Once upon a time everybody knew why measurements in quantum mechanics don't reveal pre-existing properties. It was because the act of acquiring knowledge unavoidably messes up the object being studied. What you learn is not intrinsic to the object, but a joint manifestation of the object and how you probe it to get your knowledge.

In 1935 this state of happy innocence was forever dispelled by Einstein, who with Boris Podolsky and Nathan Rosen discovered how to learn about an object by messing up only some stuff it left behind in a faraway place. They concluded that knowledge acquired in this way was indeed about pre-existing properties of the object, revealed—not created—by the act of probing the stuff left behind. Bohr, however, insisted their conclusion was unjustified, and 30 years later John Bell proved that no assignment of such pre-existing properties could agree with the quantitative predictions of quantum mechanics.

A couple of years ago Lucien Hardy [1] gave this tale an unexpected twist, by finding a charming variation of the Bell–EPR argument. Hardy's theorem is even simpler than the argument of Daniel Greenberger, Michael Home, and Anton Zeilinger that I enthused about in this column four years ago. The reason he was able to pull the trick off, and the reason, I suspect, nobody had noticed so neat an argument for so long, is that Hardy's analysis applies to data that are not correlated strongly enough to support the argument of EPR. But they do give rise to an argument every bit as seductive, which Hardy is then able to demolish with surprising ease. Parts of the formulation I give here of Hardy's gedankenexperiment are similar to those of Henry Stapp [2] and Sheldon Goldstein [3].

We consider two particles that originate from a common source and fly apart to stations at the left and right ends of a long laboratory. At the left station we can experimentally determine the answer to one of two yes–no questions, A or B. There is a choice of two other yes–no questions, M or N, to be answered by experiment on the right. Hardy provides questions A, B, M, and N, and a two-particle state |Ψ〉 for which the answers to the questions have the following features: […]