Is there an equivalent of the sonic boom for light?
A sonic boom is a shock wave which 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
It is thought that objects cannot travel faster
than c, the speed of light in vacuum
(see Relativity FAQ article on FTL travel.).
Furthermore there is no ether to act as a medium being pushed
aside like the air is pushed by an aircraft. Therefore
no light equivalent of the sonic boom can occur in vacuum.
In a medium such as water, the speed of light is
considerably less than the speed of light in vacuum.
In a medium with refractive index n the
velocity of light is vlight = c/n.
The refractive index is always greater than one* so
it is possible for a particle to travel through water
(nwater = 1.3)
or other media at a speed faster than the speed of light
in that media. When a charged particle does so, a
faint radiation is produced from the medium.
The charged particle
excites the water molecules which then return to their normal
state 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 which are in phase with
each other and can constructively interfere to form the
visible blue glow. The light propagates away in a cone
forward of the region where the interaction took place.
The half angle of the cone a can easily be
derived in terms of the velocity of the particle v
by looking at where wave fronts emitted from the track of
the particle constructively interfere.
cos(a) = vlight/v
This is analogous to the formula for the angle at which
a sonic boom propagates.
The 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 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 do not directly cause the
radiation. It actually comes from beta particles (fast
electrons) which are 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 (2 pi alpha) L sin2(a)/l2
alpha is the fine structure constant
equal to about 1/137. Notice that the refractive
index, and therefore the angle a also,
changes with wavelength l as
demonstrated when a prism produces a spectrum from
white light. This suppresses the rate at small
wavelengths in the ultraviolet and beyond.
Although Cherenkov radiation is indeed a light
equivalent of the sonic boom, there are also some
essential differences. The sonic shock wave is a
non-linear effect of sound propagation whereas light
wave propagation is always linear. The way the
waves are generated is also quite different.
* Strictly speeking the refractive
index is not always greater than one. Indeed, it is
almost always less than one for X-rays. This is because
the phase velocity of X-rays in a medium is faster
than light and the refractive index is the ratio of
phase velocities. The speed of photons is the group velocity
which is always slower than c (except when it isn't :-).
For simplicity we ignore the distinction in this article.
See the Relativity FAQ article on
faster than light (phase velocity)
for an explanation. [Thanks to Pieter Kuiper for pointing this