# Speed faster than light speed in a medium

• I
In summary, in relativistic many-body physics, particles can travel faster than the speed of light in a material if they have a high enough energy.f

hello everyone
I read this text in physics book:
"Another example is the so-called Cerenkov radiation, which consists of light waves emitted by charged particles that move through a medium
with a speed greater than the phase speed of light in that medium. The blue glow of the water that often surrounds the core of a nuclear reactor is one type of Cerenkov radiation"
Is it really speed faster than light for particles?!

hello everyone
I read this text in physics book:
"Another example is the so-called Cerenkov radiation, which consists of light waves emitted by charged particles that move through a medium
with a speed greater than the phase speed of light in that medium. The blue glow of the water that often surrounds the core of a nuclear reactor is one type of Cerenkov radiation"
Is it really speed faster than light for particles?!
The short answer to your question is that the electrons move faster than the speed of light in water, not faster than the speed of light in a vacuum. When light passes through any material it slows down so, technically an object can move faster than the light does. I will leave any other details about Cherenkov radiation to the other members here.

-Dan

• Orodruin and vanhees71
with a speed greater than the phase speed of light in that medium
Re-emphasized for the more relevant part of the statement. As mentioned above, the speed of light in a medium is not the same as that in vacuum. It is described by the index of refraction, which is around 1.3 for water and 1.5 for glass. This mesns that the speed of light in water is around 3c/4 and that in glass is around 2c/3, where c is the soeed of light in vacuum. These are the speeds that a charged particle would have to surpass to produce Cherenkov radiation.

A particle traveling at 3c/4 has a kinetic energy of around 50% of its mass, ie, ca 250 keV for an electron.

• topsquark
Are the formulas of relativity not applicable in the material environment or are they only in vacuum?

Are the formulas of relativity not applicable in the material environment or are they only in vacuum?
##c## is the speed of light in a vacuum, which is the invariant (and maximum) speed. ##\frac c n## is the speed of light in a material of refractive index ##n##. That is neither invariant nor the maximum speed.

• topsquark
Are the formulas of relativity not applicable in the material environment or are they only in vacuum?
The velocity you can never exceed is ##c##, wherever you are, and that is the quantity relativity uses. Light doesn't always travel at ##c##, though, for example because it slows down in a medium. In a medium you can go faster than light, but never faster than ##c##.

The "you can't go faster than light" rule is sloppy terminology, I'm afraid. The correct version is that "you can't go faster than the speed at which light travels in a vacuum (whether you're in a vacuum or not)".

• mfb, topsquark and malawi_glenn
Are the formulas of relativity not applicable in the material environment or are they only in vacuum?
Yes, they are applicable, you just need to apply them correctly. As pointed out, they use 'c', which is the speed of light in a vacuum.
So for example, if you wanted to use the addition of velocities formula for light moving through a material, which is, in turn, moving relative to you, the basic form is (u+v)/(1+uv/c^2)
If u is the velocity of the medium, then you would used c/n for v.

• topsquark
Yes, they are applicable, you just need to apply them correctly. As pointed out, they use 'c', which is the speed of light in a vacuum.
So for example, if you wanted to use the addition of velocities formula for light moving through a material, which is, in turn, moving relative to you, the basic form is (u+v)/(1+uv/c^2)
If u is the velocity of the medium, then you would used c/n for v.
It is worth pointing out that this is directly related to Fizeau’s measurements of the speed of light in a moving medium.

• topsquark
##c## is the speed of light in a vacuum, which is the invariant (and maximum) speed. ##\frac c n## is the speed of light in a material of refractive index ##n##. That is neither invariant nor the maximum speed.
##c/n## is the phase velocity of the light in the medium as measured in the rest frame of this medium. As such it's a scalar quantity. There's been a lot of confusion concerning relativisitic many-body physics, because in the beginning the physicists didn't get the relativistic description in the most useful and mathematically simplest form. The key to solve these problems is to define all medium-related quantities in the (local) rest frame of the medium. A good starting point is van Kampen's paper on relativistic thermodynamics:

N. G. van Kampen, Relativistic thermodynamics of moving
systems, Phys. Rev. 173, 295 (1968),
https://doi.org/10.1103/PhysRev.173.295

• topsquark