If the shutters are opened after a photon has been "deposited" in the cavities, the photosensor located between the shutters will detect (and absorb) the photon with probability 1/2.

Let's again color the marks at the backdrop: those made by atoms whose photons are detected by the sensor yellow, and those made by atoms whose photons are not detected by the sensor blue. How will the yellow and blue marks be distributed? Which Rule now applies?

Since the photon left by a "yellow" atom is no more, it is clearly impossible to determine the slit taken by a "yellow" atom. Rule B therefore holds for yellow atoms. The distribution of yellow marks is qualitatively identical to the distribution of electrons in the most beautiful experiment obtained under the conditions stipulated by Rule B.

But the sum of the yellow and blue distributions is the same as the sum of the red and green distributions. The reason this is so is that by the time we determine the color of a mark (by observing which cavity contains the photon or by opening the shutters to see whether the sensor responds), the mark is already there. The atom has already been detected. What we do after that with the photon can have no influence on the total distribution of marks. So the distribution of blue marks must be complementary to the distribution of yellow marks — their maxima and minima are exchanged.

The experiment with shutters opened

As we are entitled to infer something about an atom's behavior from the green or red color of its mark (when the shutters remain closed), so we are entitled to infer something about an atom's behavior from the yellow or blue color of its mark (when the shutters are opened).

But what? The behavior we are entitled to infer this time lacks a classical analogue. We therefore have no choice but to fall back on mathematical concepts to "describe" it. We say that the yellow atoms went through the slits in phase, and that the blue atoms went through the slits out of phase.

Since much the same mathematical concepts are employed to describing the behavior of (classical) waves, these descriptions are often given an all too literal interpretation, suggesting that under the conditions stipulated by Rule B particles actually behave like waves. (This is wrong for several reason, one of them being that if a single particle did behave like a wave in 3-dimensional space, then a system of n particles would behave like a wave in 3n-dimensional space, rather than like n waves in 3-dimensional space.) If we nevertheless speak of complementary "interference" patterns, of constructive "interference" and destructive "interference", we do not refer to the behavior of waves but simply to the difference between probability distributions calculated according to Rule A and probability distributions calculated according to Rule B. (Recall: "constructive interference" simply means that Rule B gives a large probability than Rule A, and "destructive interference" simply means that Rule B gives a smaller probability than Rule A.)

Ready for the next million-dollar question? Suppose we find that a given atom went through L. Are we entitled to believe that this very atom would also have gone through L if we had not checked through which slit it went?

Once again the answer is negative.

If we had not checked through which slit this atom went, we could have checked how it went through the slits — in phase or out of phase — and we would have found either that it went through the slits in phase or that it went through the slits out of phase. In any case we would have found that the atom went through the slits (plural) with a particular phase relation — a concept that involves both of the alternatives "through L" and "through R" and therefore is inconsistent with the notion that this particular atom, all by itself, whether observed or not, went through L.

M. O. Scully, B.-G. Englert, and H. Walther, "Quantum optical tests of complementarity," Nature 351, No. 6322, 111–116 (1991).

B.-G. Englert, M. O. Scully, H. Walther, "The duality in matter and light,'' Scientific American 271, No. 6, 56–61 (December 1994).

U. Mohrhoff, "Objectivity, retrocausation, and the experiment of Englert, Scully and Walther,'' American Journal of Physics 67, 330–-335 (1999).