Back to Bohr: Quantum Jumps in Schroedinger's Wave Mechanics

TL;DR

This paper explores the measurement problem in quantum mechanics by analyzing wave function collapse and quantum jumps within wave mechanics, using a scattering array of harmonic oscillators to interpret inelastic scattering as quantum jumps.

Contribution

It introduces a model of a scattering array of harmonic oscillators to interpret quantum jumps and wave function collapse within wave mechanics, emphasizing an epistemic view of the wave function.

Findings

Wave function collapse occurs around single oscillator sites during inelastic scattering.

Inelastic scattering states are superpositions of possible scattering events.

Quantum jumps correspond to actual inelastic scattering events.

Abstract

The measurement problem of quantum mechanics concerns the question under which circumstances coherent wave evolution becomes disrupted to produce eigenstates of observables, instead of evolving superpositions of eigenstates. The problem needs to be addressed already within wave mechanics, before second quantization, because low-energy interactions can be dominated by particle-preserving potential interactions. We discuss a scattering array of harmonic oscillators which can detect particles penetrating the array through interaction with a short-range potential. Evolution of the wave function of scattered particles, combined with Heisenberg's assertion that quantum jumps persist in wave mechanics, indicates that the wave function will collapse around single oscillator sites if the scattering is inelastic, while it will not collapse around single sites for elastic scattering. The Born rule for position observation is then equivalent to the statement that the wave function for inelastic scattering amounts to an epistemic superposition of possible scattering states, in the sense that it describes a sum of probability amplitudes for inelastic scattering off different scattering centers, whereas at most one inelastic scattering event can happen at any moment in time. Within this epistemic interpretation of the wave function, the actual underlying inelastic scattering event corresponds to a quantum jump, whereas the continuously evolving wave function only describes the continuous evolution of probability amplitudes for scattering off different sites. Quantum jumps then yield definite position observations as defined by the spatial resolution of the oscillator array.