The Many-to-One Principle: Erasure as the Universal Substrate of Definiteness, Selection, and Physical Law

Abstract

We propose that a single information-theoretic operation — the many-to-one map on a physical system's state space, followed by inaccessibility of the discarded alternatives — is the missing universal principle underlying defmiteness, selection, irreversibility, and the emergence of classical structure across every scale of physical reality. We call this the Many-to-One Principle (M1P). By the Bennett–Landauer theorem, every such map dissipates at least Q \geq k_B T \ln 2 per bit of Shannon entropy reduced. We argue that this bound is not merely a constraint on computation but the generative signature of physical definiteness itself: wherever alternatives become a single definite record, M1P is operating, and wherever M1P operates, a thermodynamic cost is paid. We show that M1P unifies quantum measurement, decoherence, natural selection, neural commitment, protein folding, cosmological structure formation, and the arrow of time under one formal structure — a many-to-one map on an accessible state space. We do not claim that M1P derives the Second Law, explains consciousness, or replaces quantum mechanics. We claim something narrower and more radical: that the textbook separation between "physics," "computation," "biology," and "mind" obscures a single operation they all instantiate, and that recognizing this operation as universal reorganizes what we should expect a fundamental theory to look like.