The Heisenberg Interpretation of Quantum Mechanics

In his book `Physics and Philosophy', Werner Heisenberg posited a distinction between the quantum and the classical worlds, which he characterized in terms of "potentialities or possibilities" versus "things and facts". However, the standard quantum formalism does not express such distinctions.
In this talk, we present a concrete implementation of this distinction into the quantum formalism, resulting in what will be called the Heisenberg interpretation of quantum mechanics. The modification of the formalism mainly involves replacing state reduction by a composition of two maps between the Hilbert space and a set of corresponding classical states. These maps represent the emergence and submergence of a classical state from a quantum state from interactions currently labeled as "measurements". This modified formalism has a number of advantages over the Copenhagen interpretation and sets the stage for experimental predictions which are not obvious under the standard formalism.