The duck's wake
This is the first translation I'm doing of one of my French science popularization blog posts.
When I was preparing my PhD thesis a few years ago, I was also doing weekly hour-long preparation sessions for groups of three students to train them for the engineering schools contests. In these sessions, each student is given a problem that he must solve on a chalkboard.
The students were often brilliant and showed a great physical sense.
One of my favorite problems was the following: "the duck's wake". The student was supposed to figure out both the questions and the answers. Great exercise if you ask me and very revealing of the student's qualities or lack thereof. Here are some of the things you could say on this subject...
Let's simplify and suppose that the duck is a dimensionless point. When it moves on the water surface, it casts waves. Let's imagine these circular waves travel at an approximately constant speed (in reality they don't, more on that later). There are two possibilities: the duck can move slower than the waves, in which case the first wave will always be ahead of all the others, or the duck is "supersonic" and the waves will form a triangular wake. The first question you can ask yourself is to determine the relation between the angle of the wake and the speed of the duck. As could be expected, the faster the duck, the sharper the angle. The angle would be 180 degrees if the duck had the exact speed of the waves: the wavefront would be a line perpendicular to the direction of the duck and it would move with it.
The triangle that the wave's enveloppe creates is really a shockwave similar to the one that a supersonic plane emits. The supersonic bang is just the shockwave. Contrary to popular belief, the bang is not emitted by the plane as it passes the speed of sound but is continually emitted as long as it travels faster than sound. The thing is that the places where the bang can be heard move at the speed of sound. What you hear when a supersonic plane flies by is thus, to summarize: silence as long as you're outside the sound cone, a bang as you enter it, and the noise of the plane after that.
The second question you could ask is the repartition of energy in the shockwave. The result of the calculation is really surprising: the energy diverges and becomes infinite at the tip of the cone. This means that you would need infinite energy to go above the speed of sound. I suppose that's one reason why people used to think it was impossible. Of course, it's not really infinite in practice, just very expensive because no plane or duck is a point.
So now we know that any object that travels faster than the waves it emits emits these waves as a shockwave that packs most of its energy in its enveloppe. This phenomenon is commonly observed for surface waves (a duck's or a boat's wake) as well as for sound (supersonic planes). Now can it be observed for lightwaves?
A priori, no physical object can travel faster than the speed of light in a vacuum, so this phenomenon looks like something that would be out of the question. Nevertheless, light doesn't always travel in a vacuum. In any medium, light travels slower than the speed of light in a vacuum. It is thus possible to travel faster than light in a medium. The shockwave that the theory predicts does exist and is a commonly observed phenomenon called Cerenkov radiation. It is this radiation that is used in some neutrino detection devices.
Neutrinos are subtle particles. They have a very low mass (it's only recently that we've discovered thay have one), they don't have an electrical charge, don't participate in the strong force and the only way they interact with anything is through improbable weak interactions (gravitation can be neglected for detection purposes, the neutrino masses being so small). Despite their being very common particles in the universe (billions of neutrinos go through us every second), as they rarely interact with ordinary matter that is made from electrons, protons and neutrons, their detection is very difficult. Some detectors use the Cerenkov effect. When a neutrino interacts inside the detector, a particle such as an electron can be emitted with a faster than light speed. This particle emits light while decelerating (any charged particle accelerating emits electromagnetic waves). The resulting shockwave is then measured by detectors, from which we can deduce the trajectory of the charged particle, which gives us the direction of the neutrino that created it.
This is how you can start from the duck's wake and end up discussing the detection of neutrinos. That's just one illustration of the extraordinary explicative power of physics...
UPDATE: comments pointed out that the angle of the wake of the duck (or of a boat, or of whatever moves fast enough) does not depend on the speed of the object, as the good Lord Kelvin showed. It is constant at approximately 39 degrees. This is because the speed of the waves depends on the wavelength in such a subtle way as to cancel the dispersion that a single wavelength wave would show. Our simplistic calculation is still perfectly valid for cases where such dispersion doesn't exist, such as Çerenkov radiation.