We show how trajectories can be reintroduced in quantum mechanics provided that its spatial continuum is modelled by a variable real number (qr-number) continuum. Such a continuum can be constructed using only standard Hilbert space entities. In this approach, the geometry of atoms and subatomic objects differs from that of classical objects. The systems that are non-local when measured in the classical space-time continuum may be localized in the quantum continuum. We compare trajectories in this new description of space-time with (...) the corresponding Bohmian picture. (shrink)

The double slit experiment for a massive scalar particle is described using intuitionistic logic with quantum real numbers as the numerical values of the particle's position and momentum. The model assigns physical reality to single quantum particles. Its truth values are given open subsets of state space interpreted as the ontological conditions of a particle. Each condition determines quantum real number values for all the particle's attributes. Questions, unanswerable in the standard theories, concerning the behaviour of single particles in the (...) experiment are answered. (shrink)