This paper published in Synthese shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or “toy” model of quantum mechanics over sets (QM/sets).
Counting Direct-sum Decompositions
March 28, 2016 by
This paper uses elementary methods to derive the formulas for and to tablulate (in the case q = 2) two related q-analogs of the Stirling numbers of the second kind and the Bell numbers for direct-sum decompositions (vector space analogs of set partitions) of a finite vector space over a finite field with q elements.
The Existence-Information Duality
October 30, 2015 by
The development of the logic of partitions (dual to the usual Boolean logic of subsets) and logical information theory bring out a fundamental duality between existence (e.g., elements of a subset) and information (e.g., distinctions of a partition). This leads in a more meta-physical vein to two different conceptions of reality, one of which provides the realistic interpretation of quantum mechanics.
Partition Logic talk slides Ljubljana
September 23, 2015 by
Slides from talk on Partition Logic at University of Ljubljana Sept. 8, 2015.
On the Objective Indefiniteness Interpretation of Quantum Mechanics
August 28, 2015 by
Classical physics and quantum physics suggest two different meta-physical conceptions of reality: the classical notion of a objectively definite reality “all the way down,” and the quantum conception of an objectively indefinite type of reality. Part of the problem of interpreting quantum mechanics (QM) is the problem of making sense out of an objectively indefinite reality. Our sense-making strategy is to follow the math by showing that the mathematical way to describe indefiniteness is by partitions (quotient sets or equivalence relations).
Why Delayed Choice Experiments do Not imply Retrocausality
January 23, 2015 by
This is the on-line first version (unpaginated) of my first publication in quantum mechanics. It shows how delayed-choice experiments should be interpreted so they do not imply retrocausality.
Partitions and Objective Indefiniteness in Quantum Mechanics
January 9, 2014 by
The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality–that is described mathematically by partitions. Our sense-making strategy is implemented by developing the mathematics of partitions at the connected conceptual levels of sets and vector spaces. Set concepts are transported to (complex) vector spaces to yield the mathematical machinery of full QM, and the complex vector space concepts of full QM are transported to the set-like vector spaces over ℤ₂ to yield the rather fulsome pedagogical model of quantum mechanics over sets or QM/sets.
Introduction to Partition Logic
January 1, 2014 by
This is an introductory treatment of partition logic which also shows the extension to logical information theory and the possible killer application to quantum mechanics.
Quantum mechanics over sets
October 24, 2013 by
This paper gives a toy model of quantum mechanics over the field 2, where the vectors can be interpreted as subsets of a universe set, and hence the name: “Quantum mechanics over sets.” It gives the “logic” of QM in the old-fashioned sense of the essential logic of a theory pared down to operations on sets (vectors over 2). This includes the simplest logical treatment of the double-slit experiment, Bell’s Theorem, the probability calculus based on Born’s Rule, and much else (all restated in the context of sets).
Seminar in Quantum Information Theory II
December 10, 2012 by
These are the slides from a seminar in quantum information theory and related topics in the Computer Science Department of UC/Riverside during the Spring quarter 2012.