave like waves. This happens because a photon can take multiple paths simultaneously. This strange property is known as superposition.
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For years, scientists have struggled to explain this using classical ideas. Even Richard Feynman argued that it would require calculating an infinite number of paths. That approach quickly becomes impossible in practice.
Slotine and Lohmiller approached the problem differently by asking whether classical physics might also permit multiple possible paths. If that were true, they would not need to calculate infinite possibilities. Instead, a small number of paths might be enough.
They returned to the principle of least action and modified it. Then they added another key idea: density. Density, in this context, represents the probability that a particle will take a given path.
Lohmiller explains it with a simple example. Imagine spraying water from a hose toward a wall. Most water hits the center, but some droplets scatter to the sides. This spread forms a pattern. And that pattern reflects probability.
Using this idea, the team adjusted the classical equations. They included both multiple paths and density. When they applied this to the double-slit experiment, the results were striking. Instead of calculating infinite paths, they only needed two, one through each slit.
Despite this simplification, their results matched exactly with the predictions of the Schrödinger equation. That means a classical framework could reproduce quantum behavior with precision.
“We found that both equations are mathematically identical when we include density,” Slotine says.
This does not mean quantum physics disappears. Instead, it shows that classical tools can describe it in a new way.
The team tested their method on other quantum phenomena as well. One example is quantum tunneling. In this process, particles pass through barriers that should be impossible to cross. Classical physics cannot explain this behavior. Yet the new formulation successfully predicts it.
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The researchers also modeled the electron in a hydrogen atom. They showed that its quantum wave pattern could be derived from a classical orbit.
They even revisited the famous Einstein-Podolsky-Rosen experiment, which explores quantum entanglement. This experiment helped shape modern quantum theory. The new approach offers a fresh perspective on it.
Together, these results suggest a deeper unity in physics. What once seemed like separate worlds may follow the same underlying rules. The implications can be far-reaching.
In quantum computing, scientists deal with complex systems that are difficult to model. These systems often involve nonlinear energies that require approximations. The new method can simplify those calculations.
It may also help researchers study problems that combine quantum physics with general relativity. These areas remain some of the biggest challenges in science.
Slotine believes the approach can make quantum systems easier to understand and predict.
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“At least in principle, we can now describe quantum behavior using simple classical tools,” he says.
This does not entirely remove the mystery of quantum mechanics. But it shows that some of its complexity may come from how we choose to describe it. By changing the mathematical lens, the strange becomes more familiar.
The study offers a new perspective on a long-standing problem. It suggests that the gap between classical and quantum physics may not be as wide as it once seemed. And in that overlap, scientists may find simpler ways to understand the universe.
