Some%20persistent%20puzzles%20in%20background%20independent%20approaches%20to%20quantum%20gravity

1

• Some persistent puzzles in background independent
  approaches to quantum gravity
• Lee Smolin
• Perimeter Institute for Theoretical Physics and
  UW
• Work by and with Fotini Markopoulou,
• Mohammad Ansari, Sundance O. Bilson-Thompson,
  Hal Finkel,
• Jacob Foster, Isabeau Premont-Schwarz, Yidun Wan
• 1) What has loop quantum gravity accomplished
  for sure?
• What are the persistent hard problems?
• Non-locality problem or opportunity?
• Particle physics from non-local edges.
• A bimetric low energy limit

2

• Some persistent puzzles in background independent
  approaches to quantum gravity
• and a possible remedy to them
• Lee Smolin
• Perimeter Institute for Theoretical Physics and
  UW
• Work by and with Fotini Markopoulou,
• Mohammad Ansari, Sundance O. Bilson-Thompson,
  Hal Finkel,
• Jacob Foster, Isabeau Premont-Schwarz, Yidun Wan
• 1) What has loop quantum gravity accomplished
  for sure?
• What are the persistent hard problems?
• Non-locality problem or opportunity?
• Particle physics from non-local edges.
• A bimetric low energy limit

3

• What has loop quantum gravity accomplished for
  sure!
• A Quantum geometries spin networks for algebra
  A
• Quantum spacetimes spin nets evolve by local
  rules.
• Derivations of A and B from classical
  diffeomorphism
• invariant theories.
• Applications black holes, cosmology,
  phenomenology, etc.
• There is lots of good news. Steady progress.
• But there are also several persistent unsolved
  problems.

4
Unification We claim we can include any
standard matter, SUSY and the theory stays
finite consistent. BUT what about anomalous
chiral gauge theories??? Is there fermion
doubling as there is in lattice gauge
theory? In that case can LQG really include the
standard model? Is there a spin statistics
theorem? There are many LQG/spin foam models.
Are there criteria to pick out one that should
describe nature? If LQG is even roughly right,
the right version should have implications for
the problem of unification.
5
Interpretation of quantum cosmology Several
claims, but still open. Evolving constants of
motion YES, but how to implement in the real
theory?? Relational quantum theory (Crane,
Rovelli, et al) Sounds good in principle, but
what determines the boundaries between different
domains? Quantum and algebraic causal histories
(Markopoulou et al) Also sounds good, but
requires a fixed causal structure. (Terno
reports on some developments) What is an event
when we sum over causal histories? Maybe quantum
theory should come from quantum gravity and not
the other way around??
6
The emergence of classical spacetime
geometry. -We can assume ansatzs for
semi-classical, coherent or weave states and
derive predictions from them. But we cant know
if these are predictions of the theory unless we
can find the ground state and show that
classical geometry emerges. There are new
approaches to this problem to be discussed
here. Rovelli et al propagator Markopoulou et
al particles as decoherence free subspaces Why
cant we find the Hamiltonian operator for
asymptotically flat b.c. and show that it is
positive definite on physical states? Why
is this so hard? What if the quantum hamiltonian
is not positive definite?
7

• Three possibilities
• 0 The theory is wrong
• Those spin foam models from which classical
  spacetime emerges
• are very special. This is a criteria to pick
  out good theories.
• (Perhaps they are supersymmetric, and underlie
  string theory.)
• The emergence of spacetime is generic.
• Shouldnt 2 be right? You dont need to get the
  details of atomic
• dynamics remotely right to understand why the air
  in the room is
• uniform, or understand why metals form at low
  temperature.
• We then need a general, thermodynamic type
  argument.
• Also, phenomenology predictions, low energy
  symmetry should

8

• There is one issue which matters the two types
  of moves
• Expansion moves Exchange moves
• Hamiltonian constraint gives only expansion
  moves.
• Spin foams give both (finite evolution, crossing
  symmetry)
• How then could spin foam models be precisely
  derived from the
• Hamiltonian quantum theory? Do we have to choose
  between them?
• Claim expansion moves are necessary for
  generating long distance
• correlations, hence, emergence of spacetime.
• Possible ways out regulate in space and time,
  master constraint???

9
The problem of non-locality Two kinds of
locality Microlocality connectivity of a
single spin net graph causal structure of a
single spin foam history. Macrolocality nearby
in the classical metric that emerges Issues Sem
iclassical states may involve superpositions of
large numbers of graphs. Their notions of
locality may not agree. Which notion of
locality emerges as macrolocality? Similar
issue for histories. Are there states
contributing to a semiclassical state for a
classical metric qab whose connectivity is
non-local with respect to qab?
10
Weaves Spherically symmetric case
Metric
Consider a set of N spherical spheres, between
which there are shells. This gives rise to a
coarse grained geometry In the form of a list
g Ai, Vi . Gg gt is a weave state that
matches this
But there are non-local weaves that equally well
satisfy these conditions
11
Local weave all links cross only one sphere.
A 6,8, 10 V 3,4,5,6
12
The conditions are equally well satisfied by
non-local weaves
A 6,8, 10 V 3,4,5,6
13
So the weave conditions do not imply
locality. There seems nothing that guarantees
that microscopic locality defined by the
connectivity of a given spinnet goes over into
locality of a semi-classical or coherent
state from which classial geometry would
emerge. Furthermore, there is a problem
suppressing non-local links, as there are
potentially so many more of them. This is the
inverse problem.
14
The inverse problem is a general problem for
background independent approaches to quantum
gravity
Its easy to approximate smooth fields with
discrete structures.
15
The inverse problem is a general problem for
background Independent approaches to quantum
gravity
Its easy to approximate smooth fields with
combinatoric structures.
But generic graphs do not embed in manifolds of
low dimension, preserving even approximate
distances.
?
Those that do satisfy constraints unnatural in
the discrete context,
16
One reason for worry We believe the universe
starts in a non-classical state and
then classical spacetime emerges as it evolves.
So the initial states should not approximate any
classical geometry. The evolution is by local
moves. Will these generate local
spacetime? Local moves are unlikely to remove
non-local edges. So once there in the initial
state, they are defects, trapped
in! Combinatorial definition of non-local
edge smallest cycle containing the edge is
very large.
17
Exchange moves can increase the non-local edges.
Perform a 2 to 2 move
1
1/2
1/2
1/2
1/2
1/2
1/2
18
Exchange moves can increase the non-local edges.
Perform a 2 to 2 move
1
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1
1/2
1/2
1/2
19
Exchange moves can increase the non-local edges.
Perform a 2 to 2 move
1
1/2
1/2
1/2
1/2
1/2
1/2
The two left and two right edges can now
evolve away from each other, leading to two
non-local edges.
1/2
1/2
1/2
1
1/2
1/2
1/2
20

• LQG cosmological scenario
• Universe starts with a random spinnet
• Expands by a combination of expansion and
  exchange moves
• Becomes local (low valence nodes) decorated with
  a small number
• of the original links, which are now non-local.
• What really happens?
• Hal Finkel will report on a series of numerical
  experiments
• using stochastic evolution with various mixes of
  evolution moves
• No quantum mechanics
• No labels, only graphs
• Random start 200 nodes
• Grow to 5,000 nodes
• Vary R exchange moves/expansion moves

21
R1
Initial local red nonlocal magenta Added
local black nonlocal green
22
R1 blowup
23
Initial local red nonlocal magenta Added
local black nonlocal green
R1 blowup
24
Initial local red nonlocal magenta Added
local black nonlocal green
R1 blowup
Expansion dominated phase spiky, not a random
sampling of any manifold
25
R100
26
Initial local red nonlocal magenta Added
local black nonlocal green
R100 blowup
27
Initial local red nonlocal magenta Added
local black nonlocal green
R100 blowup
28
Initial local red nonlocal magenta Added
local black nonlocal green
Exchange dominated phase Well mixed, spikiness
eliminated. Lots of non-locality created by local
exchange moves!!! For details see Hal Finkels
talk
R100 blowup
29
Compare R100 to R1
R1
R100
Tentative conclusion dominance by exchange moves
is needed to recover macro-geometry Is this a
problem for Hamiltonian evolution??
30
Suppose the ground state is contaminated by a
small proportion of non-local links (locality
defects)?? What is the effect of a small
proportion of non-local edges in a regular
lattice field theory? If this room had a small
proportion of non-local link, with no two nodes
in the room connected, but instead connecting to
nodes at cosmological distances, could we
tell? Yidun Wan studied the Ising model on a
lattice contaminated by random non-local links.
Rnon-local links/local links 20/8001/40
31
The critical phenomena is the same, but the
Curie temperature increases slightly.
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Tentative conclusions To a certain point, the
effect of non-local defects on the lattice is
just to raise the critical temperature,
Correlation functions alone apparently cannot
detect small amounts of non-locality, at least
away from Tc. For details, see Yidun Wans talk.
34

• What are we to do about the inverse problem and
• the locality problem?

35

• What are we to do about the inverse problem and
• the locality problem?
• Hope that the problem is solved by dynamics, i.e.
  there
• is an action, natural in the discrete setting,
  that forces
• the discrete system to condense to approximate a
• low dimensional spacetime.
• Little evidence of this so far

36

• What are we to do about the inverse problem and
• the locality problem?
• Hope that the problem is solved by dynamics, i.e.
  there
• is an action, natural in the discrete setting,
  that forces
• the discrete system to condense to approximate a
• low dimensional spacetime.
• Little evidence of this so far
• The theories are wrong.
• But these appear to be generic problems!!!

37

• What are we to do about the inverse problem and
• the locality problem?
• Hope that the problem is solved by dynamics, i.e.
  there
• is an action, natural in the discrete setting,
  that forces
• the discrete system to condense to approximate a
• low dimensional spacetime.
• Little evidence of this so far
• The theories are wrong.
• But these appear to be generic problems!!!
• Assume a sparse distribution of non-local links
  are
• locked in from the early universe and hence
  connect to
• cosmological scales. See what this implies for
  physics.

38

• We have been studying the effects of small
  amounts of
• nonlocality in semiclassical states
• matter from non-locality
• large macroscopic corrections to the low energy
• limit (MOND-like effects)
• Cosmological implications
• Hidden variables theories of quantum mechanics
• gr-qc/0311059 PRD 04

39

• We have been studying the effects of small
  amounts of
• nonlocality in semiclassical states
• matter from non-locality
• large macroscopic corrections to the low energy
• limit (MOND-like effects)
• Cosmological implications
• Hidden variables theories of quantum mechanics
• Discussed at Marseille gr-qc/0311059 PRD 04

40
Consider LQG coupled to Yang-Mills with gauge
group G
A network with a non-local link labeled (j1/2,
r fundamental) looks to a local observer like a
spin 1/2 particle in the fundamental rep. of G.
(1/2,N)
So we naturally get fermions, and unlike SUSY in
the fundamental representation of any gauge
fields.
41
So a small amount of non-locality is nothing to
be afraid of. A spinnet w/ non-local links looks
just like a local spinnet with particles.
42
So a small amount of non-locality is nothing to
be afraid of. A spinnet w/ non-local links looks
just like a local spinnet with particles. But
this implies that the dynamics and interactions
of matter fields are already determined by the
dynamics of the gravity and gauge fields. Could
this work? Model trivalent spinnets (21)
with local moves.
fm gr-qc/9704013
43
Relation between fermion and gravity
dynamics pure gravity amplitude
i
k
i
k
Aijn klm
n
m
j
l
j
l
Let the i1/2 line be non-local
k
i
k
A1/2jn klm
n
m
j
l
j
l
This is a propagation amplitude for a fermion
k
Y
k
A1/2jn klm
Y
n
m
j
l
j
44
Lets look at this in detail
1
Y
1
A1/2 1/2 1/2 111
Y
1/2
1
1/2
1
1/2
1
The standard LQG fermion amplitude has the form
1
1
Y
Y
F1
1/2
1/2
1
1
1
We have to do this twice to reproduce the pure
gravity move
F12 A1/2 1/2 1/2 111
j
45
Interactions come from moves that are local
microscopically, but non local macroscopically
A spin-1 boson
1/2
1/2
B
1
1/2
1/2
46
Interactions come from moves that are local
microscopically, but non local macroscopically
A spin-1 boson as a non-local link w/ j1
1
1/2
1/2
1/2
1/2
1/2
B
1
1
1/2
1/2
1/2
1/2
1/2
47
Interactions come from moves that are local
microscopically, but non local macroscopically
Perform a 2 to 2 move
1
1/2
1/2
1/2
1/2
1/2
B
1
1
1/2
1/2
1/2
1/2
1/2
48
Interactions come from moves that are local
microscopically, but non local macroscopically
Perform a 2 to 2 move
1
1/2
1/2
1/2
1/2
1/2
B
1
1
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1
1
1/2
1/2
1/2
49
Interactions come from moves that are local
microscopically, but non local macroscopically
Locally this looks like
1
1/2
1/2
1/2
1/2
1/2
B
1
1
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
y
1
y
1
1
1/2
1/2
1/2
1/2
50
Interactions come from moves that are local
microscopically, but non local macroscopically
Locally this looks like
So if the pure gravity amplitude is
1/2
1/2
i
k
B
1
i
k
1/2
Aijn klm
n
m
1/2
j
l
j
l
1/2
The amplitude for matter interaction comes from
the pure gravity evolution amplitude. Amp B -gt
y y A1/2 1/2/1 1/2 1//2 1
y
1
y
1/2
51

• Matter without matter J A Wheeler
• Works also when coupling to gauge fields are
  included.
• Just label edges by reps of SU(2) X G.
• Pair creation possibly implies spin-statistics
  connection.
• Dowker, Sorkin, Balachandran.....
• CPTgravity CPTmatter same for CP, T
  etc
• Does CP breaking in matter imply CP breaking in
  gravity?
• We get a tower or particles of increasing spin,
  just like
• Regge trajectories in string theory.
• This gives a unification in which fermions appear
  in
• fundamental representations of gauge groups-
• unlike SUSY where they appear in adjoint reps-
• but like nature.

52
But we still have to input the gauge group.
53
But we still have to input the gauge
group. Could there be a version where we input
as little as possible, and we get out
the standard model, as observed?
54
But we still have to input the gauge
group. Could there be a version where we input
as little as possible, and we get out
the standard model, as observed? Minimal model
no labels, just graphs... too simple...
55
But we still have to input the gauge
group. Could there be a version where we input
as little as possible, and we get out
the standard model, as observed? Minimal model
no labels, just graphs... too simple... Next
simplest model Ribbon graphs
56
Lets play a simple game
(Bilson-Thompson) Basis States Oriented,
twisted ribbon graphs, embedded in S3 topology,
up to topological class. There is a label,
which is twisting
t0
t1
t-1
57
Rule 1 Twist number is conserved at nodes.
We will be interested in states with triplets of
edges
58
Some possible topologies for triplets
Left braid
Right braid
unbraid
Each strand also can be twisted
0
59
Two more rules Rule 2 Conservation of
braiding number across nodes. Rule 3 No
states with both and - twists in a single
triplet. Topological embeddings of ribbon graphs
modulo these rules span a Hilbert space
Hedges

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Assume this theory has a low energy limit,
defined in terms of an emergent 31 dimensional
spacetime metric. Assume that in the low energy
limit the resulting effective dynamics is
Poincare invariant. What do the twisted braid
states look like?
62
Classification of braided states
(Bilson-Thompson hep-ph/0503213)
Interpretation Twist charge in units of
e/3 Braiding left and right fermion number
63
Spin 1/2 states q 0
0 0 0
0 0 0
64
Spin 1/2 states q 0
nL
nR
0 0 0
0 0 0
65
Spin 1/2 states q 0 q 1
nL
nR
0 0 0
0 0 0


- - -
- - -
66
Spin 1/2 states q 0 q 1
nL
nR
0 0 0
0 0 0
eL
eR
e-L
e-R


- - -
- - -
67
Spin 1/2 states q 0 q 1 q
2/3
nL
nR
0 0 0
0 0 0
eL
eR
e-L
e-R


- - -
- - -
uR
uL
0
0
0
0
0
0
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• The 30 fermion states of the first generation are
  all here.
• Color is naturally explained as place in the
  braid. It is clear
• why only the charge 1/3 and 2/3 states have
  color. 24 states
• There are only two neutral states, one left, one
  right handed.
• There are four q 1 states
• There is a general
• flavor/colour index
• R1,...,15
• Fermion helicity, Rgt

70
To get statistics and independence of left and
right states we need another rule
Assume that the physical states live in a
subspace that satisfies the additional rule for
non-coincident edges
q Y q-1 Y
Y
But not necessarily the other recoupling rules
71
As a result under physical braiding (not
coincident), ends of ribbons in 2d surfaces
behave as anyons.
This means that individual ribbons could never
behave as relativistic particles in 31
dimensions.
q
If q9 -1 the triplets braid as fermions, so
they can move as particles in 3d.
So for triplets
q9
q eip/9
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So projected onto braids
-

Under the rules assumed. the left and right
braids, in all their twisted states, are
independent Y Left Y Right
Single ribbons cannot behave as particles in 3d.
They are anyons. They can live as ribbons in
31 but as particles only in 21 But triplets
can!
73
P projection operator onto triplet states

P
-
74
Suppose this works, so that the observed fermions
are all ends of non-local links. So the
probability of a link being non-local is at
least 1080/10180 10-100 There could be many
more non-local links and we could still be in a
very sparse domain. The effects of non-locality
may only become apparent when one looks out to
cosmological scales. Could there be macroscopic
non-local effects that only appear on
cosmological scales? These would be effects that
are characterized by the cosmological constant
scale L L-1/2
75

• There are anomalies in the CMB data at the scale
  L L -1/2

One interpretation no power on scales larger
than L-1/2

• Neutrino masses are at the scale L m r1/4
  lP-1/2 L1/4 .1 eV
• We should expect anomalies at the acceleration
  scale given by
• ac c2/L 10-8 cm/sec2

76

• The Pioneer Anomaly is at the scale ac

a is approximately 8 10-8 cm/sec2
astro-ph/0104064, 0208046
77

• The anomalous galaxy rotation curves are
  characterized by
• an acceleration scale near ac
• The Tully Fischer Relation
• Galaxies have flat rotation curves, with velocity
  V astro-ph/0204521
• k Ga0 M V4
• a0 1.2 10-8 cm/sec2 ac
• k mass/luminosity ratio

78
The MOND phenomenological law accounts for this
A modification of Newtons law of gravitational
acceleration holding low in the acceleration
limit Newtonian gravitational acceleration
aN - GM/r2 Milgrams Law aN gta0
aaN aN lta0
a-(aNa0)1/2 a0 1.2 10-8 cm/sec2 ? L
c2/6 This calls for non-locality as the force
falls slower than 1/r2
79
Fits to data
Galaxy rotation curves
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• The MOND formula does embarrassingly well!
• Could MOND be a consequence of quantum gravity?
• In particular since it suggests non-locality,
  could it
• be non-locality from quantum gravity?
• Basic idea
• The low energy limit of quantum gravity is a
  bi-metric theory
• (Markopoulou)

83
Bi-metric theories as the low energy limit of
quantum gravity Usual bimetric theories
have two classical metrics, differing by other
degrees of freedom gab f2 (qab Ba Bb
) qab satisfies something like einstein
eqs propagation of matter is determined by
gab. The proposal is that the difference arises
from mismatch of macro and microlocality.
84

• Bi-metric theories as the low energy limit of
  quantum gravity
• Markopoulou, Premont-Schwarz, ls to appear
  
• From a given quantum gravity state Y gt we
  extract two metrics
• Micro-metric matches geometry operators
• lt Y V Y gt and lt YA Y gt
• treats non-local links the same as local links
• satisfies approximate Einstein equations
• Macro-metric derived from propagation of matter
• ignores non-local links beyond matter
  scale.

85
Recall Spherically symmetric, static weave
Consider a set of N spherical spheres, between
which there are shells. This gives rise to a list
of areas g Ai, Vi . Gg gt is a weave state
that matches this
But there are non-local weaves that equally well
satisfy these conditions
86
The macro metric counts local and non-local edges
differently Rules 1) Macro and micro
metrics agree for local weaves 2) Macro metric
gives less weight in areas for non-local
edges and less weight in volume for ends of
non-local edges. 3) Both are static.
The disagreement about areas leads to a mapping
r and r refer to the same physical surface, given
different areas by the two metrics The
non-locality does not affect the other
components, so the lapse is
87
The macrometric determines orbits of stars
according to
To reproduce the observations (MOND law) we need
But the micrometric must be approx Schwarzchild,
n2 1 - 2 GR/r
r02 2GML r gt r for r gt r0
which tells us
Can the distribution of non-local links be chosen
to reproduce this, keeping the macro-spatial
geometry flat to zeroth order in
GM/r? YES (Note an upper cutoff rlt R er0 )
88
C ( r ) dr number of outgoing non-local links
crossing the shell at r. D ( r ) dr
number of ingoing non-local links crossing
the shell at r. Da0 area deficit from a
non-local edge Dv0 volume deficit from a
non-local edge
89
Conclusions Non-locality does not necessarily
kill a theory, it may be hard to observe
directly. Non-local links leads to a new
unification of matter with geometry and
forces. Maybe it is hard to derive classical GR
as the low energy limit because the low energy
limit is a bimetric theory?? Bimetric theory can
roughly account for effects of non-local links in
semiclassical or weave states. Non-locality,
modeled by such a bimetric theory, might be able
to account for observed astrophysical
deviations from Newtons laws.
90
THE END