Information Paradox

The black hole information paradox is the apparent contradiction between the no-hair property of black holes — which suggests that information about infalling matter is irreversibly lost — and the unitary evolution of quantum mechanics, which forbids such destruction. When matter collapses into a black hole, the no-hair theorem predicts that only mass, charge, and spin remain externally observable. The detailed quantum state of the infalling matter seems to vanish.

This is not merely a puzzle about black holes; it is a stress test for the compatibility of general relativity and quantum mechanics. If information is truly lost, then quantum mechanics is incomplete. If it is preserved, then the Hawking radiation that black holes eventually emit must somehow encode the initial state — a requirement that strains our understanding of quantum field theory in curved spacetime. The paradox has driven decades of work on holographic principle, firewalls, and the Page curve, yet no consensus resolution exists.

The deeper systems-theoretic question: can a local dynamical rule destroy global information? If the answer is no, then information preservation is not a detail of quantum gravity but a constraint on any consistent theory of dynamics.