Speed of light is a constant. How?

• back2square1
In summary, the speed of light is a constant that doesn't change, but the index of refraction will always be 1 when light goes from one medium to the other because that is the ratio between the speed of light in two different media.

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.

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.

back2square1 said:
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.
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.

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back2square1 said:
,
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 . . .

m4r35n357 said:
[..] 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:

back2square1 said:
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.

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.

fishtail said:
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/

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.

Dickfore said:
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.

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).

m4r35n357 said:
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.

Dickfore said:
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.

harrylin said:
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.

harrylin said:
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/

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

And THANKS Everyone !

Dickfore said:
[..] 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:

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back2square1 said:
[..] 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

1. What does it mean that the speed of light is constant?

The speed of light, denoted by the symbol c, is a fundamental constant of the universe. It refers to the speed at which light travels in a vacuum, and it is approximately 299,792,458 meters per second. This means that no matter where or when you measure it, light will always travel at the same speed.

2. How was the speed of light first measured?

The first measurement of the speed of light was attempted by Danish astronomer Ole Rømer in the 17th century. He observed the timing of the eclipses of Jupiter's moons and noticed that the eclipses appeared to occur later when Earth was farther away from Jupiter. This difference in timing allowed him to calculate the speed of light to be about 220,000 kilometers per second, which is quite close to the actual value.

3. Why is the speed of light considered to be the cosmic speed limit?

According to Einstein's theory of relativity, the speed of light is the maximum speed at which energy, information, or anything else in the universe can travel. This is because as an object approaches the speed of light, its mass increases and it requires more and more energy to accelerate it further. Therefore, it is impossible for anything with mass to reach or exceed the speed of light.

4. How is the speed of light related to time and space?

Einstein's theory of relativity also states that time and space are not absolute, but are relative to the observer's frame of reference. This means that the speed of light is the same for all observers, regardless of their relative motion. This also leads to the concept of time dilation, where time appears to pass slower for objects moving at high speeds.

5. Can the speed of light ever change?

Based on current understanding, the speed of light is considered to be a fundamental constant that cannot be changed. However, there are theories that suggest that the speed of light may have been faster in the early universe, or that it may vary in different regions of space. These theories are still being studied and are not widely accepted in the scientific community.