Lessons from the Information Paradox (2012.05770v2)

Abstract: We review recent progress on the information paradox. We explain why exponentially small correlations in the radiation emitted by a black hole are sufficient to resolve the original paradox put forward by Hawking. We then describe a refinement of the paradox that makes essential reference to the black-hole interior. This analysis leads to a broadly-applicable physical principle: in a theory of quantum gravity, a copy of all the information on a Cauchy slice is also available near the boundary of the slice. This principle can be made precise and established -- under weak assumptions, and using only low-energy techniques -- in asymptotically global AdS and in four dimensional asymptotically flat spacetime. When applied to black holes, this principle tells us that the exterior of the black hole always retains a complete copy of the information in the interior. We show that accounting for this redundancy provides a resolution of the information paradox for evaporating black holes and, conversely, that ignoring this redundancy leads to paradoxes even in the absence of black holes. We relate this perspective to recent computations of the Page curve for holographic CFTs coupled to nongravitational baths. But we argue that such models may provide an inaccurate picture of the rate at which information can be extracted from evaporating black holes in asymptotically flat space. We discuss large black holes dual to typical states in AdS/CFT and the new paradoxes that arise in this setting. These paradoxes also extend to the eternal black hole. They can be resolved by assuming that the map between the boundary CFT and the black-hole interior is state dependent. We discuss the consistency of state-dependent bulk reconstructions. We conclude by examining the viability of arguments for firewalls, fuzzballs and other kinds of structure at the horizon.

• The paper demonstrates that exponentially small corrections in Hawking radiation preserve information and ensure unitary evolution in black holes.
• The paper establishes that holography of information encodes complete bulk details on the boundary, overturning the notion of isolated black hole interiors.
• The paper argues that state-dependent interior reconstructions reconcile existing paradoxes and guide future quantum gravity research.

Analyzing the Resolution of the Information Paradox in Quantum Gravity

The paper "Lessons from the Information Paradox" by Suvrat Raju offers a rigorous exploration of the longstanding conundrum associated with black hole information loss, initially posed by Hawking in the 1970s. The core puzzle, known as the information paradox, revolves around the apparent contradiction between quantum mechanics, which dictates unitary evolution of states, and the nature of Hawking radiation, which seems to suggest that information about initial states is lost when a black hole evaporates.

Resolution through Exponentially Small Correlations

Hawking's original formulation of the information paradox was predicated on the semi-classical calculation that black holes emit radiation purely characterized by their mass, charge, and angular momentum, and seemingly not by the details of the infalling matter. However, Raju emphasizes that small, yet vital, exponential corrections in the emitted radiation are sufficient to resolve the paradox. These corrections ensure that information about the initial state is preserved, albeit not detectable through leading-order calculations. This insight hinges on recognizing the critical role of quantum statistical mechanics, whereby exponentially small differences between pure and mixed states are indistinguishable by low-order observables.

Holography of Information Principle

A significant advance in resolving the paradox stems from understanding how information is encoded in quantum gravity through the "holography of information" principle. Raju clarifies that in a gravitational setting, complete information about a region of space is redundantly available at its boundary. This principle dismantles the notion that black hole interiors are informationally isolated from their exteriors.

By applying this principle, it becomes clear that the information from the black hole interior is always duplicated at the exterior, rendering traditional notions of information "falling into" a black hole obsolete. This redundancy is elucidated, particularly in scenarios considering global Anti-de Sitter (AdS) space and asymptotically flat spacetimes, where gravitational constraints make the boundary theory sufficient to retrieve the complete bulk information.

Implications for Quantum Gravity and Black Holes

The implications of Raju's analysis are vast, affecting both theoretical and practical domains within quantum gravity. Importantly, the paper negates the necessity of drastic proposals like firewalls and fuzzball models that previously attempted to explain information retention at black holes, which often conflict with the expected behavior of low-energy effective field theory. Instead, it suggests that what seems like information loss is a misinterpretation based on ignoring subtleties of how gravity encodes information holographically.

The principle of holography of information not only resolves paradoxes involving black holes but plays a broader role in understanding quantum gravity's fundamental features. It shapes future directions by highlighting areas where known physics may be sufficiently robust to extend results to currently speculative settings such as evaporating black holes.

State Dependence and Interior Reconstructions

Raju's discussion also revisits the debate on whether black hole interiors can be described by "state-dependent" operators. The paper aligns towards a nuanced understanding where such dependencies are necessary to account for interior states within a holistic framework. Ensuring consistency with quantum mechanics while using state-dependent frameworks remains a focal challenge that demands further theoretical refinement.

Paradoxes Revisited

Moreover, Raju reanalyzes paradoxes tied to large AdS black holes and suggests that they can be addressed by refining how we relate boundary conformal field theory (CFT) dynamics to bulk geometrical data, specifically within state-dependent constructs.

Conclusion

In summarizing, "Lessons from the Information Paradox" articulates a newfound clarity in resolving one of theoretical physics' most challenging paradoxes by employing sophisticated notions of quantum information theory and gravitational holography. It provides a compelling narrative that stabilizes our understanding of black holes within quantum gravity, thereby bridging gaps that have persisted since Hawking's groundbreaking insights. Future explorations will undoubtedly continue to refine these concepts, addressing remaining questions on the nature of spacetime and quantum information processing in gravitational contexts.