Observables and the future of quantum gravity

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Observables and the future of quantum gravity

• Donald Marolf, UCSB
• Niels Bohr Institute
• August 16, 2006

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Classical General Relativity

• Diffeomorphism Invariance ? Relativity

xa ? xa xa(x)
Only relations between physical events are
observable.
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The problem of time

• In cosmology,

and H, A 0.
Relativity Advancing the time coordinate does
not change the invariant relations between events.
S
Classical GR Use relational observables
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Quantum Theory?

• How to construct relational quantum observables
  in the effective theory?
• What are their properties?
• How do they reproduce local physics?

Progress to date

• Relational QFT observables exist!
• Pesudo-local
• However, IR effects are important!

Future

• Large cosmologies and eternal inflation.

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Outline

• Systems with boundaries (Asymptotically Flat
  space, AdS)
• 01 models
• d1 cosmologies and IR effects

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1. Systems with boundaries

• Commonly discussed observable The S-matrix

Reminder Diffeos which act on the Bndy are not
gauge.
E.g. (asymptotic) Poincare transformations are
symmetries w/non-zero generators
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More generally, any quantity evaluated on the
Bndy is an observable.
AdS
Asympt. Flat
Expect additional observables at i0 analytic
continuation of S-matrix
y
z
Z
x
i0
i0
x
y
ltf(x) f(y) f(z)gt
Ashtekar-Romano representation of i0.
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More local observables?
(A challenge for AdS/CFT)
We do not measure bndy observables in the
lab. Our labs do not stretch to the boundary!

• No truly local observables

But, perhaps pseudo-local? I.e., approximate
local observables in appropriate circumstances.
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Looks easy if make use of Boundary!
or, fix coordinates on boundary and fix gauge
ExampleAdS
fa (o - m2)xa
x
Z g exp(iS)
g exp(iS) d(f) DFP
Observables are relative to boundary.
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Q1 Are pseudo-local obs. independent of boundary
obs.?

• Classically Yes, black holes can have internal
  dynamics not seen at the boundary.
• Quantum? AdS/CFT suggests no.Boundary theory
  is dual to bulk.

CFT microstates account for black hole entropy
expect these to capture all details of black hole
microstates.
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Q2 How are pseudo-local obs. related to boundary
obs?

• What is the dictionary?
• How to get info out of black holes?
• How does the bulk arise as an effective
  description of the CFT?

Exciting progress, but radial direction remains a
chalenge.(See talk by D.B.)
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2. Cosmology

• What if no boundary to space?

Classical relational observables
Take d scalar fields, Za Z1,Z2,Zd in config.
where Zaxa selects unique event.
fZaxa
or, more generally,
fZaxa
See also DeWitt, or Ambjorn others in DT
literature.
Quantum Theory?
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01 models reparametrization-invariant QM

• E.g., mini-superspace models.
• Canonical example is free particle

Define
Can show
1) is a well-defined observable. 2)
Closely related to Newton-Wigner operators. 3)
Unitary Evolution
References CQG 12 (1995) 1199 gr-qc/9404053.
CQG 12 (1995) 2469
gr-qc/9412016.
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Well-defined observable
Note
1) Just QM (no QFT), so integrand is
well-defined. 2) Integral converges sinceas
.
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Well-defined observable
Observable Commutes with H p2 m2 !
For A A(p,q), we have
Integrand w is proportional to N.
Integrand of commutator is total derivative
QED
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In general
Consider any 01 (QM) system w/ diffeo inv. and
an asymptotic clock dof. I.e.
as .
1) Bounded functions A on the phase space define
observables (A)ct. 2) In the approximation that
c ? c const is a symmetry (ideal clock),
evolution is unitary
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3. Restore Space
(Giddings, DM, Hartle hep-th/0512200)
Simple model d free scalar fields, Za
Z1,Z2,Zd.
Restrictions
Set GN 0 Flat Minkowski space. Take Zs free.
No self-interactions, no interactions with other
scalar field (f, with A A(f)). Linear
background Za lxa dZa, quantize dZa.
Operators renormalized by covariant
point-splitting. (Preserves tensor character
under diffeos.)
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Results d gt 21

• These operators are well-defined andapproximate
  local observables

where xaixai/l, and when
Smearing scale
and
In particular, cannot take s to zero
Together,
Background energy density sets bound on
resolution!
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Turn gravity back on.

• Propagating gravitons not a problem(perturbative
  effective field theory)
• But, also Coulomb field from energy density r.?
  Can only instrument finite region of size R.

R
If no black hole or grav collapse resolution ?
Thinning of degrees of freedom, but thinner than
holography. Expect that our observables are not
complete set! Are others less local?
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IR Effects
R
Z-vacuum outside

• Operators integrate over vacuum region.
• Vacuum not an eigenstate of any local operator.
  Via quantum fluctuations, vacuum can
  impersonate instrumented region.
• Small finite probability exp(-z2/s2)
  exp(-R2/d2)
• but, infinite volume ? divergent fluctuations

not well-defined in infinite spacetimes.
Requires IR cut-off on space may reflect
fundamental structure of quantum gravity.
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Large Finite Universes are OK
(Multigrid)
Gaussian sampling? exponential suppression. Vacuum
not resolved, just distinguished from R.
R
L ltlt exp(Rl/s)
d4, d 1/TeV
L
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does not exist in infinite space

• Note differs from gauge fixed observables
  attached to boundary.
• Coordinates anchored to bndy have no energy
  density no back reaction no problems!
• Recall OK because translations are not gauge.
• But in finite volume, all diffeos are gauge.
• No continuity two distinct classes of
  observables.

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The future??

• If there are no better observables,
• For ,
• Will the universe become fuzzy as ?
• Will this help us understand L and the
  landscape?

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Summary

• Non-trivial to build Observables for quantum
  gravity.
• However, becomes easy with a boundary Bndy
  observables, and pseudo-local observables
  anchored to bndy. (e.g., AdS)
• Fully relational observables can exist w/o bndy,
  but IR divergences!
• Fuzzy future?
• Fundamental distinction between finite and
  infinite universes?