On the Role of Quantum Events in Double-Slit Experiments

TL;DR

This paper presents a novel interpretation of quantum events in double-slit experiments by modeling external influences as boundary conditions, linking wave-particle dualism to basis choices in a Hilbert space framework.

Contribution

It introduces a new formulation of the Schrödinger equation as an external influence boundary condition, offering a fresh perspective on wave-particle duality.

Findings

Wave-particle dualism corresponds to basis choice in Hilbert space.

External influences can be modeled as boundary conditions in Schrödinger's equation.

The approach unifies classical and quantum descriptions through Hilbert space geometry.

Abstract

We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external influences for a given physical system is then equivalent to the Hilbert space of a quantum system without spin. We discuss the double-slit experiment in the context of this approach and show that wave-particle dualism reduces to the choice of a basis in the geometrical construction of the Hilbert space of small external influences.