New Quantum Weirdness: Balls That Don't Roll Off Cliffs

Quantum particles continue to behave in ways traditional particles do not

By George Musser

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A good working definition of quantum mechanics is that things are the exact opposite of what you thought they were. Empty space is full, particles are waves, and cats can be both alive and dead at the same time. Recently a group of physicists studied another quantum head spinner. You might innocently think that when a particle rolls across a tabletop and reaches the edge, it will fall off. Sorry. In fact, a quantum particle under the right conditions stays on the table and rolls back.

This effect is the converse of the well-known (if no less astounding) phenomenon of quantum tunneling. If you kick a soccer ball up a hill too slowly, it will come back down. But if you kick a quantum particle up a hill at the same speed, it can make it up and over. The particle will have “tunneled” across (although no actual tunnel is involved). This process explains how particles can escape atomic nuclei, causing radioactive alpha decay. And it is the basis of many electronic devices.

In tunneling, the particle can do something the ball never does. Conversely, the particle might not do something the ball always does. If you kick a soccer ball toward the edge of a cliff, it will always fall off. But if you kick a particle toward the edge, it can bounce back to you. The particle is like one of those little toy robots that senses the edge of a table or staircase and reverses course, except that the particle has no internal mechanism to pull off its stunt. It naturally does the exact opposite of what the forces acting on it would indicate. The researchers behind the analysis—Pedro L. Garrido of the University of Granada in Spain, Jani Lukkarinen of the University of Helsinki, and Sheldon Goldstein and Roderich Tumulka, both at Rutgers University—call this phenomenon “antitunneling.”

In both cases, the explanation lies in the wave nature of particles, which in turn reflects the fact that a quantum particle generally has an ambiguous location. The wave describes the range of locations where it could be found. This wave behaves much like ordinary waves such as sound. Whenever any wave encounters a barrier that is not absolutely rigid, some of the wave will penetrate into the barrier, albeit with diminishing intensity. If the barrier is not too thick, the wave can reemerge on the other side. That is analogous to tunneling.

For antitunneling, the analogy is that whenever any wave encounters any abrupt change of conditions—even ones more favorable to its propagation—some of it will reflect back. Something similar happens when a scuba diver looks up and sees the sea surface acting as a mirror. To be sufficiently abrupt, the distance over which conditions change must be shorter than the wavelength (which for a particle is related to momentum). If the change is too gradual, the wave will simply go along, and the particle will act like a soccer ball after all.

Garrido and his colleagues undertook a numerical analysis to rule out the possibility that the phenomenon was an artifact of idealized assumptions. They also calculated how long a particle will tend to roll around the table before going over the edge; it gets longer the higher the table is. David Griffiths of Reed College, author of a widely used introductory quantum mechanics textbook (the second edition of which gives a version of antitunneling as a student exercise), calls it “a very sweet paradox.” Physicist Frank Wilczek of the Massachusetts Institute of Technology says, “It’s a solid analysis, and it points out an interesting phenomenon I hadn’t been consciously aware of.”

Antitunneling might have applications for building laboratory particle traps, describing nuclear decay or exploring the foundations of quantum mechanics, but its main appeal is to remind physicists how a nearly century-old theory has lost none of its capacity to surprise.