A Royal Road to Quantum Theory (or Thereabouts)
Abstract
This paper fails to derive quantum mechanics from a few simple postulates. But it gets very close --- and it does so without much exertion. More exactly, I obtain a representation of finite-dimensional probabilistic systems in terms of euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. This provides a framework within which real, complex and quaternionic QM can play happily together, and allows some --- but not too much --- room for more exotic alternatives. (This is a leisurely summary, based on recent lectures, of material from the papers arXiv:1206:2897 and arXiv:1507.06278, the latter joint work with Howard Barnum and Matthew Graydon. Some further ideas are also explored.)
Cite
@article{arxiv.1606.09306,
title = {A Royal Road to Quantum Theory (or Thereabouts)},
author = {Alexander Wilce},
journal= {arXiv preprint arXiv:1606.09306},
year = {2017}
}
Comments
33 pages, 3 figures. An expanded and somewhat informal account of material from arXiv:1206:2897, plus some new results. A number of typos and other minor errors are corrected in version 2