Max Born, a German physicist, formulated the Born rule in 1926 while working on the foundations of quantum mechanics. The Born rule provides a probabilistic interpretation of the wave function, linking it to the probability of obtaining specific measurement outcomes.
At the time, quantum mechanics was still in its early stages of development, and there were debates and discussions about the interpretation of the wave function. Born's key insight came from considering the wave function as a mathematical tool to describe the state of a quantum system rather than a physical entity itself.
Born proposed that the square of the amplitude of the wave function, known as the wave function's modulus squared, is directly related to the probability density of finding a particle in a particular state. In other words, the probability of observing a particle in a given state is proportional to the square of the absolute value of the wave function.
This idea of relating probabilities to the wave function was a departure from the earlier ideas of wave mechanics, which focused primarily on the deterministic aspects of the wave function and did not explicitly incorporate probabilities. Born's probabilistic interpretation provided a bridge between the mathematical formalism of quantum mechanics and experimental observations, enabling the calculation of measurable quantities.
It's worth noting that the development of the Born rule was also influenced by the work of other physicists of that time, such as Werner Heisenberg and Pascual Jordan, who were exploring similar ideas regarding the probabilistic nature of quantum phenomena.
The Born rule, with its probabilistic interpretation, has since become an essential part of quantum mechanics and is widely accepted as a fundamental principle. It allows for the calculation of probabilities and statistical distributions of measurement outcomes, which have been confirmed through numerous experimental tests and observations. While the Born rule itself cannot be derived from other principles of quantum mechanics, its effectiveness in predicting experimental results has solidified its significance in the field.