  Quantum and classical mechanics share a common algebraic formalism which is
expressed naturally in the language of category theory. A third realization of
this formalism is the so-called hyperbolic quantum mechanics where
split-complex numbers replace the usual complex numbers. We introduce and
explore the corresponding generalization of C*-algebras and prove that
hyperbolic quantum mechanics is not a viable candidate for describing Nature.
Quantum and classical mechanics are the only acceptable theories of Nature
which are invariant under tensorial composition.
