Why Be Regular? Part I
Abstract
We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. We first critique a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who argues that the non-regular "position" and "momentum" representations of the Weyl algebra demonstrate that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. We show that there are obstacles to such an intepretation of non-regular representations. In Part II, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods.
Cite
@article{arxiv.1805.05568,
title = {Why Be Regular? Part I},
author = {Benjamin Feintzeig and JB and Manchak and Sarita Rosenstock and James Owen Weatherall},
journal= {arXiv preprint arXiv:1805.05568},
year = {2018}
}
Comments
32 pages, part I of a series