Structural Instability and Quantum Lying in the Many-worlds (Relative State) Interpretation

Abstract

The stability of dynamical systems against perturbations (variations in initial conditions/model parameters) is a property referred to as structural stability. The study of sensitivity to perturbation is essential because in experiment initial conditions are not fixed, nor are model parameters known, to arbitrarily high precision. Additionally, if a physical system under study exhibits stability (insensitivity to initial conditions) then a theoretical description of the system must exhibit structural stability. Consequently, stability can be a useful indicator of the correctness of a theoretical formulation. In this work the many-worlds interpretation is considered. It is first demonstrated that the interpretation admits a class of special states, herein referred to as "quantum liar states," because they indicate disagreement between the recorded result of a measurement and the actual state of a system. It is then demonstrated that the many-worlds interpretation is not structurally stable against the introduction of quantum liar states.