Replica Wormholes and Quantum Hair

Replica Wormholes and Quantum Hair 

https://arxiv.org/abs/2404.02331

Xavier Calmet, Stephen D.H. Hsu 

We discuss recent applications of Euclidean path integrals to the black hole information problem. In calculations with replica wormholes as the next-to-leading order correction to the Gibbons-Hawking saddlepoint, the radiation density matrix approaches a pure state at late times, following the Page curve. We compare unitary evaporation of black holes (in real time), mediated by calculable quantum hair effects, with the replica wormhole results. Both replica wormhole and quantum hair approaches imply that radiation states are macroscopic superpositions of spacetime backgrounds, invalidating firewall and monogamy of entanglement constructions. Importantly, identification of modes inside the horizon with radiation modes (i.e., large scale nonlocality across the horizon) is not required to provide a physical picture of unitary evaporation. Radiation modes can encode the interior information while still remaining independent degrees of freedom.

Wormholes dominate the Gibbons-Hawking saddlepoint of the Euclidean path integral after the Page time. This is because wormholes can connect the interiors of any two black holes i,j. At late times the number of such pairs grows as the dimensionality of the radiation Hilbert space squared. 

The wormholes connect BHs with macroscopically different recoil trajectories. This means the radiation approaches a pure state that is a macroscopic superposition - very similar to what our quantum hair expressions indicate.

Quantum Hair During Gravitational Collapse (published version in Physical Review D)

https://journals.aps.org/prd/pdf/10.1103/PhysRevD.108.086012

This is a follow up to our earlier work on quantum gravitational corrections to the exterior graviton field of a compact object, also known as quantum hair. 

Here we follow the gravitational collapse of a dust ball and show that the quantum hair persists through the formation of a black hole horizon. The detailed calculations are possible due to an effective field theory formulation of quantum gravity in the long wavelength, low spacetime curvature limit.

Quantum Hair in Electrodynamics and Gravity (Eur. Phys. J. Plus)

This is the published version of the arxiv preprint previously discussed here.

We found it interesting that quantum hair can already be found using the familiar Euler-Heisenberg effective action, which results from integrating out the electron in QED. 

The paper also contains a general argument for why solutions to the semiclassical field equations resulting from the effective action (both in gravity and QED) carry more information about the state of the source than in classical physics. 

From the Conclusions: 

The quantum effective actions for both electrodynamics and gravity lead to field equations which couple a compact source (charge current or energy-momentum tensor) to external fields (electromagnetic or graviton field) in a manner which, generically, leads to quantum memory and quantum hair effects. External solutions of the field equations deviate, due to quantum corrections, from the familiar classical forms that satisfy the Gauss law. As a specific consequence, more information about the interior source configuration is encoded in the external field than in the classical theory. 

As specific applications, we considered semiclassical sources (large black hole, macroscopic charge distribution), which allowed us to solve the quantum corrected field equations by expanding around a classical solution. However, fully quantum statements regarding quantum hair are also possible, which do not, for example, require a semiclassical source. In [1–3] it was shown that the quantum state of a compact source (e.g., in an energy eigenstate or superposition thereof) determines certain aspects of the quantum state of its external field. In principle, measurements of the external fields can fully determine the interior state of a black hole.

Quantum Hair During Gravitational Collapse

This is a follow up to our earlier work on quantum gravitational corrections to the exterior graviton field of a compact object, also known as quantum hair. Here we follow the gravitational collapse of a dust ball and show that the quantum hair persists through the formation of a black hole horizon.

The detailed calculations are possible due to an effective field theory formulation of quantum gravity in the long wavelength, low spacetime curvature limit.
 

Quantum Hair During Gravitational Collapse 

https://arxiv.org/abs/2305.09466 

X. Calmet, R. Casadio, S. Hsu, F. Kuipers 

We consider quantum gravitational corrections to the Oppenheimer-Snyder metric describing time-dependent dust ball collapse. The interior metric also describes Friedmann-Lemaitre-Robertson-Walker cosmology and our results are interpreted in that context. The exterior corrections are an example of quantum hair, and are shown to persist throughout the collapse. Our results show the quantum hair survives throughout the horizon formation and that the internal state of the resulting black hole is accessible to outside observers.

 

 

Quantum gravitational corrections to particle creation by black holes (Physics Letters B)

This is the published version of our preprint https://arxiv.org/abs/2303.00310.

Quantum gravitational corrections to particle creation by black holes 

X. Calmet, S. Hsu, M. Sebastianutti 

We calculate quantum gravitational corrections to the amplitude for the emission of a Hawking particle by a black hole. We show explicitly how the amplitudes depend on quantum corrections to the exterior metric (quantum hair). This reveals the mechanism by which information escapes the black hole. The quantum state of the black hole is reflected in the quantum state of the exterior metric, which in turn influences the emission of Hawking quanta.

In earlier work we showed that the quantum state of a black hole is reflected in the quantum state of the exterior metric (outside the horizon). This violates classical intuitions, but can be shown explicitly using long wavelength effective field theory.

We calculated examples of small corrections to the external spacetime geometry which are sensitive to the internal BH state. In this paper we show that these corrections in turn affect Hawking radiation amplitudes. 

This means that the Hawking radiation state depends on the internal BH state. At the quantum level the hole is not black! We derive the results using both Hawking's original method and the tunneling method of Parikh and Wilczek.

 

While the focus of the new paper is explicit calculations, the big picture statement is:

The quantum state of the BH is reflected in the quantum state of its external gravitational field, which forms the background where the Hawking radiation originates. Radiation amplitudes are NOT independent of interior state.

Decoherence and Quantum Measurement: The Missing Lecture

This is an elementary lecture for students which discusses quantum measurement from the modern perspective of decoherence.

Decoherence and Quantum Measurement: The Missing Lecture 

arXiv:2212.02391 [quant-ph]  

We give an elementary account of quantum measurement and related topics from the modern perspective of decoherence. The discussion should be comprehensible to students who have completed a basic course in quantum mechanics with exposure to concepts such as Hilbert space, density matrices, and von Neumann projection (``wavefunction collapse'').

See also: 

Ten Years of Quantum Coherence and Decoherence 

Macroscopic Superposition States in Isolated Quantum Systems 

Macroscopic Superpositions in Isolated Systems (talk video + slides)

Discovering the Multiverse: Quantum Mechanics and Hugh Everett III, with Peter Byrne — Manifold #22

 

Peter Byrne is an investigative reporter and science writer based in Northern California. His popular biography, The Many Worlds of Hugh Everett III - Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family (Oxford University Press, 2010) was followed by publication of The Everett Interpretation of Quantum Mechanics, Collected Works 1957-1980, (Princeton University Press, 2012), co-edited with philosopher of science Jeffrey A. Barrett of UC Irvine. 

Everett's formulation of quantum mechanics, which implies the existence of a quantum multiverse, is favored by a significant (and growing) fraction of working physicists. 

Steve and Peter discuss: 

0:00 How Peter Byrne came to write a biography of Hugh Everett 

18:09 Everett’s personal life and groundbreaking thesis as a catalyst for the book 

24:00 Everett and Decoherence 

31:25 Reaction of other physicists to Everett’s many worlds theory 

40:46 Steve’s take on Everett’s many worlds theory 

43:41 Peter on the bifurcation of science and philosophy 

49:21 Everett’s post-academic life 

52:58 How Hugh Everett is remembered now 

References: 

Many Worlds posts on Infoproc 

Conversations with Dieter Zeh 

Macroscopic Superpositions in Isolated Systems 

Transcript

Quantum Hair in Electrodynamics and Gravity (arXiv:2209.12798)

New paper!

Quantum Hair in Electrodynamics and Gravity 

Xavier Calmet, Stephen D. H. Hsu 

arXiv:2209.12798 

We demonstrate the existence of quantum hair in electrodynamics and gravity using effective action techniques. In the case of electrodynamics we use the Euler-Heisenberg effective action while in the case of quantum gravity we use the unique effective action. We give a general formulation of these effects which applies to both theories and discuss analogies and differences between them. Furthermore, we present a QED analog to black hole evaporation. Spontaneous pair production in the external field of a ball of charge is analogous to Hawking radiation from black holes. Assuming spherical symmetry, the Gauss law prevents the external field from depending on the density profile of the ball. Quantum corrections violate these expectations, showing that quantum radiation can encode classically forbidden information about the source.

We found it interesting that quantum hair can already be found using the familiar Euler-Heisenberg effective action, which results from integrating out the electron in QED.

The paper also contains a general argument for why solutions to the semiclassical field equations resulting from the effective action (both in gravity and QED) carry more information about the state of the source than in classical physics.

From the Conclusions:

The quantum effective actions for both electrodynamics and gravity lead to field equations which couple a compact source (charge current or energy-momentum tensor) to external fields (electromagnetic or graviton field) in a manner which, generically, leads to quantum memory and quantum hair effects. External solutions of the field equations deviate, due to quantum corrections, from the familiar classical forms that satisfy the Gauss law. As a specific consequence, more information about the interior source configuration is encoded in the external field than in the classical theory. 

As specific applications, we considered semiclassical sources (large black hole, macroscopic charge distribution), which allowed us to solve the quantum corrected field equations by expanding around a classical solution. However, fully quantum statements regarding quantum hair are also possible, which do not, for example, require a semiclassical source. In [1–3] it was shown that the quantum state of a compact source (e.g., in an energy eigenstate or superposition thereof) determines certain aspects of the quantum state of its external field. In principle, measurements of the external fields can fully determine the interior state of a black hole.

A Brief History of Hawking's Information Paradox (European Physics Letters)

This is a short review of our recent work on black hole information for European Physics Letters.

A Brief History of Hawking's Information Paradox 

European Physics Letters 139 (2022) 49001

Xavier Calmet and Stephen D. H. Hsu 

Abstract 

In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in entangled macroscopic superposition states of the radiation. 

DOI: 10.1209/0295-5075/ac81e8

arXiv version: https://arxiv.org/abs/2207.08671

From Conclusions:

... The radiation amplitudes computed by Hawking, which describe thermal radiation emitted from a black hole at temperature T, already describe a broad distribution of possible radiation types, spins, and momenta emitted at each stage. Thus, even in the semiclassical approximation there are many distinct patterns of radiation in (6). The set of possible final states is already complex even at leading order, resulting in very different coarse grained patterns of energy-momentum density. Small corrections to the amplitudes α(E, r) due to quantum hair do not qualitatively change this situation, but they are necessary to unitarize the evaporation and they determine the precise relations between components of the entangled state. 

Importantly, no special assumptions about the amplitudes α(E, r) need to be made to determine that the factorized form of the state (2) does not hold. Factorization is assumed in essentially every formulation of the information paradox, but in reality is violated because the external graviton state depends on the internal black hole state. 

Known quantum gravitational effects leading to quantum hair are extremely small and thus difficult to probe experimentally or detect via observations. We cannot prove that our solution to the information paradox is unique. However, the consequences of quantum hair lead, without any speculative theoretical assumptions, to plausible unitary evaporation of black holes. The properties of quantum hair and the evaporation amplitude (6) can be deduced using only long wavelength properties of quantum gravity – they do not rely on assumptions about Planck scale physics or a specific short distance completion. Therefore, Occam’s razor favors quantum hair.

Quantum Hair and Black Hole Information, University of Amsterdam, 17 Jun 2022

 

As promised, video from my talk in Amsterdam. 

Seminar at the Institute of Physics, University of Amsterdam, 17 Jun 2022. 

Title: Quantum Hair and Black Hole Information 

Abstract: I discuss recent results concerning the quantum state of the gravitational field of a compact matter source such as a black hole. These results demonstrate the existence of quantum hair, violating the classical No Hair Theorems. I then discuss how this quantum hair affects Hawking radiation, allowing unitary evaporation of black holes. Small corrections to leading order Hawking radiation amplitudes, with weak dependence on the external graviton state, are sufficient to produce a pure final radiation state. The radiation state violates the factorization assumption made in standard formulations of the information paradox. These conclusions are consequences of long wavelength properties of quantum gravity: no special assumptions are made concerning short distance (Planckian) physics. 

Slides

Institute of Physics, University of Amsterdam:

Amsterdam, Utrecht, Split, Hvar

Last week I was in Amsterdam and Utrecht to give seminars on quantum hair and black hole information at the Universities of Utrecht and Amsterdam. The organizers told me I was the first external visitor to give an in-person talk since the COVID lockdowns. 

The Utrecht seminar went over 2 hours (unfortunately, 't Hooft was away) and the other over 90 minutes. 

I will post video of the seminars at some point. 

Now I am at the John Bell Institute on Hvar, Croatia for a special workshop on the black hole information puzzle. 

This is the view of the Adriatic from the John Bell Institute, and the beach:

 

Institute of Physics, University of Amsterdam:

Seminar on Black Hole Information and Quantum Hair, Yangzhou University (video)

 

Center for Gravitation and Cosmology, Yangzhou University (May 16 2022) 

There were several good questions at the end, and a discussion of the following rather fundamental topic.

In the conventional description of quantum measurement a pure state evolves into a mixed state, with probabilities of distinct outcomes (non-unitary von Neumann projection). 

See, e.g., 

Against Measurement (John Bell)

Black holes and decoherence 

What Hawking suggested is that a black hole (i.e., gravity) causes pure states to evolve into mixed states. But if pure states already evolve into mixed states in ordinary quantum mechanics, why is it problematic for black hole physics (gravity) to have this effect? 

Title: Quantum Hair and Black Hole Information 

Abstract: I discuss recent results concerning the quantum state of the gravitational field of a compact matter source such as a black hole. These results demonstrate the existence of quantum hair, violating the classical No Hair Theorems. I then discuss how this quantum hair affects Hawking radiation, allowing unitary evaporation of black holes. Small corrections to leading order Hawking radiation amplitudes, with weak dependence on the external graviton state, are sufficient to produce a pure final radiation state. The radiation state violates the factorization assumption made in standard formulations of the information paradox. These conclusions are consequences of long wavelength properties of quantum gravity: no special assumptions are made concerning short distance (Planckian) physics.

Slides.

Quantum Hair and Black Hole Information -- Quantum Gravity and All of That seminar series (video)

 

May 5 2022 talk in the international seminar series Quantum Gravity and All of That. 

The talk is pitched at a slightly more expert audience than previous versions I have given. 

There are interesting comments by and discussions with G. Veneziano, V. Rubakov, Suvrat Raju and others during the seminar. 

The Zoom client on ChromeOS does not allow me to see others in the meeting when I share my slides fullscreen. So at times I was not sure whose questions I was responding to! 

Slides.

Title: Quantum Hair and Black Hole Information 

Abstract: I discuss recent results concerning the quantum state of the gravitational field of a compact matter source such as a black hole. These results demonstrate the existence of quantum hair, violating the classical No Hair Theorems. I then discuss how this quantum hair affects Hawking radiation, allowing unitary evaporation of black holes. Small corrections to leading order Hawking radiation amplitudes, with weak dependence on the external graviton state, are sufficient to produce a pure final radiation state. The radiation state violates the factorization assumption made in standard formulations of the information paradox. These conclusions are consequences of long wavelength properties of quantum gravity: no special assumptions are made concerning short distance (Planckian) physics.

Has Hawking's Black Hole Information Paradox Been Resolved? (Video of MSU Theory Seminar 4/22/2022)

 

Theory seminar at Michigan State University April 22 2022. 

Title: Has Hawking's Black Hole Information Paradox Been Resolved? 

Abstract: In 1976 Stephen Hawking argued that black holes cause pure states to evolve into mixed states. Put another way, quantum information that falls into a black hole does not escape in the form of radiation. Rather, it vanishes completely from our universe, thereby violating a fundamental property of quantum mechanics called unitarity. I give a pedagogical introduction to this paradox, suitable for non-experts. Then I discuss recent results concerning the quantum state of the gravitational field of a compact matter source. These results demonstrate the existence of quantum hair, violating the classical No Hair Theorems. I then discuss how this quantum hair affects Hawking radiation, allowing unitary evaporation of black holes. 

Slides.

Black Hole Information and Quantum Hair in 10 minutes! (video)

 

This is a very nice 10 minute introduction to the black hole information paradox, and to our work on quantum hair. 

See earlier discussion Quantum Hair from Gravity (published version in Physical Review Letters). 

Parth G's video already has more than 10x as many views as my academic talk! Slides

Scott Aaronson: Quantum Computing, Unsolvable Problems, & Artificial Intelligence — Manifold podcast #9

 

Scott Aaronson is the David J. Bruton Centennial Professor of Computer Science at The University of Texas at Austin, and director of its Quantum Information Center. Previously, he taught for nine years in Electrical Engineering and Computer Science at MIT. His research interests center around the capabilities and limits of quantum computers, and computational complexity theory more generally. 

Scott also writes the blog Shtetl Optimized: https://scottaaronson.blog/ 

Steve and Scott discuss: 

1. Scott's childhood and education, first exposure to mathematics and computers. 

2. How he became interested in computational complexity, pursuing it rather than AI/ML. 

3. The development of quantum computation and quantum information theory from the 1980s to the present. 

4. Scott's work on quantum supremacy. 

5. AGI, AI Safety

ManifoldOne page. Transcript.

Quantum Hair from Gravity (published version in Physical Review Letters)

This is the published version of our paper on Quantum Hair on black holes, in Physical Review Letters:

Quantum Hair from Gravity 

Xavier Calmet, Roberto Casadio, Stephen D. H. Hsu, and Folkert Kuipers 

Phys. Rev. Lett. 128, 111301 – Published 17 March 2022 

We explore the relationship between the quantum state of a compact matter source and of its asymptotic graviton field. For a matter source in an energy eigenstate, the graviton state is determined at leading order by the energy eigenvalue. Insofar as there are no accidental energy degeneracies there is a one to one map between graviton states on the boundary of spacetime and the matter source states. Effective field theory allows us to compute a purely quantum gravitational effect which causes the subleading asymptotic behavior of the graviton state to depend on the internal structure of the source. This establishes the existence of ubiquitous quantum hair due to gravitational effects.

The paper establishes that the quantum state of the graviton field (equivalently, the spacetime metric) of a compact matter source depends on the quantum state of the source. This can be established without a short distance theory of quantum gravity -- i.e., near the Planck length. Our results are long wavelength effects and are insensitive to the details of short distance physics, such as whether gravitons are excitations of strings, or something else, at the most fundamental level.

Classical theorems in General Relativity indicate that black holes are nearly featureless -- only a few aspects of the hole, such as its total mass, charge, and angular momentum, are manifested in its asymptotic gravitational field. We show that this "no hair" property does not extend to the quantum realm. Indeed at the quantum level the situation is the opposite: the full quantum state of the compact object can be recovered from the asymptotic graviton state.

In this companion paper we show how these results resolve Hawking's black hole information paradox, which has been an open problem for 46 years.

Quantum hair and black hole information 

Physics Letters B Volume 827, 10 April 2022, 136995 

Xavier Calmet and Stephen D.H. Hsu 

It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity.

Note to experts: the companion paper explains why Mathur's Theorem (i.e., entanglement entropy must always increase by ~ln 2 with each emitted qubit) is evaded once one considers BH evolution in the full radiation Hilbert space. The radiation Hilbert space is much larger than the small subspace which remains after conditioning on any specific spacetime background or BH recoil trajectory. Even exponentially small entanglement between different radiation states (mediated by quantum hair) can unitarize the evaporation process.

This is also explained in detail in the talk video and slides linked below.

Press coverage:

BBC

Guardian

Independent

Earlier discussion, with more background on the Hawking paradox. See especially the important work by Suvrat Raju and collaborators: 

Quantum Hair and Black Hole Information (December 2021) 

Has Hawking's Black Hole Information Paradox Been Resolved? (November 2021)

Video of seminar and slides.

Vlatko Vedral: Oxford Theoretical Physicist on Quantum Superposition of Living Creatures — Manifold Podcast #7

 

Vlatko Vedral is Professor in the Department of Physics at the University of Oxford and Centre for Quantum Technologies (CQT) at the National University of Singapore. He is known for his research on the theory of Entanglement and Quantum Information Theory. 

Steve and Vlatko discuss: 

1. History of quantum information theory, entanglement, and quantum computing 

2. Recent lab experiments that create superposition states of macroscopic objects, including a living creature (tardigrade) 

3. Whether quantum mechanics implies the existence of many worlds: are you in a superposition state right now? 

4. Present status and future of quantum computing

Resources 

Web page: https://www.vlatkovedral.com/ 

Entanglement Between Superconducting Qubits and a Tardigrade: https://arxiv.org/pdf/2112.07978.pdf 

Macroscopic Superposition States: entanglement of a macroscopic living organism (tardigrade) with a superconducting qubit (Infoproc blog discussion including Sidney Coleman talk Quantum Mechanics In Your Face!) 

Quantum Hair and Black Hole Information (Physics Letters B published version)

This is the published version of our recent arxiv preprint, previously discussed here.

Quantum hair and black hole information 

https://doi.org/10.1016/j.physletb.2022.136995 

Abstract 

It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity.

The earlier paper, which established the existence of quantum hair, has been accepted by PRL and should also appear soon. 

Seminar video and slides. 

From the paper:

4. Conclusion 

Hawking's information paradox has been the focus of intense interest for almost 50 years. In his 1992 lecture on the subject, John Preskill wrote [5] 

I conclude that the information loss paradox may well presage a revolution in fundamental physics. 

The resolution described here is conservative: the quantum state of the exterior gravity field is determined by the interior black hole state, allowing the latter to influence Hawking radiation produced at the horizon. Two distinct quantum states of the black hole may produce the same semiclassical external geometry, but the graviton states differ at the quantum level. The relationship between interior and exterior quantum states is not governed by classical no-hair theorems. Indeed, it has gradually been appreciated that gravity itself prevents the localization of quantum information [4], [9], [10], [11], [21], [22], [23], even behind a horizon. We stress that all formulations of the paradox require a degree of factorization between the black hole internal state and the radiation (see, e.g., (6)), which is clearly not true of our equation (4). 

Certain aspects of our expressions (2)-(4) are very clear: the black hole information is spread over many branches of the final radiation state, and macroscopic superpositions of different spacetime geometries play a role in the evaporation. Some of the difficulty in resolving the paradox may originate from a reluctance to accept these aspects of quantum dynamics.

Black Hole Information and Quantum Hair: seminar video and slides

 

This is video of a seminar I gave at the University of Sussex. Slides.

Has Hawking's Black Hole Information Paradox Been Resolved? Quantum Hair and Black Hole Information 

Abstract: In 1976 Stephen Hawking argued that black holes cause pure states to evolve into mixed states. Put another way, quantum information that falls into a black hole does not escape in the form of radiation. Rather, it vanishes completely from our universe, thereby violating a fundamental property of quantum mechanics called unitarity. I give a pedagogical introduction to this paradox, suitable for non-experts. Then I discuss recent results concerning the quantum state of the gravitational field of a compact matter source. These results demonstrate the existence of quantum hair, violating the classical No Hair Theorems. I then discuss how this quantum hair affects Hawking radiation, allowing unitary evaporation of black holes.

See this related blog post: Has Hawking's Black Hole Information Paradox Been Resolved?

In the talk I mention an introductory colloquium on the history of black holes and the connection to entropy and information. See slides.