Foundations of Physics

, Volume 44, Issue 6, pp 678–688

On the Traversal Time of Barriers


DOI: 10.1007/s10701-014-9804-2

Cite this article as:
Aichmann, H. & Nimtz, G. Found Phys (2014) 44: 678. doi:10.1007/s10701-014-9804-2


Fifty years ago Hartman studied the barrier transmission time of wave packets (J Appl Phys 33:3427–3433, 1962). He was inspired by the tunneling experiments across thin insulating layers at that time. For opaque barriers he calculated faster than light propagation and a transmission time independent of barrier length, which is called the Hartman effect. A faster than light (FTL or superluminal) wave packet velocity was deduced in analog tunneling experiments with microwaves and with infrared light thirty years later. Recently, the conjectured zero time of electron tunneling was claimed to have been observed in ionizing helium inside the barrier. The calculated and measured short tunneling time arises at the barrier front. This tunneling time was found to be universal for elastic fields as well as for electromagnetic fields. Remarkable is that the delay time is the same for the reflected and the transmitted waves in the case of symmetric barriers. Several theoretical physicists predicted this strange nature of the tunneling process. However, even with this background many members of the physics community do not accept a FTL signal velocity interpretation of the experimental tunneling results. Instead a luminal front velocity was calculated to explain the FTL experimental results frequently. However, Brillouin stated in his book on wave propagation and group velocity that the front velocity is given by the group velocity of wave packets in the case of physical signals, which have only finite frequency bandwidths. Some studies assumed barriers to be cavities and the observed tunneling time does represent the cavity lifetime. We are going to discus these continuing misleading interpretations, which are found in journals and in textbooks till today.


Faster than light velocity Front velocity Universal tunneling time Special theory of relativity Einstein causality Sommerfeld–Brillouin velocity analysis 

Mathematics Subject Classification

42.25.-p 42.50.Ct 03.65.-w 03.65.Ud 06.30.Gv 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Bad NauheimGermany
  2. 2.II. Physikalisches InstitutUniversität zu KölnKölnGermany