1210.6371 (Jeffrey Bub)

Quantum Correlations and the Measurement Problem    [PDF]

Jeffrey Bub

The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are probabilistic correlations that lie outside the classical correlation polytope, which has the structure of a simplex. The replacement of the classical simplex as the structure representing probabilistic correlations by the quantum convex set is the analogue in quantum mechanics of the replacement of Newton's Euclidean space and time by Minkowski spacetime in special relativity. The 'no go' hidden variable theorems tell us that we can't shoe-horn these correlations into the classical simplex by supposing that something has been left out of the story. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of non-simplex theories. This paper is an elaboration of these ideas, and its consequences for the measurement problem of quantum mechanics. A large part of the difficulty is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable is only apparent and depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation resolves the problem.

View original: http://arxiv.org/abs/1210.6371