# Speed of light

1. Dec 9, 2012

### mcafej

Ok, so I just watched the nova fabric of the cosmos (blew my mind). Anyways, suppose I jumped on top of a beam of light and road it as it traveled out into space. Now, suppose that as I was traveling out there, another person is coming at me in the exact opposite direction on another beam of light. According to Einstein, if I was holding a radar gun, it would still say that the person on the other beam of light was only going 671 million mph (roughly), but what I don't understand is that if we are going opposite directions, why would my radar gun not change? I understand that if i flew by an observer on a beam of light, space would warp in order to not allow me to exceed the speed of light, but how would I perceive the person coming at me if we were both on a beam of light? Obviously it would only be an instant that we would see each other, but how would we perceive time relative to each other? If I looked at my watch and he looked at his, and I could somehow see the speed of his watch, which would be ticking faster and which would slow down?

This is something that I have found fascinating, and I believe it is true, but it just blows my mind, and I'm really interested in it.

2. Dec 9, 2012

### ghwellsjr

According to Einstein, you need to talk about speeds of objects and light with respect to or with reference to a coordinate frame. That's why it is called a reference frame. In Special Relativity, the coordinates of this frame are not warped, however, objects traveling at high speeds in this frame can be "warped", if by that you mean their clocks will run slower than the coordinate time of the frame and their rulers will be compressed along the direction of motion.

Also, according to Einstein, you are correct that you cannot exceed the speed of light but you also cannot achieve the speed of light. But your question will work even with speeds less than that of light so let's do it at 99% of the speed of light, Ok? Let's say that you are traveling at 99%c in one direction and far away is another observer coming towards you at the same speed (both speeds according to a frame of reference).

Your radar gun will determine that the other observer is not traveling at 198%c but rather 99.995%c. Look up "velocity addition" in wikipedia to see the formula to make this calculation.

As you are approaching the other observer, you will see his watch running faster than yours by a factor of 200. So during the time that your watch ticks out 1 second, you will see his tick 200 seconds. But he will also see yours ticking 200 times faster than his. Look up "relativistic Doppler" in wikipedia for the formula for this.

Then as you pass each other and look back at the other one, you each will see the other ones watch ticking more slowly than your own by a factor of 1/200.

Does this help clarify things for you?