# For a Split Second, a (Simulated) Particle Went Backward in Time

But the arrow of time takes its direction not only from big numbers. According to quantum theory, that paradoxical body of rules governing the subatomic universe, not even a single particle can reverse its own course through time.

The uncertainty principle, which lies at the heart of quantum mechanics, states that, at any given moment, either the location or the velocity of a subatomic particle can be specified, but not both. As a result, a particle such as an electron, or a system of them, is represented by a mathematical entity called a wave function, whose magnitude is a measure of the probability of finding a particle in a particular place or condition.

The wave function extends throughout space and time. The law describing its evolution, known as the Schrödinger equation, after Austrian physicist Erwin Schrödinger​, is equally valid running forward or backward. But getting a wave function to go in reverse is no small trick.

Dr. Vinokur likened the challenge to sending a speeding billiard ball back to where it started. Seems easy: Just hit it with a cue stick. But if it’s a quantum ball, the uncertainty principle kicks in: You can know how hard to hit the ball, or in which direction to hit it, but not both.

“Because of the uncertainty principle, the quantum ball will never return back to the point of the origin,” Dr. Vinokur said.

Moreover, in quantum mechanics, the ball is actually a wave: Once its location is known, it spreads like ripples on a pond and evolves. Making it go backward takes more than a nudge with a cue stick. It requires reversing the phases of the waves, turning crests into troughs, and so forth, an operation too complex for nature to accomplish on its own.