Ontological equivalence of matrix mechanics and wave mechanics

Ascertain whether Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics describe the same physical reality or merely compute empirically equivalent outcomes, despite their formal equivalence within Hilbert-space theory.

Background

After demonstrating the procedural unification of matrix and wave mechanics and recalling von Neumann’s formal equivalence, the essay emphasizes a remaining philosophical question about their ontological status. It asks whether the two formalisms are not only mathematically equivalent but also describe the same reality.

This unresolved issue underscores the paper’s central theme: formal unification does not necessarily resolve epistemic or metaphysical differences between representational and operational modes of understanding in quantum theory.