wavefunction collapse

Before you look, a quantum system can be a superposition of many possibilities at once; the instant you measure, you find exactly one. Wavefunction collapse is the name for that abrupt jump from a spread-out superposition to a single definite outcome. It is the most conceptually loaded piece of the formalism and the crux of the measurement problem.

The precise statement is the projection postulate. If you measure observable A on |psi> and obtain the eigenvalue a_n, the state is instantaneously replaced by (projected onto) the corresponding eigenstate |a_n>, renormalized. This update is discontinuous, probabilistic (the outcome is chosen by the Born rule), and non-unitary — it stands in stark contrast to the smooth, deterministic, unitary evolution given by the Schrodinger equation between measurements. That is why re-measuring immediately reproduces the same value: the state is now already an eigenstate.

The essential honesty: collapse is a postulate, and what it really is remains interpretation-dependent and unresolved. The Copenhagen interpretation takes it as a genuine physical process; the many-worlds interpretation denies collapse happens at all and keeps only unitary evolution, with apparent collapse being branching; decoherence explains why interference between outcomes becomes unobservable for macroscopic apparatus but does not by itself pick a single outcome. No experiment yet distinguishes these, and the tension between smooth Schrodinger evolution and sudden collapse is the unsolved measurement problem.