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A Royal Road to Quantum Theory (or Thereabouts)

Department of Mathematics, Susquehanna University, Selinsgrove, PA 17870, USA
Entropy 2018, 20(4), 227; https://doi.org/10.3390/e20040227
Received: 15 January 2018 / Revised: 14 March 2018 / Accepted: 19 March 2018 / Published: 26 March 2018
(This article belongs to the Special Issue Quantum Information and Foundations)
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Abstract

This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, 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, developing the connection between conjugate systems and the possibility of forming stable measurement records and making connections between this approach and the categorical approach to quantum theory.) View Full-Text
Keywords: reconstruction of quantum mechanics; conjugate systems; Jordan algebras reconstruction of quantum mechanics; conjugate systems; Jordan algebras
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Wilce, A. A Royal Road to Quantum Theory (or Thereabouts). Entropy 2018, 20, 227.

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