 The main challenge for AMI is to justify the assumption that there is a preferred partition of the universe and to provide some idea about what this factorization should look like. AMI also faces another problem. A non-atomic quantum system \(S^{\sigma}\), defined as composite of atomic quantum systems, does not necessarily have properties that correspond to the outcomes of measurements. The reason is that the system \(S^{\sigma}\) might be in the quantum state \(\varrho^{\sigma}\) with an eigenprojector \(\Pi^{\sigma}\) such that \(\mathrm{Tr}^{\sigma}(\varrho^{\sigma}\Pi^{\sigma}) = 1\). This implies that if one measured the property represented by \(\Pi^{\sigma}\), one would obtain a positive outcome with probability 1. But it may be the case that the projector \(\Pi^{\sigma}\) is not a composite of atomic properties and, therefore, according to AMI, it is not a property possessed by the composite quantum system \(S^{\sigma}\). 