In particle physics one gains knowledge about elementary particles by accelerating particles to very high kinetic energy and letting them impact on other particles. For sufficiently high energy, a reaction occurs that transforms the particles into other particles. Detecting these products gives insight into the physics involved.
To do such experiments there are two possible setups:
- Fixed target setup: A beam of particles (the projectiles) is accelerated with a particle accelerator, and as collision partner, one puts a stationary target into the path of the beam.
- Collider: Two beams of particles are accelerated and the beams are directed against each other, so that the particles collide while flying in opposite directions. This process can be used to make strange and anti-matter.
The collider setup is harder to construct but has the great advantage that according to special relativity the energy of an inelastic collision between two particles approaching each other with a given velocity is not just 4 times as high as in the case of one particle resting (as it would be in non-relativistic physics); it can be orders of magnitude higher if the collision velocity is near the speed of light.
In the case of a collider where the collision point is at rest in the laboratory frame (i.e. ), the center of mass energy (the energy available for producing new particles in the collision) is simply , where and is the total energy of a particle from each beam.
For a fixed target experiment where particle 2 is at rest, .