# Does this* refraction experiment correctly conclude faster than light travel?

This question asks if a particular experiment is correct in its conclusion.

This experiment, conducted by Alfred Leitner, is shown in a 1975 physics instructional movie. It claims that the experiment proves faster than light travel by the phase speed of the light.

Is this conclusion correct, based on the experiment?

The claim can be seen at about 3/5 and 7/8 ths in the movie, however you will really need to watch the whole thing if you want to understand the claim. dont worry, you will find it easy to watch and worth watching.

• The answer is almost certainly no, it is not traveling faster than light, unless you mean little exceptions like particles moving faster than light does in a certain material. But I don't think anyone will want to watch 35 minutes to find out what exactly is wrong. Can you direct us to the part where the claim or explanation is made? May 2, 2014 at 22:12
• This isn't the best forum for suggesting others watching neat videos. It's probably better to summarize the experiments & conclusions in your own words.
– BMS
May 2, 2014 at 22:27
• @YungHummmma: Actually, Alfred Leitner made some really well-done videos on topics like this and superfluidity. In this case, Leitner is correct in saying that phase velocities can exceed $c$. May 2, 2014 at 22:43
• It happens because glass has electronic transitions around that region, and the blue-end of the Lorentz curves dip the refractive index below 1, so the phase-velocity winds up being faster than light. It's for a similar reason why glass has increasing refractive index at wavelengths below the electronic transition frequency (which is why prisms work). May 2, 2014 at 23:17
• "its a very engaging 35 minutes. watch it." So, you want people to not only help you out but to invest more than half-an-hour or their time before they can even begin? And you can't even be bothered to describe the set up here? Really? May 3, 2014 at 1:00

Yes, it is entirely possible for a phase velocity to be faster than $c$, indeed to be arbitrarily fast.

The experiment shown is a very good demonstration of that. When the sodium vapor prism is turned on, one side of the resonance diffracts one way, the other the other way, which can only happen if one side has an index of refraction less than $1$. One subtlety is that you have to watch the image as the vapor turns on; it is technically possible for there to be a small resonance on top of a larger one, such that the "upward" (smaller $n$) deflected light in the pattern was still overall deflected downward, in which case all the frequencies you see had $n > 1$. This is not the case in this experiment, but even if it were all you would have to do to see $n < 1$ is look at even higher frequencies past the larger resonance.

One way to accommodate yourself to this notion is to imagine a long line of people doing "the wave" (raising their arms from time-to-time so as to make a wavelike pattern). If you give everyone instructions beforehand as to when exactly they should raise their arms, you can make a disturbance propagate down the line at any speed you wish. The key is that information was distributed in advance.

With light waves, we are often tacitly in the regime where the light has been on for some time and any initial transient effects have died away. In this way, information has had time to travel through the medium. If the electric field peaks at $x_0$ at time $t_0$, the wave can very well be set up such that the electric field at $x_0 + 1\ \mathrm{m}$ peaks before $t_0 + 3\ \mathrm{ns}$.

This effect is important in focusing X-ray telescopes, like Chandra or NuSTAR, since, as your video mentions, very high frequencies have phase velocities faster than $c$ in most materials and thus have indices of refraction less than $1$. Some familiar results from optics are reversed in these conditions: For instance, X-rays entering a material from vacuum refract away from the normal the the surface, and for small enough grazing angles there is total external reflection.

To preempt the inevitable followup, even group velocities can be faster than $c$, since group velocities are not necessarily the same as signal velocities, but that's a topic for another question.

• +1 Fantastic analogy with "the wave". I've never been able to explain this to others non-mathematically and this is something high schoolers can understand, extremely accurate (unlike most high school analogies) and moreover lets one see the transfer of information issue clearly " ..information was distributed in advance". May 4, 2014 at 1:04

The movie is correct that the phase velocity of light traveling through a material can be greater than c.

The phase velocity of a De Broglie wave can also be greater than c. In fact, for a particle at rest phase velocity is infinite for a De Broglie wave. See http://arxiv.org/ftp/arxiv/papers/0712/0712.0967.pdf

None of this implies that a signal or particle is travel faster than c.