When you throw a ball in the air, the equations of classical physics will tell you exactly what path the ball will take as it falls, and when and where it will land. But if you were to squeeze that same ball down to the size of an atom or smaller, it would behave in ways beyond anything that classical physics can predict.
Or so we've thought.
MIT scientists have now shown that certain mathematical ideas from everyday classical physics can be used to describe the often weird and nonintuitive behavior that occurs at the quantum, subatomic scale.
In a paper appearing today in the journal Proceedings of the Royal Society A Mathematical Physical and Engineering Science, the team shows that the motion of a quantum object can be calculated by applying an idea from classical physics known as "least action." With their new formulation, they show they can arrive at exactly the same solution as the Schrödinger equation—the main description of quantum mechanics—for a number of textbook quantum-mechanical scenarios, including the double-slit experiment and quantum tunneling.
Such mysterious phenomena, that could only be understood through equations of quantum mechanics, can now also be described using the team's new classical formulation. In essence, the researchers have built an exact mathematical bridge between the classical, everyday physical world and the world that happens at dimensions smaller than an atom.
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