I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and the (...) boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)

Two principles of locality used in discussions about quantum mechanics are distinguished. The intuitive no-action-at-a distance requirement is called physical locality. There is also a mathematical requirement of a kind of factorizability which is referred to as "locality". It is argued in this paper that factorizability is not necessary for physical locality. Ways of producing models that are physically local although not factorizable which are concerned with correlations between the behavior of pairs of particles are suggested. These models can account (...) for all the quantum mechanical single and joint probabilities. (shrink)