Why is it that a noncanonical transformation that leaves H invariant does not map a solution into another? Or, in view of the discussions on consequence II, why is it that an experiment and its transformed version do not give the same result when the transformation that leaves H invariant is not canonical? It is best to consider an example. Consider the potential given in Exercise 2.8.3. Suppose I release a particle at (x=a,y=0) with (px=b,py=0) and you release one in the transformed state in which (x=0,y=a) and (px=b,py=0), i.e., you rotate the coordinates but not the momenta. This is a noncanonical transformation that leaves H invariant. Convince yourself that at later times the states of the two particles are not related by the same transformation. Try to understand what goes wrong in the general case.