A one-world interpretation of quantum mechanics

The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules of probability theory apply to it when it interacts with a quantum system. Under mild assumptions, we recover the unitary dynamics, collapse and Born rule postulates from quantum theory. Nonetheless, there is no decoherence, because the quantum state remains pure conditioned on the classical trajectory. This results in one world, rather than many-worlds. Our main technical tool is to exploit a change of measure on the space of classical paths, the functional form of which is shown to characterise the quantum dynamics and Born rules of a class of quantum-like theories.