Wave function collapse is the process by which a quantum system transitions from a superposition to a single definite state upon measurement.When a particle is measured, it is as if it suddenly realizes it is being observed and stops playing tricks, choosing one specific state. This instantaneous choice is the wave function collapse.
Erwin Schrödinger introduced the wave function in 1926. Max Born at the same time gave a probabilistic interpretation, but the measurement mechanism remained a mystery. John von Neumann in 1932 introduced the projection postulate (collapse) as a separate process, distinct from unitary evolution. John Stewart Bell in 1964 showed that any hidden-variable theory reproducing quantum predictions must be nonlocal, which was experimentally confirmed by Alain Aspect in the 1980s. The question of whether collapse is a physical process or merely an update of knowledge remains open.
According to the measurement postulate (Born's rule), if a system is in superposition |ψ⟩ = Σ c_i |φ_i⟩, and observable A with eigenvectors |φ_i⟩ is measured, then the probability of outcome i is |⟨φ_i|ψ⟩|² = |c_i|². As a result of measurement, the state collapses to |φ_i⟩. This process is described by the projection operator P_i = |φ_i⟩⟨φ_i|. Mathematically, collapse represents an irreversible transformation that turns the superposition into a statistical mixture described by the density matrix ρ = Σ |c_i|² |φ_i⟩⟨φ_i|. In dynamical collapse models (e.g., Ghirardi-Rimini-Weber), nonlinear stochastic terms are added to the Schrödinger equation so that collapse occurs objectively.
If you measure identical particles many times, the distribution of results will match the probabilities predicted by the wave function before collapse.





















