Obtaining the Born Rule from the Many-Worlds Interpretation of Everettian Mechanics: A Deterministic Approach to the Measurement Problem

In this project, we explore how the Born rule, which yields the probabilities of outcomes following a quantum measurement, arises from the many-worlds interpretation (MWI) of Everettian mechanics, in context of the measurement problem. The measurement problem is based on the phenomenon of superposition collapse upon observation, as posited by the Copenhagen interpretation. In contrast, the MWI suggests that when a measurement is made, the universe branches into multiple, non-interacting worlds, with each containing a different outcome. In the case of a pair of entangled particles in a spin-state superposition, we demonstrate how the Born rule emerges from branching, where the relative frequencies of outcomes across all branches matches with the probabilities given by the square of the wavefunction's amplitude. This framework put forth by Everettian mechanics addresses the measurement problem by providing a deterministic-evolution approach that still preserves the randomness of measurements. In addition, we explore further implications of entangled states and the role of observers within this context, in how their entanglement with the measurement reinforces the Born Rule. Our analysis incorporates entanglement mechanics and the Hilbert Space formalism to model our outcomes, offering a perspective on the MWI's implications on non-locality, which is key to fundamental theorems like Bell's theorem.