Interaction-Free Measurements

1 The Penrose bomb testing problem I am greatly indebted to Roger Penrose. I have learned very much from his papers, from his exciting books, and from our (too short) conversations. I am most grateful to Roger for developing the idea of Avshalom Elitzur and myself on interaction-free measurements (IFM). The version of IFM Penrose described in his book (1994) is conceptually different from our original proposal, and although it is much more difficult for practical applications it has the advantage of demonstrating even more striking quantum phenomena. So I will start with presenting Pen rose's version of IFM. Suppose we have a pile of bombs equipped with super-sensitive triggers. The good bombs have a tiny mirror which is connected to a detonator such that if any particle (photon) " touches " the mirror, the mirror bounces and the bomb explodes. Some of the bombs are duds in which the mirror is rigidly connected to the massive body of the bomb. Classically, the only way to verify that a bomb is good is to touch the mirror, but then a good bomb will explode. Our task is to test a bomb without exploding it. We are not allowed to make errors in our test, i.e., to say that a bomb is good while it is a dud, but we may sometimes cause an explosion. There cannot be a solution by weighting the bomb, or touching the mirror from the side, or any other similar way: the only observable physical difference between a good bomb and a dud is that the good bomb will explode when a single particle will touch the mirror, and the dud will not. Thus, the solution of this task seems to be logically impossible: the only difference between the bombs is that one explodes and the other does not and we are asked to test a bomb without exploding it. Nevertheless, quantum mechanics provides a solution to the problem in a surprisingly simple way. The method uses the well known Mach-Zehnder interferometer which is shown in Fig. 1. The photons reach the first beam splitter which has transmission coefficient 1/2. The transmitted and reflected parts of their waves are then reflected by two mirrors and finally reunite at another similar beam splitter. Two detectors collect the photons after they pass through the second beam splitter. It is possible to arrange the positions of the beam splitters …