- 14 Separability , Preferred Bases , and the Nonconservation of Quantities

A solution to the preferred basis problem of Everett’s relative state formalism is presented. The solution does not rely on detailed properties of the observer, apart from the necessity of having at least one distinct state for each possible measurement result, and an initial state. It is argued that our concept that one entity is distinct from another arises from an approximation that the Hilbert space is factorisable in a manner compatible with the Hamiltonian. Conservation of angular momentum is shown to be inconsistent with the Copenhagen interpretation of quantum mechanics. In particular, it is not consistent to suppose that the measuring device absorbs angular momentum lost by the quantum system during measurement. It is shown that it is theoretically possible to observe violations of conservation of quantities whose associated operators commute with the Hamiltonian. This is explainable in the context of the “many-worlds” picture as the storage of some of the quantity in the relative signs of the superimposed worlds. A simple method of “generating” angular momentum is described. An example is given of a device which can turn a beam of spin-up particles into a beam of spin-down particles, without itself absorbing any angular momentum. This method cannot be used to generate energy. [email protected]