  We examine certain nonassociative deformations of quantum mechanics and
gravity in three dimensions related to the dynamics of electrons in uniform
distributions of magnetic charge. We describe a quantitative framework for
nonassociative quantum mechanics in this setting, which exhibits new effects
compared to ordinary quantum mechanics with sourceless magnetic fields, and the
extent to which these theoretical consequences may be experimentally testable.
We relate this theory to noncommutative Jordanian quantum mechanics, and show
that its underlying algebra can be obtained as a contraction of the alternative
algebra of octonions. The uncontracted octonion algebra conjecturally describes
a nonassociative deformation of three-dimensional quantum gravity induced by
magnetic monopoles, which we propose is realised by a non-geometric
Kaluza-Klein monopole background in M-theory.
