3.4.4.4 Wave-Function Collapse
In his same 1927 paper on the uncertainty principle, Heisenberg introduced the concept of wave-function collapse. In 1932, von Neumann incorporated this concept into the mathematical formulation of Quantum Mechanics, as we shall see in section 4.6.
As we have already described above, the quantum system is always in a superposition state which evolves according to the Schroedinger equation, until a measurement is made, thus causing the wave-function to collapse to just one of the basis states, and the property being measured uniquely acquires the eigenvalue of that particular state. After the collapse, the system again evolves according to the Schroedinger equation.
The wave-function collapse is a fundamental problem in the interpretation of Quantum Mechanics, known as the measurement problem, or the effect of the observer, as we shall describe it further in section 4.4.5, so some interpretations discard this collapse process and reformulate the relation between measurement apparatus and the system. The existence of the wave-function collapse is required in the Copenhagen interpretation, the objective collapse interpretations, the transactional interpretation, and the von Neumann interpretation in which consciousness causes the collapse. In many other interpretations, the collapse of wave-function is considered a redundant or optional approximation.
The significance to the wave-function varies from one interpretation to another, depending of whether it merely encodes the observer’s knowledge of the system, or if it is physically real. The collapse itself is a forced expression for the observation or measurement which requires replacing the description of an uncertain state of a system by a description of the system in a definite state that was obtained by the measurement.