A ‘problem of time’ in the multiplicative scheme for then-site hopper

Abstract

Quantum Measure Theory (QMT) is an approach to quantum mechanics, based on the path integral, in which quantum theory is conceived of as a generalised stochastic process. One of the postulates of QMT is that events with zero quantum measure do not occur, however this is not sufficient to give a full picture of the quantum world. Determining the other postulates is a work in progress and this paper investigates a proposal called the Multiplicative Scheme for QMT in which the physical world corresponds, essentially, to a set of histories from the path integral. This scheme is applied to Sorkin's n-site hopper, a discrete, unitary model of a single particle on a ring of n sites, motivated by free Schrödinger propagation. It is shown that the multiplicative scheme's global features lead to the conclusion that no non-trivial, time-finite event can occur.

Understanding quantum mechanics: a review and synthesis in precise language

“…A central question in this approach is 'what corresponds to the physical world?' One suggestion is that the physical world is represented by an answer to every yes-no physical question that can be asked about the world, once the class of spacetime histories has been fixed [534]. 3.…”