Abstract
This is a transcription of a conference proceedings from 1985. It reviews the Jordan algebra formulation of quantum mechanics. A possible novelty is the discussion of time evolution; the associator takes over the role of i times the commutator in the standard density matrix formulation, and for the Jordan algebra of complex Hermitian matrices this implies a Hamiltonian of the form H= i[x,y] + λ I for traceless Hermitian x,y and real number λ. Other possibilities for time evolution in the Jordan formulation are briefly considered.