The Classical and the Quantum World

Gary E. Bowman

This introductory chapter outlines the differences between classical physics and quantum physics by positing three imaginary worlds. World 1 is governed by the laws of classical Newtonian mechanics, World 2 by classical field physics, and World 3 by quantum physics. The point is that classical physics deals with well-defined, continuously-existing physical quantities, including trajectories, while quantum physics is fundamentally about physical quantities defined in terms of probability functions.

Nicolaas P. Landsman

Kohei Morita, Kohei Morita

One of the problems of the many worlds interpretation (MWI) of quantum mechanics is about the ontological status of multiple worlds. In the MWI, the multiple worlds are quasi-classical, and the quasi-classical worlds are considered as emergence and pattern. However, the ontological understanding about the quasi-classical realms remains ambiguous. This article aims to clarify the ontological status of the quasi-classicality in the MWI. In particular, the notion of emergence and pattern has been investigated in the philosophy of science. The investigation about these notions provides a refined ontology of many worlds interpretation.

Marco Bellini, Silvia Viciani, Alessandro Zavatta

Josep Lumbreras, Hailan Ma, Jayne Thompson +1 more

World models provide digital simulacra of the true world, allowing agents to be trained and tested before costly real-world deployment. At each time step, they receive an action and generate an observation and reward matching the statistics of the true world. In complex environments where present outcomes depend on events far in the past, this requires memory. One might expect that, by increasing memory, we can always build a model accurately enough to align the optimal agent policies of the real and virtual worlds. We show that this is false for classical world models, even when the true world itself is classical. We construct true worlds for which every finite classical model fails along the same possible trajectory: it either loses the ability to distinguish actions when the true world clearly prefers one, or repeatedly assigns the highest expected reward to suboptimal actions. Its expected-reward estimates also retain a nonvanishing average error. In contrast, each such true world admits a quantum world model using a single qutrit that reproduces it exactly: its reward estimates and preferred actions always match those of the true world, ensuring that the optimal policies of the real and virtual worlds remain perfectly aligned.