This statement is to be understood in the following way. Let \(\HC_S\) be the Hilbert spaces of an isolated individual system \(S\), \(\HC_R\) that of the rest of the world, so \(\HC=\HC_S\otimes\HC_R\) is the Hilbert space of the total system. The properties of \(S\) must be represented by a projective decomposition of \(\HC_S\), or by a consistent family of such properties. That \(S\) is isolated means there is no interaction between \(S\) and \(R\), which is to say that for any two times \(t\) and \(t'\) during the period of interest the time development operator of the total system factors: