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Quantum Gravity Past, Present and Future

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Quantum Gravity past, present and future carlo rovelli vancouver 2017 loop quantum gravity, Many directions of investigation string theory, Hořava–Lifshitz theory, supergravity, Vastly different numbers of researchers involved asymptotic safety, AdS-CFT-like dualities A few offer rather complete twistor theory, tentative theories of quantum gravity causal set theory, entropic gravity, Most are highly incomplete emergent gravity, non-commutative geometry, Several are related, boundaries are fluid group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, Several are only vaguely connected to the actual problem of quantum gravity shape dynamics, ’t Hooft theory non-quantization of geometry Many offer useful insights … loop quantum causal dynamical gravity triangulations string theory asymptotic Hořava–Lifshitz safety group field AdS-CFT theory dualities twistor theory shape dynamics causal set supergravity theory Penrose nonlinear quantum dynamics non-commutative geometry Violation of QM non-quantized geometry entropic ’t Hooft emergent gravity theory gravity Several are related Herman Verlinde at LOOP17 in Warsaw No major physical assumptions over GR&QM No infinity in the small loop quantum causal dynamical Infinity gravity triangulations in the small Supersymmetry string High dimensions theory Strings Lorentz Violation asymptotic Hořava–Lifshitz safety group field AdS-CFT theory dualities twistor theory Mostly still shape dynamics causal set classical supergravity theory Penrose nonlinear quantum dynamics non-commutative geometry Violation of QM non-quantized geometry entropic ’t Hooft emergent gravity theory gravity Discriminatory questions: Is Lorentz symmetry violated at the Planck scale or not? Are there supersymmetric particles or not? Is Quantum Mechanics violated in the presence of gravity or not? Are there physical degrees of freedom at any arbitrary small scale or not? Is geometry discrete i the small? Lorentz violations Infinite d.o.f. Supersymmetry QM violations Geometry is discrete? at Planck scale at Planck scale Strings No No Yes No No Loops No No No No Yes Hojava Lifshitz Yes Yes No No No Asymptotic safety No Yes No No No Nonlinear quantum No Yes No Yes No dynamics Your favorite … … … … … We do have existing and possibly developing empirical evidence Empirical evidence: 1: Lorentz invariance Violation of Lorentz invariance → Renormalizability Observation has already ruled out theories S. Liberati, Class. Quant. Grav. 30, 133001 (2013) Lorentz violating solutions of QG are under empirical stress Is Lorentz invariance compatible with discreteness ? Yes! Classical discreteness breaks Lorentz invariance. Quantum discreteness does not ! Cfr rotational invariance: If a classical vector component can take only discrete values only, then SO(3) is broken. But if quantum vector can have discrete eigenvalues in a SO(3) invariant theory L L(β) Lorentz invariance and quantum discreteness are compatible => Geometry is quantum geometry Empirical evidence: 2: Supersymmetry Once again, no sign of supersymmetry Solution of QG using supersymmetry are under empirical stress A point about philosophy of science: - Popper’s falsification: theories are either “OK” or “proved wrong”. - Bayesian “confirmation”: we have “degrees of confidence” in theories; these are are lowered, of enhanced, by empirical (dis-)confirmation. Karl Popper Bruno De Finetti Not seeing a giraffe in the forests of Canada during a hike, does not prove that there are no giraffes in the forests of Canada A point about philosophy of science: - Popper’s falsification: theories are either “OK” or “proved wrong”. - Bayesian “confirmation”: we have “degrees of confidence” in theories; these are are lowered, of enhanced, by empirical (dis-)confirmation. Karl Popper Bruno De Finetti Not seeing a giraffe in the forests of Canada during a hike, does not prove that there are no giraffes in the forests of Canada But if for thirty years nobody sees a giraffe… And we have now heard that supersymmetry is “going to be seen soon” for more than thirty years…. Empirical evidence: 3: Lab experiments Analog systems Test the consequences of an assumption. Not the assumption themselves. Planck scale effects NOT predicted by most QG theories in the lab Violations of QM suggested by QG Quantum property Can falsify the hypothesis that the of the metric gravitational field is classical. Is the metric a Can falsify the hypothesis that the quantum entity? gravitational field is classical. S Bose, A Mazumdar, GW Morley, H Ulbricht, M Toroš, M Paternostro, A Geraci, P Barker, MS Kim, G Milburn: A Spin Entanglement Witness for Quantum Gravity, 2017. C Marletto, V Vedral: An entanglement-based test of quantum gravity using two massive particles, 2017. Empirical evidence: 4: The Sky a) Early Universe: “Quantum cosmology” b) Black holes: Disruption of the photon ring Planck Stars Quantum Cosmology A: In the early universe, quantum gravity effects cannot be disregarded These leave traces in the current universe. Few degrees of freedom. Gravity is quantum, spacetime is dynamical Schrödinger equation → Wheeler de Witt equation Absence of a preferred time variable. Quantum Cosmology H: How to understand quantum theory of “the whole”. All degrees of freedom of the Universe. Absence of external observer? The problems raised by this would exist also if relativistic gravity did not exist. Quantum Cosmology A is a totally different problem from Quantum Cosmology H Large activity to describe the physics of the very early universe, and find traces in the CMB Notice: this is all physics of few degrees of freedom! Great effort to find testable consequences of the theories in course b) Black holes Small effects pile up over time - Wide quantum fluctuations of the metric Giddings - Boson condensate of low energy gravitons Dvali - Fluctuations of the causal structure allowing black hole to decay Haggard, Barrau, Vidotto, CR - Wide quantum fluctuations of the metric Theoretical reason: to bring information out of the hole Observable consequence: Event Horizon Telescope Possibly visible distortion of the photon ring Imaging an Event Horizon: Mitigation of Scattering toward Sagittarius A* Fish et al 2014 - Fluctuations of the causal structure allowing black hole to decay /KPMQYUMK 5EJYCT\UEJKNF 3WCPVWOTGIKQP 5EJYCT\UEJKNF /KPMQYUMK Exploding holes /KPMQYUMK 3WCPVWOTGIKQP 5EJYCT\UEJKNF /KPMQYUMK Exploding holes At MG2 and in a paper ’79-’81 Frolov, Vilkovinski ‘79 Sean A. Hayward in ’06 Stephen, t’Hooft, Whithing ‘93 Valeri Frolov In ’05 Ashtekar, Bojowald ’05 [see M. Smerlak’s talk] Grigori A. Vilkovisky (left) Modesto ‘06 In ’93 Abhay Ashtekar Hayward ’06 Cristopher R. Stephens Martin Bojowald 2 Hajicek Kieffer ’01 1 Gerard ’t Hooft region 3 Haggard, Rovelli ’15 Bernard F. Whiting Figure 2: Penrose diagram for the gravitational collapse inside the event horizon (Region 1 and region 2) and outside the event horizon (Region3). Solving the constraints equations (9) we obtain the known results for the classical dust matter gravi- tational collapse [8]. 2GravitationalcollapseinAshtekarvariables In this section we study the gravitational collapse in Ashtekar variables [12]. In particular we will express the Hamiltonian constraint inside and outside the matter and the constraints P1 and P2 in terms of the symmetric reduced Ashtekar connection [13], [14]. 2.1 Ashtekar variables In LQG the fundamental variables are the Ashtekar variables:theyconsistofanSU(2) connection i a Aa and the electric field Ei ,wherea, b, c, =1, 2, 3aretensorialindicesonthespatialsectionand ··· a i, j, k, =1, 2, 3areindicesinthesu(2) algebra. The density weighted triad Ei is related to the ···i a 1 abc j k i j triad ea by the relation Ei = 2 ϵ ϵijk eb ec .Themetricisrelatedtothetriadbyqab = ea eb δij . Equivalently, ab a b ij det(q) q = Ei Ej δ . (10) ! i a The rest of the relation between the variables (Aa,Ei )andtheADMvariables(qab,Kab)isgivenby i i b ij Aa = Γa + γ KabEj δ (11) i where γ is the Immirzi parameter and Γa is the spin connection of the triad, namely the solution of i i j k Cartan’s equation: ∂[aeb] + ϵjk Γ[aeb] =0. The action is 1 3 a a i S = dt d x 2Tr(E A˙ a) N N a N i , (12) κγ Σ − − H − H − G " " # $ where N a is the shift vector, N is the lapse function and N i is the Lagrange multiplier for the Gauss a a i a constraint i.WehaveintroducedalsothenotationE[1] = E ∂a = Ei τ ∂a and A[1] = Aadx = i i a G A τ dx .Thefunctions , a and i are respectively the Hamiltonian, diffeomorphism and Gauss a H H G 4 /KPMQYUMK 3WCPVWOTGIKQP 5EJYCT\UEJKNF /KPMQYUMK A technical result in classical GR: The following metric is an exact vacuum solution, of the Einstein equations outside a finite spacetime region (grey), plus an ingoing and outgoing null shell, I The metric is determined by two constants: ds2 = F (u, v)dudv + r2(u, v)(d✓2 + sin2✓dφ2) − III II v u F (u ,v )=1,r(u ,v )= I − I . Region I I I I I I 2 vI < 0. 3 32m r r r F (u, v)= e 2m 1 e 2m = uv. Region II r − 2m I ⇣ ⌘ 1 uI uI Matching rI (uI ,vI )=r(u, v) u(uI )= 1+ e 4m . vo 4m 3 ⇣ ⌘ 32m rq Region III F (uq,vq)= e 2m ,rq = vq uq. rq − Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling Hal Haggard, CR I I ➜ Choose a “Boundary” surface around the quantum region. /KPMQYUMK 3WCPVWOTGIKQP 5EJYCT\UEJKNF /KPMQYUMK Spin network Spinfoam Primordial black holes! A real-time FRB 5 Figure 2. The full-Stokes parameters of FRB 140514 recorded in the centre beam of the multibeam receiver with BPSR. Total intensity, and Stokes Q, U,andV are represented in black, red, green, and blue, respectively. FRB 140514 has 21 7% (3-σ)circularpolarisation ± averaged over the pulse, and a 1-σ upper limit on linear polarisation of L<10%. On the leading edge of the pulse the circular polarisation is 42 9% (5-σ)ofthetotalintensity.Thedatahavebeensmoothedfromaninitialsamplingof64µsusingaGaussianfilteroffull-width ± half-maximum 90 µs.
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