A "problem of time" in the multiplicative scheme for the $n$-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.

24 pages, 2 figures. Now published in J. Phys. A: Math. Theor. under CC-BY. New version expands section 3.1 and corrects typos

References in corpus (3)

• Quantum Dynamics without the Wave Function
• The birth of spacetime atoms as the passage of time
• An exercise in "anhomomorphic logic"

Cited by in corpus (1)

• Understanding quantum mechanics: a review and synthesis in precise language