Fotini Markopoulou- Quantum Gravity and Emergent Locality

8/3/2019 Fotini Markopoulou- Quantum Gravity and Emergent Locality

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QUANTUM GRAVITYAND EMERGENT LOCALITY

Fotini MarkopoulouPerimeter Institute


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QUANTUM GRAVITYAND EMERGENT LOCALITY

QUANTUM GRAPHITY:a background independent condensedmatter model of emergent space

Fotini MarkopoulouPerimeter Institute

T. Konopka, FM & L.Smolin, hep-th/0611197

also with: O. Dreyer, S. Severini


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Preview

geometrogenesis

phase transition

Permutation symmetry No locality (no space) Relational

High-Translations Local Relational

Low- ground state


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Outline.

1. Motivation

2. Quantum Graphity: A Model of emergent space (time)

3. Could we observe this? Early universe application

4. Discussion


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1. Emergence of near-flat geometry in low-energy limit of background

independent quantum gravity: long-standing challenge.

Motivation for the model.

cf. Ambjorn talk


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2. Locality: underutilized.

combinatorial quantum geometry classical geometry

: quantum geometry

spin foam vertex properties




cf. Ambjorn talk

i j

k

l

local statements


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cf. Ambjorn talk

FM&L.Smolin, gr-qc/0702044

2. Locality: underutilized.

combinatorial quantum geometry classical geometry

: quantum geometry

spin foam vertex properties

nodes one-edge perturbations locality is unstable

locality?

i j

k

l

local statements


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Phase transition + background independence

micro-locality macro-locality

background independence means dynamics determines locality.

phase transition

O.Dreyer, hep-th/0409048

FM&D.Kribs, gr-qc/0510052

FM, gr-qc/0703097


2. Locality, cont.


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Phase transition + background independence

micro-locality macro-locality

background independence means dynamics determines locality.

phase transition

O.Dreyer, hep-th/0409048

FM&D.Kribs, gr-qc/0510052

FM, gr-qc/0703097


2. Locality, cont.

Lots of other hints: AdS/CFT, black holes, causets,...


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3. Background independence vs emergent gravity

Geometry and gravity are only

classical, emergent concepts.

- condensed matter approaches(e.g. Volovik)

- string theory

Background independence:dynamical nature of

spacetime geometry

What is the role of the lattice/geometry

and the symmetries of the lattice?


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3. Background independence vs emergent gravity

Geometry and gravity are only

classical, emergent concepts.

- condensed matter approaches(e.g. Volovik)

- string theory

Background independence:dynamical nature of

spacetime geometry

What is the role of the lattice/geometry

and the symmetries of the lattice?

Reconcile:

Background independence: no fundamental geometric degrees of freedom

Today: background independent condensed matter models.Dreyer 04, 06, Lloyd 05,FM&Kribs 05, FM07.

Background independence is normally implemented by a superposition

of quantum geometries: - loop quantum gravity- dynamical triangulations- causal sets


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4. Matter vs Geometry.

New results on emergent matter are suitable for a background independent

treatment:

5. No fundamental locality large-scale observational consequences of

quantum gravity.


gauge theory -like

excitations

and fermions

M.Levin & X-G.Wen, hep-th/0507118


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The model: kinematics.

Complete graph : vertices, edges.

one-edge state space:

edge on

edge off

total state space:


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The model: dynamics.


want ground state


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want ground state

turns off edges and has minimum when all edges have degree .

E.g., for ,


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want ground state

values:

strings

turns off edges and has minimum when all edges have degree .

E.g., for ,


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want ground state

does not likeopen strings tension

wants all


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want ground state

length of loop

cf. kinetic energy


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want ground state

length of loop

cf. kinetic energy


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want ground state

length of loop

cf. kinetic energy


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want ground state

length of loop

Let . There is a preferred loop length :

cf. kinetic energy


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erases edges to give lattice with extension



makes lattice regular and gives macro-matter


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Matter.

and are generalizations of the rotor model ofstring-net

condensation of Levin and Wen to a dynamical lattice.

tension K.E. : ground state has almost no strings

tension K.E. : ground state is a superposition of many closed strings,

i.e., string-net condensed:

high-energy charged excitations: open strings

emergent gauge theory.

M.Levin & X-G.Wen, hep-th/0507118


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Ground state geometry plus matter.

Local lattice: large average distance .

Small vertex degree

Loops of average size .

Possibly also regular?

For number of minimal loops

is maximized by the honeycomb lattice:

In our model: the balance between tension and K.E. controls both the

loop size when the lattice is dynamical and gives the matter.

T.Konopka, FM& S.Severini

Plus string condensation on the ground state

lattice, as in string nets.


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Summary of quantum graphity.

geometrogenesis

phase transition

Permutation symmetry No locality

Relational -dimensional no subsystems external time

micro-matter

Translations Local

Relational large low-dimensional subsystems external and internal time

macro-matter and dynamicalgeometry

Model has 4 couplings ( ) and 3 parameters ( ).

Some obey generic conditions:

Some have to be adjusted:

High- Low-


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Cosmology of emergent space.

Horizon problem

This is an extrapolation

of our causal and localstructure to the initial time


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Horizon problem



inflation


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In our model:


Horizon problem



inflation


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In our model:


Horizon problem



inflation


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In our model:


Horizon problem



inflation

Are the CMB correlations a consequence of pre-geometry?

Compare, e.g., to the phenomenology of discretization.

A geometrogenesis scenario has the potential of large-scale effects.

C


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Comments.

1. Time, temperature?

Emergent space or emergent spacetime?

Time-reparametrization invariance as the noiseless sector of atheory with time: T. Konopka and FM, gr-qc/0601028.

Does the temperature imply a bath?

Internal vs external time and geometry.Internal: subsystems observing subsystems. Our emergent space

gives emergent spacecetime internally.

2. The terms that give rise to matter are also responsible for the geometry

of the lattice: we dont just erase edges, we also order them.

This is a new use for unification.

T d


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To do.

Understand the ground state

Graph theory analysis of the terms in the Hamiltonian

Cosmology: perturbations

Effective disordered locality description

Understand the role of the temperature


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Fotini Markopoulou- Quantum Gravity and Emergent Locality

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