Quantum Systems Based Upon Galois Fields — From Sub-Quantum to Super-Quantum Correlations

Abstract

Dedicated to Freeman Dyson on the occasion of his 90th birthdayIn this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.

Interference and Oscillation in Nambu Quantum Mechanics

“…Various proposals for alternative QM theories can be found in the literature. The field/division algebra over which the state space is constructed has been modified from C to R [10], H [11], O [12][13][14], and the finite fields F q [15][16][17][18][19][20][21]. Non-linear corrections to the Schrödinger equation have been considered by Weinberg [22,23].…”

The Nakano–Nishijima–Gell-Mann Formula from Discrete Galois Fields

“…Recently, with the development of quantum information, Galois fields have begun to be used to construct space-time models as error-correcting codes [33]. Further application of Galois fields is expected in the foundation of quantum physics [34] and time crystal with discrete space-time symmetry [20][21][22][23][24].…”

The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields

“…Recently, with the development of quantum information, Galois fields have begun to be used to construct space-time models as error-correcting codes [31]. Further application of Galois fields is expected in the foundation of quantum physics [32] and time crystal with discrete space-time symmetry [20][21][22][23][24].…”