Born rule: quantum probability as classical probability

Understand

I provide a simple derivation of the Born rule as giving a classical probability, that is, the ratio of the measure of favorable states of the system to the measure of its total possible states.

• In classical systems, the probability is due to the fact that the same macrostate can be realized in different ways as a microstate.
• Despite the radical differences between quantum and classical systems, I show that the same can be applied to quantum systems, and the result is the Born rule.
• This works only if the basis is continuous (an eigenbasis of observables with continuous spectra), but all known physically realistic measurements involve a continuous basis (the position basis).