On Virtual Phonons, Photons, and Electrons

Abstract

A macroscopic realization of the strange virtual particles is presented. The classical Helmholtz and the quantum mechanical Schr\"odinger equations are analogous differential equations. Their imaginary solutions are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary solutions of this differential equation point to strange consequences: They are non local, they are not observable, and they described as virtual particles. During the last two decades QED calculations of the imaginary solutions have been experimentally confirmed for phonons, photons, and for electrons. The experimental proofs of the predictions of the non-relativistic quantum mechanics and of the Wigner phase time approach for the elastic, the electromagnetic and the Schr\"odinger fields will be presented in this article. The results are zero tunneling time and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured barrier interaction time (i.e. the barrier transmission time) scales approximately inversely with the particle energy.