Understanding the quantum measurement problem is closely associated with understanding wave function collapse. Motivated by Breuer's claim that it is impossible for an observer to distinguish all states of a system in which it is contained, wave function collapse is tied to self observation in the Schmidt biorthonormal decomposition of entangled systems. This approach provides quantum mechanics in general and relational quantum mechanics in particular with a clean, well motivated explanation of the measurement process and wave function collapse. Relational quantum mechanics 1 provides a parsimonious interpretation of quantum mechanics that has many compelling features. However the nature of the measurement process and wave function collapse is left rather vague. In this paper their nature is clarified using the Schmidt biorthonormal decomposition and self observation. While the arguments are presented in the frame work of relational quantum mechanics they are quite general, depending only on the quantum state being described by a probability amplitude.

In the last decades huge theoretical effort was devoted to the development of consistent theoretical models, aiming to solve the so-called "measurement problem", to which John Bell dedicated part of his thoughts. Among these, the Dynamical Reduction Models possess the unique characteristic to be experimentally testable, thus enabling to set experimental upper bounds on the reduction rate parameter λ characterizing these models. Analysing the X-ray spectrum emitted by an isolated slab of Germanium, we set the most stringent limit on the parameter λ up to date.

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