# A small question relating LHC

1. Sep 20, 2008

### pixel01

Hi all,
I've learnt that the LHC has just started. There are two beams of protons which travel clockwise and anti-clockwise at nearly the speed of light. Then the two beams are to colide into each other. My question is whether the speed of one beam compared to the other is at nearly 2 c ?

2. Sep 20, 2008

### mgb_phys

Yes the closing speed is 2c, if you were travelling with one bunch of particles you would measure the other bunch approaching you at c (although what you would measure this with - I'm not sure)

This doesn't violate relativity in any way, no THING is travelling at 2c, just the rate of decrease of the distance between them.

Last edited: Sep 20, 2008
3. Sep 20, 2008

### astromandi

The speed of one beam wrt other is 'c'. NOT 2c

4. Sep 20, 2008

### George Jones

Staff Emeritus
Just before collision, the coordinate distance in the frame of the Earth between bunches of particles traveling in opposite directions decreases at the rate of (nearly) 2c. This is what mgb_phys meant by "closing speed."

5. Sep 20, 2008

### pixel01

So if one man stood on one beam, he would see the second moving at 2c ?. In other way, one beam would travel at 2c if the other beam was considered the frame?

6. Sep 20, 2008

### Fredrik

Staff Emeritus
If the speed of one beam is u and the speed of the other v (both relative to the ground), then the speed of one of the beams relative to the other is

$$\frac{u+v}{1+uv/c^2}$$

For example, if u=v=0.99c (exactly), then the result is (0.99+0.99)c/(1+0.99*0.99)=0.99994949750012... c.