Wave-function collapse

In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation"). It is the essence of measurement in quantum mechanics and connects the wave function with classical observables like position and momentum. Collapse is one of two processes by which quantum systems evolve in time; the other is continuous evolution via the Schrödinger equation. However, in this role, collapse is merely a black box for thermodynamically irreversible interaction with a classical environment. Calculations of quantum decoherence predict apparent wave function collapse when a superposition forms between the quantum system's states and the environment's states. Significantly, the combined wave function of the system and environment continue to obey the Schrödinger equation.

In 1927, Werner Heisenberg used the idea of wave function reduction to explain quantum measurement. Nevertheless, it was debated, for if collapse were a fundamental physical phenomenon, rather than just the epiphenomenon of some other process, it would mean nature was fundamentally , i.e. nondeterministic, an undesirable property for a theory. This issue remained until quantum decoherence entered mainstream opinion after its reformulation in the 1980s. Decoherence explains the perception of wave function collapse in terms of interacting large- and small-scale quantum systems, and is commonly taught at post-introductory level (e.g. the Cohen-Tannoudji textbook). The quantum filtering approach and the introduction of quantum causality non-demolition principle allows for a classical-environment derivation of wave function collapse from the stochastic Schrödinger equation.

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