All waves have a zero tunneling time
-
Günter Nimtz
und
Horst Aichmann
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 E2 = (ħk)2c2 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).
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Artikel in diesem Heft
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Artikel in diesem Heft
- Frontmatter
- General
- Rapid Communication
- All waves have a zero tunneling time
- Atomic, Molecular & Chemical Physics
- Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals
- Dynamical Systems & Nonlinear Phenomena
- Dynamics of liquid drop on a vibrating micro-perforated plate
- Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions
- Evolution of nonlinear stationary formations in a quantum plasma at finite temperature
- Solid State Physics & Materials Science
- Effect of ZnO nanoparticles on optical textures and image analysis properties of 7O.O5 liquid crystalline compound
- First-principles study on band gaps and transport properties of van der Waals WSe2/WTe2 heterostructure
- Dirac cones for graph models of multilayer AA-stacked graphene sheets
