The foundation for parallel worlds begins with the fundamental mystery of quantum mechanics, specifically the phenomenon known as superposition. When particles are not being observed, quantum theory suggests they exist in all possible states simultaneously, like a coin that spins in the air being both heads and tails until it lands and we observe the result. The famous thought experiment of Schrödinger's cat illustrates this peculiar aspect of quantum reality, where a cat in a sealed box can be simultaneously alive and dead until someone opens the box to observe its state.
The mathematical formalism of quantum mechanics describes reality through wave functions, complex mathematical entities that encode all possible states of a quantum system. These wave functions evolve according to Schrödinger's equation, which is completely deterministic and reversible, yet when we make measurements, we observe only one specific outcome from all the possibilities contained within the wave function. This discrepancy between the smooth evolution of the wave function and the discrete, random outcomes of measurements constitutes what physicists call the measurement problem.