# Information Loss and Unitary Quantum Gravity

## Overview

RU is a certificate engine for universality and obstructions in constrained nonnegative propagation. Host structures supply finite inputs. Outputs are audited certificates or finite obstruction witnesses.

## RU fit

- **Fit level:** Low

## RU instantiation hooks

- Host-context for why protected sectors and operator algebra structure matter; RU enters only after extracting a finite positive propagation model from a controlled sector.
- Pairs naturally with the bootstrap truncation bridge and the moduli-chamber global report step.

## Purpose

Show why the black hole information problem is not a side story but a stress test for any theory that claims to unify quantum mechanics with gravity, and show what the string-theory method stack contributes that is reusable outside the original context.

This document is written to keep two commitments at once:

- be explicit about what is solid and what is conditional on regimes (large N, AdS, supersymmetry, semiclassical control)
- still make the RU-host suitability claim concrete: string theory supplies working models and tools that change what can be computed

## The paradox in one clean form

Hawking’s semiclassical calculation suggests that an evaporating black hole emits radiation that is (to excellent approximation) thermal. If the black hole forms from a pure quantum state and evaporates completely into thermal mixed radiation, then pure states evolve to mixed states, contradicting unitary time evolution.

Even if you do not accept the strongest form of the paradox, the tension is real:

- semiclassical gravity plus ordinary locality near the horizon strongly suggests approximately thermal radiation
- quantum mechanics strongly suggests global unitarity
- black holes in gravity have entropy, so whatever the microscopic degrees of freedom are, they must be counted and must evolve consistently

## What string theory contributes, in a reusable way

### Microstate accounting in protected sectors

In supersymmetric (BPS) settings, string theory can count microscopic states and match the Bekenstein–Hawking entropy of certain black holes. This is a example example of turning a geometric thermodynamic law into a microscopic counting problem. Strominger–Vafa is the standard anchor.

What is reusable here is not just the result but the method:

- identify a sector protected by symmetry so the count does not change as coupling changes
- count states where the description is weakly coupled
- argue that the same count applies when the gravitational description is valid

This is exactly the bridge Wray emphasizes: in weak coupling the entropy becomes a field theory question on branes, and the answer matches gravity in the protected regime. (Wray PDF around page 255; see curated excerpt `black_hole_entropy_as_field_theory_question`.)

### Holography as a unitarity model

The holographic principle, specialized to AdS/CFT, provides explicit quantum systems without gravity (a boundary QFT) that reproduce gravitational physics in the bulk. In such models, unitarity is built into the boundary description, so the gravity side inherits strong evidence for unitary evolution.

This does not mean every black hole in every spacetime is solved. It does mean that there exist fully defined quantum theories in which black holes appear on the gravity side but the underlying description is manifestly unitary.

Wray’s notes make this conceptual move explicit: the “puzzles about black holes” motivate the transition into holography and AdS/CFT. (Wray PDF around pages 242–259; see curated excerpt `chapter_transition_black_holes_to_holography` and the AdS/CFT excerpts.)

### The Page curve and modern semiclassical tools (islands)

A concrete target for “unitary evaporation” is the Page curve: the fine-grained entropy of Hawking radiation should rise early, then fall back to zero if the total evolution is unitary. Page’s 1993 computation for random states gives the expected shape in a generic unitary system.

Recent semiclassical gravity computations in controlled settings reproduce a Page-curve-like behavior using the “island” rule and replica wormholes.

What string theory contributes here is again a method stack rather than a single headline:

- holographic duality provides a nonperturbative definition that makes unitarity plausible
- semiclassical gravity in AdS-like models provides a calculational arena where entropy can be computed with gravitational saddles
- quantum information language (entanglement wedge ideas, generalized entropy) supplies the right observable and the right variational principle

A good orientation example is Harlow’s lectures, which were written precisely to connect holography, black holes, and quantum information.

## What is settled, what is conditional, what is open

| Claim | Status | Why it is believed | Main caveat |
|---|---|---|---|
| Certain supersymmetric black hole entropies admit microscopic counting matching gravity | Solid in its regime | Protected BPS counting plus explicit constructions | Applies to special, symmetry-protected black holes |
| AdS/CFT provides unitary quantum models with black holes on the gravity side | Solid as a framework | The boundary QFT is an ordinary unitary quantum system | These are AdS asymptotics and usually large N limits |
| Page-curve behavior can be reproduced in controlled semiclassical models | Strong progress, actively refined | Replica wormholes and islands match the expected entropy behavior | Best understood in simplified settings and controlled limits |
| A universally accepted local, horizon-scale mechanism for information release in generic evaporation exists | Not settled | Competing narratives exist (complementarity, firewalls, islands, state dependence) | Sensitive to assumptions about locality and interior reconstruction |

Firewalls sharpen the tradeoffs between purity of radiation, effective field theory near the horizon, and a smooth horizon for infalling observers.

## The “host suitability for RU instantiation” takeaway

The information problem is reducible into RU certificates to keep around because it forces precision about what a UV completion must do.

An RU reduction target is credible here because the host data supplies:

- explicit microscopic degrees of freedom in settings where gravity would otherwise be only thermodynamic
- a duality framework where unitarity is inherited from an ordinary QFT
- concrete calculational technology for entanglement in gravity, which has become a general tool well beyond the original paradox