# How can muons travel faster than light through ice?

When a neutrino traveling through ice hits and interacts with an oxygen atom, muons are created.

Cherenkov radiation can be created when muons travel through ice faster than light and create a coherent shock wave with some high frequent radiation.

As a charged particle (e.g. muons) travels, it disrupts the local electromagnetic field in its medium. In particular, the medium becomes electrically polarized by the particle's electric field.

But why can muons travel faster than light through ice while it probably has more interaction with the atoms because of his mass of 105,66 MeV/c² and charge?

• If you like this question you may also enjoy reading this and this Phys.SE posts. Mar 29, 2016 at 20:39
• Put simply: muons have mass, so they can't decelerate instantaneously like photons can. So if a relativistic muon suddenly hits a block of ice, it can't avoid travelling faster than local (ice-based) light speed, at least until it has time to decelerate. Mar 29, 2016 at 22:58

The first thing to understand is that light moves slower in a material medium than in a vacuum. The ratio of the speed in vacuum to the speed in the material is called the "index of refraction" of the material.

Only the speed of light in vacuum represents the cosmic speed limit.

The muons don't move faster than "the speed of light", they move faster than "the speed of light in ice" which is allowed.

Secondly the $106 \,\mathrm{MeV/c^2}$ is not the muon's charge but its mass. A muon's charge is the same as that of an electron: $e = 1.602 \times 10^{-19}\,\mathrm{C}$.

• +1 Good & valid points, but perhaps an exploration as to what it is that slows down light in ice and why that doesn't affect muons equally would address the original question more directly? Mar 29, 2016 at 17:27
• This sentence most directly answers the OP's question: "Only the speed of light in vacuum represent the cosmic speed limit." Mar 29, 2016 at 21:16
• I don't see that this addresses the OP's question at all. They are not asking why the speed of light in a medium isn't the ultimate speed limit in that medium. They are asking why muons, in particular, are not slowed down more than light is by electromagnetic interactions.
– zwol
Mar 30, 2016 at 20:07

It's the muon's mass that decreases the effects of electrical interactions and lets them penetrate far into dense matter. Also, muons decay so rapidly that if they are not moving at relativistic speeds, they don't last long enough to have much of an effect on anything. So, a muon has tremendous momentum relative to photons or electrons.

Muons are identical to electrons, including their charge and "size" but have 1,000 times the mass. With a huge mass moving at relativistic speeds, they shrug of electrical charge or magnetic interactions that would stop an electron or photon.

Image having two ping pong balls, one full of air with just the mass of the plastic shell, the second filled with lead. You target a stand of cane or reeds with both balls. The air filled you toss with your hand. The lead filled, you fire out of cannon. Which will travel farther through the impeding stalks?

Light/photons moving though any medium except vacuum interacts with the electrical and magnetic fields of the medium as well as being absorbed and then reemitted. Since photons have no mass, they are easily influenced and retarded by ambient electrical and magnetic fields in ordinary matter. Muons have mass, a lot of it by atomic particle standards, and they always move at near the speed of light in a vacuum, regardless of the medium they form in or transit.

Cherenkov radiation can be thought of as a kind of shockwave generated as the muon or other particle compresses the ambient electrical and magnetic fields in a medium until they form photons. It's been analogized to the visible shockwave created by aircraft breaking the sound barrier in humid air. The compression cause the ambient moisture to condense into a visible fog.

• Nit. Muon are "only" about 200 times the mass of an electron, not 1000 times. Mar 30, 2016 at 1:40

The index of refraction is an electronic property, directly dependent upon the electric permittivity of the media, and ultimately depends upon the free electron density. As the energy of the photon increases, the interactions with the electrons decrease, so that x-rays are barely retarded at all, though they are scattered by the electrons of the atoms. Of course, the Cerenkov radiation is in the optical range, and so is slowed by the ice by the refractive index.

The net effect is that light travels at c/n in the ice; for ice n=1.3, so for light in ice it travels about 3/4 c.

The muons are created inside the ice when a high energy neutrino is absorbed. The muons which are traveling faster than 3/4 c are the ones which create the Cerenkov radiation; the slower ones will just create ion trails, and not the optical shock waves.

All of the muons interact with charged particles, leading to your question of why they travel faster than light in ice, leading to Cerenkov radiation. Because the ones which generate Cerenkov radiation are traveling at relativistic speeds, this reduces the effective cross section for scattering. They will barely see the electron clouds, but instead scatter of the nucleus.

For those curious as to why light slows down in the ice, I've repeated my previous answer to this question:

Transparent materials (glass, air) transmit images; if the image is distorted or indistinct, we know that the material is altering the coherence of the optical information. That is, what started out at the beginning has not arrived all at the same time. With enough distortion the image is completely lost.

So what is required for a transparent medium to successfully transmit an image? Since light is a physical wave, the transparent medium must preserve the coherence of the phase information of the light. In a typical glass the phase front is slightly slowed while traveling through the glass; this slowing is encoded in the index of refraction, $n = c/v$.

If the material absorbs some frequencies, the material will appear to be colored; a photon that is absorbed (depending on the energy level structure) can be re-emitted, but this will be at (a) a random time later, and (b) in a random direction. No image for this color! There is an exception: stimulated emission, which is the key to building a laser. But this is not how images are transmitted in a passive material.

The process that transmits images can be summed up as Coherent Forward Scattering: Coherent, because otherwise the image integrity is reduced; Forward, because the image is transmitted in this direction, through the material; and Scattering, the remaining available generalized mechanism at the quantum level.

The result is quite like the Huyghen's wavelet model for light transmission: the photons are the waves that are scattered coherently, and because it is coherent, they are able to interfere both constructively and destructively to maintain the coherence of the overall phase front.

It is the interference that slows the phase velocity through through the material; the individual photons continue to "move" at the speed of light, $c$, but the effective motion of the phase front is slowed.

Richard Feynman devotes some time to this in his lectures on QED: The Strange Theory of Light and Matter

• "muons are also traveling at relativistic speeds" ... and the light isn't? - That is, it apparently isn't just the speed of travel which causes the difference in the magnitude of scattering between muons and photons, so what is the cause?
– R.M.
Mar 29, 2016 at 20:14
• @R.M.: I've clarified this for you. Mar 30, 2016 at 20:33
• Thanks, but I still think you're omitting why the muons (apparently) aren't subject to the same considerations that slow the photons. If photons interact with the ice and are slowed, wouldn't muons also likewise interact and also get slowed? What's the key difference between photons and muons which slows the "top speed" for light, but not for muons?
– R.M.
Mar 30, 2016 at 20:53
• @R.M.: high energy photons (x-rays, gamma rays) travel much faster through ice or glass (or steel) than their low-energy counterparts such as Cerenkov radiation. The effective index of refraction for x-rays is very close to 1; the same will be true for these relativistic muons. Mar 30, 2016 at 21:46