Universal tunneling time for all fields

Abstract

Tunneling is an important physical process. The observation that particles surmount a high mountain in spite of the fact that they don't have the necessary energy cannot be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies pointed towards a universal tunneling time (Haibel,Esposito). Experiments and calculations have shown that the tunneling time of opaque photonic barriers (optical mirrors, e.g.) equals approximately the reciprocal frequency of the corresponding electromagnetic wave. The tunneling process is described by virtual photons. Virtual particles like photons or electrons are not observable. However, from the theoretical point of view, they represent necessary intermediate states between observable real states. In the case of tunneling there is a virtual particle between the incident and the transmitted particle. Tunneling modes have a purely imaginary wave number. They represent solutions of the Schroedinger equation and of the classical Helmholtz equation. Recent experimental and theoretical data of electron and sound tunneling confirmed the conjecture that the tunneling process is characterized by a universal tunneling time independent of the kind of field. Tunneling proceeds at a time of the order of the reciprocal frequency of the wave.