Born Rule and its Interpretation

Ruth E. Kastner

Lev Vaidman A

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.

Qian Li

Abstract In this paper, we analyze the thought experiment of "Wigner's friend" and point out that new understanding should be made to Born's rule and measurement process: Born's rule is no longer seen as a rule based on the history of the quantum system's, and the measurement results are no longer directly related to the state of the measured object before the measurement. Inspired by Everett III and H. Zurek's views, we believe that Born's rule reflects the coordination between different parts of the measured results in quantum entanglement systems, so it has nothing to do with the history of particles themselves but rather with the history records. A new interpretation of quantum mechanics is proposed, which is an objective interpretation. Under this interpretation, micro-particles can also be assigned definite states before being observed. Based on this interpretation, Wigner's friend-like scenarios or paradoxes extending Wigner's friend-like scenarios can be effectively explained. The new interpretation brings brand-new perspectives to many quantum phenomena. We also point out potential applications of the new interpretation in the future.

Robert B. Griffiths

John B. DeBrota, Christopher A. Fuchs, Jacques Pienaar +1 more

The authors use Bayesian probability theory to extend the ``QBism'' interpretation of quantum mechanics by showing how one may derive Born's rule from a set of assumptions where the state and measurement are described relative to a ``reference measurement.'' The result gives insight into Born's rule, even if one does not support the subjective interpretation of quantum mechanics underlying QBism.