Bornregelen

Bornregelen is the term used in several Nordic and Germanic languages for Born’s rule, a foundational postulate in quantum mechanics named after Max Born. It provides the probabilistic interpretation of the quantum state and connects the mathematical description of a system to observable outcomes.

In its standard form, the rule states that the probability density of finding a particle at position x, given a normalized wavefunction ψ(x,t), is P(x,t) = |ψ(x,t)|^2. For a measurement with discrete outcomes corresponding to eigenstates |φ_i⟩, the probability of obtaining outcome i is P_i = |⟨φ_i|ψ⟩|^2. In the density-matrix formalism, probabilities are written as P_i = Tr(ρ Π_i), where ρ is the state and Π_i is the projector onto the outcome subspace.

History and role: Born introduced this probabilistic interpretation in 1926, addressing how complex wavefunctions relate to experimental statistics. Since then, Bornregelen has become a central component of the standard formulation of quantum mechanics and a universal tool for predicting measurement results.

Interpretations and derivations: While the Born rule is typically treated as a postulate, various theoretical approaches have sought to derive it from deeper principles. Gleason’s theorem provides a mathematical route under certain assumptions, and contemporary discussions also consider derivations from symmetry, information-theoretic considerations, or foundational interpretations of quantum theory.

Applications and significance: The rule underpins the calculation of outcomes in quantum experiments, spectroscopy, quantum computing, and quantum communication. It remains a focal point in discussions of quantum foundations and the nature of probability in quantum mechanics.