Generalized Uncertainty Principle: Implications for Black Hole Complementarity

TL;DR

This paper explores how the generalized uncertainty principle (GUP), motivated by quantum gravity considerations, impacts black hole complementarity, potentially resolving conflicts with quantum mechanics but raising new questions about the principle's validity.

Contribution

It analyzes the role of GUP in black hole complementarity, showing that GUP can preserve complementarity under certain N-dependent assumptions.

Findings

GUP may prevent violation of complementarity with large N rescaling.

Complementarity can be maintained if GUP's N-dependence is assumed.

Raises questions about the actual form of GUP and the validity of complementarity.

Abstract

At the heart of the black hole information loss paradox and the firewall controversy lies the conflict between quantum mechanics and general relativity. Much has been said about quantum corrections to general relativity, but much less in the opposite direction. It is therefore crucial to examine possible corrections to quantum mechanics due to gravity. Indeed, the Heisenberg Uncertainty Principle is one profound feature of quantum mechanics, which nevertheless may receive correction when gravitational effects become important. Such generalized uncertainty principle [GUP] has been motivated from not only quite general considerations of quantum mechanics and gravity, but also string theoretic arguments. We examine the role of GUP in the context of black hole complementarity. We find that while complementarity can be violated by large N rescaling if one assumes only the Heisenberg's Uncertainty Principle, the application of GUP may save complementarity, but only if certain N-dependence is also assumed. This raises two important questions beyond the scope of this work, i.e., whether GUP really has the proposed form of N-dependence, and whether black hole complementarity is indeed correct.