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 6

*n* 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.