Cerenkov radiation and the speed of light

[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 :

Another of your statements is "Light will slow down when entering an
optically dense medium." Actually this is not quite true. While it
is true that we measure a lower AVERAGE speed of the light through a
medium, the propagation of light through the medium, between atoms, is
actually at the normal vacuum speed of light, c. What happens is that
the light moves at speed c between atoms, but photons are "absorbed"
by the atoms. By "absorption" I mean that the energy of the
photon causes an electron of the atom to be kicked to a higher energy
level, and the photon ceases to exist. Then, after a very small time
delay, the electron goes back to its original (usually ground state)
energy and "emits" a photon of the same energy (and thus same
frequency and thus same wavelength) as the original "absorbed" photon.
(In fluorescent materials the energy of the photon is downshifted, but
I am talking here of "elastic", or non-energy shifting, absorptions.)
It is this very small time delay which makes us measure the average
"speed of light" through the medium as slower than the vacuum speed of
light. But, again, between atoms the light does travel at the speed
c.

At source : http://www.madsci.org/posts/archives/1998-05/893732585.Ph.r.html"

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...

 

[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.

 

[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...

 

[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 :-)

 

[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 !

 

[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)

 

[Bob_for_short]

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

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.

 

[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...

 

[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 :-/

 

[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) ?

 

[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.. :/

 

[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.

 

[malawi_glenn]

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

Cheers

 

[337]

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

Cheers

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.

 

[Naty1]

Here is the Physicsforum FAQ

Do Photons Move Slower in a Solid Medium?

Contributed by ZapperZ. Edited and corrected by Gokul43201 and inha

This question appears often because it has been shown that in a normal, dispersive solid such as glass, the speed of light is slower than it is in vacuum. This FAQ will strictly deal with that scenario only and will not address light transport in anomalous medium, atomic vapor, metals, etc., and will only consider light within the visible range.

The process of describing light transport via the quantum mechanical description isn't trivial. The use of photons to explain such process involves the understanding of not just the properties of photons, but also the quantum mechanical properties of the material itself (something one learns in Solid State Physics). So this explanation will attempt to only provide a very general and rough idea of the process.

A common explanation that has been provided is that a photon moving through the material still moves at the speed of c, but when it encounters the atom of the material, it is absorbed by the atom via an atomic transition. After a very slight delay, a photon is then re-emitted. This explanation is incorrect and inconsistent with empirical observations. If this is what actually occurs, then the absorption spectrum will be discrete because atoms have only discrete energy states. Yet, in glass for example, we see almost the whole visible spectrum being transmitted with no discrete disruption in the measured speed. In fact, the index of refraction (which reflects the speed of light through that medium) varies continuously, rather than abruptly, with the frequency of light.

Secondly, if that assertion is true, then the index of refraction would ONLY depend on the type of atom in the material, and nothing else, since the atom is responsible for the absorption of the photon. Again, if this is true, then we see a problem when we apply this to carbon, let's say. The index of refraction of graphite and diamond are different from each other. Yet, both are made up of carbon atoms. In fact, if we look at graphite alone, the index of refraction is different along different crystal directions. Obviously, materials with identical atoms can have different index of refraction. So it points to the evidence that it may have nothing to do with an "atomic transition".

When atoms and molecules form a solid, they start to lose most of their individual identity and form a "collective behavior" with other atoms. It is as the result of this collective behavior that one obtains a metal, insulator, semiconductor, etc. Almost all of the properties of solids that we are familiar with are the results of the collective properties of the solid as a whole, not the properties of the individual atoms. The same applies to how a photon moves through a solid.

A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

Moral of the story: the properties of a solid that we are familiar with have more to do with the "collective" behavior of a large number of atoms interacting with each other. In most cases, these do not reflect the properties of the individual, isolated atoms.

 

[malawi_glenn]

yeah but we want formulas and references

 

[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...

 

[Bob_for_short]

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

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.

 

[Bob_for_short]

...I'm not certain this is possible for any photo-molecular event to emit a photon with the same wavelength as the absorbed one. Besides - this seems to back the claim and the group-speed of light is actually slower in a higher-density medium...

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.

 

[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.

 

[malawi_glenn]

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 $c = 1/\sqrt{\epsilon_{o}\mu_{o}}$

We have already discussed that in this particular thread! :D

 

[Bob_for_short]

...So, the speed in any medium would be a new relation, taking into account the change in the constants? Like, $c_{r} = 1/\sqrt{\epsilon_{r}\mu_{r}}$

Yes, it is so. In a medium those constants can depend on the EMW frequency and be complex in a general case.

 

[DecayProduct]

We have already discussed that in this particular thread! :D

Indeed, it was you I was referencing when I said it had been stated. Like I said, I'm by no means an expert on the subject, and maybe that's why I don't find it confusing.

But it seems pretty straight forward to me why the speed of light changes inside of a dielectric medium. The new "vacuum" has become more viscous with the interactions of each atom within the medium, changing the fundamental relationship between the electric and magnetic constants. Maybe it's like sliding across smooth ice, as compared to sliding across carpet?

 

[337]

PD - what you say is correct - but it refers to phase-speed, not group-speed of light.

 

[DecayProduct]

PD - what you say is correct - but it refers to phase-speed, not group-speed of light.

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

When light enters materials its energy is absorbed. In the case of transparent materials (dielectrics) this energy is quickly re-radiated. However, this absorption and re-radiation introduces a delay. As light propagates through dielectric material it undergoes continuous absorption and re-radiation. Therefore when the speed of light in a medium is said to be less than c, this should be read as the speed of energy propagation at the macroscopic level. At an atomic level, electromagnetic waves always travel at c in the empty space between atoms. Two factors influence this slowing; stronger absorption leading to shorter path length between each re-radiation cycle and longer delays. The slowing is therefore the product of these two factors. This reduction in speed is also responsible for bending of light at an interface between two materials with different refractive indices, a phenomenon known as refraction.

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.

 

[337]

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.

 

[337]

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 ?

 

[337]

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.

From source : http://en.wikipedia.org/wiki/%C4%8Cerenkov_radiation"

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 ?

 

[DecayProduct]

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.

 

[337]

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.

 

[Bob S]

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.

 

[337]

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 ?

 

[malawi_glenn]

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 ?

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)

 

[Bob S]

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 similar 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.

 

[Bob S]

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.