Black Holes, Quantum Mechanics, and Firewalls

Transcription

1 Black Holes, Quantum Mechanics, and Firewalls Joseph Polchinski Simons Symposium, NYC 11/18/13

2 A Brief History of the Black Hole Information Paradox:

3 A Brief History of the Black Hole Information Paradox: In 1976, Stephen Hawking argued that black holes destroy information, in a way that requires a modification of the principles of quantum mechanics.

4 A Brief History of the Black Hole Information Paradox: In 1976, Stephen Hawking argued that black holes destroy information, in a way that requires a modification of the principles of quantum mechanics. In 2004, he changed his mind.

5 A Brief History of the Black Hole Information Paradox: In 1976, Stephen Hawking argued that black holes destroy information, in a way that requires a modification of the principles of quantum mechanics. In 2004, he changed his mind. In 2012, some radicals from Santa Barbara argued that if QM is not modified, the black hole interior is very different from what general relativity predicts.

6 A Brief History of the Black Hole Information Paradox: In 1976, Stephen Hawking argued that black holes destroy information, in a way that requires a modification of the principles of quantum mechanics. In 2004, he changed his mind. In 2012, some radicals from Santa Barbara argued that if QM is not modified, the black hole interior is very different from what general relativity predicts. The information paradox is one of the great thought experiments in the history of physics.

7 Thought experiments have played a major role in the discovery of the laws of physics. Example: Maxwell s equations

8 Thought experiments have played a major role in the discovery of the laws of physics. Example: Maxwell s equations Coulomb/Gauss: charges produce electric fields (1785/1835) Ampere: currents produce magnetic fields (1826) Faraday: changing magnetic fields produce electric fields (1831) Maxwell: changing electric fields produce magnetic fields (1861)

9 The equations before Maxwell: a simple thought experiment reveals their incompleteness

10 Maxwell s simple thought experiment: x capacitor Experiment: put a capacitor in an alternating current. Measure the magnetic field at x. The incomplete set of equations gives two different answers. This can be fixed by adding one more term.

11 Adding Maxwell s term fixed everything, and gave an unexpected bonus: Faraday Maxwell magnetic electric magnetic electric magnetic electric... = electromagnetic wave speed = = speed of light (to few % accuracy)

12 Why was this discovered via a thought experiment and not a real experiment? In order to see the effect if was necessary to reach the nanosecond time scale. Heinrich Hertz observed this directly 25 years later, using sparks to drive a circuit at nanosecond time scales. Why was a thought experiment successful? All but one term was already known! Thought experiments are useful in exposing incompleteness and inconsistency of a theory.

13 In quantum gravity we have the same problem: The natural time scale is the Planck time, 5 t P = hg /c = sec far beyond the reach of direct experiment. But we also have the same advantage: The theories of quantum mechanics and general relativity are each very well tested and successful in their own regimes. Thought experiments can expose inconsistencies.

14 singularity time horizon horizon singularity Black holes have proven to be useful arenas for the confrontation of quantum mechanics and general relativity

15 Confronting quantum mechanics with general relativity in a black hole leads to two conflicts: The entropy puzzle (Bekenstein, Hawking, ) The information paradox (Hawking, 1976). Latest incarnation: the firewall.

16 The entropy puzzle: General relativity describes black holes as smooth geometries, without `hair. Quantum mechanics points to an atomic or bit substructure. Evidence for the latter: Information storage limit (Bekenstein) The black hole temperature (Hawking, 1974). A further lesson: the holographic principle.

17 Bekenstein: calculate number of bits of information that a black hole can contain, as a function of its radius R. Minimum energy to add one bit: hc/r Total energy of a black hole of radius R: c4r/g. # of bits = energy/(energy per bit) = c3r2/hg. Hawking: black holes radiate with a temperature kt = hc/r. Total entropy (number of bits) = energy/kt - = c3r2/hg. What are these bits?

18 The holographic principle: the Bekenstein-Hawking result for the number of bits in a black hole is interesting: 2 - = R2/l cr2/hg Planck For most systems the number of bits is proportional to the volume, R3. This suggests that the fundamental degrees of freedom of a gravitating system live on its surface: the holographic principle ( t Hooft, Susskind 93) If so, this would be fundamentally different from any system that we are familiar with, a radical change in the nature of space.

19 Uses both QM and GR, but the horizon is a region of low curvature, so this calculation should be reliable. horizon singularity To introduce the information problem, we need to talk about Hawking radiation. Virtual particles are created by quantum fluctuations. In the black hole geometry, one can fall into the singularity and the second escape, carrying away energy.

20 time As a result, the black hole eventually emits all of its energy and disappears, leaving only the outgoing Hawking radiation.

21 Hawking: the final state of the outgoing radiation is independent of the initial state, or of anything thrown in: information is lost. Not consistent with Schrodingerlike evolution, God not only plays dice, He sometimes throws the dice where they cannot be seen. time Rather,

22 The difference is the horizon: information would have to travel faster than light. time Note: if we burn a book, information is scrambled but not destroyed: Schrodinger s equation still holds.

23 Going around in circles ( ): Information loss Information carried away by the Hawking radiation Remnants

24 How this was resolved: Many quantum systems have been found to have the surprising property of duality : two seemingly different systems that are actually the same. When one description becomes highly quantum, the second becomes classical and simple. Maldacena (1997) found a duality between a quantum mechanical black hole and a much more ordinary system, a gas of strongly interacting particles (similar to quarks and gluons).

25 Maldacena s duality: = Like Maxwell, an unexpected connection between widely different areas of physics citations. The most complete construction of quantum gravity to date.

26 = Consequences: Quarks + gluons obey ordinary QM: info can t be lost. Provides the bits predicted by Bekenstein and Hawking. Holographic: the bits live on the surface.

27 = Consequences: Quarks + gluons obey ordinary QM: info can t be lost. Provides the bits predicted by Bekenstein and Hawking. Holographic: the bits live on the surface. In 2004, Hawking conceded.

28 So where do we stand? The holographic principle is very different from previous physical laws. How does it work in detail? Especially, how does it work in an expanding spacetime? (Maldacena s duality works in a special box, anti-de Sitter space - AdS). The interior of a black hole is a lot like Big Bang (in reverse), so maybe this is a good place to start? Where exactly did Hawking go wrong: how does the information get out? Hawking s original argument was so stimulating because it presented sharp alternatives, none of which seemed satisfactory

29 Things that were widely believed: Information is not lost. An observer who says outside the black hole sees nothing unusual. An observer who falls through the horizon sees nothing unusual. Black hole complementarity: information doesn t actually travel faster than light. The outside observer sees it come out, the infalling observer sees it inside, and they can t compare notes a new relativity principle ( t Hooft, Susskind).

30 Things that were widely believed: Information is not lost. An observer who says outside the black hole sees nothing unusual. An observer who falls through the horizon sees nothing unusual. Actually these are inconsistent! They imply an impossible quantum state for the Hawking radiation. (Ahmed Almheiri, Don Marolf, JP, Jamie Sully)

31 b Basically, one runs Hawking s original argument backwards: The Hawking pair is produced in an entangled state, > > > > Conservation of information requires that the Hawking photons be entangled with each other (a pure state). a c b QM does not allow this, entanglement is monogamous! a b c a b c ( > > > > > vs. > ( > > > >

32 ( > > > > > vs. > ( > > > > information loss firewall! Sort of like breaking a chemical bond, losing the entanglement across the horizon implies a higher energy state.

33 instead of Once again, a sharp conflict between quantum mechanics and spacetime

34 After a year and >100 papers, there is no consensus. Most attempts to evade the firewall require loosening the rules of quantum mechanics, but there is no clear framework for this: Strong complementarity (no global Hilbert space) Limits on quantum computation (Harlow & Hayden 12) Final state boundary condition at the black hole singularity (Horowitz & Maldacena 03; Preskill & Lloyd 13). EPR = ER (Spacetime from entanglement, Maldacena & Susskind 13). Nonlinear observables (Papadodimas & Raju 12, Verlinde2 12). All of these are preliminary frameworks, not theories.

35 If firewalls exist, how and when do they form? There are ideas, in which the singularity expands, but nothing definite. Are there any observational effects for black holes? Some ideas would lead to this, but the argument is consistent with the exterior being exactly as in the usual picture, except perhaps for very subtle quantum effects. Are there any consequences for cosmology? Too early to say. Are cosmological horizons like black hole horizons? Is there a version of the information problem? Most important, this may give us a new lever on applying holography to cosmology.

36 Conclusion: Thought experiments with black holes have led to some surprising discoveries: black hole bits, the holographic principle, Maldacena s duality. The latest thought experiment presents new challenges, and we can hope that it will lead us to a more complete theory of quantum gravity.