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
