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.
References
[1] J. C. Bose, Double Prisms Experiment, Science and Culture, 2008, p. 408.Search in Google Scholar
[2] A. Sommerfeld, Optics, Lectures on Theoretical Physics Vol. IV, § SC, San Diego, Academic Press, 1954.Search in Google Scholar
[3] G. Nimtz, A. Haibel, R.-M. Vetter, A. Haibel, and G. Nimtz, “Monografie scientifiche, serie fisiche, Roma,” Proceedings Int. Conf., TAQMSB, Napoli, 2000, pp. 125–138. A. Haibel, G. Nimtz, Ann. Phys.(Leipzig) 10, 707 (2001).10.1002/1521-3889(200108)10:8<707::AID-ANDP707>3.0.CO;2-RSearch in Google Scholar
[4] A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett., vol. 58, p. 774, 1991, G. Nimtz and H. Aichmann, Z. Naturforsch. 72, 881 (2017). https://doi.org/10.1063/1.104544.Search in Google Scholar
[5] S. Esposito, “On a universal photonic tunnelling time,” Phys. Rev. E, vol. 64, p. 026609, 2001. https://doi.org/10.1103/physreve.64.026609.Search in Google Scholar
[6] H. Aichmann and G. Nimtz, “On the traversal time of barriers,” Found. Phys., vol. 44, p. 678, 2014. https://doi.org/10.1007/s10701-014-9804-2.Search in Google Scholar
[7] A. Enders and G. Nimtz, “On superluminal barrier traversal,” J. Phys. I, vol. 2, p. 169, 1992. https://doi.org/10.1051/jp1:1992236.10.1051/jp1:1992236Search in Google Scholar
[8] M. Alonso and E. J. Finn, “Fundamental university physics, vol. III,” Am. J. Phys., vol. 37, p. 235, 1969. https://doi.org/10.1119/1.1975492.Search in Google Scholar
[9] R. Ramos, D. Spierings, I. Racicot, A. M. Steinberg, arXiv:1907.13523v1, 31.Jul 2019; S. Potnis et al., Phys. Rev. Lett. 118, 060402 (2017).Search in Google Scholar
[10] U. S. Sainadh, H. Xu, X. Wang, et al.., “Attosecond angular streaking and tunnelling time in atomic hydrogen,” Nature, vol. 568, p. 75, 2019. https://doi.org/10.1038/s41586-019-1028-3.Search in Google Scholar
[11] P. Eckle, A. N. Pfeiffer, C. Cirelli, et al.., “Attosecond ionization and tunneling delay time measurements in helium,” Science, vol. 322, p. 1525, 2008. https://doi.org/10.1126/science.1163439.Search in Google Scholar
[12] T. Hartman, “Tunneling of a wave packet,” J. Appl. Phys., vol. 33, p. 3427, 1962. https://doi.org/10.1063/1.1702424.Search in Google Scholar
[13] A. Enders and G. Nimtz, “Evanescent-mode propagation and quantum tunneling,” Phys. Rev.E, vol. 48, p. 632, 1994.10.1103/PhysRevE.48.632Search in Google Scholar
[14] R. Ramos, D. Spierings, I. Racicot, and A. M. Steinberg, “Measurement of the time spent by a tunnelling atom within the barrier region,” Nature, vol. 583, p. 529, 2020. https://doi.org/10.1038/s41586-020-2490-7.Search in Google Scholar
[15] G. Nimtz, “Macroscopic virtual particles exist,” Z. Naturforsch. A, vol. 74, no. 5, p. 363, 2019. https://doi.org/10.1515/zna-2019-0020.Search in Google Scholar
[16] C. K. Carniglia and L. Mandel, “Quantization of evanescent electromagnetic waves,” Phys. Rev. D, vol. 3, p. 280, 1971. https://doi.org/10.1103/physrevd.3.280.Search in Google Scholar
[17] S. T. Ali, “Evanescent waves in quantum electrodynamics with unquantized sources,” Phys. Rev. D, vol. 7, p. 1668, 1972.10.1103/PhysRevD.7.1668Search in Google Scholar
[18] A. Stahlhofen and G. Nimtz, “Evanescent modes are virtual photons,” Europhys. Lett., vol. 76, p. 189, 2006. https://doi.org/10.1209/epl/i2006-10271-9.Search in Google Scholar
[19] E. Merzbacher, Quantum Mechanics, 2nd ed. New York, John Wiley & Sons, 1970.Search in Google Scholar
[20] L. Brillouin, Wave Propagation in Periodic Structures, Chap. VIII, New York, Dover Publications, 1953.Search in Google Scholar
[21] G. Nimtz, “Do evanescent modes violate relativistic causality?,” LNP, vol. 702, p. 506, 2006.10.1063/1.2218191Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
