DOCSLIB.ORG

Naked Firewalls Phys

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Naked Firewalls Phys Naked Firewalls Phys. Rev. Lett. 116, 161304 (2016) Pisin Chen, Yen Chin Ong, Don N. Page, Misao Sasaki, and Dong-han Yeom 2016 July 8 Introduction In the firewall proposal, it is assumed that a firewall lies near the event horizon and should not be observable except by infalling observers, who are presumably terminated at the firewall. However, if the firewall is located near where the horizon would have been, based on the spacetime evolution up to that time, later quantum fluctuations of the Hawking emission rate can cause the `teleological' event horizon to have migrated to the inside of the firewall location, rendering the firewall naked. In principle, the firewall can be arbitrarily far outside the horizon. This casts doubt about the notion that firewalls are the `most conservative' solution to the information loss paradox. The AMPS Argument Almheiri, Marolf, Polchinski and Sully (AMPS) argued that local quantum field theory, unitarity, and no-drama (the assumption that infalling observers should not experience anything unusual at the event horizon if the black hole is sufficiently large) cannot all be consistent with each other for the Hawking evaporation of a black hole with a finite number of quantum states given by the Bekenstein-Hawking entropy. AMPS suggested that the `most conservative' resolution to this inherent inconsistency between the various assumptions is to give up no-drama. Instead, an infalling observer would be terminated once he or she hits the so-called firewall. This seems rather surprising, because the curvature is negligibly small at the event horizon of a sufficiently large black hole, and thus one would expect nothing special but low energy physics. The Heart of the AMPS Argument Assuming unitarity, the information contained inside a black hole should eventually be recovered from the Hawking radiation. The late time radiation purifies the earlier radiation, so the late time radiation should be maximally entangled with the earlier radiation. By the monogamy of quantum entanglement, the late time radiation cannot also be maximally entangled with the interior of the black hole. This means that the field configuration across the event horizon is generically not continuous, which leads to a divergent local energy density. More explicitly, the quantum field 2 Hamiltonian contains terms like (@r ') . The derivative is divergent at some r = R if the field configuration is not continuous across R. This is the firewall. The Location of a Firewall Usually it is thought that a firewall lies on or just inside an old black hole event horizon. Of course in quantum mechanics there are no sharp boundaries, and the position of an event horizon should be uncertain, up to perhaps fluctuations of the order of the Planck length. That is to say, a firewall is presumably like a stretched horizon, with the crucial difference that anything that hits a firewall gets incinerated instead of just passing right through. By the nature of the event horizon, if the firewall lies either inside or exactly on the horizon, then it is completely invisible to the observers outside. For a firewall that is not too far outside the event horizon, it is still doubtful that it is perceptible to far-away observers, since it would seem that such a firewall would be well hidden inside the Planckian region of the local thermal atmosphere. Causality Assumption for Firewalls Here we make the assumption that a firewall, if it exists, has a location determined by the past history of the Hawking evaporating black hole spacetime and is near where the event horizon would be if the evaporation rate were smooth, without quantum fluctuations. Then we show that quantum fluctuations of the evaporation rate in the future can move the event horizon to the inside of the firewall location, rendering it naked. Vaidya Metric Assumption For simplicity, we shall approximate the metric near the horizon of an evaporating black hole by the Vaidya metric with a negative energy influx: 2M(v) ds2 = − 1 − dv 2 + 2dvdr + r 2dΩ2: (1) r Here M(v) is the mass of the black hole, which is decreasing as a function of the advanced time v. For a smooth evaporation rate of a spherical black hole emitting mainly photons and gravitons, we shall take (in Planck units) dM α M_ ≡ = − ; (2) dv M2 where α is a constant which, in my Ph.D. thesis of forty years ago, I numerically evaluated to be about 3:7474 × 10−5. Location of the Event Horizon with Smooth Evaporation The apparent horizon is located at rApH = 2M(v), whereas the event horizon is generated by radially outgoing null geodesics, dr 1 2M(v) r_ ≡ = 1 − ; (3) dv 2 r on the boundary of such null geodesics reaching out to future null infinity, instead of falling in to the singularity that is believed to be inside the black hole. For a smooth evaporation rate M_ ≡ dM=dv = −α=M2, the event horizon is given by the solution to Eq. (3) such that it does not diverge exponentially far away from the apparent horizon in the future. If we define u ≡ 1 − r=(2M) and p ≡ −4M_ and assume that n ≡ −d ln p=d ln M is constant, then one can show that the event horizon is at u = p + (n − 2)p2 + (n − 1)(2n − 5)p3 + (6n3 − 28n2 + 37n − 14)p4 + O(p5): (4) The Adiabatic Horizon For a smooth Hawking evaporation into massless particles with p ≡ −4M_ = 4α=M2, so that n = 2, one finds that the event horizon is at 2 3 6 rEH = 2M[1 − 4α=M + O(α =M )]: (5) For a general spherical metric, the covariant generalization of f_ along an outward null direction toward the future is f_ ≡ df =dv ≡ Nα@f =@xα, with outward null vector Nα normalized α so thatr _ ≡ dr=dv ≡ N r,α = (1=2)rr · rr ≡ (1=2) − M=r. Note that dM=dv = −α=M2 implies that d2(M3)=dv 2 = 0, but since r ≈ 2M, we have d2(r 3 )=dv 2 ≈ 0 as well. Let us EH EH therefore define an adiabatic horizon at rAdH by the outer root of d2 @ @ (r 3 ) ≡ Nα Nβ r 3 = 0: (6) dv 2 AdH @xα @xβ AdH The Location of the Adiabatic Horizon The location of the adiabatic horizon is very near where the event horizon would be if the future evolution of the latter followed the adiabatic mass evolution law dM=dv = −α=M2. One can show that rAdH is equivalent to the location where the gradient vector of (1=4)r(r 2) · r(r 2) = r 2rr · rr ≡ r 2 − 2Mr (which, incidentally, α 2 defines M) is in the outward null direction, or N (r rr · rr),α = 0, which gives M_ = (1=2) − (3=2)(M=r) + (M=r)2 and 4M r ≡ : (7) AdH p 3 − 1 + 16M_ When dM=dv = −α=M2 holds, this expression agrees with 2 3 6 rEH = 2M[1 − 4α=M + O(α =M )] to the order given. The Fourth-Root Horizon For fluctuating evaporation, a smoother approximation for the horizon is the fourth-root horizon at rq 4 2 r4rH ≡ (2M) + (32α) − 32α: (8) The inverse of this relation is M = (1=2)(r 4 + 64αr 2 )1=4. If one 4rH 4rH had a model evaporating black hole for which the event horizon (say denoted by r) were exactly at the fourth-root horizon, so that r = r , then using Eqs. (3) and (8) and the definition ≡ 8α=M2 4rH p pp leads to −M2M_ /α = 2 1 + 2[1 − 1 + 2 − ]/, which is p very close to 1 for M 4 α ( 1), but then it decreases to a minimum near 0.954142 at ≈ 0:398463 before increasing to 2 as the mass goes to zero and diverges, with −M2M_ /α always staying finite and remaining within a factor of 2 of unity and hence giving M_ ∼ −α=M2 as M decreases to zero. The Smoothed Horizon An even smoother approximation for the location of the event horizon is the smoothed horizon at Z 1 1+2a y 1+a y rSmH (v)≡2 dyM(v −4M(v)y) 2 exp − − 2 exp − (9) 0 a a 2a 2a for a positive smoothing parameter a. Then if M(v) had a linear dependence on v over the range where the integrand is significant, this would give the extrapolation rSmH (v) = 2M(v + 4M(v)), the radius of the apparent horizon at a time greater than v by the inverse of the surface gravity, which is what the first two terms of 2 3 6 _ 2 rEH =2M[1−4α=M +O(α =M )] give for constant M =−α=M . A plausible value of the smoothing parameter might be a ∼ ln(M(v)) 1, giving smoothing over roughly the scrambling time ∼ M(v) ln(M(v)). Location of the Firewall near the Smoothed Horizon We shall assume that the firewall, if it exists, is close to where the event horizon would be if the black hole evolves smoothly and adiabatically according to dM=dv = −α=M2, as perhaps well estimated by the smoothed horizon for some suitable value of the smoothing parameter a. However, the actual event horizon depends on the future evolution of the spacetime, and not just on that of its past. Therefore, quantum fluctuations in the future spacetime can lead the event horizon to deviate significantly from the smoothed horizon. If the mass loss rate exceeds the adiabatic formula, then the event horizon will be inside the smoothed horizon. As a result a firewall located at the smoothed horizon would become naked, visible from future null infinity.
Load more

Recommended publications
  • Stephen Hawking: 'There Are No Black Holes' Notion of an 'Event Horizon', from Which Nothing Can Escape, Is Incompatible with Quantum Theory, Physicist Claims
    NATURE | NEWS Stephen Hawking: 'There are no black holes' Notion of an 'event horizon', from which nothing can escape, is incompatible with quantum theory, physicist claims. Zeeya Merali 24 January 2014 Artist's impression VICTOR HABBICK VISIONS/SPL/Getty The defining characteristic of a black hole may have to give, if the two pillars of modern physics — general relativity and quantum theory — are both correct. Most physicists foolhardy enough to write a paper claiming that “there are no black holes” — at least not in the sense we usually imagine — would probably be dismissed as cranks. But when the call to redefine these cosmic crunchers comes from Stephen Hawking, it’s worth taking notice. In a paper posted online, the physicist, based at the University of Cambridge, UK, and one of the creators of modern black-hole theory, does away with the notion of an event horizon, the invisible boundary thought to shroud every black hole, beyond which nothing, not even light, can escape. In its stead, Hawking’s radical proposal is a much more benign “apparent horizon”, “There is no escape from which only temporarily holds matter and energy prisoner before eventually a black hole in classical releasing them, albeit in a more garbled form. theory, but quantum theory enables energy “There is no escape from a black hole in classical theory,” Hawking told Nature. Peter van den Berg/Photoshot and information to Quantum theory, however, “enables energy and information to escape from a escape.” black hole”. A full explanation of the process, the physicist admits, would require a theory that successfully merges gravity with the other fundamental forces of nature.
    [Show full text]
  • Black Hole Weather Forcasting
    NTU Physics Department Chih-Hung Wu 吳智弘 I. Spacetime Locality and ER=EPR Conjecture II. Construction of the Counter-example III. Debate with Professor J. Maldacena J. Maldacena and L.Susskind, “Cool horizon for entangled black holes”, Fortsch. Phys. 61 (2013) 781-811 arXiv:1306.0533 Pisin Chen, Chih-Hung Wu, Dong-hanYeom. ”Broken bridges: A counter-example of the ER=EPR conjecture”, arXiv:1608.08695, Aug 30, 2016 Locality(Impossibility of superluminal signal) 1.Quantum Theory-EPR entanglement 2.General Relativity-ER bridge Violation of Locality?---NO! ER bridge should remain un-traversable even in the quantum theory. En /2 e nLR m n In AdS/CFT framework, an eternal AdS- Schwarzschild BH and the Penrose diagram: En /2 e nLR m n Maximally entangled J. Maldacena, “Eternal black hole in AdS” JHEP 0304 (2003) 021 ,arXiv:0106112 Consider such a scenario: A large number of particles, entangled into separate Bell pairs, and separate them when we collapse each side to form two distant black holes, the two black holes will be entangled. Now they make a conjecture that they will also be connected by an Einstein-Rosen bridge. ER=EPR Known: EREPR Conjecture: EPRER How to realize in the usual Hawking radiation scenario? Second black hole= early half of HR. Step 1: Generate an entangled system Step 2: Formation of the ER bridge Step 3: Collapsing of the bubble Step 4: Evaporation of the black hole Step 5: Communication via ER bridge Assumption: GR with N massless scalar fields 11N S gd4 x ()()() 2 U f 2 i 22i1 The potential has two minima: (AdS space) Background (false vacuum) True vacuum 0 Prepared in advance (e.g.
    [Show full text]
  • A Hole in the Black Hole
    Open Journal of Mathematics and Physics | Volume 2, Article 78, 2020 | ISSN: 2674-5747 https://doi.org/10.31219/osf.io/js7rf | published: 7 Feb 2020 | https://ojmp.wordpress.com DA [microresearch] Diamond Open Access A hole in the black hole Open Physics Collaboration∗† April 19, 2020 Abstract Supposedly, matter falls inside the black hole whenever it reaches its event horizon. The Planck scale, however, imposes a limit on how much matter can occupy the center of a black hole. It is shown here that the density of matter exceeds Planck density in the singularity, and as a result, spacetime tears apart. After the black hole is formed, matter flows from its center to its border due to a topological force, namely, the increase on the tear of spacetime due to its limit until it reaches back to the event horizon, generating the firewall phenomenon. We conclude that there is no spacetime inside black holes. We propose a solution to the black hole information paradox. keywords: black hole information paradox, singularity, firewall, entropy, topology, quantum gravity Introduction 1. Black holes are controversial astronomical objects [1] exhibiting such a strong gravitational field that nothing–not even light–can escape from inside it [2]. ∗All authors with their affiliations appear at the end of this paper. †Corresponding author: mplobo@uft.edu.br | Join the Open Physics Collaboration 1 2. A black hole is formed when the density of matter exceeds the amount supported by spacetime. 3. It is believed that at or near the event horizon, there are high-energy quanta, known as the black hole firewall [3].
    [Show full text]
  • Naked Firewalls Phys
    Naked Firewalls Phys. Rev. Lett. 116, 161304 (2016) Pisin Chen, Yen Chin Ong, Don N. Page, Misao Sasaki, and Dong-han Yeom 2016 May 19 Introduction In the firewall proposal, it is assumed that the firewall lies near the event horizon and should not be observable except by infalling observers, who are presumably terminated at the firewall. However, if the firewall is located near where the horizon would have been, based on the spacetime evolution up to that time, later quantum fluctuations of the Hawking emission rate can cause the `teleological' event horizon to have migrated to the inside of the firewall location, rendering the firewall naked. In principle, the firewall can be arbitrarily far outside the horizon. This casts doubt about the notion that a firewall is the `most conservative' solution to the information loss paradox. The AMPS Argument Almheiri, Marolf, Polchinski and Sully (AMPS) argued that local quantum field theory, unitarity, and no-drama (the assumption that infalling observers should not experience anything unusual at the event horizon if the black hole is sufficiently large) cannot all be consistent with each other for the Hawking evaporation of a black hole with a finite number of quantum states given by the Bekenstein-Hawking entropy. AMPS suggested that the `most conservative' resolution to this inherent inconsistency between the various assumptions is to give up no-drama. Instead, an infalling observer would be terminated once he or she hits the so-called firewall. This seems rather surprising, because the curvature is negligibly small at the event horizon of a sufficiently large black hole, and thus one would expect nothing special but low energy physics.
    [Show full text]
  • Firewalls and the Quantum Properties of Black Holes
    Firewalls and the Quantum Properties of Black Holes A thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Science degree in Physics from the College of William and Mary by Dylan Louis Veyrat Advisor: Marc Sher Senior Research Coordinator: Gina Hoatson Date: May 10, 2015 1 Abstract With the proposal of black hole complementarity as a solution to the information paradox resulting from the existence of black holes, a new problem has become apparent. Complementarity requires a vio- lation of monogamy of entanglement that can be avoided in one of two ways: a violation of Einstein’s equivalence principle, or a reworking of Quantum Field Theory [1]. The existence of a barrier of high-energy quanta - or “firewall” - at the event horizon is the first of these two resolutions, and this paper aims to discuss it, for Schwarzschild as well as Kerr and Reissner-Nordstr¨omblack holes, and to compare it to alternate proposals. 1 Introduction, Hawking Radiation While black holes continue to present problems for the physical theories of today, quite a few steps have been made in the direction of understanding the physics describing them, and, consequently, in the direction of a consistent theory of quantum gravity. Two of the most central concepts in the effort to understand black holes are the black hole information paradox and the existence of Hawking radiation [2]. Perhaps the most apparent result of black holes (which are a consequence of general relativity) that disagrees with quantum principles is the possibility of information loss. Since the only possible direction in which to pass through the event horizon is in, toward the singularity, it would seem that information 2 entering a black hole could never be retrieved.
    [Show full text]
  • Wormholes Untangle a Black Hole Paradox
    Quanta Magazine Wormholes Untangle a Black Hole Paradox A bold new idea aims to link two famously discordant descriptions of nature. In doing so, it may also reveal how space-time owes its existence to the spooky connections of quantum information. By K.C. Cole One hundred years after Albert Einstein developed his general theory of relativity, physicists are still stuck with perhaps the biggest incompatibility problem in the universe. The smoothly warped space- time landscape that Einstein described is like a painting by Salvador Dalí — seamless, unbroken, geometric. But the quantum particles that occupy this space are more like something from Georges Seurat: pointillist, discrete, described by probabilities. At their core, the two descriptions contradict each other. Yet a bold new strain of thinking suggests that quantum correlations between specks of impressionist paint actually create not just Dalí’s landscape, but the canvases that both sit on, as well as the three-dimensional space around them. And Einstein, as he so often does, sits right in the center of it all, still turning things upside-down from beyond the grave. Like initials carved in a tree, ER = EPR, as the new idea is known, is a shorthand that joins two ideas proposed by Einstein in 1935. One involved the paradox implied by what he called “spooky action at a distance” between quantum particles (the EPR paradox, named for its authors, Einstein, Boris Podolsky and Nathan Rosen). The other showed how two black holes could be connected through far reaches of space through “wormholes” (ER, for Einstein-Rosen bridges). At the time that Einstein put forth these ideas — and for most of the eight decades since — they were thought to be entirely unrelated.
    [Show full text]
  • Black Hole Physics
    Black Hole Entropy, Hawking Radiation and Information Paradox 王卓骁 Major: planetary formation THCA Student Seminar Advisor: Doug Lin 2017/11/24 Outline • Over view of black hole physics • Black hole thermodynamics, black hole entropy • Hawking radiation • Information paradox • Recent ambitious hypothesis: Over view of black hole physics • 1784, first idea about black hole, John Michell and Laplace • 1915, general relativity built by Einstein, curvature V.S. matter • 1916, Schwarzschild got the general spherically symmetric, vacuum solution 2GM r = s c2 Over view of black hole physics Event Horizon 2GM r = s c2 Event Horizon Over view of black hole physics Event Horizon • What is event horizon? Schwarzschild solution e.g. world line light cone • Far away observer: space timeslope boundary, “point of no return” Schwarzschild Coordinates. Red line denoted outgoing light rays, while blue for ingoing. Fig. by Quinzacara 2014 Over view of black hole physics Event Horizon • What is event horizon? Schwarzschild solution e.g. • Far away observer: space time boundary, “point of no return” Equivalence Principle. • Traveling astronaut: nothing strange when passing through credit: Andrew Hamilton (JILA) t⇤ = t (r⇤ r) ± − Eddington-Finkelstein Coordinates. Red line denoted outgoing light rays, while blue for ingoing. Fig. by Quinzacara 2014 Over view of black hole physics Stellar evolution Chandrasekhar, 1931 < 1.4 M☉ Oppenheimer, 1939 < 3 M☉ credit: http://chandra.harvard.edu/xray_sources/stellar_evolution.html Over view of black hole physics • 1960s, Kerr solution, Newman solution, no-hair theorem • 1967, pulsar discovered, compact objects became realistic • 1970s, Bardeen, Bekenstein, Carter, Hawking led to BH thermodynamics. Involving QFT, Hawking radiation emerged.
    [Show full text]
  • Black Holes Information, Entanglement, Complementarity
    I. Review of the information problem and black hole complementarity II. The firewall argument III. Responses and open questions Hawking radiation singularity horizon star Hawking’s argument: The Hawking process is a quantum effect, and produces a superposition, + The two photons are entangled; the outside (unprimed) photon by itself is in a mixed state. Hawking’s argument: The net result is a highly entangled state, roughly When the evaporation is completed, the inside (primed) degrees of free- dom are gone, leaving the Hawking radiation in a highly mixed state. Pure → mixed evolution. Counterintuition: for an ordinary burning object, the apparent evolution from a pure to mixed state is a result of coarse- graining, not an exact statement. Perhaps Hawking has missed subtle phases. But the entanglement is not sensitive to small corrections: to turn into a pure state would need O(1) admixture of at each step (cf. Mathur 0909.1038, also Giddings 1108.2015). The difference is that an ordinary burning object does not have a horizon. The Page argument (hep-th/9306083): S 3 O(RS ) t Red: Scoarse (= SBekenstein-Hawking) of evaporating black hole. Blue: (SvN of radiation) = (Sent. of rad. + BH) ≤ (SvN of BH), according to Hawking ’76. Deviations from Hawking must begin when the black hole is still large (green). 3/4 Asides: RS = M in Planck units, remnants, A vs. A S O(R3) t Old vs. young black holes. Hayden and Preskill 0708.4025: a message thrown into an old black hole can be read almost immediately from the Hawking radiation, if we have collected the first half+ε of the radiation.
    [Show full text]
  • Complementarity Is Not Enough Arxiv:1207.5192V2 [Hep-Th] 15 Oct
    Prepared for submission to JHEP Complementarity Is Not Enough Raphael Boussoa;b aCenter for Theoretical Physics and Department of Physics, University of California, Berkeley, CA 94720, U.S.A. bLawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A. Abstract: The near-horizon field B of an old black hole is maximally entangled with the early Hawking radiation R, by unitarity of the S-matrix. But B must be maximally entangled with the black hole interior A, by the equivalence principle. Causal patch complementarity fails to reconcile these conflicting requirements. The system B can be probed by a freely falling observer while there is still time to turn around and remain outside the black hole. Therefore, the entangled state of the BR system is dictated by unitarity even in the infalling patch. If, by monogamy of entanglement, B is not entangled with A, the horizon is replaced by a singularity or “firewall". To illustrate the radical nature of the ideas that are needed, I briefly discuss two approaches for avoiding a firewall: the identification of A with a subsystem of R; and a combination of patch complementarity with the Horowitz-Maldacena final-state proposal. arXiv:1207.5192v2 [hep-th] 15 Oct 2012 Contents 1 The Firewall Paradox1 2 Why Complementarity is Not Enough3 3 Three Choices5 3.1 Information Loss for the Outside Observer5 3.2 Firewalls6 3.3 Breakdown of Effective Quantum Field Theory8 3.3.1 Identification of Hilbert Spaces8 3.3.2 Final State Quantum Mechanics 10 1 The Firewall Paradox Almheiri, Marolf, Polchinski and Sully [1] have exhibited a profound paradox.
    [Show full text]
  • The Black Hole Firewall Paradox
    The Black Hole Firewall Paradox Dissertation by Tycho Sikkenk Supervised by Professor Fay Dokwer Department of Physics, Imperial College London In Partial Fulfillment of the Requirements for the Degree of Master of Science (MSc) June-September 2013 (Submitted September 20, 2013) \Nobody has the slightest idea what is going on." Joe Polchinski on the Firewall Paradox, KITP Fuzz or Fire Conference, August 2013 2 Abstract Famously, the quantum treatment of black holes predicts the appearance of Hawking radi- ation emanating from the black hole. Detailed analysis of the behaviour of the wave modes in the proximity of the horizon in the Schwarzschild background shows that the Hawking modes will be entangled with partner modes at the interior of the black hole, so that an observer far removed from the black hole will detect a mixed state. Thus, it seems that the collapse and subsequent evaporation of the black hole caused by emission the Hawking radiation is not unitary. Information is lost during the process and the state of the black hole is independent of that of the initial configuration of the spacetime. The solution to this paradox was found in the notion of black hole complementarity, which postulates that the observer at infinity will measure a different reality than an infalling spectator. Further support dispelling the conclu- sions of the information paradox came with the holographic principle and the gauge/gravity duality of the AdS/CFT correspondence, that conclusively proved that even the life cycle of an AdS black hole is governed by a unitary matrix of the conformal field theory on the boundary of the spacetime.
    [Show full text]
  • Wormhole and Entanglement (Non-)Detection in the ER=EPR Correspondence
    CALT-TH-2015-048 Wormhole and Entanglement (Non-)Detection in the ER=EPR Correspondence Ning Bao,1,2 Jason Pollack,2 and Grant N. Remmen2 1Institute for Quantum Information and Matter and 2Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA Abstract The recently proposed ER=EPR correspondence postulates the existence of wormholes (Einstein- Rosen bridges) between entangled states (such as EPR pairs). Entanglement is famously known to be unobservable in quantum mechanics, in that there exists no observable (or, equivalently, projector) that can accurately pick out whether a generic state is entangled. Many features of the geometry of spacetime, however, are observables, so one might worry that the presence or absence of a wormhole could identify an entangled state in ER=EPR, violating quantum mechanics, specifically, the property of state-independence of observables. In this note, we establish that this cannot occur: there is no measurement in general relativity that unambigu- ously detects the presence of a generic wormhole geometry. This statement is the ER=EPR dual of the undetectability of entanglement. arXiv:1509.05426v1 [hep-th] 17 Sep 2015 e-mail: ningbao@theory.caltech.edu, jpollack@theory.caltech.edu, gremmen@theory.caltech.edu Contents 1 Introduction 2 2 Entanglement is Not an Observable3 3 Setup 4 4 The Single-Observer Case6 5 The Multiple-Observer Case8 6 Conclusions 11 1 Introduction Black holes are the paradigmatic example of a system where both field-theoretic and gravitational considerations are important. Black hole thermodynamics and the area theorem [1,2] already pro- vided a relationship between entanglement and geometry, while the classic black hole information paradox [3] and its potential resolution via complementarity [4–6] pointed at the subtlety of the needed quantum mechanical description.
    [Show full text]
  • [0.91]The Subtle Unphysical Hypothesis of the Firewall Theorem
    entropy Article The Subtle Unphysical Hypothesis of the Firewall Theorem Carlo Rovelli Centre de Physique Théorique, Aix-Marseille Université, Université de Toulon, CNRS, F-13288 Marseille, France; rovelli@cpt.univ-mrs.fr Received: 12 August 2019; Accepted: 24 August 2019; Published: 27 August 2019 Abstract: The black-hole firewall theorem derives a suspicious consequence (large energy-momentum density at the horizon of a black hole) from a set of seemingly reasonable hypotheses. I point out the hypothesis that is likely to be unrealistic (a hypothesis not always sufficiently made explicit) and discuss the subtle confusion at its origin: mixing-up of two different notions of entropy and misusing the entropy bound. Keywords: black hole entropy; information paradox; entropy 1. Confusing Two Distinct Entropies What happens at the horizon of a real black hole? What would you experience if you crossed it with a starship? We should be able to answer plausibly with established physics, since a horizon can be a low-curvature region where there is no obvious reason for unknown physics (like quantum gravity) to play a big role. Yet, today, theoreticians disagree on the answer. General relativity suggests that nothing particularly remarkable happens in a sufficiently small region around a point on the horizon. However, a portion of the theoretical physics community convinced itself that the starship crossing the horizon will be burned to ashes by a “firewall”: a strong-energy momentum density around the horizon, generated by quantum field theoretical effects. This conviction is supported by the firewall theorem [1], which proves the existence of such large energy-momentum, on the basis of a few seemingly reasonable hypotheses.
    [Show full text]