No, quantum mechanics does not imply that we can't talk about the world in the third person or as being shared by multiple observers. While quantum mechanics introduces probabilistic behavior and the concept of wave functions, it does not invalidate the notion of an objective reality that can be described and observed by multiple observers.
In the framework of quantum mechanics, the wave function describes the state of a system, and when a measurement is made, the wave function "collapses" to a specific outcome. This collapse is often interpreted as a selection of one possibility out of a range of possible outcomes. However, once the collapse occurs, the observed outcome becomes an objective fact that can be described and discussed by different observers.
Quantum mechanics provides a mathematical formalism to calculate the probabilities of different outcomes and to describe the behavior of particles and systems at the microscopic level. These probabilities can be consistent across multiple observers, and experimental results in quantum mechanics are reproducible and verifiable by different researchers.
In practical terms, while quantum mechanics introduces some inherent uncertainty at the microscopic scale, it does not undermine the ability to describe and discuss the world in a third-person manner or from a shared perspective. The principles of classical physics, which are based on determinism and causality, emerge as approximations in certain macroscopic regimes where quantum effects become negligible.
Therefore, we can still talk about the world in objective terms, as shared by multiple observers, even within the framework of quantum mechanics.