Yasunori Nomura. UC Berkeley; LBNL; Kavli IPMU

Transcription

1 Yasunori Nomura UC Berkeley; LBNL; Kavli IPMU

2 Why black holes? Testing grounds for theories of quantum gravity Even most basic questions remain debatable Do black holes evolve unitarily? Does an infalling observer pass the event horizon smoothly? Are dynamics local outside the stretched horizon? S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D14 (1976) A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arxiv: [hep-th]] involves all three pillars of modern physics: Quantum mechanics, General relativity, and Statistical mechanics

3 In this talk, I present a picture that aims to give affirmative answers to these questions. I will argue that a key to address these issues is to understand the emergence of semiclassical spacetime. d.o.f.s described by semiclassical theory is only a tiny subset of the whole d.o.f.s in the microscopic theory. Physics of BH information concerns these vast d.o.f.s which must be viewed as delocalized from the semiclassical viewpoint. Mostly based on with Fabio Sanches and Sean Weinberg The black hole interior in quantum gravity, Phys. Rev. Lett. 114 (2015) [arxiv: [hep-th]] Relativeness in quantum gravity: limitations and frame dependence of semiclassical descriptions, JHEP 04 (2015) 158 [arxiv: [hep-th]] earlier work with Varela and Weinberg, e.g., , , , ; See also Y. Nomura and N. Salzetta, Why Firewalls Need Not Exist, Phys. Lett. B761 (2016) 62 [ ].

4 Quantum Mechanics and Black Holes Information loss paradox same at the semiclassical level horizon Hawking radiation Hawking radiation A B information is lost?? Hawking ( 76)

5 Quantum Mechanics and Black Holes Information loss paradox same at the semiclassical level horizon Hawking radiation Hawking radiation A B information is lost?? No Hawking ( 76) Quantum mechanically different final states The whole information is sent back in Hawking radiation (in a form of quantum correlations) cf. AdS/CFT, classically burning stuffs,

6 From a falling observer s viewpoint: horizon A Distant observer: Information will be outside at late times. (sent back in Hawking radiation) Falling observer: Information will be inside at late times. (carried with him/her) B Objects simply fall in cf. equivalence principle Which is correct? Note: Quantum mechanics prohibits faithful copy of information (no-cloning theorem) + + (superposition principle) ( + )( + )

7 From a falling observer s viewpoint: horizon There is no contradiction! A Distant observer: Information will be outside at late times. (sent back in Hawking radiation) Falling observer: Information will be inside at late times. (carried with him/her) B Objects simply fall in cf. equivalence principle Which is correct? Both are correct! One cannot be both distant and falling observers at the same time. Black hole complementarity Susskind, Thorlacius, Uglum ( 93); Stephens, t Hooft, Whiting ( 93)

8 Including both (late) Hawking radiation and interior spacetime in a single description is overcounting! Equal-time hypersurfaces must be chosen carefully. This is a hypothesis beyond QFT in curved spacetime. nice slice (nothing wrong in general relativity) A hope was that with such a careful choice, semiclassical field theory gives a good (local) description of physics viewed from a single observer. cf. Hayden, Preskil ( 07); Sekino, Susskind ( 08);

9 Complementarity Does Not Seem Enough Firewall argument(s) Almheiri, Marolf, Polchinski, (Stanford), Sully ( 13 14) Entanglement argument Monogamity of entanglement prevents unitarity and smoothness incompatible Typicality argument Typical states in quantum gravity do not seem to have smooth interior

10 Complementarity Does Not Seem Enough Firewall argument(s) Almheiri, Marolf, Polchinski, (Stanford), Sully ( 13 14) Entanglement argument Monogamity of entanglement prevents unitarity and smoothness incompatible Typicality argument Typical states in quantum gravity do not seem to have smooth interior

11 Complementarity Does Not Seem Enough Firewall argument(s) Almheiri, Marolf, Polchinski, (Stanford), Sully ( 13 14) Entanglement argument Monogamity of entanglement prevents unitarity and smoothness incompatible Smooth horizon: t t Unitarity: e + e - > e + e - > + e - e + > x x e + e - > 0> 0> L 0> R + 1> L 1> R + S Minkowski Rindler (infalling) (Schwarzschild) t Page ( 93)

12 The entanglement argument for firewalls The problem for black hole information can be formulated in a single causal patch Monogamity of entanglement smooth horizon: A B unitarity: B C Fig. by Preskil These two structures cannot both be true. Unitarity Smooth horizon = firewall

13 Note: the black hole thermal atmosphere zone is thick (below we set l P = 1) r* = r + 2M ln r - 2M 2M A clash of basic principles! Unitarity (of black hole evolution) Local physics outside the stretched horizon Equivalence principle (~ smooth horizon)

14 Quantum Evolution of BHs without Firewalls What is Bekenstein-Hawking entropy? Dynamically formed black hole Time scale of evolution (Hawking emission): t ~ M The black hole state involves a superposition of E ~ M ~ 1/M Y.N., Sanches, Weinberg (2014) How many independent ways are there to superpose the energy eigenstates to obtain the same black hole geometry within this precision? Ψ(M)> = c 1 E 1 > + c 2 E 2 > + c 3 E 3 > + The logarithm of this number: S BH = A 4 M+ M M E

15 Quantum Evolution of BHs without Firewalls What is Bekenstein-Hawking entropy? Dynamically formed black hole Time scale of evolution (Hawking emission): t ~ M The black hole state involves a superposition of E ~ M ~ 1/M Y.N., Sanches, Weinberg (2014) How many independent ways are there to superpose the energy eigenstates to obtain the same black hole geometry within this precision? Ψ(M)> = c 1 E 1 > + c 2 E 2 > + c 3 E 3 > + The logarithm of this number: S BH = A 4ħ M+ M M E Classically, the number is a continuous infinity! Quantum mechanics reduces the number of states (not a new quantum hair )

16 Black hole information is carried by spacetime slightly different M Where is the information? In QM, information is stored nonlocally in general. (Local dynamics, non-local state) A black hole is quasi static entropy density Entropy is mostly at the horizon cf. V(r) ~ -M/r O(1) entropy at the edge of the zone not «O(1) fractionally only ~ O(1 / A), but enough to affect evaporation! There are O(M 2 ~ A) steps!

17 The (correct) picture of Hawking emission: (ingoing) negative energy excitation Emission occurs at the edge of the zone No need to carry information from the horizon! r 2M r ~ 3M r* There is no outgoing mode in the zone in the semiclassical picture. The monogamity argument does not apply!

18 The (correct) picture of Hawking emission: (ingoing) negative energy excitation Emission occurs at the edge of the zone No need to carry information from the horizon! r 2M r ~ 3M r* There is no outgoing mode in the zone in the semiclassical picture. The monogamity argument does not apply! At the microscopic level Ψ 1 (M)> Ψ 2 (M)> Ψ 3 (M)> Ψ 4 (M)> Ψ 2n (M)>?

19 The (correct) picture of Hawking emission: (ingoing) negative energy excitation Emission occurs at the edge of the zone No need to carry information from the horizon! r 2M r ~ 3M r* There is no outgoing mode in the zone in the semiclassical picture. The monogamity argument does not apply! At the microscopic level Ψ 1 (M)> Ψ 2 (M)> Ψ 3 (M)> Ψ 4 (M)> Ψ 2n (M)>? Ψ* 1 (M)> r 1 > Ψ* 2 (M)> r 2 > Ψ* 3 (M)> r 1 > Ψ* 4 (M)> r 2 > Ψ* 2n (M)> r 2 > : negative energy excitation * But the relaxation afterward Ψ* 1 (M)> Ψ* 2 (M)> Ψ* 2n (M)> Ψ 1 (M - δm)> Ψ 2 (M - δm)> Ψ n (M - δm)> does not seem to be possible

20 The (correct) picture of Hawking emission: (ingoing) negative energy excitation Emission occurs at the edge of the zone (information extracted directly from spacetime there) r 2M r ~ 3M r* = r + 2M ln r - 2M 2M There is no outgoing mode in the zone in the semiclassical picture. The monogamity argument does not apply! At the microscopic level Ψ 1 (M)> Ψ 2 (M)> Ψ 3 (M)> Ψ 4 (M)> Ψ 2n (M)> Ψ* 1 (M)> r 1 > Ψ* 1 (M)> r 2 > Ψ* 2 (M)> r 1 > Ψ* 2 (M)> r 2 > Ψ* n (M)> r 2 > Negative energy excitation carries negative entropy! E ~ S Information extraction from BHs occurs through ingoing negative information.

21 What was wrong with the naïve Hawking pair-creation picture? Relevant process occurs at the horizon. Created pairs are maximally entangled.

22 What was wrong with the naïve Hawking pair-creation picture? Relevant process occurs at the horizon. at the edge of the zone (a macroscopic distance away from the horizon) Created pairs are maximally entangled. are not (the origin of the information transfer to the far exterior region) BH information is carried nonlocally by spacetime.

23 What was wrong with the naïve Hawking pair-creation picture? Relevant process occurs at the horizon. at the edge of the zone (a macroscopic distance away from the horizon) Created pairs are maximally entangled. are not (the origin of the information transfer to the far exterior region) BH information is carried nonlocally by spacetime. Note: Time reversal process vs generic incoming radiation Semiclassical picture breaks down at large distances, but only in a subtle way.

24 A successful reference frame change possible T highly boosted w.r.t. the BH s rest frame X In a frame whose spatial origin falls from a distance: r 0 2M > O(M) Space/time scale between any detector clicks (even if blueshfited) are T ~ X ~ O(M) approx. Minkowski r 0 Distribution of information depends on the frame Extreme relativeness A key to understand the quantum nature of spacetime c.f. Y.N., Salzetta, Sanches, Weinberg, Toward a Holographic Theory for General Spacetime, Implications for Boltzmann brains Y.N., A Note on Boltzmann Brain, arxiv: Solution to the firewall paradox of the Boltzmann brain problem

25 Summary Information/firewall problem in black hole quantum physics a picture for the emergence of semiclassical spacetime vast d.o.f.s (Bekenstein-Hawking entropy) partial classicalization coarse-graining (quantum) matter in spacetime QFT (in curved spacetime) coarse-graining classical theory microscopic theory of quantum gravity Quantum information of spacetime Black hole information concerns d.o.f.s coarse-grained here. Their dynamics cannot be described in the semiclassical picture. How spacetime and gravity emerge in a full theory of quantum gravity? We need a true holographic understanding c.f. Y.N., Salzetta, Sanches, Weinberg, Toward a Holographic Theory for General Spacetime,

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27 A successful reference frame change possible T highly boosted w.r.t. the BH s rest frame r 0 X In a frame whose spatial origin falls from a distance: r 0 2M > O(M) Space/time scale between any detector clicks (even if blueshfited) are T ~ X ~ O(M) approx. Minkowski Distribution of information depends on the frame Extreme relativeness A key to understand the quantum nature of spacetime c.f. Y.N., Salzetta, Sanches, Weinberg, Toward a Holographic Theory for General Spacetime,