Situated Observation and the Quantum Measurement Problem

H. D. Zeh

Volkher B. Scholz, Reinhard F. Werner

The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing the observables are then acting non-trivially only on one of the tensor factors. However, the same situation can also be modelled by just using one joint Hilbert space, and requiring that all operators associated to different observers commute, i.e. are jointly measurable without causing disturbance. The problem of Tsirelson is now to decide the question whether all quantum correlation functions between two independent observers derived from commuting observables can also be expressed using observables defined on a Hilbert space of tensor product form. Tsirelson showed already that the distinction is irrelevant in the case that the ambient Hilbert space is of finite dimension. We show here that the problem is equivalent to the question whether all quantum correlation functions can be approximated by correlation function derived from finite-dimensional systems. We also discuss some physical examples which fulfill this requirement.

Časlav Brukner

Edgar Shaghoulian

The measurement problem in quantum mechanics is almost exclusively discussed in situations where gravity is ignored. We discuss some recent developments in our understanding of quantum gravity and argue that they significantly alter the problem. Quantum gravity may even resolve one of the thorniest questions in discussions of the measurement problem: who collapses the wavefunction of the entire universe?

Nancy Delaney Cartwright

Abstract Precursing now popular ‘spontaneous reduction’ views, this chapter argues that the measurement problem in quantum mechanics is not a problem of measurement at all. Reductions happen in a variety of circumstances and are particularly important in the preparation of quantum states. But there is no reason to think there is any simple physical characterization of situations in which reduction of the wave packet occurs from when it does not. There is a difference in the mathematical characteristics of the evolution operator between the two (unitary operators versus non‐unitary), but this mathematical difference need mark no interesting physical difference distinguishing the situations to which operators apply.

Gregg S. Jaeger