# Relativistic energy and momentum in particle collisions

1. Apr 29, 2010

### swe91

1. The problem statement, all variables and given/known data
Two particle P and Q each of restmass m0 and moving in collision course at 2/3c in the laboratory frame of reference.
In the same collision but in particle P's frame of reference, P is at rest.
2. Relevant equations
As the total energy of the particles depends on the frame of reference, do the observers in each frame of reference agree on the number of particles and photons formed in the collision?
3. The attempt at a solution
From
E=$$\gamma$$m0c2
p=$$\gamma$$m0v
where v=v' from relativistic velocity addition.
and
E2=p2c2+m02c4
I can conclude that the total energy and momentum of the the collision differs. Furthermore, as I do not se how the available energy for particle formation can be the same when the total energy is different, I would conclude that the number of particles would differ depending on the reference frame. However, this does not feel right. As the collision takes place at a "single point" in space, wouldn't it be measured the same from all inertial frames of reference?

2. Apr 29, 2010

### nickjer

Hmmm.... Well it is true that momentum and energy change between different frames. People use the invariant rest mass to solve problems like this. But "number" of particles shouldn't be affected by relativity. The energy of the final products may be different but the total number of products won't change.

3. May 2, 2010