<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The goals of this paper fall into three related areas: (i) we present an overview of a universal algebraic paradigm in which measurement specialists can construct formal models of measurement in a unified manner and systematically reason about a large class classical measurement operations, (ii) we construct convenient von Neumann quantity algebras and quantity-channels between them to represent measurements, and introduce the dual framework of state spaces and state-channels between them to investigate the statistical structure of measurements, and (iii) we provide several detailed examples that illustrate the power and versatility of algebraic approaches to measurement procedures.</p></abstract>

The goals of this paper fall into three related areas: (i) we present an overview of a universal algebraic paradigm in which measurement specialists can construct formal models of measurement in a unified manner and systematically reason about a large class classical measurement operations, (ii) we construct convenient von Neumann quantity algebras and quantity-channels between them to represent measurements, and introduce the dual framework of state spaces and state-channels between them to investigate the statistical structure of measurements, and (iii) we provide several detailed examples that illustrate the power and versatility of algebraic approaches to measurement procedures.

Algebraic Frameworks for Measurement in the Natural Sciences

Departments of Philosophy, Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA 19104, USA

Measurement Science Review

{"article-title":"Algebraic Frameworks for Measurement in the Natural Sciences"}

The goals of this paper fall into three related areas: (i) we present an overview of a universal algebraic paradigm in which measurement specialists can...

Algebraic Frameworks for Measurement in the Natural Sciences

Published Online: Dec 15, 2012

Page range: 213 - 233

DOI: https://doi.org/10.2478/v10048-012-0032-7

This content is open access.