Erratum to: On Virtual Phonons, Photons, and Electrons

Abstract

A macroscopic realization of the peculiar virtual particles is presented. The classical Helmholtz and the Schrödinger equations are differential equations of the same mathematical structure. The solutions with an imaginary wave number 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 wave numbers point to strange consequences: The waves are non-local, they are not observable, and they are described as virtual particles. During the last two decades QED calculations of the solutions with an imaginary wave number have been experimentally confirmed for phonons, photons, and electrons. The experimental proofs of the predictions of non-relativistic quantum mechanics and the Wigner phase time approach for the elastic, electromagnetic and Schrödinger fields will be presented in this article. The results are zero time in the barrier and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured tunneling time scalesThe online version of the original article can be found under doi:10.1007/s10701-009-9356-z.G. Nimtz ( ) II. Physikalisches Institut, Universität zu Köln, Zülpicherstrasse 77, 50937 Köln, Germany e-mail: G. Nimtz@uni-koeln.de 1222 Found Phys (2010) 40: 1221-1230 approximately inversely with the particle energy. Actually, the tunneling time is given only by the barrier boundary interaction time, as zero time is spent inside a barrier.

Can One Transmit Energy Faster Than Light

“…In regard to Nimtz [1][2] and Walker [3], in both there papers, on tunnelling particles and EM fields in the near field from a dipole antenna, that go faster than light, what is the mechanism for energy to behave in this way?…”

“…Gunter Nimtz [1] says in his paper on tunnelling that the refractive index plays a role of the potential for electromagnetic evanescent modes in wave mechanical tunnelling. This is the same with the principle of least action, where light takes the shortest path in a medium in refraction through glass for example.…”

“…Then one finds a possible explanation for the mechanism of why one superluminal speeds in tunnelling and EM fields in the near-field, that in the reducing the refractive index of the vacuum, ZPF field being reduced, allows light to be superluminal and consider the engineering of the vacuum, to send energy faster than light. TUNNELLING I begin in listing the effects found Gunter Nimtz in his paper [1]. In Nimtz's paper, it's found that tunnelling of particles in the barrier are nonlocal, instantly spread out with the same amplitude over the whole barrier space.…”

“…One then naturally asks if one could understand the mechanism of this, that one might be able to send energy faster than the speed of light. With these considerations it has been shown by Gunter Nimtz [1][2] that tunnelling through a potential barrier are superluminal in the barrier, and that Walker [3] showed that EM fields are superluminal in the near-field of an transmitter and reduce to the speed of light in the far field. Talaaki Musha [4] in a number of experiments, shows in his paper that photons travel at superluminal speeds in the electromagnetic near-field of the source.…”

“…That he found information signal can be propagated superluminally, that it can be reflected by a moving frame and arrive at the source before the information was transmitted, enabling causality to be violated [9]. I introduce each characteristic findings of the paper of Nimtz [1][2] and Walker [3] and there is consideration of the work of Bajlo [10] where he detected for the first-time advanced waves, where such advanced potentials are considered to be reflecting the symmetry exhibited by time, in the advanced and retarded solutions of Maxwell's equations, that reflect two flows of time, and that this is related to the German Mathematician (1918) Emmy Noethe's theorem, due to conservation laws and the principle of least action, which is also applied to laws of refraction in the tunnelling medium to superluminal speeds through an potential barrier and the superluminal EM fields in the near-field. One then considers what the mechanism is, of why energy behaves this way to be superluminal, and if one can understand this mechanism, that one could send energy faster than light.…”