[Physics FAQ] - [Copyright]

Updated 1998.
Original by Philip Gibbs 1997.

Is there an equivalent of the sonic boom for light?

A sonic boom is a shock wave that propagates from an aircraft or other object which is going faster than sound through the air (or other medium).  In subsonic flight air is deflected smoothly around the wings.  In supersonic flight this cannot happen, because the effect of the aircraft wings pushing the air ahead cannot travel faster than sound.  The result is a sudden pressure change or shock wave which propagates away from the aircraft in a cone at the speed of sound.

Objects cannot travel faster than c, the speed of light in vacuum (see the FAQ article on faster-than-light travel).  But for light there is no ether to act as a medium being pushed aside like the air that is pushed by an aircraft.  The result is that there is no equivalent of a sonic boom for light moving in a vacuum.

But light needn't always move in a vacuum.  The phase velocity of light in a medium with refractive index n is vlight = c/n.  (See the FAQ article on faster-than-light travel for an explanation of phase velocity.)  For example, water has a refractive index of about 1.3, so the speed of light in water is considerably less than the speed of light in vacuum.  Furthermore, it's in fact possible for a particle to move through a medium such as water at a speed faster than the speed of light in that medium—though not faster than the speed of light in a vacuum.

When a charged particle does move through a medium at a speed higher than the speed of light in that medium, a faint radiation is produced by the medium.  In water, for example, the charged particle excites the water molecules, which then return to their normal state by emitting photons of blue light.  Because the particle is moving faster than the speed of light in water, it can trigger a cascade of photons that are in phase with each other and can interfere constructively to form a visible blue glow.  The light propagates in a cone forward of the region where the interaction took place.  An expression for the cone's half angle θ can easily be derived in terms of the speed v of the particle, by examining where wave fronts emitted from the track of the particle interfere constructively:

             cos θ = vlight/ v .

This is analogous to the formula for the angle at which a sonic boom propagates.

This effect, known as Cherenkov radiation, was observed as a faint blue glow by Pavel Cherenkov in 1934 when he was asked to look at the effects of radioactivity in liquids.  The explanation for the light was provided by Ilya Franc and Igor Tamm.  It is possible to detect the Cherenkov radiation as it forms circles on a surface, and it can be used to measure the speed and direction the particle was travelling in.  It is therefore a very useful means of studying the products of particle collisions and cosmic rays.

The blue glow in the water surrounding nuclear reactors is Cherenkov radiation.  The water is there to stop neutrons; but neutrons are uncharged and so do not themselves directly cause the radiation.  The Cherenkov radiation actually comes from beta particles (fast electrons) emitted by fission products.  For most media blue light predominates over longer wavelengths of light, because the number of quanta emitted as Cherenkov radiation in a wavelength interval dl at wavelength l over a path length L is given by

             dl  2πα  L sin2θ/ l 2,

where α is the fine structure constant, equal to about 1/137.  Notice that the refractive index, and therefore the angle θ, changes with wavelength l as demonstrated when a prism produces a spectrum from white light.  This suppresses the rate at the small wavelengths of ultraviolet and beyond.

Although Cherenkov radiation is indeed an equivalent of the sonic boom for light, there are some essential differences between it and a real sonic boom (for sound).  For sound, the shock wave is a non-linear effect of sound propagation, whereas for light, wave propagation is always linear.  The means by which the waves are generated also differ for sound and for light.

A Side Note on the Refractive Index

Strictly speaking, the refractive index of a medium need not be greater than one.  Indeed, it is almost always less than one for X rays, which means that the phase velocity of X rays in a medium is greater than c (since the refractive index is the ratio of phase velocity in vacuum (c) to phase velocity in the medium).  The speed of the X ray photons is their group velocity, which will be less than c.  For simplicity, we have ignored the distinction in velocities in this article.  See the Relativity FAQ article on faster than light (phase velocity) for an explanation.  (Thanks to Pieter Kuiper for pointing this out.)