- Hartman effect
The delay time for a tunneling
particle is independent of the thickness of the opaque barrier. This is called the Hartman effect and might result in particles traveling faster thanlight .The Hartman effect is the tunnelling effect through a barrier where the tunnelling time tends to a constant for large barriers. [J.C. Martinez, and E. Polatdemir, "Origin of the Hartman effect", "Physics Letters A", Vol 351, Iss 1-2, 20 February 2006, pp31-36.] This was first described by
Thomas Hartman in 1962. [T. E. Hartman, "Tunneling of a wave packet", "J. Appl. Phys." 33, 3427 (1962).] This could, for instance, be the gap between two prisms. When the prisms are in contact, the light passes straight through, but when there is a gap, the light is refracted. There is a finite probability that the photon will tunnel across the gap rather than follow the refracted path. For large gaps between the prisms the tunnelling time approaches a constant and thus the photons appear to have crossed with a superluminal speed. [G. Nimtz, A. A. Stahlhofen, "Macroscopic violation of special relativity", 5 Aug 2007 available as eprint [http://arxiv.org/abs/0708.0681] ]However, an analysis by Herbert Winful from the University of Michigan suggests that the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than c, because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate". [Winful, H, "Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox", "Physics Reports", Vol 436, Iss 1-2, December 2006, pp1-69.] Winful means by this that the photons crossing the barrier are virtual photons only existing in the interaction and could not be propagated into the outside world.
References
*T. E. Hartman, "Tunneling of a wave packet", "J. Appl. Phys." 33, 3427 (1962).
*J.C. Martinez, and E. Polatdemir, "Origin of the Hartman effect", "Physics Letters A", Vol 351, Iss 1-2, 20 February 2006, pp31-36.
*H. Winful, "Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox", "Physics Reports", Vol 436, Iss 1-2, December 2006, pp1-69.
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