# What is a current view on Nimtz (FTL) effect?

1. Aug 16, 2013

### Dmitry67

Based on WIKI, there is no consensus, as I understand, experimentally the effect is confirmed, but there are different interpretations trying to explain that there is no FTL.

There are several discussions about Group velocity vs Phase velocity, but I think it we produce very short impulses we can simply talk about the Front velocity. In such case, the interpretation on the results must be unambiguous, right?

As it does not happen, I am missing something important

2. Aug 16, 2013

### vanhees71

I thought this nonsense has just disappeared from the news (some years ago it made it to the prime-time news in German TV; with real physics achievements like the discovery of the Higgs boson you don't have a chance for that ;-)) and got forgotten.

IMHO this issue is well understood and solved for over 100 years. The question about apparantly superluminal signal velocities in wave propagation through media for signals with frequencies close to a resonance region of the medium, where anomalous dispersion occurs (and nothing else happens in the frequency region of evanescent modes in wave guides), has been solved by Sommerfeld in 1907 in a very short note, answering the corresponding question by Willy Wien on this issue. At this time, the special theory of relativity was quite new and all these issues had to be understood and explained (as the not so simple issues on the Lorentz-transformation properties of physical quantities like temperature, particle density, etc.). Later in 1913 this issue has been worked out very carefully by Sommerfeld and Brillouin in two famous papers in the Annalen der Physik.

The short answer is that the stationary-phase method for the evaluation of the Fourier integral defining the wave packet in the medium, which usually leads to the idea of group velocity ($\vec{v}_g=\partial \omega/\partial \vec{k}$) is not applicable anymore for modes in the region of anomalous dispersion, and the interpretation of the group velocity as the velocity of the "center of the wave packet" becomes obsolete. The group velocity can become easily larger than the speed of light, but it doesn't tell you anything about signal propagation anymore. What happens in reality is that the wave packet becomes very much deformed moving through the medium and there is no well-defined "center of the wave packet" anymore. Thus the group velocity doesn't give a good idea on what's happening concerning the speed of signal propagation. As Sommerfeld and Brillouin have shown, within their quite simple classical model for dispersion of em. waves, the wave front propagates precisely with the speed of light. At the first impact the medium looks as the vacuum since the electrons (or other charges making up the medium, relevant for the considered signal) have first to get excited from the equilibrium position. Then they send out em. waves due to the perturbation of the signal, which gets superimposed with the original em.-wave perturbation. The very first impact leads to a rapidly oscillating signal, the socalled Sommerfeld forerunner, followed by another slower oscillating signal, the Brillouin forerunner. Then, if you have a very long wave train at a relatively sharply peaked spectrum around one frequency, the medium comes to a stationary state, and after some time you have a plain-wave propagation inside the medium governed by the fractional index, giving the usual phase velocity in the medium as it should be. All is nicely described by Sommerfeld and Brillouin using marvelous applications of complex-function analysis. You find a somewhat simplified (but still far from trivia!) treatment of this theory in Sommerfeld, Lectures on Theoretical Physics, Vol. IV (Optics).

Last but not least one should mention that not much changes from this qualitative picture, when invoking a quantum theoretical treatment of dispersion (in linear-response approximation). Then you also find that the signal propagates according to the retarded in-medium propagator for the electromagnetic wave, which by construction within QED fulfills Einstein causality and thus again nothing moves faster than light which is not allowed to do so!

3. Aug 16, 2013

### Bill_K

Wikipedia has a brief discussion of the Sommerfeld and Brillouin precursors.

4. Aug 16, 2013

### DennisN

5. Aug 17, 2013

### Dmitry67

Thank you, all

6. Aug 17, 2013

### vanhees71

This single-photon precursor study is simply beautiful. No Nimtz nonsense but good old Sommerfeld and Brillouin observed, as expected. Also Ref. [10] of the PRL is very nice to read.