Classical Mechanics as an Emergent Compression of Quantum Information

Abstract

The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a compressed, lower-information representation of quantum reality. Quantum mechanics encodes significantly more information through superposition, entanglement, and phase coherence, which are lost due to decoherence, phase averaging, and measurement, reducing the system to a classical probability distribution. This transition is quantified using Kolmogorov complexity, where classical systems require \( O(N) \) bits of information, while quantum descriptions require \( O(2^N) \), showing an exponential reduction in complexity. Further justification comes from Ehrenfest's theorem, which ensures that quantum expectation values obey Newton's laws, and path integral suppression, which eliminates non-classical trajectories when \( S \gg \hbar \). Thus, rather than viewing quantum mechanics as an extension of classical mechanics, we argue that classical mechanics is a lossy, computationally reduced encoding of quantum physics, emerging from a systematic loss of quantum correlations.