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Zeitschrift für Naturforschung A

On timeless macroscopic spaces

Günter Nimtz, Horst Aichmann

Published Feb 27, 2023• 1 citation
Publisher

Abstract

Abstract Sommerfeld and other physicists pointed out that tunneling is no classical process. The arguments are that the tunneling wave’s momentum is imaginary and its energy is negative. However, what is the time τ spent inside a barrier? Brillouin conjectured that the non-classical behaviour is valid for waves of all fields, i.e. for electromagnetic and acoustic waves as well as for Schrödinger waves.

DOI
10.1515/zna-2022-0271

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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.

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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).

Zeitschrift für Naturforschung A•Feb 19, 2021•3 citations
Abstract Sommerfeld and other physicists pointed out that tunneling is no classical process. The arguments are that the tunneling wave’s momentum is imaginary and its energy is negative. However, what is the time τ spent inside a barrier? Brillouin conjectured that the non-classical behaviour is valid for waves of all fields, i.e. for electromagnetic and acoustic waves as well as for Schrödinger waves.
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.
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.
We begin the Article with confusing citations in published papers on the question recently: how much time does a wave packet spend in a tunnelling barrier? ..a particle tunnelling through a barrier appears to do so in zero time 1. .. The pulse transit through the barrier itself seems to be instantaneous 2. ..tunnelling is unlike to be an instantaneous process 3. ..ionization time is close to zero 4. ..all waves have a zero tunneling time [5]. ..Our results are inconsistent with claims that tunnelling takes zero time 6
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.
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.
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).