Can you increase the speed of light?

[Agent M27]

We were covering Lorentz Transformations yesterday in class and going over the derivation from Gallilean transformations. Obviously everyone knows that in Gallilean Transform, it is basically velocity addition depending on which refrence frame the observer is in. When dealing with speeds approaching c, Lorentz is needed to account for the unchanging speed as measured by different observers in different refrence frames. Ok. All of this applies to c as measured in a vacuum, but how would it relate when passing through some medium? I am in the early stages of relativity and my understanding of optics is limited, so bare with me even if this is a frivolous question.

Take the speed of light in water. I don't know by what factor c decreases as it travels in water, but I know it does. If there was an infinite volume through which a submarine could travel, and if the sub was able to travel at .9c, at what velocity would the photons emenate, as measured by an observer in a non inertial refrence frame with respect to the sub? On the surface with my limited understanding I feel that the velocity measured would be equal to that of c in a vacuum. So there would be a small amount of velocity addition due to the refraction index, just not quite .9c + c. Is this correct, or am I totally off on this tangent thought? My professor could not give me an answer, but this does not preclude that there is no answer, just probably outside of his spectrum of knowledge. Thanks in advance.

Joe

 

[Frame Dragger]

We were covering Lorentz Transformations yesterday in class and going over the derivation from Gallilean transformations. Obviously everyone knows that in Gallilean Transform, it is basically velocity addition depending on which refrence frame the observer is in. When dealing with speeds approaching c, Lorentz is needed to account for the unchanging speed as measured by different observers in different refrence frames. Ok. All of this applies to c as measured in a vacuum, but how would it relate when passing through some medium? I am in the early stages of relativity and my understanding of optics is limited, so bare with me even if this is a frivolous question.

Take the speed of light in water. I don't know by what factor c decreases as it travels in water, but I know it does. If there was an infinite volume through which a submarine could travel, and if the sub was able to travel at .9c, at what velocity would the photons emenate, as measured by an observer in a non inertial refrence frame with respect to the sub? On the surface with my limited understanding I feel that the velocity measured would be equal to that of c in a vacuum. So there would be a small amount of velocity addition due to the refraction index, just not quite .9c + c. Is this correct, or am I totally off on this tangent thought? My professor could not give me an answer, but this does not preclude that there is no answer, just probably outside of his spectrum of knowledge. Thanks in advance.

Joe

The derived value of the speed of light in a vacuum is the upper limit of c. There is a delay for the observer, which is why there is such a thing as diffraction of light in water. Ask any surf-spear fisher, and they'll tell you it appears that fish are displaced by a certain amount according to depth, etc. They aim accordingly, but if the fish were on a given trajectory a computer could calculate an intercept course before the fish appears to reach a given area from the frame of the fisherman above the water.

 

[Ich]

That sounds a lot like http://en.wikipedia.org/wiki/Fizeau_experiment" .

 

[Frame Dragger]

That sounds a lot like http://en.wikipedia.org/wiki/Fizeau_experiment" .

Not a complete coincidence. ;)

 

[Naty1]

Hi M27:

See for a brief explanation:

http://en.wikipedia.org/wiki/Speed_of_light#In_a_medium


so you ARE off on tangent, but all of us have tried those tangents as well//

not to worry...

 

[Agent M27]

The Fizeau experiment is pretty interesting. Now as I interpret it this is only dealing with a stationary photon emitter and pulsing photons through a moving medium, which I believe is the v in: V(1-$$\frac{1}{n^{2}}$$. Can I use these equations to apply a moving photon emitter, moving at .8c or so? When I worked through some calculation I assumed that I would subtract V(1-$$\frac{1}{n^{2}}$$ if the water was moving toward the emitter and I would add V(1-$$\frac{1}{n^{2}}$$ if the water was moving in the direction of the photon, is this correct? Thanks in advance.

Joe

 

[Ich]

Can I use these equations to apply a moving photon emitter, moving at .8c or so?

Any ray of light moves in the ``stationary'' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

It makes no difference.

 

[Naty1]

I think Ich and the reference I posted have the same answer...NO..

if you read wikipedia you will see that light moves at c between emission and absorption in a medium...end of story...

you can't speed light up and slow it down in the matter you posted...but different substances will overall "slow light" in a sense...hence refraction...

 

[Agent M27]

Gotcha, thanks a lot. I was tired when I was reading before, but now it is sinking in.

Joe

 

[PhilDSP]

If you must use photons that travel faster than c then you need to find a material which has a permittivity less than 1 - the permittivity of vacuum. Light velocity has a dependency on permittivity. This would be making an assumption that vacuum actual contains something that polarizes an electric field (that it doesn't happen by magic) and that whatever that is can be reduced.

However, even that is not enough because changing the permittivity without a counter adjustment to magnetic permeability will only induce refraction.

PS. The numeric value of electric permittivity varies depending on which system of measurements you're using.-------------------------------------------------------------------------------------

Captain Picard: Q, how do we divert the asteroid from its trajectory that will collide with the planet? The Enterprise can't generate the power needed.

Q: That's easy. Just change the gravitational constant of the universe.

 

[Frame Dragger]

If you must use photons that travel faster than c then you need to find a material which has a permittivity less than 1 - the permittivity of vacuum. Light velocity has a dependency on permittivity. This would be making an assumption that vacuum actual contains something that polarizes an electric field (that it doesn't happen by magic) and that whatever that is can be reduced.

However, even that is not enough because changing the permittivity without a counter adjustment to magnetic permeability will only induce refraction.

PS. The numeric value of electric permittivity varies depending on which system of measurements you're using.


-------------------------------------------------------------------------------------

Captain Picard: Q, how do we divert the asteroid from its trajectory that will collide with the planet? The Enterprise can't generate the power needed.

Q: That's easy. Just change the gravitational constant of the universe.

I think a bit of research into Čerenkov Radiation would be illuminating (rimshot!) for the OP as an example of what really happens when light 'brakes' between mediums.

 

[Agent M27]

That is a pretty cool experiment, thanks Frame Dragger, it was illuminating! I guess it comes down to the brass tacks that nothing is going to go faster than light, but it is curious how it travels faster through that meidum than it otherwise would. You have sent me on a hunt for more information. Cheers and take care.

Joe

 

[Frame Dragger]

That is a pretty cool experiment, thanks Frame Dragger, it was illuminating! I guess it comes down to the brass tacks that nothing is going to go faster than light, but it is curious how it travels faster through that meidum than it otherwise would. You have sent me on a hunt for more information. Cheers and take care.

Joe

Thank you, and very funny with the pun. Remember: the blue glow means we're all dead.

I agree that the propogration of light through various mediums is weird and amazing. Very cool, as you say.