Space representing all possible states of the universe. A point in phase space completely describes the state at a given instant. In a classic Newtonian world with n particles, there would be 6n dimensions in its phase space; three spatial dimensions and three momentum dimensions for each particle, representing its position and momentum vector.

A Hamiltonian function describes the evolution of points in phase space over time. Not only points are interesting, but solids as well. For instance, a hypersphere in phase space with radius one would describe all possible universes described by measurements with an rms error of one. An interesting theorem by Joseph Liouville proves that for any given region in phase space, the volume will remain the same. However, this does not confine the region; it continually spreads out and grows more and more convoluted.