# Cerenkov radiation and the speed of light

1. Jul 8, 2009

### 337

While reading up on Cerenkov radiation, the first question that came to mind was "Why would light travel slower in a higher density medium (water) ?" I found the following explanation :

Is this correct ? I know that the vast majority of photon absorption-emission events result in an emitted photon with a longer wavelength than the absorbed one - and within the emission band-widths of the absorbing molecule. What exactly is the difference between the 2 absorption types described here (the none wavelength-shifting, and the wavelength-shifting) ?

Another thing is - in any energetic interaction, all the participants "get something" for their trouble, if a molecule absorbs and emits the same wavelength of photon, what does the molecule get out of this "deal" ? (I also think that theoretically, the wavelength of the photon can not be exactly the same, the laws of thermodynamics ensure some losses).

Can the Cerenkov radiation be compared to aurora boralis, or any other photonic emission resulting from charged particles traveling through a magnetic field ?

And finally : As far as we know at this stage, the speed of light is an absolute and a limit within any local reference frame. When a photon looses energy, the energy loss expresses itself in a wavelength shift, not a lower speed. So if the explanation given above for the lower speed of light in water is not correct - what is ? I can not imagine anything other than higher dimensions causing this....

Last edited by a moderator: May 4, 2017
2. Jul 8, 2009

### Bob_for_short

"Absorption and emission" explanation is wrong. In a transparent medium bound electrons do participate but they oscillate and radiate so no delay occurs. The resulting EMF has different velocity due to this collective effect.

3. Jul 8, 2009

### 337

From what you're saying - I understand that the cause of the Cerenkov radiation is the interaction is between the magnetic field generated by the (faster than light) moving charged-particle, and bound electrons in the medium (which has equivalence to aurora boralis, only here the magnetic field is moving instead of the charged particles).

However, this does not explain WHY the speed of light in a higher-density medium (like water) is lower.

Normally photon (EM) -photon interaction would result in interference and wavelength shift - but not a lower speed......

4. Jul 8, 2009

### malawi_glenn

The speed of light in medium is related to the permittivity and permeability of a material, this is basic electrodynamics, look at the wave-equation :-)

5. Jul 8, 2009

### 337

In the case of permittivity and permeability, I would expect the outcome to be a change in polarization or phase, not a lower speed of light !!

6. Jul 8, 2009

### malawi_glenn

But have you looked at the wave equation? the speed is 1/sqrt(epsilon * mu)

(This is not even particle physics, but classical physics)

7. Jul 8, 2009

### Bob_for_short

But in a medium there is no just photon-EM "interaction" (superposition you mean). In a medium there are also currents and charges so the resulting field may have different dispersion law including velocity change. In a transparency "window" the medium EM properties are described with Re(n)>1, Im(n)=0. This gives v<c with no fading in space.

Last edited: Jul 8, 2009
8. Jul 8, 2009

### 337

Glenn :

If you mean < Epsilon * Mu = 1/(V^2) > it indicates phase velocity of EM radiation and although under certain circumstances it may exceed the speed of light in a vacuum, it is not the "group velocity" and does not mean energy or information are traveling faster than light.

Besides - the phase velocity is frequency dependent, so if that were correct, the absolute speed of light would be frequency dependent, which it is obviously not.....

So also here - no explanation as to why the speed of light is lower in higher density media....

9. Jul 8, 2009

### malawi_glenn

but when we talk about "speed of light" we speak about the phase velocity right? It was a loong time ago since I had electrodynamics ;-)

You should also mention if you are after the "photon" i.e. light on "atomic level" or "light" as "macroscopic" property. Cherenkov radiation deals with the macroscopic, hence this is classical mechanics, not particle physics :-/

10. Jul 8, 2009

### 337

I read the description of "Cerenkov radiation" which simply said "speed of light", that is something very different to phase-speed, then I ran into the description I quoted in my first post and also there the term phase-speed is not mentioned. It just didn't square with common sense :

When I look at a prism it is obvious that photons (VIS range) have different breaking indices depending on their wavelength (result of change is phase speed), however - the "group speed" of any of those photons has to be identical and unchanging within the local reference frame.

Additionally - on an astronomical scale, when observing distant objects, photons of various wavelengths emitted by a single event arrive here together (for detection), if phase-speed was the same as group-speed, I would expect photons of different wavelengths to arrive at different times (since space is not the vacuum we once thought it was and the great distances make for a cumulative effect). This is a great relief

Anyway, so the speed of light is the same also in water (within a local reference frame), Cerenkov radiation is the result of charged particles released into water at speads higher than the phase-speed of light in water, is this not equivalent to aurora boralis (northern lights) ?

11. Jul 8, 2009

### malawi_glenn

aurora boralis is ionization of atoms in the atmosphere due to solar wind particles.

I just recall that when we talk about speed of light, we mean the phase-velocity, and that was also written in the wiki article on speed of light, so I might have rembered correctly, but I am a novice in classical electrodynamics.. :/

12. Jul 8, 2009

### Bob_for_short

I think you have to read some opto-electronics sources (optical wave-guides) - the things like the phase and the group velocities are well considered in them (as well as different mechanisms of the information losses).

Concerning the light velocity, you should know that in presence of charges and currents (bound or free) the light (EMW) velocity is not obliged to be c: the EMV equations are not so simple, neither their solutions.

Last edited: Jul 8, 2009
13. Jul 8, 2009

### malawi_glenn

hey Bob! Can you please submit some of these "sources"? I want to learn these things (again).

Cheers

14. Jul 8, 2009

### 337

Second that. Because to the best of my current understanding only properties of space-time and mass-energy can cause changes in C (local)..... If there is more - I absolutely want to know.

15. Jul 8, 2009

### Naty1

Here is the Physicsforum FAQ

16. Jul 8, 2009

### malawi_glenn

yeah but we want formulas and references

17. Jul 8, 2009

### 337

Ok : now I finally had time to read the whole thing. The lattice behavior makes more sense, however - as with any photo-molecular event - I would still expect the photon (after having been "rejected" by the lattice) to have a slightly longer wavelength due to energy losses, and since the energy losses depend on the path-length of the photon in the lattice, the wavelength shift would depend on it too, but I don't think this is the case......

Last edited: Jul 9, 2009
18. Jul 8, 2009

### Bob_for_short

No, unfortunately, I cannot. At least, I have myself to brows Internet to find something.
I know this subject just because I learned it on purpose in 2001 to find a work in this field.
Optical waveguides, fibers, etc. cover this subject well. Try to find something available online.

19. Jul 8, 2009

### Bob_for_short

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.

20. Jul 8, 2009

### DecayProduct

I myself am still struggling with the fundamentals of college algebra and calculus, so forgive me if I am totally off base here.

The speed of light in the vacuum is a relation between the permittivity of the vacuum, and the permeability of the vacuum. It's already been stated, but the relation is $c_{o} = 1/\sqrt{\epsilon_{o}\mu_{o}}$

Passing through matter, aren't the constants altered by the presence of the mater, resulting in a different relative permittivity and permeability? So, the speed in any medium would be a new relation, taking into account the change in the constants? Like, $c_{r} = 1/\sqrt{\epsilon_{r}\mu_{r}}$

P.S.: I also don't think the auroras are a result of cerenkov radiation, but are due to excited gas molecules emitting light, similar to a neon sign.

Last edited: Jul 8, 2009