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Revision and enlargement of this page is now permanently stalled - this page is no longer updated.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

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

The Berkeley group gives a general overview of their research at

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

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

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

Some other papers of Chiao's Berkeley group are also online, e.g.

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

A description of the equivalence between these microwave-experiments and quantum mechanical tunneling is described in

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

Nimtz's reply and general observations on causality and his experiments can be found in

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

Supplements: (May 5, 1999 and Jan 29, 2001)

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

II. Superluminal quantum phenomena

III. Causality, superluminality and relativity