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arXiv:0709.2736

Comment on "Macroscopic violation of special relativity" by Nimtz and Stahlhofen [arXiv:0708.0681v1]

Herbert G. Winful

Published Sep 18, 2007• 5 citations
arXivHTMLPDF

Abstract

A recent paper by G. Nimtz and A. A. Stahlhofen [arXiv:0708.0681v1] makes the following claims: (1) that the authors have observed a macroscopic violation of special relativity, (2) that they have demonstrated quantum mechanical behavior of evanescent modes on a meter-length scale, and (3) that barriers are crossed in zero time, implying superluminal (faster than light), and indeed, infinite tunneling velocity. Here I suggest that all these claims are erroneous and are based on a misinterpretation of a purely classical measurement accurately described by Maxwell's equations.

DOI
10.48550/arxiv.0709.2736

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Feynman one of the founders of Quantum Electronic Dynamics (QED) introduced in his diagrams virtual particles as intermediate states of an interaction process. Such virtual particles are not observable, however, from the theoretical point of view they represent necessary intermediate states between observable real states. Such virtual particles were introduced for describing the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual photons are evanescent modes known from optics. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes are present in the optical processes of total reflection and in undersized wave guides for instance. The most prominent example of the occurrence of evanescent modes is frustrated total internal reflection at double prisms. In 1949 Sommerfeld \cite{Sommerfeld} pointed out that this optical phenomenon represents the analogy of quantum mechanical tunneling. The evanescent modes and tunneling violate the theory of special relativity, obviously, they represent the exception which proves the special theory of relativity. We demonstrate the quantum mechanical behavior of evanescent modes \textbf{with digital microwave} signals at a macroscopic scale of the order of a meter and show that evanescent modes are well described by virtual photons as predicted by former QED calculations.

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A recent paper by G. Nimtz and A. A. Stahlhofen [arXiv:0708.0681v1] makes the following claims: (1) that the authors have observed a macroscopic violation of special relativity, (2) that they have demonstrated quantum mechanical behavior of evanescent modes on a meter-length scale, and (3) that barriers are crossed in zero time, implying superluminal (faster than light), and indeed, infinite tunneling velocity. Here I suggest that all these claims are erroneous and are based on a misinterpretation of a purely classical measurement accurately described by Maxwell's equations.
Feynman one of the founders of Quantum Electronic Dynamics (QED) introduced in his diagrams virtual particles as intermediate states of an interaction process. Such virtual particles are not observable, however, from the theoretical point of view they represent necessary intermediate states between observable real states. Such virtual particles were introduced for describing the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual photons are evanescent modes known from optics. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes are present in the optical processes of total reflection and in undersized wave guides for instance. The most prominent example of the occurrence of evanescent modes is frustrated total internal reflection at double prisms. In 1949 Sommerfeld \cite{Sommerfeld} pointed out that this optical phenomenon represents the analogy of quantum mechanical tunneling. The evanescent modes and tunneling violate the theory of special relativity, obviously, they represent the exception which proves the special theory of relativity. We demonstrate the quantum mechanical behavior of evanescent modes \textbf{with digital microwave} signals at a macroscopic scale of the order of a meter and show that evanescent modes are well described by virtual photons as predicted by former QED calculations.
Photonic tunnelling experiments have shown that i) the Einstein energy relation is violated, ii) the tunnelling process is non‐local, iii) the signal velocity is faster than light, i.e. superluminal, iv) the tunnelling signal is not observable, since photonic tunnelling is described by virtual photons, and v) according to the experimental results the signal velocity is infinite inside the barriers, implying that tunnelling instantaneously acts at a distance. We think these properties are not compatible with the claims of many text books on Special Relativity, see for instance Refs. [1].
Abstract Zero tunneling time and thereby a faster than light traversal velocity was calculated nearly a hundred years ago and has been observed recently. We report about experimental results and estimations, which confirm the zero time tunneling for elastic as well as for electromagnetic and Schrödinger waves. Zero time tunneling was first observed with microwaves 1992 (H. Aichmann and G. Nimtz, Found. Phys., vol. 44, p. 678, 2014; A. Enders and G. Nimtz, J. Phys. I, vol. 2, p. 169, 1992). In 2008, zero time was also observed for tunneling electrons (P. Eckle, A. N. Pfeiffer, C. Cirelli, et al., Science, vol. 322, p. 1525, 2008). Presumably, this effect took place with atoms quite recently (R. Ramos, D. Spierings, I. Racicot, and A. M. Steinberg, Nature, vol. 583, p. 529, 2020). The Einstein relation E 2 = (ħk)2 c 2 is not satisfied in the tunneling process, since the wave number k is imaginary (E is the total energy, ħ the Planck constant, and c the vacuum velocity of light), Zero time tunneling is described by virtual photons (A. Stahlhofen and G. Nimtz, Europhys. Lett., vol. 76, p. 189, 2006). The tunneling process itself violates the Special Theory of Relativity. Remarkably, Brillouin conjectured that wave mechanics is valid for all waves independent of their field (L. Brillouin, Wave Propagation in Periodic Structures, Chap. VIII, New York, Dover Publications, 1953).
Evanescent modes or the tunnelling process are characterized by an imaginary wave number. These special solutions of the Helmholtz and of the Schrödinger equations first noticed in connection with the total reflection were said to have no physical meaning about 200 years ago. Last century the tunnelling problem in quantum mechanics has been described by the phase time approach. The phase time approach yields the group velocity of a wave packet (see e.g. Hartman, 1962). Nowadays the phase time approach is used in network analyzers to determine the group velocity of an electromagnetic wave in devices. We have reported about superluminal signal velocities in photonic tunnelling. It was observed that the superluminal photonic tunnelling time data measured in the time domain are in agreement with the calculated phase time data. This result is also in agreement with the definition of the barrier transition time given in the Federal Standard 1037 C (NTIA, USA 2000). Thus we have added further credibility to the assumption that the photonic tunnelling results are representative for quantum mechanical tunnelling of particles.
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 between 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 mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes exist 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 tunneling 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.
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 between 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 mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes exist 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 tunneling 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.