# How is light speed constant and in all directions ?

1. Jul 24, 2013

### B4ssHunter

this is my first post so please go easy on me : D

My question basically is :

how does time dilation work if you are moving towards a source of light ?

if i am moving with a speed , 150 km/s and there is a light beam moving in the same direction as i am with a speed of 300km/s , according to classical mechanics i would observe the light ray with a relative speed of 150 km/s , but then time dilation comes into play and makes my time two times as slower , so it makes 150km/ 1/2 a second , which makes 300km/s and fixes everything\

now to the main point , if i am moving towards a light ray
with a velocity of 150 km/s
according to classical mechanics i should observe it coming at me with a speed of 450 km/h ..
now how am i supposed to measure it at 300 km/s ?
even if time dilation works , it would even increase my observed speed of the light ray , not decrease it to 300 .. help please
* i am still a high school student so please no tough equations *

2. Jul 24, 2013

### Staff: Mentor

300000 km/s.
It is not just time dilation, but also a shift of simultaneity (=the basis of your velocity measurements). That is the main point actually, and its effect is different for the two light beams.

3. Jul 24, 2013

### B4ssHunter

can you give me a quick explanation on how simultaneity would affect my results here ?
* i wrote 300 for the sake of simplicity *

4. Jul 24, 2013

### Staff: Mentor

I don't know how to compress this to a quick explanation.
The basic idea: It is pointless to ask what happened "today" at some point far away, as different observers (even if they are all at earth) will disagree on the definition of "today". Therefore, the question "how long ago was the light emitted?" does not have a frame-independent answer - but you need that value to calculate the speed.

5. Jul 24, 2013

### HallsofIvy

Staff Emeritus
How does writing the wrong number simplify anything? Many writers use units in which c= 1 but you specifically wrote "km/s".

6. Jul 24, 2013

### ghwellsjr

That's a good question: how are you supposed to measure the speed of light?

Have you thought about it? If you were measuring the speed of some solid object, you would use light to observe where it was at any particular time but how do you observe light?

Whether you are traveling towards or away from a ray of light, you cannot observe it until it gets to you, correct? So in order to measure its speed, you would have to place a mirror behind you so that the light can hit it and reflect back to you. Even then, you will not be able to observe the light hitting the mirror, only when the reflection finally gets back to you, correct?

So whether you are moving towards or away from the ray of light, since you can only measure the total time it takes for the ray to make a round trip between you and the mirror, the total time will be the same either way, correct? The light can be faster for one part of the trip and slower for the other part but they will still add up to be the same and you'll never know the difference.

7. Jul 24, 2013

### Staff: Mentor

This being your first post, now would be a really good time to get in the habit of never specifying a speed without saying what it that speed is relative to. This isn't just a pedantic little nit, it is absolutely essential to making sense of relativity.

For example, you say that you're moving at 150 km/sec. I'll ask "relative to what?" Do you mean that you are moving at 150 km/hr relative to the earth under your feet? Relative to a missile approaching your spaceship in the middle of empty space light-years away from the earth? For now, let's assume that I am floating in the middle of otherwise empty space, a flash of light passes me from left to right at speed c, and then a moment later you pass me at 150 km/sec.

Now your question comes down asking how it can be that you measure the speed of the flight flash to be c relative to you and I measure it to be c relative to me, despite our relative motion - classically you'd expect these measured speed to differ by 150 km/hr.

There's an equation in the answer, but it's not a tough one. It turns out that time dilation, length contraction, and relativity of simultaneity all play together so that in this situation the speeds are related by $w=\frac{u+v}{1+uv}$ where $u$ is your speed relative to me, $v$ is the speed of the thing you're chasing (in this case, the flash of light) relative to you, and $w$ is the speed of the thing you're chasing relative to me. (I'm also measuring distance in light-seconds and time in seconds so that $c$, the speed of light, comes out to be exactly 1 - that way I don't have to clutter up the equation with a bunch of multiplying and dividing by $c$).

Try plugging various speeds into this equation (remember, the units are light-seconds per second, so the speed of light is one and everything else is less) and you'll see how the speed of light comes out the same for all observers regardless of their relative motion.

It's worth noting that if both $u$ and $v$ are very small compared to $c$, this equation reduces to the classical equation $w=u+v$. That's why we never notice relativistic effects in our daily life.

Last edited: Jul 24, 2013
8. Jul 24, 2013

### Harry Wilson

No, that isn't what happens. You are not moving in your reference frame; everything moves relative to you. When things move relative to you, you will observe THEM undergo time dilation and length contraction. You will never see your own clock slow down.
If you zoom by a space-station at 86% the speed of light, you will see their clocks slow to 50%, because you are at rest in your frame of reference. From their point of view it is you moving and them at rest, so they see YOUR clock slow by 50%. Try to figure out how this apparent paradox is resolved!
Also, the speed of light is constant in every frame, so you won't see it recede from you at c subtract your speed - it will still recede at c.

9. Jul 24, 2013

### B4ssHunter

that was a very fine answer , algaebrically
i just wished i could understand it in terms of common sense * i tried to imagine the situation *
but i guess sometimes we have to take things as they are
btw could you give me a link where i can find the derivation of this equation ?
i guess simultaneity plays a big role , i will have to read more about it

10. Jul 24, 2013