http://www.aei.mpg.de/~mpoessel/Physik/FTL/tunnelingftl.html#Supp

Faster-than-light speeds in tunneling experiments: an annotated bibliography

Revision and enlargement of this page is now permanently stalled - this page is no longer updated. Some less ancient references (as of 2001) are added in piecemeal fashion, below.

One central tenet of special relativity theory is that light speed is the greatest speed at which energy, information, signals etc. can be transmitted. In many physics-related internet newsgroups, claims have appeared that recent tunneling experiments show this assumption to be wrong, and that information can indeed be transmitted by speeds faster than that of light - the most prominent example of "information" being a Mozart symphony, having been transmitted with 4.7 times the speed of light. In this document, I've tried to collect the major references on these faster-than-light (FTL)-experiments. If I find the time, I will develop this into a written introduction on the topic of FTL speeds and tunneling, so far it is merely a (possibly incomplete) collection of references. If anyone has relevant additions/comments, I'd appreciate a mail.

Most of the references are to the technical literature, presuming that the reader has at least a basic grasp of physics. However, as usual, those articles have abstracts and conclusions, which give an overview of what the article is about. Some references that are in German are omitted here, but can be found in the german version of this page.

What's this all about, anyway?

In recent years, some physicists have conducted experiments in which faster-than-light (FTL) speeds were measured. On the other hand, Einstein's theory of special relativity gives light speed as the absolute speed limit for matter and information! If information is transmitted faster, then a host of strange effects can be produced, e.g. for some observers it looks like the information was received even before it was sent (how this comes about should be described in elementary literature on special relativity). This violation of causality is very worrysome, and thus special relativity's demand that neither matter nor information should move faster than light is a pretty fundamental one, not at all comparable to the objections some physicists had about faster-than-sound travel in the first half of this century.

So, has special relativity been disproved, now that FTL speeds have been measured? The first problem with this naive conclusion is that, while in special relativity neither information nor energy are allowed to be transmitted faster than light, but that certain velocities in connection with the phenomena of wave transmission may well excede light speed. For instance, the phase velocity of a wave or the group velocity of a wave packet are not in principle restricted below light speed. The speed connected with wave phenomena that, according to special relativity, must never exceed light speed, is the front velocity of the wave or wave packet, which roughly can be seen as the speed of the first little stirring that tells an observer "Hey, there's a wave coming". Detailled examinations of the differences between the velocities useful to describe waves can be found in the classic book

• Brillouin, L. 1960 Wave Propagation and Group Velocity. NY: Academic Press.
Basic information on quantum tunneling can be found in the introductory quantum theory literature.
Characteristic of the discussion of the FTL/tunneling experiments is that the experimental results are relatively uncontroversial - it is their interpretation that the debate is about. As far as I can see, right now there is a consensus that in neither of the experiments, FTL-front velocities have been measured, and that thus there is no contradiction to Einstein causality or to special relativity's claim that no front speed can exceed light speed. The discussion how much time a particle needs to tunnel through a barrier has been going on since the thirties and still goes on today, as far as I can tell. This discussion is about "real" tunneling experiments, like the ones a Berkeley group around Raymond Chiao has done, as well as experiments with microwaves in waveguides (that do not involve quantum mechanics) like those of Günter Nimtz et al. An overview of the discussion (including lots of further references) can be found in

•Hauge, E.H. & Støvneng 1989, Review of Modern Physics 61, S. 917--936.
The Berkeley group gives a general overview of their research at
•http://www.physics.berkeley.edu/research/chiao/research.html

An experiment of theirs, where a single photon tunnelled through a barrier and its tunneling speed (not a signal speed!) was 1.7 times light speed, is described in

•Steinberg, A.M., Kwiat, P.G. & R.Y. Chiao 1993: "Measurement of the Single-Photon Tunneling Time" in Physical Review Letter 71, S. 708--711
Articles concerned with the propagation of wave packets that happens FTL and is somewhat complicated by the fact that the waves "borrow" some energy from the medium, but does not violate causality, are
•Chiao, R.Y. 1993: "Superluminal (but causal) propagation of wavepackets in transparent media with inverted atomic populations" in Phys. Rev. A 48, B34.

• Chiao, R.Y. 1996: "Tachyon-like excitations in inverted two-level media" in Phys. Rev. Lett. 77, 1254.
Aephraim Steinberg, who is a former graduate student of Chiao's, has written two papers especially on the problem of tunneling time, which are available online at
•Aephraim M. Steinberg 1995: "Conditional probabilities in quantum theory, and the tunneling time controversy" in Phys. Rev A52, 32-42 (was preprint quant-ph/9502003).

•Aephraim M. Steinberg 1995: "How much time does a tunneling particle spend in the barrier region? " in Phys. Rev. Lett. 74, 2405-9 (was preprint quant-ph/9501015).
Some other papers of Chiao's Berkeley group are also online, e.g.
•Aephraim M. Steinberg, Raymond Y. Chiao 1995: "Sub-femtosecond determination of transmission delay times for a dielectric mirror (photonic band gap) as a function of angle of incidence" in Phys. Rev. A51, 3525/8 (was Preprint quant-ph/9501013).


• Raymond Y. Chiao, Paul G. Kwiat, Aephraim M. Steinberg: " Quantum non-locality in Two-Photon Experiments at Berkeley" (International Workshop on Laser and Quantum Optics, Nathiagali, Pakistan, 9-14 July 1994) in Quantum and Semiclassical Optics 7, 259-78 (was preprint quant-ph/950101).
Earlier experiments by Günter Nimtz of Cologne University (Universität Kön), with whose experiments most of the later newspaper articles are concerned, have been published as
• Enders, A. und G. Nimtz 1993, "Evanescent-mode propagation and quantum tunneling" in Phys. Rev. E 48, S. 632-634.


• Enders, A. und G. Nimtz 1993, J. Phys. I (France) 3, S. 1089

• Nimtz, G. et al. 1994: "Photonic Tunneling Times"in J. Phys. I (France) 4, 565.
A description of the equivalence between these microwave-experiments and quantum mechanical tunneling is described in
•Martin, Th. und Landauer, R. 1991: "Time delay of evanescent electromagnetic waves and the analogy to particle tunneling" in Phys. Rev. A 45 , S. 2611-2617.
In reaction to Nimtz' publications, a number of articles appeared which deal with a) why causality is not violated in these experiments, and b) how the results of the experiments come about. These are
•Deutch, J.M. und F.E. Low 1993: "Barrier Penetration and Superluminal Velocity" in Ann. Phys. (NY) 228, S. 184-202.

• Hass, K. und P. Busch 1994: "Causality of superluminal barrier traversal" in Phys. Lett. A 185, S. 9-13.

• Landauer, R. und Th. Martin 1994: "Barrier interaction time in tunneling" in Rev. Mod. Phys. 66, S. 217-228.

• Azbel, M. Y. 1994: "Superluminal Velocity, Tunneling Traversal Time and Causality" in Solid State Comm. 91, S. 439-441.
Nimtz's reply and general observations on causality and his experiments can be found in • Heitmann, W. und G. Nimtz 1994: "On causality proofs of superluminal barrier traversal of frequency band limited wave packets" in Phys. Lett. A 196, S. 154-158.

As far as the more recent experiments of Nimtz are concerned, especially the popular tunneling of parts of Mozart's 40th symphony with 4.7fold light speed, I have not been able to find references to a technical article yet. Heitman/Nimtz 1994 (see above) refer to it as "H. Aichmann and G. Nimtz, to be published", I haven't found it in Physics Abstracts (up to July 1996, I think I should look again soon), though.

the problem of tunneling times is also the topic of some articles I've found in the quantum physics (quant-ph) archive, namely

•Toralf Gruner, Dirk-Gunnar Welsch: Photon tunneling through absorbing dielectric barriers, Preprint quant-ph/9606008

•Andrea Begliuomini, Luciano Bracci: The tunneling time for a wave packet as measured with a physical clock Preprint quant-ph/9605045

• M. S. Marinov, Bilha Segev On the concept of the tunneling time Preprint quant-ph/9603018

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Supplements: (May 5, 1999 and Jan 29, 2001)
• Aichmann, H., G. Nimtz and H. Spieker: "Photonische Tunnelzeiten: sunb-- und superluminales Tunneln" in Verhandlungen der Deutschen Physikalischen Gesellschaft 7, 1995, S. 1258.
I'm listing this brief publication (a conference abstract) despite its being in German as it is the only publication directly referring to the tunneling of the Mozart symphony that I know of. The following article has much more content:

• Nimtz, G. and W. Heitmann: "Superluminal Photonic Tunneling and Quantum Electronics" in Progress in Quantum Electronics 21(2) (1997), S. 81-108.
Contains an expose of Nimtz' interpretation of his and other tunneling experiments.

•Chiao, R.Y. Chiao and A.M. Steinberg: "Tunneling Times and Superluminality" in Progress in Optics XXXVII (1997), S. 345-405.
Good summary of the "conventional" view why there is no faster-than-light information transfer in these tunneling experiments.

•Mitchell, M.W. and R.Y. Chiao: "Causality and negative group delays in a simple bandpass amplifier" in American Journal of Physics 66(1) (1998), S. 14-19.
Describes a very simple setup with the help of which one can understand how faster-than-light (or even negative) group and "signal"-velocities can occur without any violation of causality and without any faster-than-light information transfer.

• Diener, G.: "Superluminal group velocities and information transfer" in Physics Letters A223 (1996), S. 327-331.
General article about the pulse reshaping which, in the conventional interpretation, explains the faster-than-light (or negative) group velocities.

The following references are from the proceedings of the workshop "Superluminal(?) Velocities: Tunneling time, barrier penetration, non-trivial vacua, philosophy of physics", organized by F. W. Hehl, P. Mittelstaedt and G. Nimtz, which took place in Cologne, June 6-10, 1998.

I. Evanescent mode propagation and simulations

•A.M. Steinberg et al.: "An atom optics experiment to investigate faster-than-light tunneling" in Annalen der Physik (Leipzig), 7 (1998), S. 593-601.

• M. Büttiker and H. Thomas: "Front propagation in evanescent media" in Annalen der Physik (Leipzig), 7 (1998), S. 602-617.

•G. Nimtz: "Superluminal signal velocity" in Annalen der Physik (Leipzig), 7 (1998), S. 618-624.

• A. A. Stahlhofen and H. Druxes: "Observable tachyons in the tunneling regime?" in Annalen der Physik (Leipzig), 7 (1998), S. 625-630.

•X. Chen and C. Xiong: "Electromagnetic simulation of the evanescent mode" in Annalen der Physik (Leipzig), 7 (1998), S. 631-638.

•G. Diener: "Energy balance and energy transport velocity in dispersive media" in Annalen der Physik (Leipzig), 7 (1998), S. 639-644.

•H. D. Dahmen et al.: "Quantile motion of electromagnetic waves in wave guides of varying cross section and dispersive media" in Annalen der Physik (Leipzig), 7 (1998), S. 645-653.

•E. Capelas de Oliveira and W. A. Rodrigues Jr.:"Superluminal electromagnetic waves in free space" in Annalen der Physik (Leipzig), 7 (1998), S. 654-659.

II. Superluminal quantum phenomena

•F. E. Low: "Comments on apparent superluminal propagation" in Annalen der Physik (Leipzig), 7 (1998), S. 660-661.

•C. R. Leavens and R. Sala Mayato: "Are predicted superluminal tunneling times an artifact of using the nonrelativistic Schrödinger equation?" in Annalen der Physik (Leipzig), 7 (1998), S. 662-670.

•J. G. Muga and J. P. Palao: "Negative time delays in one dimensional absorptive collisions" in Annalen der Physik (Leipzig), 7 (1998), S. 671-678.

•S. Brouard and J. G. Muga: "Transient increase of high momenta in quantum wave-packet collisions" in Annalen der Physik (Leipzig), 7 (1998), S. 679-686.

•C. Bracher and M. Kleber: "Minimum tunneling time in quantum motion" in Annalen der Physik (Leipzig), 7 (1998), S. 687-694.

•D. Kreimer: "Locality, QED and classical electrodynamics" in Annalen der Physik (Leipzig), 7 (1998), S. 695-699.

•K. Scharnhorst: "The velocities of light in modified QED vacua" in Annalen der Physik (Leipzig), 7 (1998), S. 700-709.

•P. Mittelstaedt: "Can EPR-correlations be used for the transmission of superluminal signals?" in Annalen der Physik (Leipzig), 7 (1998), S. 710-715.

•G. C. Hegerfeldt: "Instantaneous spreading and Einstein causality in quantum theory" in Annalen der Physik (Leipzig), 7 (1998), S. 716-725.

•G. F. Melloy and A. J. Bracken: "The velocity of probability transport in quantum mechanics" in Annalen der Physik (Leipzig), 7 (1998), S. 726-731.

•H. M. Krenzlin et al.: "Wave packet tunneling" in Annalen der Physik (Leipzig), 7 (1998), S. 732-736.

III. Causality, superluminality and relativity

•P. Weingartner: "Causality in the natural sciences" in Annalen der Physik (Leipzig), 7 (1998), S. 737-747.

•U. Schelb: "On the role of a limiting velocity in constructive spacetime axiomatics" in Annalen der Physik (Leipzig), 7 (1998), S. 748-755.

•V. Gasparian et al.: "On the application of the Kramers-Kronig relations to the interaction time problem" in Annalen der Physik (Leipzig), 7 (1998), S. 756-763.

•E. Recami et al.: "Superluminal microwave propagation and special relativity" in Annalen der Physik (Leipzig), 7 (1998), S. 764-773.

•H. Goenner: "Einstein causality and the superluminal velocities of the Cologne microwave experiment" in Annalen der Physik (Leipzig), 7 (1998), S. 774-782.