# Speed of Light

## Main Question or Discussion Point

Can anyone please tell me what does SPEED OF LIGHT WITH RESPECT TO AN OBSERVER mean?
Some explain it like this: If there are two poles 10km apart, in front of an observer and he sees a ray of light passing past them, then he would see that the light would cross the poles in time 10/c. Is it correct? Coz I doubt it.

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Doc Al
Mentor
Some explain it like this: If there are two poles 10km apart, in front of an observer and he sees a ray of light passing past them, then he would see that the light would cross the poles in time 10/c. Is it correct? Coz I doubt it.
Why do you doubt it?

So, is it the right definition?
Well, then are the concepts of special relativity mastered well by you?

Doc Al
Mentor
So, is it the right definition?
That would be an example of what the speed of light with respect to some frame of reference would predict.
Well, then are the concepts of special relativity mastered well by you?

A torch is kept at a point P. Observer is at P. The torch is switched on at Q. As you say, the speed he should detect is 10/c as the light travels from Q to R.
But now, let's investigate it more closely. As the torch is switched on, the wavefront from Q takes 10/c seconds to travel from Q to P. So after the torch has been switched on, then after 10/c seconds he detects that it has been switched on. Then, as light reaches R, the observer at P realises that it has reached R 100/c seconds after it actually reaches R. So, definately, he hasn't been able to detect the correct speed and infact, to him it has appeared as if the light has decelerated.
That's the question.

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Doc Al
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Several problems here:
(1) Where do you get 100 km? Your diagram looks like a right triangle to me, with sides equal to 10 km. So the hypotenuse would be about 14.1 km, not 100 km.
(2) Any observer must take into account the travel time for the light to reach him. Only after taking that into consideration will he be able to intelligently interpret his observations. Once he does he'll agree that the light took 10km/c to reach both P and R.

lol! Sorry, actually I had different sides earlier and then after changing the sides, I forgot to change to hypotenuse and wrote the whole problem accordingly.

Anyways, what do you mean by "taking into consideration". What if the observer doesn't know the distance PQ?

Doc Al
Mentor
Anyways, what do you mean by "taking into consideration". What if the observer doesn't know the distance PQ?
If he doesn't know the distance to the source of the light, then he has no basis for interpreting his observations. All he can say is that the light reaches him at some time.

One way to view things is to imagine that there are observers stationed at all locations (including P, Q, and R) with their own synchronized clocks. Then there's no need to worry about light travel time, since all observations will be local. In other words: Observer Q will report that he sent the light beam at time T1; Observers P and R will report that they received the light at times T2 and T3. (T2 will equal T3, since they are the same distance from Q.)

Well, there is really no problem with that set up of yours.
But what I want to know is that when we say that light travels at a constant speed with respect to every observer, doesn't it mean that the light should not appear to be decelerating to the observer in my case?
For instance, assume that the room in which this experiment is being carried out filled with colloidal particles. Then wouldn't the observer see the light's path as a decelerating beam?

Doc Al
Mentor
But what I want to know is that when we say that light travels at a constant speed with respect to every observer, doesn't it mean that the light should not appear to be decelerating to the observer in my case?
What matters is what you measure, not what 'appears'. You must take into consideration the light travel time when interpreting your raw observations.
For instance, assume that the room in which this experiment is being carried out filled with colloidal particles. Then wouldn't the observer see the light's path as a decelerating beam?
It's only the speed of light in a vacuum that is the same for all observers.

Well, sir, in relativity, the thing that matters is 'what appears'. If an observer starts calculating everything, he will overcome effects such as time dilation (which occurs at high speeds).
And I know that the speed of light in VACCUM is same for all observers. But the colloidal particles can be suspended in the vaccum without any problem. Then the observer would see the path of light which would appear to be decelerating. Now this is the real problem. How do we explain the fact that he would see a decelerating beam?

Doc Al
Mentor
Well, sir, in relativity, the thing that matters is 'what appears'. If an observer starts calculating everything, he will overcome effects such as time dilation (which occurs at high speeds).
No, just the opposite. Relativistic effects such as time dilation are measured after taking into account light travel times.
And I know that the speed of light in VACCUM is same for all observers. But the colloidal particles can be suspended in the vaccum without any problem. Then the observer would see the path of light which would appear to be decelerating. Now this is the real problem. How do we explain the fact that he would see a decelerating beam?
This has nothing to do with your earlier example. It's simply due to the light NOT traveling in a vacuum. You'll get the same effect by shining light through a piece of glass. So?

Actually, it has a lot to do with my example. In my earlier example on the line QR, assume there are more equidistant points A, B, C in between Q & R. Then although the light is travelling in vaccum, when the light hits the colloidal particle at A, a wavefront from A reaches P in time T1. When the light hits the particle at B, the wavefront reaches the observer in time T2. Same with T3. As you can see, PA, PB PC are hypotenuses of different triangles. And so T3>T2>T1. That's why I'm saying it appears to be decelerating.

ghwellsjr
Gold Member
A torch is kept at a point P. Observer is at P. The torch is switched on at Q. As you say, the speed he should detect is 10/c as the light travels from Q to R.
But now, let's investigate it more closely. As the torch is switched on, the wavefront from Q takes 10/c seconds to travel from Q to P. So after the torch has been switched on, then after 10/c seconds he detects that it has been switched on. Then, as light reaches R, the observer at P realises that it has reached R 100/c seconds after it actually reaches R. So, definately, he hasn't been able to detect the correct speed and infact, to him it has appeared as if the light has decelerated.
That's the question.
Aside from the error on the distance PR, I cannot understand your experiment. First you say the torch is at P. Then you say the torch is switched on at Q. And then you say the light travels from Q to R. Did you mean that the torch is at Q and not at P? Is the idea that there is a wire going from P to Q and that the observer at P turns on a switch which causes the torch to come on at Q or did you just mean it comes on some time all by itself. Is there just one observer at P. What is at R?

Doc Al
Mentor
Actually, it has a lot to do with my example. In my earlier example on the line QR, assume there are more equidistant points A, B, C in between Q & R. Then although the light is travelling in vaccum, when the light hits the colloidal particle at A, a wavefront from A reaches P in time T1. When the light hits the particle at B, the wavefront reaches the observer in time T2. Same with T3. As you can see, PA, PB PC are hypotenuses of different triangles. And so T3>T2>T1. That's why I'm saying it appears to be decelerating.
I really don't see your point. All observers will measure the time it takes for light to travel (in vacuum) from one point to another to be D/c, where D is the distance between the points. The fact that things may 'appear' to decelerate when you ignore light travel time is irrelevant.

Doc Al
Mentor
Did you mean that the torch is at Q and not at P?
I think that's what he meant.

HallsofIvy
Homework Helper
A little more detail on "speed with respect to an observer".

Suppose you are standing on the side of a road and a person throws a ball to you at, say 30 mph. It's speed "with respect" to you (or "relative to you") would be 30 mph.

Now, suppose another person, driving down the road toward the thrower, at 20 mph, were to reach out an catch the ball. The speed of the ball "with respect to" this person (and how hard it would hit his hand) would be (by classical mechanics) 30+ 20= 50 mph.

Finally, suppose that instead of throwing a ball the first person shines a light toward you. Its speed "with respect to you" is "c" mph. Classical mechanics would say that the speed of that light, "with respect to a person driving toward it at 20 mph" would be c+ 20 mph. But experimental evidence shows that that is not true. The speed of light coming toward a person, no matter how fast he was moving relative to you would still be exactly "c". That is why "relativity" was needed to replace classical mechanics for objects moving at very high relative speeds.

(Relativity would say that the ball thrown at 30 mph would hit the car, coming toward it at 20 mph, at slightly less than 50 mph but at those low speeds the difference would be too small to be measurable.)

Drakkith
Staff Emeritus
Here's an example. Lets say I take a laser pointer and shine it toward a stationary observer, observer A, 10 KM distant. Observer A measures how long it takes a small portion of the photons to travel through a 1 meter tube. He will find that they travel at c.

Now, lets say that we have another observer, observer B, traveling at 50% c directly away from observer A and myself so that my laser will pass by him at a distance of say one foot. That observer measures the speed of some of those photons in my laser as it passes by him as well. Observer B measures the speed as ALSO being c. So observer A and observer B both measure the laser as moving at the same speed even though they are both moving at completely different velocities in relation to the laser. The difference here is that Observer B measures the FREQUENCY of those photons as being LESS than observer A. The light from my laser with be shifted toward the red side of the spectrum. The light will be redder to him than it was to observer A.

Sorry. Actually, this all error was because of editing the original diagram.
I'm now explaining to you , the whole experiment from scratch.

There is a room with suspended colloidal particles. There is no air. There are three points P, Q, R. They form a right triangle right angled at Q. The torch is at Q. The observer is at P.

Now, the torch at Q is switched on by the observer at P through a remote. The torch gets switched on and the light starts travelling towards R. As expected, it will hit the colloidal particles in its way and enlighten its path. Let us take three points on QR - A, B & C such that QA=AB=BC=CR. As the light hits the particle at A, a wavefront will be generated at A which will travel to P in time T1. The observer at P will begin to see the path just as the wavefront from A reaches him. Now, as the main beam of light travels from A to B , it will strike B and a similar wavefront would be generated that will reach P in time T2. Same with C.
As it can be clearly seen (by geometry). T1<T2<T3. So, as the light travels farther and farther, the new path enlightened by the beam will be visible after more and more time and thus the beam would appear to be decelerating.
Note that the observer at P doesn't know the distance PQ. So, he is unable to do any calculations to explain the situation.

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Doc Al
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As it can be clearly seen (by geometry). T1<T2<T3. So, as the light travels farther and farther, the new path enlightened by the beam will be visible after more and more time and thus the beam would appear to be decelerating.
What the observer at P sees is a series of reflections from the particles at A, B, and C. The time between his receipt of each reflection increases. This is exactly what one would expect to see at P if a light beam travel from Q to R, hitting equally spaced particles along the way.
Note that the observer at P doesn't know the distance PQ. So, he is unable to do any calculations to explain the situation.
Why not? He's perfectly capable of using exactly the reasoning you used above. He'll conclude that his observations are consistent with a light beam reflecting off of equally spaced particles. He can even use his observations to figure out where A, B, and C are.

The point is that 'raw' observations of light must be interpreted by taking account of the time it takes for the light to reach the observer. (Just as you did in your analysis above.) No one would ever conclude that he observed a beam of light 'slowing down' based on the observations discussed here.

ghwellsjr
Gold Member
Can anyone please tell me what does SPEED OF LIGHT WITH RESPECT TO AN OBSERVER mean?
Some explain it like this: If there are two poles 10km apart, in front of an observer and he sees a ray of light passing past them, then he would see that the light would cross the poles in time 10/c. Is it correct? Coz I doubt it.
What the observer at P sees is a series of reflections from the particles at A, B, and C. The time between his receipt of each reflection increases. This is exactly what one would expect to see at P if a light beam travel from Q to R, hitting equally spaced particles along the way.

Why not? He's perfectly capable of using exactly the reasoning you used above. He'll conclude that his observations are consistent with a light beam reflecting off of equally spaced particles. He can even use his observations to figure out where A, B, and C are.

The point is that 'raw' observations of light must be interpreted by taking account of the time it takes for the light to reach the observer. (Just as you did in your analysis above.) No one would ever conclude that he observed a beam of light 'slowing down' based on the observations discussed here.
Based on your original post and your corrected example, are you suggesting that Special Relativity is claiming that any observer will measure the speed of light as a constant even when they don't know the distances involved? Don't you think that is expecting a bit much?

It turns out that every legitimate experiment that has ever been performed to measure the speed of light gets the same value, so much so, that scientists have assigned an exact value to the speed of light which is called "c" and has a value of 299792458 meters per second. This, of course, has nothing to do with Special Relativity, it's just a statement about what we have observed about nature in the past and what we assume we will always observe about nature in the future.

But I suspect that this answer is not really what you are asking about but you will need to rephrase your question if that is the case.

ghwellsjr