On the probabilistic nature of quantum mechanics and the notion of closed systems

TL;DR

This paper examines the concept of closed systems in quantum mechanics, demonstrating that under broad conditions, a subsystem can behave as closed even with entanglement, highlighting the inherent non-determinism of quantum measurements.

Contribution

The paper provides a rigorous analysis showing that quantum subsystems can act as closed systems despite entanglement, emphasizing the probabilistic nature of quantum predictions.

Findings

Subsystems can behave as closed systems with entangled states.

Initial states and unitary evolution do not guarantee measurement predictability.

Quantum mechanics inherently exhibits non-determinism.

Abstract

The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the interaction between $P$ and $Q$, we show that the system $P$ behaves as a closed system if the initial state of $P \vee Q$ belongs to a large class of states, including ones exhibiting entanglement between $P$ and $Q$. We use our results to illustrate the non-deterministic nature of quantum mechanics. Studying a specific example, we show that assigning an initial state and a unitary time evolution to a quantum system is generally not sufficient to predict the results of a measurement with certainty.