Speed of light is a constant. How?

[back2square1]

Ok. I admit I'm completely new to Relativity (I had my first lecture today!). What I learned was that the speed of light is a absolute constant that doesn't change.
I then came into some situation like,
1. I'm driving my car with velocity v and turn on my headlights, won't the speed of light coming out of my headlights be c+v?
2. If light speed is absolute constant, then the index of refraction would always be 1 when light goes from one medium to the other because index of refraction is the ratio between the speed of light in two different media.
Someone please explain.

 

[Dickfore]

1. No, you are using the "velocity addition law" which implicitly assumes Galilean transformations are valid. You will learn in next lectures that the true transformations are the Lorentz transformation and that there is a different velocity composition law in relativity:
$$v = \frac{v' + u}{1 + \frac{v' \, u}{c^2}}$$
If you take $v' = c$ in this formula, you will get $v = c$.

2. The true postulate of relativity is that the speed of light in vacuum is a true constant and relativistic invariant. It is referred to as c. In every other material, light propagates at a slower speed. In the rest frame of the material it propagates with a speed $c/n$, where n is the refraction index of the material.

 

[harrylin]

Ok. I admit I'm completely new to Relativity (I had my first lecture today!). What I learned was that the speed of light is a absolute constant that doesn't change.

Hi, it's not clear if you refer to the first or the second postulate, or both!
Or did, perhaps, that first lecture muddle them up?! :uhh:

See the intro of http://www.fourmilab.ch/etexts/einstein/specrel/www/ :

The second postulate (the "light postulate") assumes as a law of physics that the speed of light in vacuum as determined in an inertial frame is constant (c): it's the same in all directions and not affected by the motion of the source.

And according to the first postulate (the principle of relativity), this law about the speed of light must be invariant: the same value for c must be found in any inertial reference system.

Which of those two did you refer to?

I then came into some situation like,
1. I'm driving my car with velocity v and turn on my headlights, won't the speed of light coming out of my headlights be c+v?

The second postulate states that the speed of light coming out of your headlights is constant, independent of the motion of your headlights. Thus it will still be c as determined wrt to the road as inertial reference system.

The first postulate has that the same will be obtained with a different inertial reference system. And SR solved the puzzle of how such seemingly contradictory findings can be not contradictory after all (read again the intro of Einstein's 1905 paper).

Does that help?

2. If light speed is absolute constant, then the index of refraction would always be 1 when light goes from one medium to the other because index of refraction is the ratio between the speed of light in two different media.
Someone please explain.

1.The effective speed of light as determined in refractive media is less than c.
2. In the scattering model of light the speed of the entering light wave is in fact c but a delayed secondary wave comes out of the refractive material.

See also this freshly started thread with exactly that question :grumpy::
https://www.physicsforums.com/showthread.php?t=635251

 

[m4r35n357]

,
1. I'm driving my car with velocity v and turn on my headlights, won't the speed of light coming out of my headlights be c+v?

Speaking as an amateur, I find two things puzzling here:
1. Did your lecturer really tell you that light speed is independent of the source without mentioning the SR velocity addition formula? What a master of suspense!
2. If you are a student, why not just ask your lecturer rather than posting here?
I know that if I had access to formal educational facilities I would be making use of them, and only posting here to answer questions.
Perhaps I am just having an off day . . .

 

[harrylin]

[..] I find two things puzzling here:
1. Did your lecturer really tell you that light speed is independent of the source without mentioning the SR velocity addition formula? What a master of suspense! [..]

What I found puzzling is that his/her lecturer apparently did not explain that the speed of light is independent of that of the source (=speed of headlights)!

2. If you are a student, why not just ask your lecturer rather than posting here?
I know that if I had access to formal educational facilities I would be making use of them, and only posting here to answer questions.

Yes, well, I can understand it if after a confusing lecture some people may want to hear it explained by someone else. :tongue2:

 

[HallsofIvy]

Ok. I admit I'm completely new to Relativity (I had my first lecture today!). What I learned was that the speed of light is a absolute constant that doesn't change.
I then came into some situation like,
1. I'm driving my car with velocity v and turn on my headlights, won't the speed of light coming out of my headlights be c+v?

IF you assume non-relativistic Newtonian physics, yes. But if you are talking about relativity, no that sum does not give the speed of light relative to the road. Velocities just don't combine like that in relativitity.

2. If light speed is absolute constant, then the index of refraction would always be 1 when light goes from one medium to the other because index of refraction is the ratio between the speed of light in two different media.

Relativity says that the speed of light in vacuum is constant, not in other media.

Someone please explain.

 

[fishtail]

Maybe it would be easier to understand if we say the measurement of the speed of light is the same rather than just the speed of light. Measurement implies use of clocks and measuring rods(distance). Now if moving clocks and rods vary, we can measure a constant speed of light.

 

[harrylin]

Maybe it would be easier to understand if we say the measurement of the speed of light is the same rather than just the speed of light. Measurement implies use of clocks and measuring rods(distance). Now if moving clocks and rods vary, we can measure a constant speed of light.

Yes indeed, that's an essential point. In SR jargon, following Einstein, it is common to label the inferred or "measured" speed of light (in part not even really measured but defined) as "the speed of light". This is explained in his 1905 paper, in section 1.
- http://www.fourmilab.ch/etexts/einstein/specrel/www/

Back2square1, was this emphasized in the intro lecture?

 

[Dickfore]

To the previous 2 posters, No, the speed of light IS the same according to all frames. This follows from the 1St postulate. Then, it is the reason why identically construced clocks and measuring rods measure different time intervals and lengths in different frames, without any noticable mechanical (or otherwise) deformation.

 

[harrylin]

To the previous 2 posters, No, the speed of light IS the same according to all frames. This follows from the 1St postulate. [..]

In SR the speed of light is defined as we explained, and as everyone can read. SR has no metaphysics.

 

[Dickfore]

In SR, there is a limit speed of propagation of interactions. This is the contents of the 2nd postulate. According to the 1St postulate, this limit speed must have the same value in every system.

It happens that the speed of propagation of em waves (as predicted by Electrodynamics) in free space is equal to this limit speed. Historically, it was the first example of its physical manifestation in light propagation. This is why Einstein's original paper calls the limit speed "the speed of light in vacuum". There are other examples of disturbances/interactions propagating at the same speed: the strong color force in QCD, and gravitational waves in GR. It was thought that neutrinos also traveled at this speed, but, since they have mass, they travel at subluminal speeds.

After this historical digression, let us come back to the point:
Clocks and measuring rods measure different intervals between the same two events according to different frames BECAUSE c is invariant, and NOT the other way around (c is invar, because times dilate and lengths contract).

 

[back2square1]

Speaking as an amateur, I find two things puzzling here:
1. Did your lecturer really tell you that light speed is independent of the source without mentioning the SR velocity addition formula? What a master of suspense!
2. If you are a student, why not just ask your lecturer rather than posting here?
I know that if I had access to formal educational facilities I would be making use of them, and only posting here to answer questions.
Perhaps I am just having an off day . . .

Believe me, the education system in India is collapsing. My lecturer was too stupid to explain me those things. I had my second lecturer yesterday and he started with Galilean Transformation and went all the way through Lorentz Transformations,Time dilations, Michaelson-Morley Experiment and ended up in Length contraction within just 45 (forty-five, its not a typo!) minutes. I guess, now you know what "formal educational facilities" mean here.

1. No, you are using the "velocity addition law" which implicitly assumes Galilean transformations are valid. You will learn in next lectures that the true transformations are the Lorentz transformation and that there is a different velocity composition law in relativity:
$$v = \frac{v' + u}{1 + \frac{v' \, u}{c^2}}$$
If you take $v' = c$ in this formula, you will get $v = c$.

2. The true postulate of relativity is that the speed of light in vacuum is a true constant and relativistic invariant. It is referred to as c. In every other material, light propagates at a slower speed. In the rest frame of the material it propagates with a speed $c/n$, where n is the refraction index of the material.

This really helped. Thanks.

What I found puzzling is that his/her lecturer apparently did not explain that the speed of light is independent of that of [...]

I'm a he, not a she.

Yes indeed, that's an essential point. In SR jargon, following Einstein, it is common to label the inferred or "measured" speed of light (in part not even really measured but defined) as "the speed of light". This is explained in his 1905 paper, in section 1.
- http://www.fourmilab.ch/etexts/einstein/specrel/www/

Back2square1, was this emphasized in the intro lecture?

He didn't say nothing about "measured" speed of light or whatsoever. The lecturer just used "speed of light".

And THANKS Everyone !

 

[harrylin]

[..] In SR, there is a limit speed of propagation of interactions. This is the contents of the 2nd postulate. [..]

For the real contents of the second postulate see my post #3 ... :uhh:

Clocks and measuring rods measure different intervals between the same two events according to different frames BECAUSE c is invariant, and NOT the other way around [..]

That's a bit off-topic, but a logical deduction must not be confounded with a physical cause!
SR makes the following logical deduction from observation:
invariant c => Lorentz contraction + time dilation

A similar discussion is taking place here:
https://www.physicsforums.com/showthread.php?p=4070104

 

[harrylin]

[..] I had my second lecturer yesterday and he started with Galilean Transformation and went all the way through Lorentz Transformations,Time dilations, Michaelson-Morley Experiment and ended up in Length contraction within just 45 (forty-five, its not a typo!) minutes. [..]

Hmm, well maybe he wanted to tell you everything so that you would have no questions left.

He didn't say nothing about "measured" speed of light or whatsoever. The lecturer just used "speed of light".

That's fine - if he had first defined "speed of light" as Einstein did in his first paper on that topic. That definition is not metaphysical but operational: based on rulers, clocks and convention. I cite from the intro:

"The theory to be developed is based—like all electrodynamics—on the kinematics of the rigid body, since the assertions of any such theory have to do with the relationships between rigid bodies (systems of co-ordinates), clocks, and electromagnetic processes. Insufficient consideration of this circumstance lies at the root of the difficulties which the electrodynamics of moving bodies at present encounters."

Cheers