Michael Kernaghan

About

I am an independent researcher in quantum foundations, affiliated with Pacific Quantum Systems in Vancouver, BC. My work investigates the mathematical structures of quantum mechanics — particularly contextuality, the Kochen-Specker theorem, and the algebraic number theory that controls which measurement configurations exhibit genuinely quantum behaviour.

In the 1990s I published two widely-cited results on Kochen-Specker sets: a 20-vector construction in four dimensions and, with Asher Peres, a 40-vector construction in eight dimensions connecting to GHZ paradoxes. My doctoral dissertation at the University of Western Ontario addressed contextualism and non-locality in quantum mechanics from a philosophy of science perspective.

In 2026 I returned to active research, discovering a complete algebraic classification of KS-producing number rings in dimension three — the "six algebraic islands" — unified by a norm-≤2 cancellation principle. This work produced one main paper and four PRL-style letters.

Education:

Ph.D. in History and Philosophy of Science, University of Western Ontario, 1995
M.A. in Philosophy, McMaster University, 1988

Research Interests

Quantum contextuality and the Kochen-Specker theorem
Algebraic number theory in quantum foundations
Non-locality, Bell's theorem, and hidden-variable models
Philosophy of quantum mechanics and interpretive questions
Computational methods in foundational physics (SAT solvers, graph algorithms)
Quantum advantage and nonlocal games

Publications

Citation metrics: [Google Scholar]

Papers (2026)

Kernaghan, M. "The Algebraic Landscape of Kochen-Specker Sets in Dimension Three." In preparation for Physical Review A.
Kernaghan, M. "New KS Sets from Algebraic Number Fields with Enhanced Contextual Advantage." In preparation for Physical Review Letters.
Kernaghan, M. "Graph Universality of CK-31 and the Norm-2 Boundary." In preparation for Physical Review Letters.
Kernaghan, M. "Computational Evidence for the Optimality of CK-31." In preparation for Physical Review Letters.
Kernaghan, M. "Kochen-Specker Uncolorability in Cyclotomic Fields Requires Exactly 6|n." In preparation for Physical Review Letters.

Journal Articles

Kernaghan, M. and Peres, A. "Kochen-Specker theorem for eight-dimensional space." Physics Letters A, Vol. 198, pp. 1–5, 1995. [DOI]
Kernaghan, M. "Bell-Kochen-Specker theorem for 20 vectors." Journal of Physics A: Mathematical and General, Vol. 27, L829, 1994. [DOI]

Dissertation

Kernaghan, Michael William. "Contextualism and Nonlocality in Quantum Mechanics." Ph.D. Dissertation, University of Western Ontario, 1995. [Institutional Repository] [PhilPapers]

Book Reviews

Kernaghan, Michael. Review of From Physics to Metaphysics by Michael Redhead. Dialogue, 1998.

Projects

Pacific Quantum Systems

A research initiative investigating the mathematical foundations of quantum mechanics and the questions they raise about physical reality.

Links: [Website] [GitHub]

The Contextuality & KS Set Atlas

A companion research site documenting Kochen-Specker set constructions, historical context, computational methods, and the algebraic islands classification.