Superluminal phase and group velocities: A tutorial on Sommerfeld's phase, group, and front velocities for wave motion in a medium, with applications to the "instantaneous superluminality" of electrons

TL;DR

This paper reviews Sommerfeld's concepts of phase, group, and front velocities, explores superluminal phenomena including electron charge transfer, and discusses experimental evidence and implications for superluminal effects in various media.

Contribution

It provides a comprehensive tutorial on superluminal wave velocities and applies these concepts to electron charge transfer experiments, highlighting potential superluminal effects.

Findings

Optical experiments show superluminal group velocities.

Charge transfer in metals and superconductors can exhibit superluminal-like behavior.

Discussion of ongoing experiments measuring electron charge transfer times.

Abstract

The concepts of phase, group, and front velocities introduced by Sommerfeld will be reviewed, and applied to superluminal phenomena, with a brief review of optical experiments that evince superluminal group velocities. We shall discuss the special case of "instantaneous superluminality" in the case of electrons. In particular, the charge transfer of electrons through a Fermi sea of electrons from the interior to the exterior of a normal metal will be discussed in connection with an ongoing experiment to measure the time it takes for this charge transfer process to take place in a long aluminum bar, in a generalization of Faraday's original "ice-pail" experiment. Also, the speed of the charge transfer of Cooper pairs through a bimetallic superconducting island, coupled via an input and an output Josephson junctions, will be discussed.