Abordagem Bayesiana para compatibilidade de perspectivas em mecânica quântica: uma possível solução para o Paradoxo do amigo de Wigner

Abstract

Classical and relativistic physics are permeated by a fundamental principle: the principle of relativity. This principle ensures that the laws of physics remain the same in any inertial reference frame. The situation in quantum mechanics, however, appears to be orthogonal to this approach, as different observers may use different perspectives to analyze the same system. The emblematic example of this situation is Wigner’s friend paradox, where there is a clash between unitary evolution and collapse when describing the same system. Given that two observers of the same system do not agree on how they reached their beliefs, we can investigate whether they can achieve compatibility between their perspectives and measurements through a compatibility criterion. In this work, we will examine two such criteria, namely the objectivist and the subjectivist approaches. After analyzing both versions, we will present a way to use this formalism to address the (original) Wigner’s friend problem. We will conclude that different beliefs, information, or knowledge about a system may not necessarily be identical, as long as they remain compatible, and we will establish a prescription for compatibility between perspectives that could resolve the paradox. The existence of a paradox lies in seeking agreement where there is only a demand for compatibility in the observers’ descriptions. In this work, we will use the formalism of conditional states, which treats quantum theory as a non-commutative generalization of classical Bayesian inference theory, to explore the compatibility of two different perspectives on the same system. We will provide a mathematical definition of compatibility between different perspectives (as well as a characterization theorem). Within this formalism, we establish parallels between classical variables and quantum systems, along with their quantum counterparts to the usual, joint, and conditional probability distributions, as well as the concepts of marginalization, Bayes’ theorem, and belief propagation. This will serve as the toolkit to examine two versions of the compatibility criterion.