Superluminal tunneling times without superluminal signaling: Fading of the MacColl-Hartman effect at early times

TL;DR

This paper demonstrates that the apparent superluminal tunneling times, known as the MacColl-Hartman effect, do not enable faster-than-light communication because the early-time tail of tunneling time distributions prevents superluminal signaling.

Contribution

It shows that the MacColl-Hartman effect diminishes at early times when modeled accurately, ensuring no superluminal signaling is possible.

Findings

Mean tunneling time for one particle is affected by early-time tail

Superluminal signaling is impossible with tunneling due to timing constraints

The effect fades when tunneling time distribution is modeled with steepest descent

Abstract

A curious feature of quantum tunneling known as the MacColl-Hartman effect results in the numerical observation that particles can traverse a barrier with effective superluminal speed. However, because tunneling is never certain, any attempt to use this effect to send a signal faster than light would require sending many particles. In this work, we consider sending -- in parallel, without interactions between particles -- sufficiently many particles to ensure at the least one of them tunnels. In this case, in spite of the time advance of the mean time for a single tunneling particle, the mean time to send one bit of information is larger for tunneling particles than for the same number of free photons. This removes any possibility of superluminal signaling. We show that the mean time to send one bit using N particles is determined by the early-time tail of the distribution of tunneling times for one particle and that, when this early-time tail is highly accurately modeled using steepest descent, the MacColl-Hartman effect is seen to fade away.