This book presents a new ‘partitional' approach to understanding or interpreting the math of standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM. Since at the set level, partitions are the mathematical tool to represent distinctions and indistinctions (or definiteness and indefiniteness), this approach shows how to interpret the key non-classical QM notion of superposition in terms of (objective) indefiniteness between definite alternatives (as opposed to seeing it as the sum of ‘waves'). Thus, the book develops a new mathematical, or indeed, logical, approach to the century-old problem of interpreting quantum mechanics, ensure it is of interest to philosophers of science as well as mathematicians and physicists.
Introduction: The partition renaissance.- Partitions: The logical
concept to describe indefiniteness and definiteness.- The Yoga of
Linearization.- The mathematics of quantum mechanics: the partition
analysis.- Conclusions.- Appendix: Comparisons between skeletal
partition math and QM math.
After receiving a B.S. at MIT (65) and then graduate work at Boston University culminating with a Ph.D. in mathematics (71), I taught for about 20 years in mathematics, computer science, and economics before joining the World Bank for a decade before retirement in 2003. Since then I have been doing research and writing full time mostly in logic, information theory, mathematics, and physics, first in California and now in Slovenia. I have hundreds of articles published in mathematics, information theory, economics, political economy, law, and now physicssee www.ellerman.org. My published books are: The Logic of Partitions: With Two Major Applications. Studies in Logic 101. London: College Publications, 2023. New Foundations for Information Theory: Logical Entropy and Shannon Entropy. Cham, Switzerland: Springer Nature. Putting Jurisprudence Back into Economics: On What Is Really Wrong with Todays Neoclassical Theory. Cham, Switzerland: Springer Nature, 2021. Neo-Abolitionism: Abolishing Human Rentals in Favor of Workplace Democracy, Heidelberg: Springer, 2021. The Uses of Diversity: Essays in Polycentricity. Lanham MD: Lexington Books, 2020. Helping People Help Themselves: From the World Bank to an Alternative Philosophy of Development Assistance. Foreword by Albert O. Hirschman. University of Michigan Press, 2005. South Asia edition published by Tulika Press, New Delhi, India, 2006. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Rowman & Littlefield Inc. 1995. Property and Contract in Economics: The Case for Economic Democracy. Cambridge MA: Basil Blackwell Inc. 1992. The Democratic Worker-Owned Firm. London: Unwin-Hyman Academic. 1990. Revised and published in Chinese as The Democratic Corporation 1997, Xinhua Publishing House, Beijing. Original book reprinted by Routledge Revivals, 2015. Economics, Accounting, and Property Theory. Lexington MA: D.C. Heath, 1982.
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