# Moving faster than the speed of light

Saketh
Imagine a material in which light travels slowly. (I don't know much about quantum mechanics, but I think this is a Bose-Einstein condensate.) From my knowledge of electromagnetic radiation, this material would have a very high index of refraction.

I have some questions:
1. Is classical electromagnetism (like refractive indices) sufficient to model a material in which light travels at, say, 17 meters per second? (I read about this somewhere)
2. If not, at what level of QM will I be able to model such materials?

Back to the story. Imagine that you have a slab of this light-slowing material on a table, with an extremely powerful loaded rifle aimed at the slab. You fire the rifle, and the bullet burrows into the slab with enough energy to maintain a speed always greater than 17 meters per second. This means that within the slab, the bullet is traveling faster than the speed of light.

More questions:
1. Is this possible?
2. If not, why not?
3. If so, what would happen?

Thanks. This situation just popped into my head, and I wanted to know how I could model it with physics.

Crosson
What happens is that we get the optical parallel of a sonic boom, and this is known as Cherenkov radiation. This phenomenon can be at least partially explained without QM, but of course QM effects play a role in the full description.

P.S. I am sure you could have chosen a more descriptive, less sensational/controversial, title for this thread.

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Saketh
What happens is that we get the optical parallel of a sonic boom, and this is known as Cherenkov radiation. This phenomenon can be at least partially explained without QM, but of course QM effects play a role in the full description.

Ah ha! Then my intuition was correct. I wasn't sure what you call a light sonic boom, but now I know!

Would this light be ultraviolet/purple?

P.S. I am sure you could have chosen a more descriptive, less sensational/controversial, title for this thread.

Gold Member
Would this light be ultraviolet/purple?

Hence the glow in a uranium storage pond. Very pretty.

DyslexicHobo
I don't know much about it, but I thought what appeared as "slower light", was really just regular speed light being refracted in zig-zags? Do the photons actually slow past 3.0 x 10^8 m/s?

Gold Member
That's correct. The photons travel at c. The absorbion/emission characteristics of the material determine how long it takes for the 'beam' to pass through.

The speed of light is a constant, c. The velocity of light (and recall there are two velocities we can define - group and phase velocity) is what changes when one moves from one medium to another.

Regarding the transmission of light through a medium - Transmitted light does NOT undergo any absorption or emission, transmitted light passes through the medium as a polarisation wave (i.e. a propagating disturbance in the electron "clouds" of the material).

Claude.

Gold Member
There has apparently been a misunderstanding on my part for several years, then. Can you elaborate upon the mechanism?

Crosson
There has apparently been a misunderstanding on my part for several years, then. Can you elaborate upon the mechanism?

It is very unusual for a system to be in an eigenstate of the photon number operator. This means that, in all but fairly recent and very controlled experiments first done by nobel prize winning physicist Aspect, light exists in a superposition state where it does not make sense to talk about photons as individual entities.

The original evidence for the existence of photons, the photoelectric effect and other atomic phenomena, have been mathematically explained using the classical wave theory of light, together with a quantum mechanical theory of the electron. The reason this is relatively unknown is that it is very embarassing to have Einstein's nobel prize been awarded for his explanation of the photoelectric effect using photons.

Gold Member
Well now... ain't that a kick in the pants...
So does that mean that wave/particle duality is a myth? Also, why doesn't the superposition collapse when an electron is encountered.

Crosson
The wave/particle duality is not a myth, because there are experiments that demonstrate conclusively the existence of photons. Its just that these experiments did not exist until the 1980s, and so a lot of dated discussions follow the outdated notion that photons are appropriate for treating the interaction between light and normal macroscopic materials.

A major source of this misinformation is the most popular Optics text, by Hecht. I was involved with a group who emailed the author and said, basically, "what is the deal with all these discussions of photons? Haven't you read the work of Aspect et al ?" . And his response was very totalitarian: photons exist, this is why Einstein got the nobel prize, end of discussion.

Also, why doesn't the superposition collapse when an electron is encountered.

Because collapses occur as a result of measurements. In the double slit experiment, what is being measured are positions, and this is why we have a collapse into a well defined position. If you want to collapse into a well defined number of photons, you have to measure the number of photons. As I said this was not done until relatively recently.

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There has apparently been a misunderstanding on my part for several years, then. Can you elaborate upon the mechanism?

From a classical standpoint, you can describe transmission through a transparent medium as a system of coupled oscillators. Taking a simple 1D case - Imagine a line of atoms. When the incoming EM field "hits" the first atom in the chain, the E field will cause the atom to polarise - that is, displace the electron cloud slightly from its equilibrium position. Since the E-field is sinusoidal, the response of the atom (or the position of the electron cloud if you like) also varies as a sinusoid in the linear case. Essentially what we have here is a driven oscillator, with the incoming EM wave acting as the drive force and the electron oscillating about an equilibrium point.

The oscillation of the electron on the 1st atom has its own associated EM field, which then causes the electron on the 2nd atom to oscillate. This continues down the chain. The reason the group velocity of the wave is reduced is because of the phase difference between the drive field and the response of the atom - the motion of the electron lags slightly behind the applied field. The reduction of group velocity of a wave inside a medium is due to this cumulative phase shift.

The difference between an absorbed wave and a transmitted wave is that the frequency of the transmitted wave does not lie on a resonance in the band structure of the medium, where an absorbed wave does. This means that for a transmitted wave, light cannot readily couple out of the wave and into the solid - an absorbed wave on the other hand excites plenty of phonon modes and so forth and the energy of the wave is quickly coupled into the solid.

One can also expand this picture by taking into account the fact that the response of an atom to an applied E field is nonlinear for high powers, thus accounting for the various nonlinear processes that can occur when an EM wave passes through a solid medium.

Also see ZapperZ's post on this topic - https://www.physicsforums.com/showpos...93&postcount=4 [Broken] , it is somewhat more thorough.

Claude.

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Gold Member
Thanks to both; that was most informative. I'll check out ZZ's post another time, though, since I don't have any background in such things. A bit of studying up on basic optics, phonons, oscillators, etc. would appear to be in order first so I can grasp it better.
I'd be interested to see how a laser burning through something looks under this approach.