Wave packets, "negative times" and the elephant in the room

TL;DR

This paper critiques the concept of tunnelling times in quantum mechanics, using a Mach-Zehnder interferometer analogy to show that claims of superluminal or negative times are unjustified and based on misinterpretations.

Contribution

It introduces an analogy with a tunable Mach-Zehnder interferometer to clarify the tunnelling time problem and argues against the validity of superluminal or negative time interpretations.

Findings

Wave packet delays can be explained without superluminal speeds.

Interference effects account for the apparent tunnelling times.

The analogy clarifies the role of the Uncertainty Principle in tunnelling.

Abstract

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. One such approach uses the position of the transmitted wave packet in order to infer the duration the particle spends in the barrier. Here we replace the barrier with a tuneable Mach-Zehnder interferometer (MZI). With this analogy one is able, at least in principle, to achieve any advance or delay of the wave packet sent to the chosen outgoing port. The Uncertainty Principle prevents one from combining the durations spent in each arm the MZI into a meaningful duration when both arms are engaged. There is no justification for invoking "superluminal" or "negative" times, since the particle is able to arrive at the same position (and with a higher probability) if the same initial state propagates through only one arm of the MZI. The same is true, we argue, in the case of tunnelling, where the transmitted wave packet results from destructive interference between multiple copies of the free state, delayed relative to the free propagation