Time and history in quantum tunneling

Abstract

The time a particle spends while tunneling is a subject of long dispute, whose recent history owes much to Rolf Landauer. While I do not have the space to say a great deal about the history of the tunneling time, I am going to try to argue that the tunneling time itself may have a great deal to teach us abouthistory. After an abbreviated description of some of the surprising results of optical experiments on tunneling, this paper outlines a new theoretical approach to the reconstruction of the past in quantum mechanics; for questions of particles known to have been transmitted through a tunnel barrier, this is precisely the type of formalism required. We will see that our results have much in common with earlier approaches due to Landauer and Büttiker, although the interpretations may diverge. Roughly speaking, our view is that the history of a tunneling particle may be described more completely than merely by its wavefunction. We will discuss the measurable consequences of this claim, and (briefly) an atom optics experiment being assembled at Toronto in order to test them. Finally, I will present some recent speculations about a quantifiable sense in which a tunneling particle may be ‘in two places at one time’, which we also hope to be able to test at Toronto.