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Black hole information, unitarity, and nonlocality

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Steven B. Giddings

High Energy Physics - Theory · Submitted 19 May 2006 · 47 references

Pith's verdict: Section 3.4 is a real, checkable cancellation; Section 4 is an explicitly heuristic argument, and Giddings says so — the modest conclusion holds, the mechanism is a promissory note.

T0 · AI review

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arXiv IDhep-th/0605196 (version 2)
Pith IDCEM3EFUC, Pith's permanent record of this paper and its review
CitationSteven B. Giddings. "Black hole information, unitarity, and nonlocality." arXiv:hep-th/0605196 (2006). https://pith.science/paper/CEM3EFUC
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The paper

The paper claims

Hawking's case that black holes destroy information rests on a step that may not be licensed: writing down the state of infalling matter and outgoing radiation on a single spacelike slice requires an exponentially large relative boost, and,

The reading

Hawking's argument that black holes destroy information assumes that on a spacelike slice crossing the horizon the quantum state factorizes into an inside part and an outside part, so that tracing over the inside leaves a mixed state for the radiation. This paper asks where that assumption could fail. It first rules out one popular suspect: the ultra-high-energy precursors of Hawking quanta are shown to have no physical effect, because their stress tensor outside the horizon is cancelled by that of their partners inside, and because such modes only separate from the horizon and from each other once they have energies of order $1/M$. The paper then identifies a different and more serious obstruction: comparing an infalling quantum with a Hawking quantum emitted a long time later forces a relative boost $s$ that grows as $e^{(t_2-t_1)/4M}$, while the two modes stay only a distance growing linearly in $t_2-t_1$ apart along the slice. If the paper is right, the standard derivation of information loss has not been carried out in a regime where local quantum field theory is known to apply, so the paradox is not yet a theorem.

What carries the argument

Two pieces of machinery carry the argument. The first is a cancellation: the stress tensor of the ultra-high-energy outgoing modes near the horizon, naively enormous for an infalling observer, combines with the contribution of the inside modes into an expression that is purely negative-frequency in Kruskal time, so momentum conservation leaves no large momenta in the interaction amplitude. This is the same statement as the nice-slice picture, in which the state near the horizon is the infalling vacuum for frequencies well above $1/M$. The second is a pair of competing scalings used as a diagnostic: the invariant mass-squared of an infalling quantum and a later Hawking quantum grows exponentially in the time between infall and emission, while their spatial separation along the slice grows only linearly. Feeding these into the locality bound, and estimating the graviton propagator as $G(x_1,x_2) sim 1/sigma^2$ with $sigma$ set by the geodesic that hugs the cut-off surface, yields a tree amplitude that grows large precisely where the bound is violated, signalling that the tree approximation has broken down and that the modes cannot be treated as independent degrees of freedom.

Extended reading notes

Core claim

The paper's central claim is that no simultaneous description of infalling modes and outgoing Hawking modes can be given on one spacelike slice without encountering a large kinematic invariant, $s approx E_1 E_2 e^{(t_2-t_1)/4M}$, or some other dependence on ultra-Planckian physics. The modes are confined to a region of size of order $M$, so their separation along a smooth slice grows only linearly, $sigma approx sqrt{2M/r_c},(t_2-t_1)$; an enormous relative boost at modest separation is exactly the regime where a proposed locality bound, $|x-y|^{D-3} gtrsim G_D|p+q|$, is expected to fail. Since that bound is the criterion for the Hilbert space on the slice to decompose into independent factors, the tensor-product decomposition $mathcal{H} = mathcal{H}_{text{inside}} otimes mathcal{H}_{text{outside}}$ that Hawking's argument requires has not been justified. Hence, in the author's words, a reliable argument for information loss has not been constructed, and the resolution is plausibly nonlocal dynamics intrinsic to strong gravity rather than any breakdown of quantum mechanics.

Load-bearing premise

The load-bearing premise is that the locality bound, imported from flat-space reasoning, still marks the failure of the tensor-product description when applied in a curved black hole background, where the paper itself concedes that a complete evaluation of the propagator and amplitude requires knowledge of the Planckian regime near the singularity.

Editorial extensions

If this is right

  • The information-loss argument cannot be run without invoking Planck-scale or trans-Planckian physics, so the paradox is not established within known, controlled physics.
  • The tensor-product structure of Hilbert space across a horizon is not a general feature of quantum gravity but an approximation valid only outside the extreme regime probed by large relative boosts.
  • Nonlocality of strong gravitational dynamics becomes a candidate mechanism for restoring purity, with the delay before infallen information can appear in the radiation set by a time of order $16M log M$.
  • The same nonlocal dynamics would supply a mechanism underlying holography and black hole complementarity, explaining why inside and outside observers' measurements need not commute.
  • The final-state proposal, in which the singularity carries no information, requires some nonlocal relay to move information outside; this picture supplies a candidate for that relay.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the obstruction is real, it should show up as a breakdown of any attempt to write a factorized density matrix for Hawking radiation at late retarded times, which is in principle a statement about the scaling of entanglement entropy with the emission time rather than about Planck-scale microphysics.
  • The argument suggests a general rule: whenever two probes of a curved background are related by an exponential boost while separated by only a modest proper distance, semiclassical field theory on that background should be suspect, which could be tested in analogue horizon systems where the boost factor is tunable.
  • Because the paper's diagnostic uses only the kinematics of Schwarzschild geometry, the same exponential-invariant-versus-linear-separation mismatch should appear for any horizon, including cosmological ones, which would extend the claim well beyond black hole evaporation.
Original abstract

The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arises from ultra-planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simultaneous description of modes that have fallen into the black hole and outgoing Hawking modes can be given without appearance of a large kinematic invariant, or other dependence on ultra-planckian physics; a reliable argument for information loss thus has not been constructed. This suggests that strong gravitational dynamics is important. Such dynamics has been argued to be fundamentally nonlocal in extreme situations, such as those required to investigate the fate of information.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,488 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.78 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.32 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arises from ultra-planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simultaneous description of modes that have fallen into the black hole and outgoing Hawking modes can be given without appearance of a large kinematic invariant, or other dependence on ultra-planckian physics; a reliable argument for information loss thus has not been constructed. This suggests that strong gravitational dynamics is important. Such dynamics has been argued to be fundamentally nonlocal in extreme situations, such as those required to investigate the fate of information.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. background 0.98 0.07 0.08 hedged possibility 0.98
s1 The leading contender is nonlocality. background 0.99 0.08 0.12 asserted 0.88
s2 Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. contribution 0.98 0.74 0.06 hedged possibility 0.49
s3 Suggestions that such dynamics arises from ultra-planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. result 0.93 0.77 0.09 asserted 1.00
s4 However, no simultaneous description of modes that have fallen into the black hole and outgoing Hawking modes can be given without appearance of a large kinematic invariant, or other dependence on ultra-planckian physics; a reliable argument for information loss thus has not been constructed. result 0.75 0.64 0.42 asserted 0.92
s5 This suggests that strong gravitational dynamics is important. interpretation 0.98 0.32 0.18 hedged possibility 0.98
s6 Such dynamics has been argued to be fundamentally nonlocal in extreme situations, such as those required to investigate the fate of information. interpretation 0.53 0.07 0.23 hedged possibility 0.62

What kind of paper the classifier reports this is: position or commentary 0.72 · evidence from argument 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. The Kruskal diagram for the Schwarzschild geometry, together with two kinds of time slices. An explicit construction of the first kind (solid line) is given by [14]: it consists of a segment of the hyperbola of constant r = rc for U > V , attached to the matching horizontal slice in the region U < V . The second kind (dashed) consists of a horizontal segment for U < V , which terminates at the singularity. Action of the Schwarzschild time translation t → t + α on either of these slices generates a family of slices foliating the region outside the black hole, as well as the region at…
Figure 2. The intrinsic geometry of a member of the family of slices of
Figure 3. The intrinsic geometry of a member of the family of slices of
Figure 4. A representation of the situation described in the text, on a slice avoiding the singularity. Both a Hawking mode and its inside counterpart are represented, in the process of separation from the horizon. A mode that entered the black hole at an earlier time is boosted relative to these modes by an amount exponential in this time difference, whereas its distance along the slice is linear in the time. An essential question is whether one can think of the Hilbert space on the the time slice t = t2 as decomposing into separate factors describing the infalling mode and the outgoing…

Figures reproduced from arXiv:hep-th/0605196 by the authors.

References
How the literature uses it

52 arXiv papers cite this in 67 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 51 sentences without a confident label

Cites it as support 4 papers
  • Moreover a quantum particle crossing the horizon does not experience a dramatic gravitational interaction from these fluctuations because the contributions of the transplanckian ancestors of the Hawking photons are cancelled by those of their partners on the other side of the horizon [ref] .

    The hidden horizon and black hole unitarity · The black hole paradox : singularity and horizon · 0.97

  • In fact, explicit calculations [ref] show that the presence of Hawking modes does not alter appreciably the behaviour of collapsing matter, in agreement with the common lore that a freely-falling observer will not detect a substantial amount of radiation even in a neighbourhood of the horizon (see also [ref] ). 1.5cm

    Linking the trans-Planckian and the information loss problems in black hole physics · Trans-Planckian problem · 0.98

  • This is supported by studies of high-energy scattering [ref] and by investigating locality through relational observables [ref] , and could play an important role in explaining unitarity of black hole evaporation [ref] .

    A global picture of quantum de Sitter space · The Global Picture of Eternal de Sitter space · 1.00

Cites it as background 11 papers

Discussion

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