# Cerenkov radiation and the speed of light

Normally the photon wave-length is much larger than the atomic size, so in a solid the incident wave "feels" many atoms. Bound or free electrons oscillate and radiate in all directions. That is why there is a "reflected" wave when the incident wave encounters a medium. Inside the medium there are two kind of waves - the incident and the radiated one. If your medium is a metal with free electrons, the radiated wave becomes as strong as the incident one but with the opposite phase, so the resulting wave fades with depth (skin effect). Only the "reflected wave" remains.

If your medium is optically "transparent", then the internal resulting wave may propagate far in the medium but anyway it is a collective electromagnetic mode with its own properties.

Makes perfect sense (for any type of waves) but still doesn't account for the claim that the "speed of light" (as a photon) is lower in a higher-density medium.

Last edited:
Maybe this will help, or you may have already read it, it sounds pretty similar to your original post: From Wikipedia (that universally accepted repository of absolute truths):

At this point, this is more of a solid state problem, than a high energy problem. The high energy part fell off at the aurora.

Yes, that was the first thing I read, but just like I mentioned in my first post, what does the molecule get out of it ? In absorption and re-emission events you always have energy losses expressed in wavelength shifts, (not even to mention the subject emission band-width) so this means that the wavelength shift would depend on the path-length in the medium... Does this happen ?

Other relevant questions are :

1. Do measurements confirm that the wavelength of the Cerenkov radiation depends on the initial speed of the charged particle in the water ?

2. How does Cerenkov radiation behave in other media ?

Last edited:
In an attempt to shed more photons on the subject :

While relativity holds that the speed of light in a vacuum is a universal constant (c), the speed at which light propagates in a material may be significantly less than c. For example, the speed of the propagation of light in water is only 0.75c. Matter can be accelerated beyond this speed during nuclear reactions and in particle accelerators. Cherenkov radiation results when a charged particle, most commonly an electron, travels through a dielectric (electrically insulating) medium with a speed greater than that at which light propagates in the same medium.

Moreover, the velocity that must be exceeded is the phase velocity of light rather than the group velocity of light. The phase velocity can be altered dramatically by employing a periodic medium, and in that case one can even achieve Cherenkov radiation with no minimum particle velocity—a phenomenon known as the Smith-Purcell effect. In a more complex periodic medium, such as a photonic crystal, one can also obtain a variety of other anomalous Cherenkov effects, such as radiation in a backwards direction (whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity).[2]

As a charged particle travels, it disrupts the local electromagnetic field (EM) in its medium. Electrons in the atoms of the medium will be displaced and polarized by the passing EM field of a charged particle. Photons are emitted as an insulator's electrons restore themselves to equilibrium after the disruption has passed. (In a conductor, the EM disruption can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, when a disruption which travels faster than light is propagating through the medium, the photons constructively interfere and intensify the observed radiation.

It is important to note, however, that the speed at which the photons travel is always the same. That is, the speed of light, commonly designated as c, does not change. The light appears to travel more slowly while traversing a medium due to the frequent interactions of the photons with matter. This is similar to a train that, while moving, travels at a constant velocity. If such a train were to travel on a set of tracks with many stops it would appear to be moving more slowly overall; i.e., have a lower average velocity, despite having a constant higher velocity while moving.

Wiki is also using unclear terms at first, saying "the propagation speed of light in water" which is confusing but explained later on. However, there is still a description of photons absorbed and re-emitted without any wavelength-shift, which simply makes no sense at all.... Why would a water molecule absorb a photon, benefit nothing from it, and then re-emit it although it has other relaxation options through vibration and rotation ???

Can any of you confirm or refute the Wiki explanation ?

Last edited by a moderator:
At this point, and really, all points before, I'm just guessing. But since there is no real 100% transparent material, doesn't that suggest that at least some photons don't get re-radiated? I mean, a prism will heat up if you shine some light on it. But maybe the mechanism for re-radiation is the lowest energy solution the material has. When a photon strikes an atom, the atom could react mechanically and attempt to move, but for the frequencies that the material is transparent at, the modes of vibration for the atoms may not be energetically as accessible as the quantum mechanical process by which it re-radiates.

Of course - materials have something called "extinction coefficient", which determines the path-length a photon is most likely to travel before being absorbed.

When a molecule absorbs a photon - it would generally "prefer" to release whatever energy it can through rotation and vibration to reach vacuum-state. Only when an excited molecule "has no choice" it would emit a photon. So vibration and rotation are also forms of energy-release, and then if a photon is emitted - it would naturally not have the same wavelength as the photon that was initially absorbed, because the amount of energy "left" for the photon is smaller :

(energy of absorbed photon) = (energy dissipation in interaction) + (any other form of energy release) + (energy of emitted photon)

There is no such thing as perpetual motion (because the universe is expanding), so there are losses in ANY interaction where energy is exchanged. This is my problem with the Wiki explanation of the slower light-speed in a higher-density medium..... According to this principle, there would have to be a slight red-shift with each interaction of the photon with matter, the end result would be : an increasing red-shift with increasing material density and thickness.... To the best of my knowledge, observations do not confirm that.

1. Do measurements confirm that the wavelength of the Cerenkov radiation depends on the initial speed of the charged particle in the water ?

2. How does Cerenkov radiation behave in other media ?
Cerenkov radiation is very well understood. Charged particles at near the velocity of light in vacuum will radiate energy if their velocity exceeds the velocity of light in a dielectric. Even beta decay electrons from nuclear reactor fuel rods will turn the cooling water blue from Cerenkov radiation. See Schiff "Quantum Mechanics" pages 267-271 for a thorough derivation and discussion.

I don't have that book - will have to look it up online
The only books I have at home are "Introduction to Quantum Mechanics", and "Introduction to Electrodynamics" (Griffiths) but I think they have something about EM waves in matter.....

However - the big question is still unanswered : If we are not only talking about phase-speed - what really causes photons to slow down in water ?

:uhh:

Last edited:
malawi_glenn
Homework Helper
I don't have that book - will have to look it up online

However - the big question is still unanswered : If we are not only talking about phase-speed - what really causes photons to slow down in water ?

:uhh:

But haven't we settled that the phase speed is the "speed of light"?

I don't know if we can invoke photons here, Cerenkov radiation is done in the classical regime, in the quantum mechanical picture, the particle photon always travel at speed c. (as far as I know)

However - the big question is still unanswered : If we are not only talking about phase-speed - what really causes photons to slow down in water ?
First, it is useful to understand what happens in a gas. Classically, the electric field in the photon causes the electron cloud in a molecule (which is much lighter than the nucleus) to be displaced from the positively-charged nucleus. This polarizes the molecule and creates an electric dipole moment, and therefore a dielectric constant. The square root of the dielectric constant is just the index of refraction in a gas. The same thing happens in liquids and solids, except that the molecules are in close proximity, and the polarization of nearby molecules enhances the dipole moments of the molecules. This effect, the enhancement of the dielectric constant and index of refraction in liquids and solids, is the basis for both the Clausius-Mosotti equation and the Lorenz-Lorentz Law (no relation to the Lorentz Force Law).
This is all very simlar to the effect of capacitors in electric circuits. If an extra shunt capacitance (dielectric material) is inserted into a circuit with voltage V(wt), there is a phase delay due to the impedance 1/jwC = -j/wC. This delay effectively slows down the propagation in electrical circuits, e.g., coaxial transmission lines.

I don't have [Schiff's book "Quantum Mechanics"] - will have to look it up online.
There is an abbreviated discussion of Cerenkov Radiation (spelled Cherenkov) in Jackson "Quantum Electrodynamics" 3rd Edition, pgs 638-641. Some recent astronomical telescopes are based on viewing night sky Cerenkov radiation from cosmic rays. Because the index of refraction of air is about 1.00029, these cosmic rays are very fast.

malawi_glenn
Homework Helper
That is actually a great explanation Bob_S, the one with capacitors :-D

First, it is useful to understand what happens in a gas. Classically, the electric field in the photon causes the electron cloud in a molecule (which is much lighter than the nucleus) to be displaced from the positively-charged nucleus. This polarizes the molecule and creates an electric dipole moment, and therefore a dielectric constant. The square root of the dielectric constant is just the index of refraction in a gas. The same thing happens in liquids and solids, except that the molecules are in close proximity, and the polarization of nearby molecules enhances the dipole moments of the molecules. This effect, the enhancement of the dielectric constant and index of refraction in liquids and solids, is the basis for both the Clausius-Mosotti equation and the Lorenz-Lorentz Law (no relation to the Lorentz Force Law).
This is all very simlar to the effect of capacitors in electric circuits. If an extra shunt capacitance (dielectric material) is inserted into a circuit with voltage V(wt), there is a phase delay due to the impedance 1/jwC = -j/wC. This delay effectively slows down the propagation in electrical circuits, e.g., coaxial transmission lines.

Exactly. In presence of charges and currents that react to the incident field and create their own fields (sources), there is no free photons, the EMW propagation equations are different and this explains completely the difference in comparison with the vacuum EMF solutions.

jtbell
Mentor
what really causes photons to slow down in water ?

:uhh:

The individual photons do not slow down!

The individual photons do not slow down!

They do not slow down, they just propagate with smaller velocity.

They do not slow down, they just propagate with smaller velocity.

After re-reading this post, I think 337's question kinda boils down to this: When an atom in a transparent dielectric is struck by a photon, why does the atom feel compelled to re-radiate a photon of identical energy? Why does the atom not instead just vibrate from the absorbed energy, or re-radiate at a different frequency?

Ya DP - you're right. Actually if the photon is absorbed and then re-emitted with the same wavelength - I think it is in contradiction with thermodynamics (perpetual motion) and can not be correct. From what I know so far - the speed of light (so not phase-speed) is an absolute (and a limit) within the local reference frame.

The phase-speed being slower makes perfect sense, however - all descriptions refering to it still state "speed of light" which is not phase-speed... So I find it a bit vague....

** If the photon moves at C in space and then at C' in matter, there is a transition point in space-time (from the observer's reference point) so the photon has to "slow down" somewhere.

But ok - if what actually moves slower is phase and not light, this makes sense and would also be wavelength dependent. During the coming few days I hope I'll have the time to look it up in my books.

malawi_glenn
Homework Helper
Y
The phase-speed being slower makes perfect sense, however - all descriptions refering to it still state "speed of light" which is not phase-speed... So I find it a bit vague....

** If the photon moves at C in space and then at C' in matter, there is a transition point in space-time (from the observer's reference point) so the photon has to "slow down" somewhere.

But ok - if what actually moves slower is phase and not light, this makes sense and would also be wavelength dependent. During the coming few days I hope I'll have the time to look it up in my books.

Okay as I have pointed out many times now, why is phase speed NOT equal to speed of light? I have never found another definition of speed of light besides being the phase speed.

You are then mixing light speed with photon speed, you are mixing classical physics and quantum physics, of course one will encounter some paradoxes

All the paradoxes come from lack of knowledge and too much of imagination.

Look at electrodynamics of media: there is the external field E, there is polarization field P, there is induced field D, as well there H and B. Look at the induced current jE, etc. The EMF in a medium is the resulting field, not the incident one. Learn, learn, and learn.

Last edited:
Born2bwire
Gold Member
PD - what you say is correct - but it refers to phase-speed, not group-speed of light.

They are both the same thing in this case unless we are in a special kind of medium.

$$v_g = \frac{\partial \omega}{\partial k}$$
$$k = \omega \sqrt{\epsilon\mu}$$

Last edited:
Does this change with the light's wavelength? I.e., will gamma rays travel through water faster than visible light?

malawi_glenn
Homework Helper
Does this change with the light's wavelength? I.e., will gamma rays travel through water faster than visible light?

Yes, that is why one has chromatic abbreviation in lenses

Does this change with the light's wavelength? I.e., will gamma rays travel through water faster than visible light?

n depends on frequency, that's for sure. In the gamma ray region there is an imaginary part of n responsible for absorption mechanisms.

Okay as I have pointed out many times now, why is phase speed NOT equal to speed of light? I have never found another definition of speed of light besides being the phase speed.

You are then mixing light speed with photon speed, you are mixing classical physics and quantum physics, of course one will encounter some paradoxes

A photon remains the same object (if you can call it that) with the same properties no matter what theory you dress it up in, if 2 theories create paradoxes, that means at least one of them is wrong - this is why I prefer measuring to calculating.

You mentioned earlier that photons (refering to particle-wave) of shorter wavelengths would travel faster in a medium, so if that medium is very large and I'm watching a certain event - the image I'm seeing would gradually change color from blue to yellow to red as photons of longer wavelengths arrive later ? Does this happen and is it confirmed experimentally (unfortunately there is not too much info available online...) ?

This is a complex subject - so I suppose there must have been some experiments ? I'm going to have a more extensive search, but if any of you knows anything about experimental and measurement results - please share the knowledge.

Today 2009-07-13, I found this :

(Visible) light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. X-rays, on the other hand, usually have a phase velocity above c, as evidenced by total external reflection. In addition, light can also undergo scattering and absorption. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. An example would be in the core of the sun. Energy can take about a million years to reach the surface;[80]. However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibration between the radiation and the temperature. Thus, the time is how long it takes the energy to be transferred, not the photons themselves. Once in open space, a photon from the Sun takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased in a material is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitations of the matter (quasi-particles such as phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c.

Alternatively, photons may be viewed as always traveling at c, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed. [81] A light wave made up of these photons does travel slower than the speed of light. In this view the photons are "bare", and are scattered and phase shifted, while in the view of the preceding paragraph the photons are "dressed" by their interaction with matter, and move without scattering or phase shifting, but at a lower speed.

Light of different frequencies may travel through matter at different speeds; this is called dispersion. In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering.[82]

Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal (C20H28O, Figure at right), which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and co-workers. As shown here, the absorption provokes a cis-trans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.[83][84] Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration.

At source : http://en.wikipedia.org/wiki/Photon#Photons_in_matter"

If indeed Wiki is correct - this is the best explanation :) it seems like the "slower" speed of light in transparent matter is a superposition of the photon with the changes induced in the atoms, this also explains how the photon speed remains the same and only the phase-speed changes. If anyone knows of related experiments - please post.

Last edited by a moderator: