No sooner had the radical equations of quantum mechanics been discovered than physicists identified one of the strangest phenomena the theory allows.

“Quantum tunneling” shows how profoundly particles such as electrons differ from bigger things. Throw a ball at the wall and it bounces backward; let it roll to the bottom of a valley and it stays there. But a particle will occasionally hop through the wall. It has a chance of “slipping through the mountain and escaping from the valley,” as two physicists wrote in Nature in 1928, in one of the earliest descriptions of tunneling.

Physicists quickly saw that particles’ ability to tunnel through barriers solved many mysteries. It explained various chemical bonds and radioactive decays and how hydrogen nuclei in the sun are able to overcome their mutual repulsion and fuse, producing sunlight.

But physicists became curious — mildly at first, then morbidly so. How long, they wondered, does it take for a particle to tunnel through a barrier?

The trouble was that the answer didn’t make sense.

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