We present an axiomatic modification of quantum mechanics with a
possible worlds semantics capable of
predicting essential “nonquantum” features of an observable universe model—the
topology and
dimensionality of spacetime, the
existence, the
signature and a
specific form of a metric on it, and a set of naturally preferred directions (
vistas) in spacetime unrelated to its metric properties.
Keywords Geometrical quantum mechanics - Quaternion - Principal metric - Lorentzian - Hyper-Kähler - Birkhoff category - Topos - FLRW metric - Boolean - Measurement - Propensity - Cosmology