Violations of the Born rule in cool state-dependent horizons
Donald Marolf, Joseph Polchinski
TL;DR
This work analyzes state-dependent proposals for describing infalling observers at black hole horizons. It shows that making horizon observables nonlinear functions of the global state—enough to erase firewalls for typical states—inevitably induces large violations of the Born rule, with the dimensionality of near-horizon Hilbert spaces and energy-shift arguments driving the effect. A concrete, high-dimensional Hilbert-space construction demonstrates that almost all states in an excited sector map to internal excitations rather than vacuum, making the Born-rule departures, in principle, observable by infalling observers. The authors argue the result is general across state-dependent schemes, underscoring significant conflicts between such proposals and the standard framework of quantum mechanics, while acknowledging that resolving these tensions requires further, careful theoretical work, including how to yield definite interior predictions.
Abstract
The black hole information problem has motivated many proposals for new physics. One idea, known as state-dependence, is that quantum mechanics must be generalized to describe the physics of black holes, and that fixed linear operators do not provide the fundamental description of experiences for infalling observers. Instead, such experiences are to be described by operators with an extra dependence on the global quantum state. We show that any implementation of this idea strong enough to remove firewalls from generic states requires massive violations of the Born rule. We also demonstrate a sense in which such violations are visible to infalling observers involved in preparing the initial state of the black hole. We emphasize the generality of our results; no details of any specific proposal for state-dependence are required.