[math-fun] octonionic physics
I love octonions as well as other algebraic objects in the large spectrum of non-associative mathematical laws, I investigate some of their properties and use for other parts of mathematics but I don't take for granted that the mathematics I like ought to be incorporated into the fabric of space-time. This is the contrary of the very ancient habit documented by platonic dialogs were each regular polyhedron is associated with a given "element". The current thread on the theories of one colorful Cohl Furey brings the more general problem of looking into non-associativity in mainstream mathematical physics, and by that I don't mean very very high energy physics happening hypothetically one femtosecond after the Big Bang or inside a black hole or at the Planck scale. Those are valuable pursuits, but to me three centuries of modern physics have given us remarquable inter-reactions between mathematical speculations and physics investigations at the observatory, laboratory or industrial plant scale. Take a few families of examples - complex numbers for electromagnetism (notably electric signals, filters), wave mechanics, - functional analysis, non commutativity and quantum mechanics, atomic structure, - path integrals and high energy particles collisions (QCD, quarks and gluons, etc.). Is there at least one case in this kind of current or future "core" physics where an octonionic or sedenionic model or interpretation brings an added value to our knowledge of phenomena or our prediction ability or reveal an internal structure ? (I propose not to include classical Lie algebras in this thread, although these are partially non-associative) As an example, I have heard several times of octonionic or generally 2^n-dimensional algebra based fluid mechanics but never saw something very definite or a report about a real-world problem computed in this way or an insight gleaned about the equations of fluids or the structure of space. Olivier
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Olivier Gerard