# I know im wrong but just curious

1. Jan 20, 2009

### lastman

I heard it said that there is no such thing as speed its all relative to a point of reference and also that there is no such thing as anything moving faster than the speed of light. so would a burst of light going in seperate directions relative to each other be separating faster than the speed of light? may be a dumb question just curious.

2. Jan 20, 2009

### mgb_phys

Yes you can shine a beam of light in opposite directions - the two points will be moving apart at the 2x speed of light.
When we say nothing can travel faster than light we have a very specific meaning of 'thing' (involving the transfer of information)

Search for 'lighthouse paradox' for a similair case

Last edited: Jan 21, 2009
3. Jan 20, 2009

### Tac-Tics

There is a big problem with taking the difference in speed between two beams of light moving opposite directions. The problem is that if you're moving AT the speed of light, time stops. You can't measure the speed of anything, because you don't pass through time.

Matter cannot travel at the speed of light, though, so that is not a problem at all.

But take a similar problem. Take two space ships moving in opposite directions at 90% the speed of light each. What is the second space ship's speed relative to the first?

If you asked an 18th century physicist, he'd tell you it should be 180% the speed of light (relative velocities add in classical physics). However, a modern physicist knows better. You cannot simply add velocity vectors together in relativity. You have to transform them with a Lorentz Transformation. The resulting velocity is scaled down considerably, due to the speeds involved, and the answer is less than the speed of light.

4. Jan 21, 2009

### thenewmans

I like Tac-Tics's version of the thought experiment. Let’s calculate the relative speed.

v = (v1+v2)/(1+v1*v2) = (.9+.9)/(1+.9*.9) = 1.8/1.81 = .99

So classical sees the other ship as faster than light. SR sees it as just closer to the speed of light. In order to assume the speed of light is constant, Einstein decided to let time and space be flexible. (Actually Lorentz came up with time dilation.) So to one ship, time in the other ship moves slower. Let’s use a Lorentz transformation to calculate the rate of time.

Gamma = 1/sqrt(1-v^2) = 1/sqrt(1-.99^2) = 7

So the clock on the other ship ticks off 1 second for every 7 of ours. You can actually see them moving slower.

There’s a really big problem with this thought experiment in that it takes time for light to travel between the 2 ships. Accounting for that makes the calculations much more complicated and obscures the point. So I’m discounting that delay and assuming each ship can see the other in real time.

Now here’s the fun part. The other ship sees time move slower on your ship too. How can that be? http://en.wikipedia.org/wiki/Twin_paradox

5. Jan 21, 2009

### Staff: Mentor

According to an observer who sees one burst of light go west (say) while the other go east, the two light bursts will be seen to separate at twice the speed of light. Meaning that the distance between them will increase at a rate of 2x the speed of light according to that observer. Note that nothing is observed to move faster than light, of course, this is just a calculated separation rate.

6. Jan 21, 2009

### Naty1

yes.
While all the posts here are valid according their frame of reference, when I read you question I thought along the lines of Doc Al (post #5). The key is that all speed IS relative,as implied in the above posts: different observers in varying inertial frames observe different speeds.