The Born Rule is not specifically associated with Newtonian mechanics, but rather with quantum mechanics. The Born Rule, named after physicist Max Born, provides a fundamental principle for determining the probabilities associated with the outcomes of measurements in quantum mechanics.
In quantum mechanics, the state of a system is described by a wave function. The Born Rule states that the probability of obtaining a particular measurement outcome is proportional to the squared magnitude of the corresponding component of the wave function. Mathematically, for a measurement associated with an observable represented by an operator A, the probability of obtaining a specific eigenvalue aᵢ is given by:
P(aᵢ) = |Ψ(aᵢ)|²,
where Ψ(aᵢ) represents the component of the wave function associated with the eigenvalue aᵢ.
The Born Rule is a fundamental postulate of quantum mechanics and plays a central role in determining the probabilities of measurement outcomes. It helps bridge the gap between the mathematical formalism of quantum mechanics and the empirical results obtained from measurements.