The Haunted Measurement in Quantum Theory a

We have been bothered by the problem of trying to decide when a quantum mechanical system that appears to be disordered may actually contain hidden information; namely, information that may in fact be made manifest by a later interaction. We have not been able to say much that is new about this problem as yet, but we do have an example that shows that the problem is important. An example of this type of behavior occurs in a spin echo experiment. In that case, a spin system is apparently disordered by a magnetic pulse, but a later magnetic pulse reordm the system so that, subsequently, all the spins are coherently aligned for an instant. Our example goes beyond this in that the system is apparently disordered by interacting with a macroscopic object, in which it induces a macroscopic change. All one needs to do is look at the macroscopic object to detect that a measurement has taken place. However, if one does not bother to look, the system subsequently interacts with the object again, thereby undoing the macroscopic effect and completely regaining its coherence. Thus, there is a window in time within which one can look at the macroscopic object to see that a measurement has been made. After that, it is too late. All traces of the “measurement” have disappeared. It was, alas, merely a ghost. Therefore, the measurement process has been “haunted” by a measurement that was substantial for a while, but then evaporated away. Quantum mechanical measurements are not supposed to do that. We tend to think of macroscopic effects produced by quantum systems as irreversible traces, such as a count in a detector, accompanied by an incoherent amplification process. However, the point of our opening question is how can we know when an irreversible recording process has taken place? This leads to what we call the “future generations problem.” If a particular interaction seems to us to constitute a measurement that appears to destroy the coherence of the quantum system, how do we know that no one will come along at some future time with better experimental techniques? He may then discover that the wave function in this experiment only appeared to be incoherent, and that the interaction merely scrambled up the wave function and did not irreversibly alter it. In that case, he may be able to reconstitute it and show that what we took to be a measurement was in fact only a rearrangement.