The collapse problem as a consistency problem. Is the quantum measurement hypothesis consistent with conservation laws?

Research output: Contribution to journalArticlepeer-review


In his book Mathematical Foundations of Quantum Mechanics von Neumann asserted that the state vector must collapse upon measurement of any self-adjoint operator. This assertion was based on his reading of the Compton-Simon experiment. However, comparing von Neumann's account with the Compton-Simon paper itself, we find that von Neumann had completely misinterpreted the experiment. Compton and Simon had measured two angles on the same photographic plate; in von Neumann's reading it became two successive measurements which gave identical results, where the experimenter could choose which measurement to perform first. In short, von Neumann's case for collapse simply did not exist! In quantum mechanics, superpositions of different eigenvalues of conserved observables are freely admissible, but conservation laws require successive measurements of a conserved quantity upon the same object to return the same value (if the object is isolated and moves under a Schrödinger equation). This can be guaranteed only if the first measurement has caused the state vector to collapse. Thus collapse is a consistency condition which the theory must satisfy. Consistency problems are solved by displaying examples, or models, which fulfil the conditions in question. We therefore have to construct a mathematical model of the measurement process. This requires taking a stand on whether the measuring instrument does (Bohr) or does not (von Neumann–Wigner) have a classical description. If it does not, the ‘quantum measurement problem’ is insoluble. If it does, the problem – for conserved quantities – does have a solution, given by Sewell in 2005. The model displays collapse while evolving under the Schrö- dinger equation with a time-dependent hamiltonian; it does not have to call upon the observer's ‘conscious ego’. Its existence shows that additive conservation laws are consistent with the superposition principle and Schrödinger evolution. Measurement of a conserved observable returns an eigenvalue of the observable; measurement of a non-conserved observable returns a diagonal matrix element of the observable in the basis of energy eigenvectors.

Original languageEnglish
Article number169462
JournalAnnals of Physics
StatePublished - 1 Nov 2023


  • Collapse hypothesis
  • Measurement theory
  • Superposition principle and conservation laws

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'The collapse problem as a consistency problem. Is the quantum measurement hypothesis consistent with conservation laws?'. Together they form a unique fingerprint.

Cite this