  In the Hilbert space formulation of classical mechanics (CM), pioneered by
Koopman and von Neumann (KvN), there are potentially more observables that in
the standard approach to CM. In this paper we show that actually many of those
extra observables are not invariant under a set of universal local symmetries
which appear once the KvN is extended to include the evolution of differential
forms. Because of their non-invariance, those extra observables have to be
removed. This removal makes the superposition of states in KvN, and as a
consequence also in CM, impossible.
