Project Euclid (Cornell University) · 2001 · 12 citations · 0 references
Natural SciencesPhilosophyPhysicsMathematical PhysicsQuantum MechanicsTheoretical PhysicsClassical MechanicsHilbert Space FormalismIntuitionistic LogicPhilosophy Of PhysicsQuantum PhysicsQuantum StatesBell's TheoremInterpretations Of Quantum MechanicsMany-body Quantum MechanicsQuantum HamiltonianQuantum Mechanical ModelQuantum Mechanics ModelingQuantum-to-classical Transition
Intuitionistic real numbers are constructed as sheaves on the state space of the Schrodinger representation of a CCRalgebra with a finite number of degrees of freedom. These numbers are used as the values of position and momentum variables that obey Newton's equations of motion. Heisenberg's operator equations of motion are shown to give rise to numerical equations that, on a family of open subsets of state space, are local approximations to Newton's equations of motion for the intuitionistically valued variables.