A key feature to the success of a high energy collider is the beam brightness or luminosity. The beam brightness is determined by particle motion or evolution though the accelerator chain. To first order, the motion of particles in an accelerator can be described by simple harmonic motion around an ideal trajectory or energy. This motion can be portrayed using the concept of phase space.
This talk will use the Fermilab Tevatron collider as an example of the importance of phase space in high energy colliders. The use of antiprotons in the Tevatron pose additional challenges that are clearly illustrated with the concept of phase space.