Fundamental Limit on “Interaction Free” Measurements

In a highly influential recent paper by Elitzur and Vaidman, it was pointed out that the presence of an object (often called a “bomb”) can often be discerned without it absorbing even a single photon. This “interaction free measurement” scheme and later improvements on it2–5 have received a lot of attention, both in the popular press as well as in serious scientific journals2–5,7. In this paper we wish to re-examine such measurement schemes and consider how they may be limited by the Heisenberg uncertainty principle. We would like to be very precise about what we mean by an “interaction free” measurement, and we attempt to define this in terms of a specific bomb detection experiment. We imagine that the bomb we wish to detect has a trigger that is so sensitive that it will explode if interacts in any way with any particles that are sent to probe it – I.e., if it scatters or absorbs any of these particles. This bomb trigger should be sensitive to an arbitrarily small momentum transfer from the probe particle to the bomb, as well as being sensitive to angular momentum transfer, energy transfer, and transfer of any other quantum number we could consider. We now imagine that some gnome challenges us to determine if he/she has placed this sensitive bomb within some predetermined region (denoted by the dotted box in Fig. 1). If we succeed in detecting the presence of this bomb without blowing it up, we will have performed an “interaction free” measurement. We note, however, that the measurement can only be declared to be “interaction free” if the bomb is truly an ideal detector. If the bomb trigger is unreliable, then we will never know if we have interacted with the bomb or not (This will become important below). Performing an interaction free measurement as defined above may seem impossible at first — and indeed, within classical physics such a thing would clearly be forbidden. However, by exploiting wave-particle duality, a number of groups have suggested2–5 that such measurements are in fact possible. Below, we will discuss the simplest of these proposed measurement schemes, and our results will apply more generally. In this paper we will point out that these schemes in fact do not satisfy the definition of “interaction free” given above. We then continue on to ask ourselves what precisely is achieved by these schemes. In particular, we will show that schemes can indeed claim to be “energy exchange free” (as first discussed in Ref. 4) or free from transfer of certain other quantum numbers, but are not free from transfer of all quantum numbers. Specifically, we will show that such experiments are not free of momentum transfer (although they can be made to have “minimal” momentum transfer).