Abstract
Feynman introduced virtual particles in his diagrams as intermediate states of an interaction process. They represent necessary intermediate states between observable real states. Such virtual particles were introduced to describe the interaction process be- tween an electron and a positron and for much more complicated interaction processes. Other candidates for virtual particles are evanescent modes in optics and in elastic fields. Evanescent modes have a purely imaginary wave number, they represent the mathemati- cal analogy of the tunneling solutions of the Schrodinger equation. Evanescent modes ex- ist in the forbidden frequency bands of a photonic lattice and in undersized wave guides, for instance. The most prominent example for the occurrence of evanescent modes is the frustrated total internal reflection (FTIR) at double prisms. Evanescent modes and tun- neling lie outside the bounds of the special theory of relativity. They can cause faster than light (FTL) signal velocities. We present examples of the quantum mechanical behavior of evanescent photons and phonons at a macroscopic scale. The evanescent modes of photons are described by virtual particles as predicted by former QED calculations.
Highlights
EPJ Web of Conferences wave number of the solution inside the barrier and x the barrier length). In this case the traversal time is constant independent of barrier length and the group velocity becomes proportional to the barrier length
The superluminal (FTL) transmission velocity increases with barrier length
On the other hand the Helmholtz equation equals the Schrödinger equation and their evanescent modes correspond to the Schrödinger tunneling solutions
Summary
EPJ Web of Conferences wave number of the solution inside the barrier and x the barrier length) In this case the traversal time is constant independent of barrier length and the group velocity becomes proportional to the barrier length. Ω is the angular frequency, t the time, x the distance of the prisms , and κ the imaginary wave number of the tunneling mode. The experimental data we are talking about, were reproduced in different laboratories, and they are in agreement with the Helmholtz and the Schrödinger equations and with the Wigner phase time approach. The Wigner phase (shift) time was introduced in order to obtain the interaction time of particles This time re presents the interaction time of the particles with a potential barrier. Where φ represents the phase shift due to the barrier interaction process
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