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Zeitschrift für Naturforschung A

All waves have a zero tunneling time

Günter Nimtz, Horst Aichmann

Published Feb 19, 2021• 3 citations

Abstract

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).

DOI: 10.1515/zna-2020-0299

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Since 1992 experimental evidence of superluminal (faster than light, FTL) signals are causing much excitement in the physical community and in the media. Superluminal signal velocity and zero time tunneling was first observed in an analog tunneling experiment with microwaves. Recently, the conjectured zero time of electron was claimed to be observed in ionizing helium. The FTL signal velocity was reproduced with infrared light and with various tunneling barriers in several laboratories worldwide. Remarkable, it was shown that the tunneling time is a universal quantity for elastic and for electromagnetic fields. Many theoretical physicists predicted this FTL nature of the tunneling process. However, even with this background many members of the physics community did not accept the superluminal signal velocity interpretation of the experimental results and they also ignored the universal tunneling time. The predicted and measured zero tunneling time was taken as a fantastic nonsense. A brief explanation of the misleading theoretical approaches against FTL signals due to the tunneling process is presented eventually.

Abstract Since 1931, the nonclassical process of tunneling was conjectured to have a zero-time delay in the barrier. These theories have been rejected and denied. However, photonic and recent electronic tunneling experiments have proven the zero-time prediction. Tunneling is due to virtual wave packets in electromagnetic, elastic, and Schrödinger wave fields up to the macroscopic level. In this article we cite theoretical and experimental studies on zero-time tunneling, which have proven this striking behavior.

Abstract Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not 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 point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

How much time does a tunneling wave packet spent in traversing a barrier? Quantum mechanical calculations result in zero time inside a barrier . In the nineties analogous tunneling experiments with microwaves were carried out. The results agreed with quantum mechanical calculations. Electron tunneling time is hard to measure being extremely short and parasitic effects due to the electric charge of electrons may be dominant. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now and will be presented. It appears that the tunneling time is a universal property independent of the field in question.

Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not 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 point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

The energy of a wave packet tunneling a barrier is negative and its wavenumber is imaginary. What happens with time and locality? Several studies have been published resulting in a real time.However, previous theories and recent experiments revealed that the time spent inside abarrierhas no finite value but is zero. A“zero time” observation was found in different experiments and fields. In 1953Brillouin conjectured that wave mechanics holds for all fields including elastic, electromagnetic and Schrödinger waves and possibly other areas such as neuroscience.Our report addressesboth, time andspace.