How Can the No-Collapse and the Collapse Interpretations of Quantum-Mechanics Give the Same Description?

TL;DR

This paper demonstrates that no-collapse and collapse interpretations of quantum mechanics can produce identical observable predictions when using Von Neumann-Lüders projection, clarifying their relationship and differences.

Contribution

It provides a detailed analysis showing the equivalence of the two interpretations under certain conditions and discusses their distinguishability and conceptual differences.

Findings

Both interpretations yield identical observable states under Von Neumann-Lüders projection.

Distinguishability between the interpretations exists in principle but is practically challenging.

Illustrations include simple slit experiments and Mach-Zehnder interferometers.

Abstract

It is shown that no-collapse and collapse interpretations of quantum mechanics give equal object states (which predict everything that is observable) if one bases the relevant relations on the Von Neumann-L\"uders 'projection'. This connection is elaborated in detail from simple to most general cases. Distinguishability of the two approaches, which exists in principle, is also discussed. In the very simple illustration of passing one slit physical-insight difficulties in the collapse approach are indicated. For the purpose of interference between the two wavefunction components also the Maxh-Zehnder interferometer is discussed.