"One of the most profound and mysterious principles in all of physics is the Born Rule, named after Max Born. In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The Born Rule is then very simple: it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. (The wave function is just the set of all the amplitudes.) … The Born Rule is certainly correct, as far as all of our experimental efforts have been able to discern. But why? … The status of the Born Rule depends greatly on one’s preferred formulation of quantum mechanics. … Everett, … is claiming that all the weird stuff about “measurement” and “wave function collapse” in the conventional way of thinking about quantum mechanics isn’t something we need to add on; it comes out automatically from the formalism. The trickiest thing to extract from the formalism is the Born Rule."
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Sean M. Carroll, "Why Probability in Quantum Mechanics is Given by the Wave Function Squared" (July 24, 2014)
https://en.wikiquote.org/wiki/Born_rule
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