Zeno

The arrow is drawn. You are watching. Nothing happens.

Zeno of Elea argued that a flying arrow, at any single instant, is not moving, so when does it move? About twenty-four centuries later, in 1977, Baidyanath Misra and George Sudarshan showed that quantum mechanics contains a version of the paradox that actually holds: a system observed often enough does not leave the state it started in.

The reason is in the first moments. A quantum state does not begin to change at a steady rate. For short times, the chance that it has changed grows with the square of the elapsed time. Check it n times instead of once and each check starts the clock again; you pay n small squares instead of one large one, and as n grows the total goes toward zero.

In 1990, at NIST in Boulder, Wayne Itano, Daniel Heinzen, John Bollinger and David Wineland put about 5,000 beryllium ions in a Penning trap. A 256-millisecond radio-frequency pulse was tuned to carry every ion from one hyperfine level to another. During the pulse they hit the ions with short flashes of ultraviolet light: 1, 2, 4, and so on up to 64. Each flash asked one question: which level are you in? Ions in one level scattered a few photons. Ions in the other scattered none, and were measured anyway. With one flash at the end, nearly all the ions made the transition. With 64 flashes, nearly none did. For 64 ideal measurements, \(\tfrac{1}{2}\left[1-\cos^{64}(\pi/64)\right]\) comes to under 4 percent.

What the flashes do to the wavefunction is still argued over. "Collapse" is one reading, and Leslie Ballentine published an objection to it in 1991. The suppression itself is measured.

Zeno holds the bow because you are looking.