Deriving the Probabilistic Structure of Quantum Mechanics
The Born rule is a fundamental postulate in the orthodox formulation of quantum mechanics. It says that if a system is in the (normalized) state |ψ⟩ and an observable represented by the operator O is measured, then only eigenvalues λi of O will be obtained in the measurement, with probabilities |⟨λi | ψ⟩|2, where O | λ⟩ = λi | λ⟩. This postulate provides a meaningful connection between the other postulates of quantum mechanics and experimental observations. Over the years many attempts have been made to prove, rather than postulate, the Born rule, from first principles, with the goal of clarifying the inherently probabilistic nature of quantum processes. No consensus exists as to whether this program has been entirely successful. This presentation is a brief pedagogical overview of these attempts.