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Search for an Extension of Quantum Mechanics

Giulia Gualdi, Karim Murr

What we mean by extension of quantum mechanics is a new theory, not an interpretation of it. The current status of experimental and theoretical physics is that quantum mechanics “works”, and as Steven Weinberg (Nobel Prize 1979) puts it, working in such a field of research is such that “very often you do not know what is the right problem until you are close to solving it.” We are working on changing the algebraic structure of the quantum theory prior to changing the dynamics. The first route is to enlarge the notion of a group in the sense of Évariste Galois. Instead of working with binary operations, which enter a Galois group and derivatives such as rings and fields etc, one can construct n-ary algebraic structures to represent complex quantum correlations. Another research line is to view the wavefunction, and more generally a given complex number as composed of more abstract numbers. These numbers cannot be complex numbers, otherwise we end up in a tautological argument. Due to physical constraints, we found that these numbers will most likely belong to a new algebra, different from hypercomplex numbers for instance.