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 -site hopper, a discrete, unitary model of a single particle on a ring of sites, motivated by free Schr\"odinger propagation. It is shown that the multiplicative scheme's global features lead to the conclusion that no non-trivial, time-finite event can occur.
Keywords
Cite
@article{arxiv.1706.03793,
title = {A "problem of time" in the multiplicative scheme for the $n$-site hopper},
author = {Fay Dowker and Vojtěch Havlíček and Cyprian Lewandowski and Henry Wilkes},
journal= {arXiv preprint arXiv:1706.03793},
year = {2017}
}
Comments
24 pages, 2 figures. Now published in J. Phys. A: Math. Theor. under CC-BY. New version expands section 3.1 and corrects typos