Derivation of the Born Rule from Many-Worlds Interpretation and Probability Theory
Ken‐ichi Sugiyama
The Born rule is a rule that a probability we observe a small particle like an electron is proportional to the square of the absolute value of the wave function. In this paper, we try to derive the Born rule from the many-worlds interpretation. Many researchers have tried to derive the Born rule (also called Born's rule, Born's law, or probability interpretation) from Many-Worlds Interpretation (MWI). However, no one succeeds. Thus, the derivation of Born’s rule had become an important issue for MWI. We try to derive Born’s rule by introducing an elementary event of probability theory to the quantum theory as a new method. We interpret the wave function as a manifold like a three-dimensional sphere, and interpret the absolute value of the wave function as the surface area of the manifold. We suppose that the manifold exists in the discrete space that has lattice points. We interpret a point on the surface of the manifold as a state that we cannot divide any more, an elementary state. We draw an arrow from any point to any point. We interpret an arrow as an event that we cannot divide any more, an elementary event. Probability is proportional to the number of elementary events, and the number of elementary events is the square of the number of elementary states. The number of elementary states is proportional to the surface area of the manifold, and the surface area of the manifold is the absolute value of the wave function. Therefore, the probability is proportional to the square of the absolute value of the wave function.
•Apr 1, 2014•0 citations