## Separating the possible paths

It may be argued that interference effects can occur only if the possible paths of the photon are very close together. It is possible, however, to make the alternative paths as far apart as we like by an interferometer type of arrangement as illustrated in Figure 14.6.

Let us first consider what happens from the point of view of the wave representation. The light beam arrives at mirror 1 and splits into two components; approximately half is reflected (beam I), the other half is transmitted (beam II). The two rays emerge at right angles and then travel along different paths. When each beam meets the half-silvered mirror 4, a similiar thing happens as at mirror 1. Each beam splits into reflected and transmitted components. The result is that the beams recombine. The recombined beam has two components which emerge from mirror 4 at right angles, each consisting of a 50/50

dark detector

bright detector

(semi-silvered)

bright detector

(semi-silvered)

Figure 14.6 Typical interferometer experiment.

Figure 14.6 Typical interferometer experiment.

mixture of I and II. One goes towards detector A, and the other towards detector B.

Let us assume that the interferometer is adjusted so that the two light beams leaving mirror 4, are out of phase going in the direction of detector B (the 'dark' detector), and in phase in the direction of the 'bright' detector A. The fact that no light arrives at detector B is explained by the wave theory of light on the basis of destructive interference of the two combined beams.

Next, let us try the particle representation. As we did before, we can reduce the intensity of the laser beam, until the photons are so far apart that a photon usually has long left the apparatus before the next photon enters. We continue the experiment, and discover that the result is exactly the same as in the wave representation. Even though we know that this time the photons go through the apparatus one at a time, the 'dark detector' registers no clicks. No photons manage to reach it. All the photons go to detector A.

Somehow, with two routes open, the photon is prevented from reaching detector B. Note that the two alternative routes are far apart, but we do not know which route the photon has taken. So long as both routes are available, there are no clicks from detector B!

Next, we introduce an obstacle which closes one of the routes. To make quite sure that the photon cannot get through, let us put a brick into the lower path, as in the diagram. We find that an extraordinary thing happens. The dark detector immediately begins to click! Detector A also continues registering photons, but at approximately half the rate. We now know which route the photon has taken — obviously the one without the brick. There is no alternative route open; we know that the photon must have come by the 'upper' route. All photons arrive from the left at mirror 4; half of them are transmitted to detector A, and the other half reflected to detector B.

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