Semi-Classical Subspaces, The No Synchronization Law, and More

Abstract: This paper looks at the intersection of algorithmic information theory and physics, namely quantum mechanics, thermodynamics, and black holes. We discuss theorems which characterize the barrier between the quantum world and the classical realm. The notion of a ``semi-classical subspace'' is introduced. Partial signals and partial information cloning can be obtained on quantum states in semi-classical subspaces. The No Synchronization Law is detailed, which says separate and isolated physical systems evolving over time cannot have algorithmic thermodynamic entropies that are in synch. We look at future work involving the Kolmogorov complexity of black holes.