Cerenkov radiation and the speed of light

[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.

 

[malawi_glenn]

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

 

[Bob_for_short]

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.

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]

what really causes photons to slow down in water ?

The individual photons do not slow down!

 

[Bob_for_short]

The individual photons do not slow down!

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

 

[DecayProduct]

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?

 

[337]

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 referring 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]

Y
The phase-speed being slower makes perfect sense, however - all descriptions referring 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

 

[Bob_for_short]

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 j=σE, etc. The EMF in a medium is the resulting field, not the incident one. Learn, learn, and learn.

 

[Born2bwire]

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}

 

[Raap]

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

 

[malawi_glenn]

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

 

[Bob_for_short]

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.

 

[337]

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.