Forbidden Questions

To navigate the quantum world, you have to know what questions not to ask.

In the everyday world, we get along fine assuming that a baseball, for example, had a certain momentum even before we whacked it and felt the effects. But at the quantum level, an observable effect like the push on a bat does not give us permission to regard the ball's earlier momentum as having been a "real" quantity, independent of the swinging bat. Talking about such unobserved properties is a recipe for trouble.

This takes a lot of getting used to.

I ran head on into this problem in my latest story for Physical Review Focus. I first titled the story "How Long is a Photon?" and described the experiments as measuring the "duration of individual photons." That description was wrong, and came from asking forbidden questions.

Optics experts often measure the duration of pulses that are only a few femtoseconds (10^-15 seconds) long. This is much too fast for direct electronic measurements, so they do it by making two similar pulses and measuring whether they overlap. Delaying one of the pulses by more than their length stops them from overlapping. Actually the researchers repeat the experiment with millions of pairs of pulses, each with a particular delay, to build up a picture of how the overlap varies with delay. For pulses consisting of many photons, it is natural to regard the overlap time as reflecting the length of the underlying pulses.

The new experiments look a lot like this. But the difference is critical.

Kevin O'Donnell, at CICESE in Baja California, built on earlier experiments from the Weizmann Institute in Israel. Instead of pairs of pulses, however, these groups measure pairs of photons. They get the pairs by shining a steady green laser into a special crystal, which splits about one green photon in ten million into two infrared photons. Because these two photons are created as a pair in a single quantum-mechanical process, they are "entangled": properties deduced from measurements on one will always be related to properties deduced from measurements on the other, even if the measurements are done far apart.

The nature of this connection is one of the central oddities of quantum mechanics. In fact, we could save a lot of trouble by not talking about the individual photons at all, because in a profound sense they do not exist as separate entities, even after "they" move away from each other. But our language makes it hard to talk about a pair without think of it as a pair of something.

As in the experiments on pulses, O'Donnell delays one photon with respect to the other and measures their overlap. (I can say that without saying photon, but it gets a lot more complicated.) But as he explained to me, it is not meaningful to relate this overlap to the "length" of the photons. Instead, the result of the overlap experiment at different delays is a property of the combined state of the two photons. The final story, "The Overlap of Two Photons," takes pains to describe that correctly, at the cost of clunkier language and probably losing some readers.

As another example, a researcher who measures the energy of one photon in a pair can be assured that the energy of the other will be just right, so that their combined energy equals that of the original green photon. But that doesn't mean that the photon "had" that energy before the measurement was made. More complex experiments, in fact, show that the unmolested photon does not have any particular energy.

In the current experiment, you don't go too far wrong by imagining (incorrectly) that it measures the length of a photon. But this "bad habit," as described by David Mermin in Physics Today (subscribers only, or you can google the title), of conferring reality on properties that aren't or can't be measured, is the root of much confusion. More importantly, thinking (and talking) precisely about what actually exists is key to understanding the nature of the quantum world we inhabit.