Speed of light... variable?

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Cretin42

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In some browsing I was doin, I came across an article describing (very) basically, the theory of relativity. Its main example was, if I remember correctly, as follows:
A man in a boxcar, on a track infinitely long, with a velocity great enough to show a difference, would shine a light across the boxcar, using a mirror at an angle as such: / \ with the mirror at the top. The time it takes the light to reach the end is recorded.
Now in this closed system, the light would have moved at speed V1 = (distance from flashlight to mirror + distance from mirror to other side)/time taken from the light being turned on till it reached the other side.
However, outside the closed system, because the boxcar was moving at a high speed, the actual distance traveled by the light was stretched on the X axis, giving it a greater distance/time, V2, ie light traveled faster than "normal".
I bring this up because it confuses me: I always hear the "speed of light" referred to as a constant, c. in science fiction, there is "Faster than Light" travel, etc. Is it, as I would surmise, rather just the speed of light from sources stationary relative to earth, mainly? For instance, another star in the galaxy, or another galaxy in the universe, could be traveling at, say, c/2, relative to earth, sol, whatever the standard is. Yet within the solar system/galaxy, as a closed system, light would not be restricted to our measurement of c, but would be the same as our c. relative to us, however, it would appear to be travelling at 3c/2 if in our direction, or c/2 if away.
Anyways, I have probably explained myself far too much, and could really go on, but this is surely long enough:p I'll append to this if anyone's interested, lol
 
Light (in a vacuum) always travels at c relative to the observer.

The propogation wave front of light(in cesium) can travel at at least 310 times the speed of light but this is not FTL as the whole wavefunction of a photon is not completed until much later.
 
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The weird world of Relativity

Hi Cretin42,

The speed of light in a vacuum is a constant for all observers, regardless of their relative speeds.

The boxcar example you're referring to is one way to derive the Lorentz tranformations which describe how space and time change for observers moving at constant speeds with respect to each other. The example starts by <b>assuming</b> that the speed of light is constant (one of only two assumptions which underlie the theory of relativity). Then, if you follow the example through you'll find that time in the boxcar slows down from the point of view of an external observer, and the length of the car contracts in the direction of motion, all in such a way as to keep the speed of light constant.

Regarding objects moving away from each other: suppose there are two spaceships A and B which move in opposite directions away from the Earth. A person on Earth sees both spaceships moving at, say 90% the speed of light relative to Earth. On the basis of common sense, you'd say that the spaceships are moving away from each other at 90+90=180% the speed of light as seen by each other. But common sense is a poor guide to relativity, and it turns out that velocities don't add in the common sense manner. In fact, both spaceships see the other receding at less that 100% the speed of light.
 
Thanks JR, keep forgetting about that vacuum, have corrected it now. Love how you can edit things here. Helps to save face:D
 
Thanks, guys, for the explanation. While I of course don't fully understand it (it is the theory of relativity, after all), I was thinking it may have had something to do with the time differential, but it was just a guess:p Thanks again!
 
John Devers ...

I don't know JD, a little egg-on-the-face sort of keeps things in perspective, don't you think?
 
Chagur, I'm always wiping it off but I'm learning;)

JR and Chagur, Isn't it true that light, always travels at c even in mediums?

AFAIK, the photon is never sped up or slowed down.

Photons may interact with electrons to zig zag and slow the speed of the propagation wave front it may even smear into an atom and form a polariton with a hole (which is what they call stopping light) but light really never travels at other than c when you add all it's properties together.
 
Hi all,

The propagation of light through solids is a tricky subject. In physics there are two ways to describe this:

- Either you describe the light as an incoming wave. Then you can use refraction and transmission to calculate the speed of the light within the solid and you'd notice that the wave of light has been slowed down according to the index of refraction (n) of the medium.

- Or you can describe it in a more quantummechanical way and use photons. You can then argue that the photons propagate through the solid because they get absorbed by the atoms and then re-emitted (this is an effect called fluorescence). The slowing down then occurs because there is a very small timedifference between the absorption and re-emittance of the photons.

Bye!

Crisp
 
Crisp, is there only 2 ways or are there any more that work?

Comments by the researchers on their ftl experiment.

The researchers point out that the speed limit of c for any real signal is a postulate of relativity theory, for which there is still no formal proof based on the electromagnetic theory of light.
 
Hi John Denvers,

Well, I cannot think of any other ways of explaining the propagation of light, as physicists use only the particle-wave duality of light (so you can describe it as either a particle, which is the photon explanation I gave, or as a wave, which was the other). Ofcourse there are several theories on how light propagates in a solid, one better than the other, but they are in the end variants of one of the two above theories, worked out into more detail.

Concerning special relativity: I wouldn't say that c is postulated to be the maximum speed at which information can be exchanged. The postulate in SR concerning light is where Einstein states that the speed of light, c, is constant for all observers. This implies that no information can be transferred FTL, but it's not entirely postulated that way. From experiments, it is more reasonable to assume that c is constant for all observers (this has been verified to a great accuracy in the radioactive decay of near-light speed atoms). Postulating that c is the maximum information-exchange speed is not good, because there's no experimental data to support that claim (so in a sense, the researchers you talk about have a point: the "c is the max. speed for info exchange" statement is a direct consequence of the postulates of SR - and hence a theoretical statement - but the postulates itself are backed up by experimental data, and the maths are right....).

I'd have to disagree with the researcher's statements on the electromagnetic theory of light. Some thoughts:
  • Einstein used the special property (called Lorentz invariance) of the Maxwell equations for electromagnetic radiation to formulate his theory of special relativity (SR). The Maxwell equations themselves are incompatible with Einstein's SR in a mathematical sense (the theory of SR is in 4 dimensions, Maxwell's equations are in 3).
  • However, the Maxwell equations can be adapted, or better: reformulated in 4 dimensions in such a way that they fit nicely into the theory of SR. From the Maxwell equations one can easily deduce that the speed of electromagnetic radiation (in vacuum) is c, and this statement can be generalized to SR (where coïncidently, c plays another important role).
Once again, there's no experimental prove that no information can be transfered FTL (no officially confirmed experiments have done that on a macroscopic scale), but it can be deduced with basic mathematics (which we assume to be universally right) from reasonable postulates. So the questions the researchers are asking are more of a philosophical nature than exact scientific (the famous induction problem of science philosophy).

Bye!

Crisp
 
Hello Crisp,

I have a couple of questions for you.

Einstein used the special property (called Lorentz invariance) of the Maxwell equations for electromagnetic radiation to formulate his theory of special relativity (SR). The Maxwell equations themselves are incompatible with Einstein's SR in a mathematical sense (the theory of SR is in 4 dimensions, Maxwell's equations are in 3).
Click to expand...

The Maxwell equations are 4 dimensional. They involve 3 space coordinates and a time coordinate. As I understand it they are compatible with SR, but not with Newtonian physics. Could you please explain your statement above? What "reformulation" do you believe is necessary to make Maxwell's equations compatible with SR?
 
Hi James R,

The Maxwell equations are 4 dimensional.

Ofcourse they are... I don't know what I was thinking when I wrote that they were 3 dimensional.

As I understand it they are compatible with SR, but not with Newtonian physics. Could you please explain your statement above? What "reformulation" do you believe is necessary to make Maxwell's equations compatible with SR?

Yes, the Maxwel equations are compatible with SR, because they are Lorent invariant. The "mathematical incompatible" I talked about was on the 3D vs 4D thingy, and I still haven't figured out how I came to that :).

The reformulation I talked about is not a modification, but really replacing some notation (where you write the EM Tensor F). That way, it fits in nicely with the conventional contra/covariant notation of SR.

Now, the point I tried to make in my previous post was the following: the Maxwell equations are equations for radiation, originally written in the "classical" picture of waves, while the theory of SR is essentially (in my opinion) a tool to describe the motion of particles, so at first it seems difficult to get a consistent theory that describes both. From the Maxwell equations one can see that the speed of EM radiation is c, and this still holds when the Maxwell equations are reformulated in terms of SR. (It was more the close link between SR and Maxwell eq. I tried to point out, because John Denvers talked about SR and electromagnetism).

Bye!

Crisp
 
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