We may ask, in view of this spreading throughout phase space, how is it possible at all to make predictions in classical mechanics? That is, indeed, a good question. What this spreading tells us is that, no matter how accurately we know the initial state of a system (within some reasonable limits), the uncertainties will tend to grow in time and our initial information may become almost useless. Classical mechanics is, in this kind of sense, essentially unpredictable. (Recall the concept of ‘chaos’ considered above.)
In relation to Hamiltonian Phase Spaces being incomputable in terms of the spread of particles in phase space, even though the volume of psrticles as positions and momenta are virtually unchanged.
