Unitarity and nonlocality in black hole physics Steve Giddings, UCSB Based on: hep/th-0512200 w/ Marolf & Hartle hep-th/0604072 hep-th/0605196 hep-th/0606nnn
A common meme in recent physics: Violation of locality But: When, and what is the mechanism? Can this resolve the black hole information paradox?
If locality does break down, there should be a correspondence: Nonlocal physics Local QFT + GR... but what parametrizes this limit?
An old string theory proposal (Veneziano, Gross): x> 1 p + l2 st p String uncertainty principle
More recent proposal (generic gravity): (c.f. SG & Lippert hep-th/0103231; hep-th/0604072) Consider two quanta with (x,p), (y,q). Locality bound: x y D 3 G p + q...proposed boundary of regime of local physics
Two ways to investigate locality: Describe local observation Scattering
Local observation: Obstacle in gravity: diffeo invariance Evaded by relational observables (SG, Marolf, Hartle hep-th/0512200.)... but with fundamental limitations
Toy example: the Z-model Begin with a field theory, and supplement it with a set of four free fields : Z i = 0 in a state such that, Z i Ψ Z Z i Ψ Z = λδ i µx µ
For a given local operator O(x) of the original O ξ = Then: theory, define: d 4 xo(x)e 1 σ 2 (Zi ξ i ) 2 Zi x µ...diff invt Ψ Z O ξ1 O ξn Ψ Z O(x µ 1 ) O(xµ N ) where x µ A = 1 λ δµ i ξi A
Gravitational backreaction: Quantum strong φ gravity x,p φ y,q region x y D 3 < M 2 D P p + q : Local QFT fails?
Scattering: (Discuss in string thy, but bear in mind more general context. c.f. hep-th/0604072.) Classic work of Amati, Ciafaloni, Veneziano:
Pert thy fails x y D 3 < M 2 D P p + q
So local observation, scattering, provide evidence for a nonlocality principle, stating that local physics fails when grav pert theory breaks down, e.g. when violate x y D 3 G p + q Also suggested by the black hole information paradox and BH entropy ( holographic principle ), with the additional statement: the nonlocal physics is unitary
But: does this give us a consistent picture without an information paradox? (Where is the loophole in Hawking s argument for information loss -- nonlocality??) One suggestion ( t Hooft; Susskind; Verlindes;...) : transplanckian blueshifts of incipient Hawking modes? Study using smooth slices:
- + T µν : large Infalling matter
Schwarzschild t-translating... Schwarzschild t-translating... No large interaction... Big interaction?
CM frame Schwarzschild t-translating...
Argument for info loss: Draw smooth slices Argue semiclassical approx valid ρ = T r ( Ψ Ψ )
Validity of semiclassical approximation? g µν = g 0µν + h µν S =S[g 0, φ]+ d 4 x g 0 (hlh + G N h 2 2 h + G N h µν Tµν φ + ) A measure of strength of fluctuations/coupling: gd A = G 4 N x gd 4 yt µν (x) µν,λσ (x, y)t λσ (y) Gets large when BH forms in HE collision Small in low-energy collisions (More precise diagnostics: hep-th/0606nnn)
A = G N gd 4 x gd 4 yt µν (x) µν,λσ (x, y)t λσ (y) Estimate: (x, y) 1 (x y) 2 TµνT 1 2µν s e t 2 t 1 4M Alternately: h 1 (x) d 4 y (x, y)t 1 (y) Explicitly compute for small infalling perturbation 1 (e.g. Vaidya metric) Large effect for large time diff; see explicitly e.g. in gauge appropriate for describing nice slices
Thus: straightforward attempt to justify a controlled approximation for Hawking s argument fails; Specifically: breakdown of gravitational perturbation theory; But the proposed nonlocality principle states that in precisely these circumstances we expect nonlocal but unitary physics! how the information gets out?
Conclusions: The non-perturbative physics of gravity is suggested to be nonlocal but unitary Flat space parametrization: locality bound Support for this comes from relational observables, HE scattering, BH entropy, and the paradox we would otherwise face Straightforward perturbative treatment of fluctuations on nice slices breaks down, suggesting a role for this nonlocal physics and consistent resolution of the paradox