[Paper Review] Macroscopic superpositions and black hole unitarity

Stephen D. H. Hsu|arXiv (Cornell University)|Feb 3, 2013

Black Holes and Theoretical Physics18 citations

TL;DR

The paper argues that black hole unitarity can be preserved without firewalls by recognizing that the quantum state of a black hole and its environment evolves into a superposition of macroscopically distinct spacetimes due to decoherence from Hawking radiation recoil. This superposition ensures that while some branches feature an infalling observer hitting the horizon, others show the observer escaping to future infinity, reconciling subjective experience with unitarity through the global wave function.

ABSTRACT

We discuss the black hole information problem, including the recent claim that unitarity requires a horizon firewall, emphasizing the role of decoherence and macroscopic superpositions. We consider the formation and evaporation of a large black hole as a quantum amplitude, and note that during intermediate stages (e.g., after the Page time), the amplitude is a superposition of macroscopically distinct (and decohered) spacetimes, with the black hole itself in different positions on different branches. Small but semiclassical observers (who are themselves part of the quantum amplitude) that fall into the hole on one branch will miss it entirely on other branches and instead reach future infinity. This observation can reconcile the subjective experience of an infalling observer with unitarity. We also discuss implications for the nice slice formulation of the information problem, and to complementarity.

Motivation & Objective

• To resolve the black hole information paradox by showing unitarity is compatible with the equivalence principle and the absence of firewalls.
• To clarify how semiclassical observers like Alice can experience 'no drama' while the global quantum state remains unitary.
• To demonstrate that the apparent loss of information is an artifact of restricted measurement, not true information loss.
• To reconcile the nice slice argument and complementarity with unitary evolution by recognizing superpositions of spacetimes.
• To show that the global wave function contains all information, even on low-amplitude branches where matter avoids the black hole.

Proposed method

• Model the black hole formation and evaporation as a unitary Schrödinger evolution of a global quantum state Ψ, including observers and radiation.
• Analyze the wave function's evolution to show that after the Page time, the black hole's position becomes macroscopically uncertain due to radiation recoil, leading to decohered branches.
• Identify that decoherence arises from entanglement with environmental degrees of freedom, such as gravitons, causing macroscopic separation of spacetime branches.
• Use the superposition of branches to show that observers who fall into the black hole on one branch do not on others, preserving unitarity globally.
• Introduce the concept of a 'super-observer' with access to the full global state, contrasting it with a local observer like Alice who sees only one branch.
• Apply the quantum measurement framework (analogous to Bohr's complementarity) to show that information is not lost but encoded across multiple decoherent branches.

Experimental results

Research questions

• RQ1 Can unitarity be preserved in black hole evaporation without violating the equivalence principle or requiring a firewall?
• RQ2 How does the subjective experience of an infalling observer like Alice reconcile with global unitarity?
• RQ3 What role does decoherence play in the emergence of classical spacetime structure during black hole evaporation?
• RQ4 How can information be recovered from Hawking radiation if it appears to be lost behind the horizon?
• RQ5 In what sense is complementarity realized in the context of black hole evaporation and macroscopic superpositions?

Key findings

• After the Page time, the black hole's position uncertainty grows to Δx ∼ M², leading to macroscopic superpositions of spacetimes with the black hole in different locations.
• Decoherence from radiation recoil entangles the black hole's position with environmental degrees of freedom, causing the wave function to split into non-interfering branches.
• On some branches, Alice falls into the black hole and is converted into radiation; on others, she escapes to future infinity, ensuring her presence in the final state Ψf.
• The final state Ψf contains exponentially many low-amplitude branches where information that fell into the black hole is preserved and can interfere to reconstruct the initial state.
• The global wave function Ψ evolves unitarily, and unitarity is verified only by a super-observer with access to all branches, not by local observers like Alice.
• The nice slice argument fails because it assumes a single semiclassical spacetime, while the true evolution involves a superposition of distinct spacetimes, each with different causal structures.