Another strangeness and indeed power of quantum mechanics is that quantum mechanics can test something that might have happened but did not happen. A question formulated by Elitzer and Vaidman in 1993 clearly demonstrates this property (cf. Penrose [29]). The experiment goes like this: in a fictitious scenario, there is a large collection of bombs. Each bomb has an ultra-sensitive detonator on its nose connected with a mirror. The detonator is so sensitive that a single photon hitting the mirror will set off the bomb. However, there are a large number of duds in the collection whose plungers connected with the mirrors can get stuck. The problem is then: is there any way to test the bomb so that one can identify whether a particular bomb is a dud without setting it off if it happens to be a good one?
At first thought there is no solution, for any testing procedure will set off a good bomb, because according to quantum mechanics one has to observe (shooting photons at the bomb) whether the plunger is stuck. However, there is a solution and strangely enough, we need quantum mechanics to arrive at it. The solution is illustrated in Figure 3.2. In this setup, the light source emits only one photon. Now if a bomb is dud, the mirror on its nose functions as a normal mirror. In this case, the wave function describing the photon indicates that there are two separate states, one state is the photon passing through the half-silvered mirror and heading towards the dud bomb and the other state is the photon being reflected by the half-silver mirror and taking the upper path. The setup is arranged in such a way that the length of each path is exactly the same (based on the classical Mach-Zehnder interferometer), so the state at the detectors is a superposition of the two states. According to quantum mechanics, the wave function of the photon will be canceled out at detector B. Thus, if the bomb is a dud, the detector A is always activated, and never B.
On the other hand, if we have a good bomb, the mirror on the nose of the bomb does not function as a normal mirror, but as a measuring device. This is because the bomb can tell which of the alternative states the photon is in. Now if the photon takes the lower path (it has a 50% probability), the bomb will explode. In this case we know that the photon has taken the lower path, and we have lost a good bomb. However, if the photon takes the upper path, the bomb does not explode. Then we know that the photon must have taken the upper path. In other words, a good bomb measures the upper path of the photon by not measuring a photon. And this photon has a 50-50% chance hitting detector A or B. So only if the bomb is a good one, there is a 50% chance for detector B to receive the photon. Every now and then a photon is detected at B. The detection of a photon at B indicates that the bomb must be good and it did not explode.
In quantum mechanics, a real result can come from what has not happened. This is a significant departure from classical mechanics, in which all real effects must have real causes. On the other hand, this may also be the power of quantum mechanics. A similar quantum mechanical system may provide a brand new computational possibility, for all the existing computations result from what indeed happen in a real computer.
