Cerenkov (or Cherenkov) radiation is a bit of nineteenth century physics that stumbled into the twentieth. It could have been (and to some degree was, by the physicist Heaviside) predicted in the 1880s, but this effect was discovered by accident, perhaps by the Marie and Pierre Curie. It was studied in detail by Pavel Cerenkov in the 1930s, and explained a few years later by Ilya Frank and Igor Tamm. The three of them won the 1958 Nobel prize for their work.
What was the basic observation? Cerenkov studied the blue light appearing when radioactive objects (i.e. containing atoms whose nuclei decay to other nuclei by spitting off high-energy particles, including electrons and positrons [anti-electrons]) were placed near water and other transparent materials. We now know that any electrically charged particle, such as an electron, traveling with sufficiently high energy through water, air, or any other transparent medium, will give off bluish light. This light moves outward from the particle at a particular angle to the particle’s motion.
What’s going on? As Frank and Tamm understood, this is a photonic boom, quite analogous to the sonic boom that is created by a supersonic aircraft traveling through air faster than the speed of sound, or to the bow wave of a ship sailing through water. Light in a transparent medium will traverse that medium at a speed different from the speed of light in vacuum, because of the interactions between the light and the charged particles (electrons and atomic nuclei) that make up the medium. For instance, in water light travels about 25% slower than it does in empty space! And so it is easy for a high-energy electron to travel faster than light travels in water, while remaining slower than light’s speed in vacuum. If such a particle passes through water, it creates an electromagnetic shock wave, analogous to the shock wave that a supersonic jet aircraft makes in the density of air. And that shock wave radiates out from the particle, just as the sonic shock radiates from the airplane, carrying off energy in many different forms (wavelengths) of electromagnetic radiation, including visible light. There’s more energy created at the violet end of the rainbow than at the red end, and that’s why the light looks dominantly blue to our eyes and brains.
This type of radiation is enormously useful in particle physics, since it provides a terrific way to detect high-energy particles! Not only can we observe the presence of a high-energy charged particle by observing the light that it radiates, we can learn more by studying the light in detail. The precise pattern of the light can be used to determine (a) what path did the particle take across the medium, (b) how much energy was it carrying, and even (c) something about its mass (since electrons will scatter in the medium and make a jittery ring, whereas heavier particles will not do so.) A number of very important experiments, including ones that have won Nobel prizes, rely on this type of radiation, including some of those that have played a major role in studying the properties of neutrinos, e.g. SuperKamiokande.
Cerenkov radiation is also very useful in checking whether Einstein’s theory of relativity is an accurate description of nature. Cosmic rays, particles flying in from outer space (which often hit something in the atmosphere and make a large shower of particles that can be detected by observers on the ground), can in rare cases carry extraordinarily high energy, as much as 100 million times more energy than the protons at the Large Hadron Collider. These particles are (as far as we can tell) produced many light years away from earth, in powerful astronomical events such as supernovas. Now suppose the speed of light were not an ultimate speed limit, and those particles traveled faster than the speed of light in the vacuum of outer space. Then these ultra-high-energy particles would undergo Cerenkov radiation too. And because they have so far to travel, they would lose much of their energy to this radiation. It turns out this energy loss can be very rapid, and that these particles could not travel astronomical distances and keep their ultra-high-energy unless their speed remained extremely close to or below the speed of light.
In short, if cosmic rays at ultra-high-energies could move faster than the speed of light, then we shouldn’t observe any cosmic rays at ultra-high-energies at all, because they should all lose most of their energy long before they reach earth. But we do observe them. [Tiny loophole, I think: we are almost certain most of them are charged: their properties indicate they feel the strong nuclear force, and the only stable particles that could travel such distances are protons and more generally atomic nuclei, all of which have electric charge. If you open this loophole a bit, you would reduce the constraint somewhat, but it would still be pretty strong.] So therefore we can conclude: the ultra-high-energy cosmic rays (as well as any cosmic rays at lower energy) cannot exceed the speed of light by more than a very tiny number. Estimates from the late 1990s due to the very famous physicists Sidney Coleman and Sheldon Glashow (who were the first I am aware of to make this argument, but who might well have been preceded by other authors; please let me know if you are familiar with earlier papers) put this tiny number at about ten parts in a trillion trillion. The constraints from experiment have probably improved since then. [Will try to find updated numbers, and ones without any possible loopholes.]
Similarly, the simple fact that we observe high-energy electrons puts limits on their speed relative to that of light. The most recent claim I’ve read (still trying to figure out its source) is that observation of electrons with energies up to half a TeV imply that electrons cannot exceed the speed of light by more than a part per thousand trillion.