Loop Quantum Gravity, String Theory
Current Quantum Gravity Theories, Experimental Evidence, Philosophical Implications
carlo rovelli IHES 2017 1. We have quantum gravity theories
2. We have have empirical evidence
3. There is some understanding on some issues of major philosophical relevance
i: nature of physical space ii: nature of physical time iii: relation between physical and experiential time iv: connection between relational aspects of GR and QM 1. We do have quantum gravity theories Many directions of investigation loop quantum gravity, Many directions of investigation string theory, asymptotic safety, Hořava–Lifshitz theory, supergravity, AdS-CFT-like dualities twistor theory, causal set theory, entropic gravity, emergent gravity, non-commutative geometry, group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, shape dynamics, ’t Hooft theory non-quantization of geometry … loop quantum gravity, Many directions of investigation string theory, asymptotic safety, Vastly different numbers of researchers involved Hořava–Lifshitz theory, supergravity, AdS-CFT-like dualities twistor theory, causal set theory, entropic gravity, emergent gravity, non-commutative geometry, group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, shape dynamics, ’t Hooft theory non-quantization of geometry … loop quantum gravity, Many directions of investigation string theory, asymptotic safety, Vastly different numbers of researchers involved Hořava–Lifshitz theory, supergravity, Most are highly incomplete AdS-CFT-like dualities twistor theory, causal set theory, entropic gravity, emergent gravity, non-commutative geometry, group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, shape dynamics, ’t Hooft theory non-quantization of geometry … loop quantum gravity, Many directions of investigation string theory, asymptotic safety, Vastly different numbers of researchers involved Hořava–Lifshitz theory, supergravity, Most are highly incomplete AdS-CFT-like dualities twistor theory, Several are only vaguely connected causal set theory, to the actual problem of quantum gravity entropic gravity, emergent gravity, non-commutative geometry, group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, shape dynamics, ’t Hooft theory non-quantization of geometry … loop quantum gravity, Many directions of investigation string theory, asymptotic safety, Vastly different numbers of researchers involved Hořava–Lifshitz theory, supergravity, Most are highly incomplete AdS-CFT-like dualities twistor theory, Several are only vaguely connected causal set theory, to the actual problem of quantum gravity entropic gravity, emergent gravity, Several are related, boundaries are fluid non-commutative geometry, group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, shape dynamics, ’t Hooft theory non-quantization of geometry … loop quantum gravity, Many directions of investigation string theory, asymptotic safety, Vastly different numbers of researchers involved Hořava–Lifshitz theory, supergravity, Most are highly incomplete AdS-CFT-like dualities twistor theory, Several are only vaguely connected causal set theory, to the actual problem of quantum gravity entropic gravity, emergent gravity, Several are related, boundaries are fluid non-commutative geometry, group field theory, Penrose nonlinear quantum dynamics Many offer useful insights causal dynamical triangulations, shape dynamics, ’t Hooft theory non-quantization of geometry … loop quantum gravity, Many directions of investigation string theory, asymptotic safety, Vastly different numbers of researchers involved Hořava–Lifshitz theory, supergravity, Most are highly incomplete AdS-CFT-like dualities twistor theory, Several are only vaguely connected causal set theory, to the actual problem of quantum gravity entropic gravity, emergent gravity, Several are related, boundaries are fluid non-commutative geometry, group field theory, Penrose nonlinear quantum dynamics Many offer useful insights causal dynamical triangulations, shape dynamics, A few offer rather complete ’t Hooft theory tentative theories of quantum gravity non-quantization of geometry … 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 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 non-quantized geometry entropic ’t Hooft emergent gravity theory gravity No infinity in the small 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 non-quantized geometry entropic ’t Hooft emergent gravity theory gravity No infinity in the small loop quantum causal dynamical Infinity gravity triangulations in the small
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 non-quantized geometry entropic ’t Hooft emergent gravity theory gravity No infinity in the small loop quantum causal dynamical Infinity gravity triangulations in the small
string theory
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 non-quantized geometry entropic ’t Hooft emergent gravity theory gravity No major physical assumptions over GR&QM
No infinity in the small loop quantum causal dynamical Infinity gravity triangulations in the small
string theory
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 non-quantized geometry entropic ’t Hooft emergent gravity theory gravity 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
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 non-quantized geometry entropic ’t Hooft emergent gravity theory gravity 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 non-quantized geometry entropic ’t Hooft emergent gravity theory gravity 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 … … … … … 2. We do have empirical evidence Empirical evidence: 1: Lorentz invariance 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) L L(β)
Lorentz invariance and quantum discreteness are compatible L L(β)
Lorentz invariance and quantum discreteness are compatible
=> Geometry is quantum geometry Empirical evidence: 2: Supersymmetry Empirical evidence: 2: Supersymmetry Empirical evidence: 2: Supersymmetry
Once again, no sign of supersymmetry 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”.
Karl Popper 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 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 French Alps during a hike, does not prove that there are no giraffes in French Alps 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 French Alps during a hike, does not prove that there are no giraffes in French Alps 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 French Alps during a hike, does not prove that there are no giraffes in French Alps
But if for thirty years nobody sees a giraffe… 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 French Alps during a hike, does not prove that there are no giraffes in French Alps
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…. 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 French Alps during a hike, does not prove that there are no giraffes in French Alps
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….
Solution of QG using supersymmetry are under empirical stress Empirical evidence: 3: Lab experiments (future) Empirical evidence: 3: Lab experiments
Analog systems
Planck scale effects in the lab
Violations of QM suggested by QG
Quantum property of the metric Empirical evidence: 3: Lab experiments
Analog systems
Planck scale effects in the lab
Violations of QM suggested by QG
Quantum property of the metric Empirical evidence: 3: Lab experiments
Analog systems Test the consequences of an assumption. Not the assumption themselves.
Planck scale effects in the lab
Violations of QM suggested by QG
Quantum property of the metric Empirical evidence: 3: Lab experiments
Analog systems Test the consequences of an assumption. Not the assumption themselves.
Planck scale effects in the lab NOT predicted by most QG theories
Violations of QM suggested by QG
Quantum property of the metric Empirical evidence: 3: Lab experiments
Analog systems Test the consequences of an assumption. Not the assumption themselves.
Planck scale effects in the lab NOT predicted by most QG theories
Violations of QM suggested by QG
Quantum property of the metric Empirical evidence: 3: Lab experiments
Analog systems Test the consequences of an assumption. Not the assumption themselves.
Planck scale effects in the lab NOT predicted by most QG theories
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 quantum entity?
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. 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 (future) Empirical evidence: 4: The Sky
a) Early Universe: “Quantum cosmology”
b) Black holes: Disruption of the photon ring
Planck Stars 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! 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 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 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 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 Exploding holes At MG2 and in a paper ’79-’81 Frolov, Vilkovinski ‘79
Valeri Frolov
Grigori A. Vilkovisky (left) Exploding holes At MG2 and in a paper ’79-’81 Frolov, Vilkovinski ‘79
Stephen, t’Hooft, Whithing ‘93 Valeri Frolov
Grigori A. Vilkovisky (left)
In ’93
Cristopher R. Stephens
Gerard ’t Hooft
Bernard F. Whiting Exploding holes At MG2 and in a paper ’79-’81 Frolov, Vilkovinski ‘79
Stephen, t’Hooft, Whithing ‘93 Valeri Frolov
In ’05 Ashtekar, Bojowald ’05
Grigori A. Vilkovisky (left)
In ’93 Abhay Ashtekar
Cristopher R. Stephens
Martin Bojowald
Gerard ’t Hooft
Bernard F. Whiting Exploding holes At MG2 and in a paper ’79-’81 Frolov, Vilkovinski ‘79
Stephen, t’Hooft, Whithing ‘93 Valeri Frolov
In ’05 Ashtekar, Bojowald ’05
Grigori A. Vilkovisky (left) Modesto ‘06 In ’93 Abhay Ashtekar
Cristopher R. Stephens
Martin Bojowald
2
1 Gerard ’t Hooft
region 3
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 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
1 Gerard ’t Hooft
region 3
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 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
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 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 Covariant loop quantum gravity. Full definition.
n0 l 2 L N hl = L [SU(2) /SU(2) ] (hl) =lim n State space H 3 H H !1
Kinematics Operators: where Boundary spin network (nodes, links)
Transition amplitudes W (hl)=N dhvf (hf ) A(hvf ) hf = hvf C C SU(2) v v Z Yf Y Y Bulk Dynamics
j (j+1) j 1 Vertex amplitude A(h )= dg0 (2j + 1) D (h )D (g g ) vf e mn vf jmjn e e0 SL(2,C) j Z Yf X
W =limW C e C!1 v f spinfoam (vertices, edges, faces) 8⇡ ~G =1 C Satisfies all “requirements” listed by Steve Carlip in the last talk
• Quantum theory (Hilbert space, operators, transition amplitudes) • Classical limit: GR (Barrett’s theorems) • UV qft divergences (Han and Fairbairn’s theorems) • Minimum length (Spectral properties of operators) • Black hole thermodynamics A process and its amplitude
hl Boundary state = Boundary state in ⌦ out Amplitude A = W ( )
Boundary Quantum system = “Spacetime region” Spacetime region
➜ Hamilton function: S(q,t,q’,t’) A process and its amplitude
hl Boundary state = Boundary state in ⌦ out Amplitude A = W ( )
Boundary Quantum system = “Spacetime region” Spacetime region
➜ Hamilton function: S(q,t,q’,t’)
In GR, distance and time measurements are field measurements like any other one: they are part of the boundary data of the problem Boundary values of the gravitational field = geometry of box surface = distance and time separation of measurements A process and its amplitude
hl Boundary state = Boundary state in ⌦ out Amplitude A = W ( )
Boundary Quantum system = “Spacetime region” Spacetime region
➜ Hamilton function: S(q,t,q’,t’)
In GR, distance and time measurements are field measurements like any other one: they are part of the boundary data of the problem Boundary values of the gravitational field = geometry of box surface = distance and time separation of measurements
Particle detectors = field measurements
Distance and time measurements Spacetime region = gravitational field measurements /KPMQYUMK
3WCPVWOTGIKQP 5EJYCT\UEJKNF
/KPMQYUMK Full expression for the transition amplitude: 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- )circularpolarisation ± averaged over the pulse, and a 1- upper limit on linear polarisation of L<10%. On the leading edge of the pulse the circular polarisation is 42 9% (5- )ofthetotalintensity.Thedatahavebeensmoothedfromaninitialsamplingof64µsusingaGaussianfilteroffull-width ± half-maximum 90 µs.
source given the temporal proximity of the GMRT observa- 4.5 Gamma-Ray Burst Optical/Near-Infrared tion and the FRB detection. The other two sources, GMRT2 Detector and GMRT3, correlated well with positions for known ra- After 13 hours, a trigger was sent to the Gamma-Ray Burst dio sources in the NVSS catalog with consistent flux densi- Optical/Near-Infrared Detector (GROND) operating on the ties. Subsequent observations were taken through the GMRT 2.2-m MPI/ESO telescope on La Silla in Chile (Greiner et al. ToO queue on 20 May, 3 June, and 8 June in the 325 MHz, 2008). GROND is able to observe simultaneously in J, H, 1390 MHz, and 610 MHz bands, respectively. The second and K near-infrared (NIR) bands with a 100 100 field of epoch was largely unusable due to technical di culties. The ⇥ view (FOV) and the optical g0, r0, i0,andz0 bands with a search for variablility focused on monitoring each source for 60 60 FOV. A 2 2 tiling observation was done, providing flux variations across observing epochs. All sources from the ⇥ ⇥ 61% (JHK)and22%(g0r0i0z0) coverage of the inner part first epoch appeared in the third and fourth epochs with no of the FRB error circle. The first epoch began 16 hours af- measureable change in flux densities. ter FRB 140514 with 460 second exposures, and a second epoch was taken 2.5 days after the FRB with an identical 4.4 Swift X-Ray Telescope observing setup and 690 s (g0r0i0z0)and720s(JHK)ex- posures, respectively. Limiting magnitudes for J, H,andK The first observation of the FRB 140514 field was taken us- bands were 21.1, 20.4, and 18.4 in the first epoch and 21.1, ing Swift XRT (Gehrels et al. 2004) only 8.5 hours after the 20.5, and 18.6 in the second epoch, respectively (all in the FRB was discovered at Parkes. This was the fastest Swift AB system). Of all the objects in the field, analysis iden- follow-up ever undertaken for an FRB. 4 ks of XRT data tified three variable objects, all very close to the limiting were taken in the first epoch, and a further 2 ks of data magnitude and varying on scales of 0.2 - 0.8 mag in the NIR were taken in a second epoch later that day, 23 hours af- bands identified with di↵erence imaging. Of the three ob- ter FRB 140514, to search for short term variability. A final jects one is a galaxy, another is likely to be an AGN, and epoch, 18 days later, was taken to search for long term vari- the last is a main sequence star. Both XRT1 and GMRT1 ability. Two X-ray sources were identified in the first epoch sources were also detected in the GROND infrared imaging of data within the 150 diameter of the Parkes beam. Both but were not observed to vary in the infrared bands on the sources were consistent with sources in the USNO catalog timescales probed. (Monet et al. 2003). The first source (XRT1) is located at RA = 22:34:41.49, Dec = -12:21:39.8 with RUSNO =17.5 and the second (XRT2) is located at RA = 22:34:02.33 Dec =-12:08:48.2withR =19.7.BothXRT1andXRT2 USNO 4.6 Swope Telescope appeared in all subsequent epochs with no observable vari- ability on the level of 10% and 20% for XRT1 and XRT2, An optical image of the FRB field was taken 16h51m after respectively, both calculated from photon counts from the the burst event with the 1-m Swope Telescope at Las Cam- XRT. Both sources were later found to be active galactic panas. The field was re-imaged with the Swope Telescope on nuclei (AGN). 17 May, 2 days after the FRB. No variable optical sources
c 0000 RAS, MNRAS 000,000–000 Signature: distance/energy relation
1 1/2 2Gm H0 1 ⌦⇤ 3/2 obs 2 (1 + z) 1/2 sinh (z + 1) ⇠ c v ⌦M u6 k⌦⇤ " # u ✓ ◆ t
l
A real-time FRB 5
l
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- )circularpolarisation ± averaged over the pulse, and a 1- upper limit on linear polarisation of L<10%. On the leading edge of the pulse the circular polarisation is 42 9% (5- )ofthetotalintensity.Thedatahavebeensmoothedfromaninitialsamplingof64µsusingaGaussianfilteroffull-width ± half-maximum 90 µs.
source given the temporal proximity of the GMRT observa- 4.5 Gamma-Ray Burst Optical/Near-Infrared tion and the FRB detection. The other two sources, GMRT2 Detector and GMRT3, correlated well with positions for known ra- After 13 hours, a trigger was sent to the Gamma-Ray Burst dio sources in the NVSS catalog with consistent flux densi- Optical/Near-Infrared Detector (GROND) operating on the ties. Subsequent observations were taken through the GMRT 2.2-m MPI/ESO telescope on La Silla in Chile (Greiner et al. ToO queue on 20 May, 3 June, and 8 June in the 325 MHz, 2008). GROND is able to observe simultaneously in J, H, 1390 MHz, and 610 MHz bands, respectively. The second and K near-infrared (NIR) bands with a 100 100 field of epoch was largely unusable due to technical di culties. The ⇥ view (FOV) and the optical g0, r0, i0,andz0 bands with a search for variablility focused on monitoring each source for 60 60 FOV. A 2 2 tiling observation was done, providing flux variations across observing epochs. All sources from the ⇥ ⇥ 61% (JHK)and22%(g0r0i0z0) coverage of the inner part first epoch appeared in the third and fourth epochs with no of the FRB error circle. The first epoch began 16 hours af- measureable change in flux densities. ter FRB 140514 with 460 second exposures, and a second epoch was taken 2.5 days after the FRB with an identical 4.4 Swift X-Ray Telescope observing setup and 690 s (g0r0i0z0)and720s(JHK)ex- posures, respectively. Limiting magnitudes for J, H,andK The first observation of the FRB 140514 field was taken us- bands were 21.1, 20.4, and 18.4 in the first epoch and 21.1, ing Swift XRT (Gehrels et al. 2004) only 8.5 hours after the 20.5, and 18.6 in the second epoch, respectively (all in the FRB was discovered at Parkes. This was the fastest Swift AB system). Of all the objects in the field, analysis iden- follow-up ever undertaken for an FRB. 4 ks of XRT data tified three variable objects, all very close to the limiting were taken in the first epoch, and a further 2 ks of data magnitude and varying on scales of 0.2 - 0.8 mag in the NIR were taken in a second epoch later that day, 23 hours af- bands identified with di↵erence imaging. Of the three ob- ter FRB 140514, to search for short term variability. A final jects one is a galaxy, another is likely to be an AGN, and epoch, 18 days later, was taken to search for long term vari- the last is a main sequence star. Both XRT1 and GMRT1 ability. Two X-ray sources were identified in the first epoch sources were also detected in the GROND infrared imaging of data within the 150 diameter of the Parkes beam. Both but were not observed to vary in the infrared bands on the sources were consistent with sources in the USNO catalog timescales probed. (Monet et al. 2003). The first source (XRT1) is located at RA = 22:34:41.49, Dec = -12:21:39.8 with RUSNO =17.5 and the second (XRT2) is located at RA = 22:34:02.33 Dec =-12:08:48.2withR =19.7.BothXRT1andXRT2 USNO 4.6 Swope Telescope appeared in all subsequent epochs with no observable vari- ability on the level of 10% and 20% for XRT1 and XRT2, An optical image of the FRB field was taken 16h51m after respectively, both calculated from photon counts from the the burst event with the 1-m Swope Telescope at Las Cam- XRT. Both sources were later found to be active galactic panas. The field was re-imaged with the Swope Telescope on nuclei (AGN). 17 May, 2 days after the FRB. No variable optical sources
c 0000 RAS, MNRAS 000,000–000
z 2 4 6 8 10 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- )circularpolarisation ± averaged over the pulse, and a 1- upper limit on linear polarisation of L<10%. On the leading edge of the pulse the circular polarisation is 42 9% (5- )ofthetotalintensity.Thedatahavebeensmoothedfromaninitialsamplingof64µsusingaGaussianfilteroffull-width ± half-maximum 90 µs.
source given the temporal proximity of the GMRT observa- 4.5 Gamma-Ray Burst Optical/Near-Infrared tion and the FRB detection. The other two sources, GMRT2 Detector and GMRT3, correlated well with positions for known ra- After 13 hours, a trigger was sent to the Gamma-Ray Burst dio sources in the NVSS catalog with consistent flux densi- Optical/Near-Infrared Detector (GROND) operating on the ties. Subsequent observations were taken through the GMRT 2.2-m MPI/ESO telescope on La Silla in Chile (Greiner et al. ToO queue on 20 May, 3 June, and 8 June in the 325 MHz, 2008). GROND is able to observe simultaneously in J, H, 1390 MHz, and 610 MHz bands, respectively. The second and K near-infrared (NIR) bands with a 100 100 field of epoch was largely unusable due to technical di culties. The ⇥ view (FOV) and the optical g0, r0, i0,andz0 bands with a search for variablility focused on monitoring each source for 60 60 FOV. A 2 2 tiling observation was done, providing flux variations across observing epochs. All sources from the ⇥ ⇥ 61% (JHK)and22%(g0r0i0z0) coverage of the inner part first epoch appeared in the third and fourth epochs with no of the FRB error circle. The first epoch began 16 hours af- z measureable change in flux densities. ter FRB 140514 with 460 second exposures, and a second epoch was taken 2.5 days after the FRB with an identical 4.4 Swift X-Ray Telescope observing setup and 690 s (g0r0i0z0)and720s(JHK)ex- posures, respectively. Limiting magnitudes for J, H,andK 2 4 6 8 10 The first observation of the FRB 140514 field was taken us- bands were 21.1, 20.4, and 18.4 in the first epoch and 21.1, ing Swift XRT (Gehrels et al. 2004) only 8.5 hours after the 20.5, and 18.6 in the second epoch, respectively (all in the FRB was discovered at Parkes. This was the fastest Swift AB system). Of all the objects in the field, analysis iden- follow-up ever undertaken for an FRB. 4 ks of XRT data tified three variable objects, all very close to the limiting were taken in the first epoch, and a further 2 ks of data magnitude and varying on scales of 0.2 - 0.8 mag in the NIR were taken in a second epoch later that day, 23 hours af- bands identified with di↵erence imaging. Of the three ob- ter FRB 140514, to search for short term variability. A final jects one is a galaxy, another is likely to be an AGN, and epoch, 18 days later, was taken to search for long term vari- the last is a main sequence star. Both XRT1 and GMRT1 ability. Two X-ray sources were identified in the first epoch sources were also detected in the GROND infrared imaging of data within the 150 diameter of the Parkes beam. Both but were not observed to vary in the infrared bands on the sources were consistent with sources in the USNO catalog timescales probed. (Monet et al. 2003). The first source (XRT1) is located at RA = 22:34:41.49, Dec = -12:21:39.8 with RUSNO =17.5 and the second (XRT2) is located at RA = 22:34:02.33 Dec =-12:08:48.2withR =19.7.BothXRT1andXRT2 USNO 4.6 Swope Telescope appeared in all subsequent epochs with no observable vari- ability on the level of 10% and 20% for XRT1 and XRT2, An optical image of the FRB field was taken 16h51m after respectively, both calculated from photon counts from the the burst event with the 1-m Swope Telescope at Las Cam- XRT. Both sources were later found to be active galactic panas. The field was re-imaged with the Swope Telescope on nuclei (AGN). 17 May, 2 days after the FRB. No variable optical sources
c 0000 RAS, MNRAS 000,000–000
Fast Radio Bursts and White Hole Signals Aurélien Barrau, Carlo Rovelli, Francesca Vidotto. Publications of the Astronomical Society of Australia (PASA) doi: 10.1017/pas.2017.xxx. 24
the classical evolution becomes important as quantum e ects manifest. This time can be much shorter than the Publications of the Astronomical Society of Australia (PASA) Hawking evaporation time M 3 , as short as M 2 .this doi:Fundamental 10.1017/pas.2017.xxx. Physics with the SKA:BH DarkBH Matter and is the minimal time after which quantum fluctuations of the metric can appear in the region outside the BH Astroparticles horizon. In fact, the presence of a small curvature pro- 2 portional to MBH≠ near the horizon allows us to define the ‘quantum break-time’ as the inverse of this quan- 2 Fundamental Physics withtity, that istheMBH (Haggard SKA: & Rovelli, Dark 2014, 2016). Matter As and soon as these quantum fluctuations of the geometry take Astroparticles place, the dynamics of the horizon can undergo dramatic behaviours, to the point of the very disappearance of K. Kelley1, S. Riemer-Sørensen2, E. Athanassoulathe horizon,3,C.Bœhm possibly by4,5 an, G. explosion. Bertone6, A. Bosma7,M. 8 9,10,11 6,12 Di erent approaches13,14,15 to quantum gravity converge16 in Brüggen , C. Burigana , F. Calore ,pointing S. Camera out the possibility, J.A.R. of instabilities Cembranos of quantum-,R.M.T. 17 18,19 2 13,14,15 6 Connors , Á. de la Cruz-Dombriz ,P.K.SDunsbygravitational, origin N. Fornengo that can manifest, in D. an Gaggero explo- ,M. Méndez-Isla18,19, Y. Ma21,22,23, H. Padmanabhansive24 event, A. in Pourtsidou a timescale25 shorter,P.J.Quinn than the1, evapora-M. Regis13,14, Figure 20. Radio sources above the SKA1-MID point source 26 27 28 29,30,31,32 10,33,9 34,35 sensitivity,M. Sahlén for 1000h, of M. data Sakellariadou taking, if PBHs are ,1% L.of Shao the DM. ,J.Silktion time [(Gregory, T.& Trombetti Laflamme, 1993;, F.Casadio Vazza & ,F. K. Kelley1, S. Riemer-Sørensen≥2, E. Athanassoula3,C.Bœhm4,5, G. Bertone6, A. Bosma7,M. Vidotto36, F. Villaescusa-Navarro37, C. WenigerHarms,6 and 2001, L. Wolz 2000;38 Kol & Sorkin, 2004; Emparan et al., 8 9,10,11 6,12 2003)]. In particular,13,14,15 Loop Quantum Gravity has16 re- 1BrüggenInternational, C. Centre Burigana for Radio Astronomy, F. Calore Research, (ICRAR), S. Camera University of, Western J.A.R. Australia, Cembranos Ken and,R.M.T. Julie Michael Building, 7 17 18,19 2 13,14,15 6 Fairway,Connors Crawley,, Á. Westernde la Cruz-Dombriz Australia 6009 ,P.K.SDunsbycently provided, a N. framework Fornengo to compute, explicitly D. Gaggero this ,M. detectors currently in upgrade of development phase), 2Méndez-IslaInstitute of Theoretical18,19, Y. Ma Astrophysics,21,22,23, H. University Padmanabhan of Oslo,time24 P.O. (Christodoulou, A. Box Pourtsidou 1029 Blindern, et al.,25 2016).,P.J.Quinn N-0315 Loop Oslo, Quantum1 Norway, M. Grav- Regis13,14, an3 exciting set of complementary observations will help ity removes the classical curvature singularities (Rovelli M.Aix Sahlén Marseille26, Univ,M. Sakellariadou CNRS, LAM,27 Laboratoire, L. Shao d’Astrophysique28,J.Silk29,30, de31, Marseille,32, T. Trombetti Marseille,10 France,33,9, F.26 Vazza34,35,F. to4 characterizeInstitute for the Particle presence Physics of compact Phenomenology, objects both Durham in & University,Vidotto, 2013; South Ashtekar Road, & Durham, Bojowald, DH1 2006; 3LE, Corichi United & Kingdom 36 37 6 38 l ourVidotto5 Galaxy and, F. in Villaescusa-Navarro the early Universe, and eventually, C. WenigerSingh,and 2016), L. Wolz such as the one at the BH center, becausevalue of the lifetime. Using Equation 19 we can 1 LAPTH, U. de Savoie, CNRS, BP 110, 74941 Annecy-Le-Vieux, France indeed compute the mass of BHs whose lifetime shed6 InternationalGRAPPA, light on the Institute nature Centre of of for the Physics, Radio DM in Astronomy University the universe. Researchof Amsterdam, (ICRAR),of quantum Science University spacetime Park 904, of discreteness. Western1098 XH Australia, Amsterdam, The consequences Ken Netherlandsis and the Hubble Julie time, Michael yielding an Building, explosion today. 7 7Fairway, Crawley, Western Australia 6009 of this discreteness on the dynamics can be modeledFor a lifetime in the lower end of the viable win- 2 Aix Marseille Univ, CNRS, LAM, Laboratoire d’Astrophysique de Marseille, Marseille, France dow, the Schwarzschild radius is of the order of 3.9.28 InstitutePBHs and of Theoretical Quantum Gravity Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo, NorwayR 0.2mm and the observational depth allows University of Hamburg, Gojenbergsweg 112, 21029 Hamburg,at the e Germanyective level by an e ective potential thatBH pre-≥ 3 us to detect events in all the visible Universe. To9 dateAix the Marseille search for Univ, PBHs CNRS, and for LAM, constraints Laboratoire on PBHs d’Astrophysiquevents the gravitational de Marseille, collapse Marseille, from France forming the sin- 4 INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, I-40129 Bologna, Italy has10Institute mostlyDipartimento considered for Particle di Fisica an Physicsalmost e Scienze monochromatic Phenomenology, della Terra, mass UniversitàDurhamgularity University, di Ferrara, and triggers South Via Giuseppe Road, a bounce. Durham, Saragat The DH1bounce 1, I-44122 3LE, connectsFor United the Ferrara, highest Kingdom values Italy of Ÿ, the signal is emitted with 5 energy in the GeV, but a study of the photon emission 11LAPTH, U. de Savoie, CNRS, BP 110, 74941 Annecy-Le-Vieux, France spectrum,Istituto and Nazionale the presence di Fisica of Hawking Nucleare, evaporation Sezione for di Bologna,Viaa collapsing Irnerio solution 46, I-40126 of the Einstein Bologna, equation, Italy with that the code is PHYTIA indicates that the photons with 6 z 12GRAPPA, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam,higher Netherlands density, therefore more likely to be detected, 2 4 6 8 10 PBHsLAPTh, of small CNRS, mass. Monochromatic 9 Chemin de Bellevue, mass spectrum BP-110, has Annecy-le-Vieux,the classical black 74941, hole, Annecy to an explosive Cedex, France expandingare those one, in the MeV (?). Some Short Gamma Ray 7 Figure 21. The expected wavelength (unspecified units) of the 13Aix Marseille Univ, CNRS, LAM, Laboratoire d’Astrophysique de Marseille, Marseille, France Bursts (Nakar, 2007), whose source is still unclear, are been8 Dipartimento challenged by di di Fisica,erent authors Università as unrealistic degli Studi (for di Torino,a white Via hole P. Giuria (Haggard 1, 10125 & Rovelli, Torino, 2014), Italy through an signal from black hole explosions as a function of the redshift 14University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany possible candidates in this range. z.Thecurveflattensatlargedistance:theshorterwavelength exampleINFN, Carr Istituto et al. (2017a)). Nazionale An di extended Fisica Nucleare, mass function Sezioneintermediate di Torino, Via quantum P. Giuria region. 1, 10125 This process Torino, is Italy aFor typical the lowest values of Ÿ, the peak of the signal is from smaller black holes exploding earlier get compensated by the 9 redshift. 15INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, I-40129 Bologna, Italy in the millimetres. The corresponding frequencies are is10 compatibleINAF, Istituto with di Nazionaleerent PBHs di formationAstrofisica, mechanics, Osservatorioquantum Astrofisico tunnelling di Torino, event, Strada and Osservatorio the characteristic 20, 10025 time Pino Torinese, Italy 16 Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Giuseppe Saragat 1, I-44122beyond Ferrara, the sensitivity Italy of SKA-mid. On the other hand, Departamento de Fà sica Teà rica I, Universidad Complutense de Madrid, E20840 Spain in a decay we expect a probability distribution of the from11 critical collapse to cosmic strings. Hawking evapo- at which it takes place, the hole lifetime, can be as a DM and Astroparticles 27 17 API,Istituto University Nazionale of di Amsterdam, Fisica Nucleare, Science Sezione Park 904, di Bologna,Via 1098 XH Amsterdam, Irnerio 46, I-40126Netherlands Bologna, Italy event to happen, and therefore there could be some event received signal, and possibly the source being hosted ration12 is a phenomenon that becomes relevant on a time decaying time, similar to the lifetime of conventionalhappening within SKA-mid frequency range. Further- in a known astronomical object, for instance a galaxy. 18 LAPTh, CNRS, 9 Chemin de Bellevue, BP-110, Annecy-le-Vieux, 74941, Annecy Cedex, France A further technique is available, and it is peculiar of scale13 Cosmology that depends and onGravity the mass Group, of the BH. University Its time of scale Cape Town,nuclear 7701 radioactivity. Rondebosch, The Cape resulting Town, picture South is conserva-Africamore, the details of the decay mechanism are not fully neutrino signature in many cosmological observables, 19 Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy established, leaving open the possibility of the presence decaying PBHs. BHs exploding far away are less massive, 3Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, Cape Town, South Africa withk=0.05 a lower flux of energy (Kavic, 2017), the flux of and in particular, a suppression of power on small scales is 14MBH in Planck units. This implies that within the tive in comparison to other models of non-singularof some BHs. factors that could shift the wavelength possibly directin the matter power spectrum. decayed Understanding and mea- 20 INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italyby 1-2 orders of magnitude. This makes it worthwhile to energy of the measured burst lessens with distance. 15 South African Astronomical Observatory, ObservatoryThe 7925, collapse Cape still Town, produces South a Africa horizon, but it is now a suring this e ect is also important for dark energy and age21 ofINAF, the universe Istituto only Nazionale PBHs with di Astrofisica, mass smaller Osservatorio than Astrofisico di Torino, Strada Osservatorio 20,explore 10025 for transients Pino at Torinese, the highest frequencies Italy acces- The peculiar wavelength-redshift relation can be 12 School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban, 4000, South Africa general relativity tests, as models of modified gravity 1016 kg could have evaporated, and possibly produced dynamical horizon with a finite lifetime, rathersible then to SKA-mid. a In particular, it has been suggested proven also without the knowledge of the distance of the 22 DepartamentoNAOC-UKZN Computationalde Fà sica Teà Astrophysics rica I, Universidad Centre Complutense (NUCAC), University de Madrid, of E20840KwaZulu-Natal, Spain Durban,that the quantum-gravitational4000 South Africa BH explosion may be source, by studying the radiation integrated over the or interacting DM/energy also lead to modifications of very17 high-energy cosmic rays (Barrau, 2000). As cosmic perpetual event horizon. The collapsing matterlinked contin- to FRBs ( ). A number of hints seems to support detectable past explosions. SKA HI intensity mapping small scales power (see e.g. Wright et al., 2017). 23 API,Purple University Mountain of Observatory, Amsterdam, Chinese Science Academy Park 904, of 1098 Sciences, XH Amsterdam, Nanjing 210008, Netherlands China ? rays18 of such energies are rare, constraints are derived on ues its fall after entering the trapping region, formingthis conjecture, a such as the rapid impulse, of mostly can therefore provide the desired data in this respect. Current constraints on the sum of the neutrino masses, 24 CosmologyETH Zurich, and Wolfgana-Pauli-Strasse Gravity Group, University 27, CH8093 of Cape Zurich, Town, Switzerland 7701 Rondebosch, Cape Town, South Africaextra-Galactic origin, the enormous energy flux as the Studies of the integrated emission from PBH decay has arising by combining data from the CMB, galaxy clus- 19 BH converts e ciently its mass into radiation. been started in (Barrau et al., 2016) for a large range the25 very-small-massDepartment of end Mathematics of the PBH and mass Applied spectrum. Mathematics,very University dense object of whose Cape furtherTown, 7701collapse Rondebosch, is prevented Cape by Town, South Africa tering and/or the Lyman-– forest, are M‹ 0.12 eV Institute of Cosmology & Gravitation, University of Portsmouth, Burnaby Road, Portsmouth, PO1 3FX, United Kingdom of the Ÿ parameter in the PBH lifetime. The signal has . 20 quantum pressure (referred to with the suggestingPBHs name exploding in a quantum decay present a unique (Riemer-Sørensen et al., 2014; Palanque-Delabrouille 26HawkingDepartmentSouth evaporation,African of Astronomical Physics however, and Astronomy,is Observatory, a phenomenon Uppsala Observatory pre- University, 7925, SE-751 Cape Town, 20 Uppsala, South Africa Sweden feature that makes them distinguishable from other as- been obtained using the PYTHIA code (Sjöstrand et al., 21 trophysical sources. The time at which the decay hap- 2015), which for a given initial energy computes the par- et al., 2015; Cuesta et al., 2016; Vagnozzi et al., 2017). dicted27 School in the of context Chemistry of quantum and Physics, field theory University on a fixed of KwaZulu-Natal,of Planck Star WestvilleRovelli Campus, & Vidotto Private (2014)). Bag X54001, Durban, 4000, South Africa pens is a function of the BH mass. Therefore, smaller ticle production for the process. Thedirect+decayed resulting radiation One would naively expect that enlarged those constraints would 22 Theoretical Particle Physics and Cosmology group, Physics Department, King’s College London, University of London, Strand, curvedNAOC-UKZN background. Computational This is a theory Astrophysics with a regime Centre of (NUCAC),The collapsing University matter of that KwaZulu-Natal, forms PBHs Durban,in thePBHs radia- explode 4000 earlier, South that isAfrica at a distance from us. is not thermal, but it carries a distortion due to the char- improve by using galaxy clustering at higher redshifts, 23London WC2R 2LS, UK The signal they produce also depends on their mass, acteristic redshift-wavelength relation of Figure 21. This since the available volume is much larger and the non- 28 validityPurple that Mountainmay likely breakObservatory, down when Chinese approximately Academy oftion Sciences, dominated Nanjing epoch 210008, is mainly China constituted bythe photons. smaller the BH, the shorter the wavelength in both appears for both the high energy and the low energy linear clustering e ects are weaker. Also the e ects of 24 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany half29 ofETH the massZurich, of the Wolfgana-Pauli-Strasse hole has evaporated, as 27, indicated CH8093 Zurich,Seen Switzerlandfrom the center of the hole, those photonsthe highcol- and low energy channels. Signals from distant channel, as can be seen in Figure 22 for the case of the dark energy will be smaller at higher redshift. Institut d’Astrophysique, UMR 7095 CNRS, Université Pierre et Marie Curie, 98bis Blvd Arago, 75014 Paris, France shortest lifetime. In principle the result depends on the 25 sources get redshifted, partially compensating for the The possibility of using high-redshift optical galaxy for30 instanceInstitute by of the Cosmology ‘firewall’& no-go Gravitation, theorem (Almheiri University oflapse Portsmouth, through the Burnaby trapping Road, region, Portsmouth, then expands PO1shorter passing 3FX, wavelength United due to a Kingdom smaller mass. PBH mass spectrum, but di erent hypothesis for the AIM-Paris-Saclay, CEA/DSM/IRFU, CNRS, Univ Paris 7, F-91191, Gif-sur-Yvette, France surveys (combined with CMB data, in order to lift param- 26 Generic astrophysical objects have an observed wave- mass spectrum have been tested showing that the result et31 al.,Department 2013). The of geometry Physics andaround Astronomy, a BH can Uppsala indeed University,through SE-751 an anti-trapping 20 Uppsala, region Sweden and eventually exits eter degeneracies) to provide precision measurements of 27 Department of Physics and Astronomy, The John Hopkins University, Homewood Campus, Baltimorelength that MD scale linearly 21218, with theUSA distance. On the other has only a very weak dependence [(Barrau et al., 2016)]. undergo32 BeecroftTheoretical quantum Institute Particle fluctuations of Physics Particle on anda Astrophysics time Cosmology scale shorter and group, Cosmology, Physicsthe white-hole Department Department, horizon, of King’s alwaysPhysics, College at University the speed London, of of light,hand, Oxford, University Hawking the Oxford evaporation of London, OX1ends in the 3RH,Strand, standard UK theory Finally, in the presence of the ionized ISM, decay- the neutrino masses is not new (see for example (Takada et al., 2006)). High-z advantages include accessing a 33London3 WC2R 2LS, UK when BHs, of any initial mass, reach the Planck size ing PBHs can produce a radio pulse of the order of than IstitutoMBH,whenthee Nazionale ects di Fisica of the Nucleare, Hawking evaporation Sezione di Ferrara,process Via is thusGiuseppe extremely Saragat fast. 1, On I-44122 the other Ferrara, hand,and Italyproducefor an a signal with such wavelength. The phe- 1GHz (Rees, 1977; Blandford, 1977). This frequency larger comoving volume for a given survey area, and a 28 Figure≥ 22. The di use emission of the low energy channel, and 34 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdamnomenon described 14476, above Germany gives a completely di erent is fully within the sensitivity of SKA-mid. Furthermore, haveUniversity not not yet of significantly Hamburg, Gojenbergsweg modified the size 112, of 21029 the Hamburg,observer sitting Germany outside the horizon, a huge but finite red- below the di use emission of the high energy channel. We show here wider range of scales in the linear or quasi-linear regime. 29 e ect, the modified relation between wavelength and red- it is interestingly close to that of an FRB. The emission 35 Institut d’Astrophysique, UMR 7095 CNRS, Université Pierre et Marie Curie, 98bis Blvd Arago, 75014 Paris, France the ones for the shortest BH lifetime, i.e. the lowest Ÿ parameter. However, the detection of galaxies at high redshifts be- hole.Istituto As any di classical Radio Astronomia,system, the hole INAF, has Via a charac- Gobetti 101,shift 40122, stretches Italy this time to cosmological times. Thisshift (Barrau time, et al., 2014) represented by the flattenedThe unitsmechanism, in the ordinate in this case, axis are relies not on specified: the presence the normalisation of a shell comes more di cult and expensive, and shot noise e ects 30 curve (Figure 21). Observation of a burst whose sourceof the spectrum depends on the percentage of PBHs as DM. teristic36 InstituteAIM-Paris-Saclay, timescale for Mathematics, after which CEA/DSM/IRFU, the Astrophysics the departure CNRS, and from Particle Univ Parisproperly Physics 7, F-91191, (IMAPP), called the Gif-sur-Yvette, hole Radboud lifetime, University, as France discussed P.O. before Box 9010, has 6500 GL Nijmegen, The of relativistic charged particles produced in the explo- may dominate. In (Takada et al., 2006), a space-based 31 has a known distance will allow us to see whether data sion. The shell behaves as a superconductor that expels 2 NetherlandsDepartment of Physics and Astronomy, The John Hopkins University, Homewood Campus, Baltimorefits such a MD curve. If 21218, so, it would USA represent a signature of the interstellar magnetic field from a spherical volume galaxy survey with a 300 deg sky coverage at redshifts 32 3.5
Keywords: keyword1 – keyword2 – keyword3 – keyword4 – keyword5 Quantum Gravity observations are not absurd anymore.
- Decrease the Bayesian confidence of some current theories (absence of supersymmetry at energy where it was expected)
- Already rules out theories (Lorentz invariance) - Suggested astrophysical observations motivating astronomers (Cosmology+Black holes)
- Interesting laboratory experiments (Entanglement via gravity)
(Result of a pool at a recent conference (3rd Karl Schwarzschild Meeting on Gravitational Physics and the Gauge/Gravity Correspondence, Frankfurt am Main, July 2017): 80% of the participants expect observational evidence for quantum gravity observations within the next decade.) Progress has happened along some research directions
Theoretical Empirical success Empirical failure Theoretical success Key open issue failure
AdS-CFT Low-energy super Standard model Strings None Non-fundamental Lack of predictivity symmetry parameters appliacations Strings Loops None Low energy limit Infinite graph limit
Lorentz violation at Hojava-Lifshitz None Renormalizability Other scale? Planck scale
Increase evidence of Asymptotic savety None Computing amplitudes Loops fixed point
Your favorite … … … … … Loops open problems in the late 80’ Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops open problems in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
• Definition of the Hilbert space • Mathematical foundation • Coupling matter • Recovering low energy GR • Problem of time • Observables • Application to early universe • Produce verifiable physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions Loops Strings open problems open problems in the late 80’ in the late 80’
Definition of the • Finding a fundamental Hilbert space • formulation of the theory Mathematical • Deriving SU(3)xSU(2)xU(1) foundation • from first principles • Coupling matter • Computing the parameters • Recovering low of the standard model energy GR • Supersymmetry breaking • Problem of time • Compactification • Observables • Extend to the non- • Application to early perturbative regime universe • Produce tentative verifiable • Produce verifiable physical predictions physical predictions 3. There is some convergence on some issues of major philosophical relevance
i: nature of physical space ii: nature of physical time iii: relation between physical and experiential time iv: connection between relational aspects of GR and QM i: nature of physical space space
relation entity
Aristotle Newton Descartes
Space is an entity independent from its content
Aristotle : Substance Aristotle : Substance
Descartes: Res extensa Aristotle : Substance
Descartes: Res extensa
Newton: Time Space Particles Aristotle : Substance
Descartes: Res extensa
Newton: Time Space Particles
Faraday-Maxwell: Fields Particles Aristotle : Substance
Descartes: Res extensa
Newton: Time Space Particles
Faraday-Maxwell: Fields Particles
Einstein 05: Spacetime Aristotle : Substance
Descartes: Res extensa
Newton: Time Space Particles
Faraday-Maxwell: Fields Particles
Einstein 05: Spacetime
Einstein 15: Covariant Fields Aristotle : Substance
Descartes: Res extensa
Newton: Time Space Particles
Faraday-Maxwell: Fields Particles
Einstein 05: Spacetime
Einstein 15: Covariant Fields
Quanta: Quantum fields Aristotle : Substance
Descartes: Res extensa
Newton: Time Space Particles
Faraday-Maxwell: Fields Particles
Einstein 05: Spacetime
Einstein 15: Covariant Fields
Quanta: Quantum fields
Quantum gravity: Covariant quantum fields →
Quantum electromagnetic field: quanta of light
→
Quantum gravitational space: quanta of space
“Emergence” → physical space is granular jl
vn →
Space has a granular structure: spin networks Covariant loop quantum gravity. Full definition.
n0 l 2 L N hl = L [SU(2) /SU(2) ] (hl) =lim n State space H 3 H H !1
Kinematics Operators: where Boundary spin network (nodes, links)
Transition amplitudes W (hl)=N dhvf (hf ) A(hvf ) hf = hvf C C SU(2) v v Z Yf Y Y Bulk Dynamics
j (j+1) j 1 Vertex amplitude A(h )= dg0 (2j + 1) D (h )D (g g ) vf e mn vf jmjn e e0 SL(2,C) j Z Yf X
W =limW C e C!1 v f spinfoam (vertices, edges, faces) 8⇡ ~G =1 C ii: nature of physical time Covariant loop quantum gravity. Full definition.
n0 l 2 L N hl = L [SU(2) /SU(2) ] (hl) =lim n State space H 3 H H !1
Kinematics Operators: where Boundary spin network (nodes, links)
Transition amplitudes W (hl)=N dhvf (hf ) A(hvf ) hf = hvf C C SU(2) v v Z Yf Y Y Bulk Dynamics
j (j+1) j 1 Vertex amplitude A(h )= dg0 (2j + 1) D (h )D (g g ) vf e mn vf jmjn e e0 SL(2,C) j Z Yf X
W =limW C e C!1 v f spinfoam (vertices, edges, faces) 8⇡ ~G =1 C Galileo
Doctors A
Time: t B
What we observe: A, B, ...
Newton: A(t), B(t), ...
But we actually only see: A(B), B(A) ....
→ the world can be described without t At the elementary level Nature is not organized in terms of evolution in time. iii: relation between physical and experiential time “Experiential Time” is a complex layer of structures and properties which appear (emerge) at different level of approximations and descriptions of the world:
Internal flow: Diff invariant qft Connes’s flow of the vonN. algebra Connes, A. & Rovelli, C. Von Neumann algebra automorphisms and time thermodynamics relation in general covariant quantum theories. Class.Quant. Grav. 11, 2899–2918 (1994).
Flow and energy: Statistical mechanics: Thermal time (Tomita flow)
Unicity, present: Non-relativistic limit
Orientation -> traces (Perspectival?) low past entropy: Price, H. Time’s Arrow. (Oxford University Press, 1996). Rovelli, C. Is Time’s Arrow Perspectival? 6 (2015). Replicating systems with memory: Biology and evolution
“Sense of flowing time”, identity as narration Brain’s memory and anticipation D. Buonomano, Your Brain is a Time Machine: The Neuroscience and Physics of Time, Norton, New York, 2017. Moral: do not search in elementary physics what is not in elementary physics iv: connection between relational aspects of GR and QM A process and its amplitude
hl Boundary state = Boundary state in ⌦ out Amplitude A = W ( )
Boundary Quantum system = “Spacetime region” Spacetime region
➜ Hamilton function: S(q,t,q’,t’) A process and its amplitude
hl Boundary state = Boundary state in ⌦ out Amplitude A = W ( )
Boundary Quantum system = “Spacetime region” Spacetime region
➜ Hamilton function: S(q,t,q’,t’)
In GR, distance and time measurements are field measurements like any other one: they are part of the boundary data of the problem Boundary values of the gravitational field = geometry of box surface = distance and time separation of measurements A process and its amplitude
hl Boundary state = Boundary state in ⌦ out Amplitude A = W ( )
Boundary Quantum system = “Spacetime region” Spacetime region
➜ Hamilton function: S(q,t,q’,t’)
In GR, distance and time measurements are field measurements like any other one: they are part of the boundary data of the problem Boundary values of the gravitational field = geometry of box surface = distance and time separation of measurements
Particle detectors = field measurements
Distance and time measurements Spacetime region = gravitational field measurements GR: localization of a system is relative to other systems
QM: events for system isare relative to other systems
Boundary
“Spacetime region”
Understand the world as a net of system influencing one another 1. We do have quantum gravity theories (We do not know which is right)
2. We do have have some empirical evidence (Rule out and/or disfavour some theories, but no positive support yet)
3. Results towards issues of philosophical relevance
i: nature of physical space (“material”, discrete)
ii: nature of physical time (absent at the fundamental level)
iii: relation between physical and experiential time
(Time is a multilayer concept, Experiencial time is understood in terms of theormodynamics, biology, brain sciences.)
iv: connection between relational aspects of GR and QM (Understand the world as a net of system influencing one another.)