Tunnelling times, Larmor clock, and the elephant in the room

E. Akhmatskaya,D. Sokolovski

doi:10.1038/s41598-021-89247-8

Abstract

A controversy surrounding the “tunnelling time problem” stems from the seeming inability of quantum mechanics to provide, in the usual way, a definition of the duration a particle is supposed to spend in a given region of space. For this reason, the problem is often approached from an “operational” angle. Typically, one tries to mimic, in a quantum case, an experiment which yields the desired result for a classical particle. One such approach is based on the use of a Larmor clock. We show that the difficulty with applying a non-perturbing Larmor clock in order to “time” a classically forbidden transition arises from the quantum Uncertainty Principle. We also demonstrate that for this reason a Larmor time (in fact, any Larmor time) cannot be interpreted as a physical time interval. We provide a theoretical description of the quantities measured by the clock.

Highlights

A controversy surrounding the “tunnelling time problem” stems from the seeming inability of quantum mechanics to provide, in the usual way, a definition of the duration a particle is supposed to spend in a given region of space
The Uncertainty Principle (UP) in its most general form reads “one cannot design equipment in any way to determine which of two alternatives is taken, without, at the same time, destroying the pattern of interference”[3]
One immediate problem with the method is that if the WS result is used to estimate the time spent by the particle in the barrier, this time turns out to be shorter than the barrier width divided by the speed of light. This apparently “superluminal behaviour” does not lead to a conflict with Einstein’s relativity for the simple reason that, in accordance with the Uncertainty Principle, the WS time cannot be interpreted as a physical time interval spent by a tunnelling particle in the barrier[6]