Cycles of Time: An Extraordinary New View of the Universe

by Roger Penrose

For a system of d degrees of freedom, the configuration space would be a d-dimensional space. For example, if the system consisted of q point particles p1, p2, …, pq (each without any internal degrees of freedom), then the configuration space would have 3q dimensions. This is because each individual particle requires just three coordinates to determine its position, so there are 3q coordinates overall, whereby a single point P of configuration space defines the locations of all of p1, p2,…, pq together (see Fig. 1.4). In more complicated situations, where there are internal degrees of freedom as above, we would have more degrees of freedom for each such particle, but the general idea is the same.