Against symmetry Lee Smolin Perimeter Institute for Theoretical Physics

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Against symmetryLee SmolinPerimeter
Institute for Theoretical Physics

• Platonism verses Relationalism
• What physicists mean by relationalism
• General relativity is a (partly) relational
  theory
• Relational space and time in quantum gravity
• Relationalism and reductionism
• The link to Darwin
• Relational quantum theory
• Conclusions

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Two traditions in the search for fundamental
physics
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The Platonic tradition There is another realm in
which the laws are revealed in their most
perfect form. Symmetry perfection Lack of
symmetrydecaydistance from the perfect realm
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The Platonic tradition There is another realm in
which the laws are revealed in their most
perfect form. Symmetry perfection Lack of
symmetrydecaydistance from the perfect realm
A symmetry is a substitution of one entity for
another that does not change any physical
property of either.
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The Platonic tradition There is another realm in
which the laws are revealed in their most
perfect form. Symmetry perfection Lack of
symmetrydecaydistance from the perfect
realm In its modern version The perfect realm
is found in the limit of short distance of high
energy The imperfect realm of our experience is
the result of symmetry breaking A more unified
theory is one that has more symmetry Elementary
particles are classified by how they transform
under the symmetry. The ground state has as much
symmetry as possible. There is a spacetime
background which is characterized by maximal
symmetry.
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The Leibnizian tradition The principle of
identity of the indescrernible implies that
there are no two distinct entities with the same
properties. Hence when the laws of nature are
expressed in terms of fundamental entities there
can be no symmetries. This implies There are
no absolute properties defined with respect to
an eternally unchanging background. Instead,
each existing entity has relational properties,
given by their relation to all the rest.
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Leibnizian
Platonic
Space absolute, eternal emergent,
relational, background
evolving Properties defined with respect
all defined relationally to the
background Dynamics background
background dependent independent Symmetr
ies maximal none Classical
Newtonian general relativity theory
dynamics Present string theory loop
quantum gravity, Incarnation causal sets,
dynamical triangulations, NCG etc.
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The search for a complete theory by the
background dependent route. This has been the
main pre-occupation of theoretical physicists the
last 40 years. It is now pretty clear that we
have failed. Why we have failed is a question
that may be of interest for philosophers. The
big ideas have been 1) unification. All
elementary particles and forces arise from
different states or solutions of one elementary
entity. 2) symmetry Unification is to be
achieved by increasing the symmetry of physical
law (for example by increasing the dimension.)
Our world then corresponds to one particularly
asymmetric solution to symmetric physical laws.
First try unified field theory. Einstein,
Weyl, Kaluza, Klein, 1920-1955 Second try
string theory. 1984-2005
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The big hope There exists exactly one
consistent unified theory of all the
interactions and particles. The present
evidence There is evidence that string theories
(on fixed backgrounds) are consistent to 2nd
order in a certain approximation scheme. There
is evidence that there are at least 10500
distinct string theories, which at least to low
order provide unifications of gauge
fields, gravity and fermions, consistent with
positive cosmological constant. However, of the
much smaller number that are understood in
any detail, all make predictions that disagree
with observations. It has been conjectured
that all string theories are unified in one
big background independent theory M theory. But,
in spite of much effort by many smart people,
this theory has never been written down.
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Another big hope The more things are unified,
the most symmetry the theory has, and the more
unique it should be and the fewer free parameters
it should have. The results to date The
standard model of elementary particle physics 20
free parameters Its simplest supersymmetric
extension 125 free parameters The
number of distinct string theories that could
reproduce them 10500 So it appears that the
more symmetry and the more unification, the more
free parameters and the less uniqueness. WHY?
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The background dependent approach has one more
move to play The anthropic hope There are a
vast number of unified theories, and a vast
number of regions of the universe where they may
act. Out of all of these, there will be a very
small fraction where the laws of physics allow
the existence of intelligent life. We find
ourselves in one of these. Because the number
of universes and theories is so vast, theory can
make no prediction except those that follow from
requiring our own existence. (Susskind,
Schwartz, Douglas, Linde, Polchinski and
others...) The result is a reducto ad absurdum
of taking the background dependent approach, in
which, recently, good people have found no
alternative but to seriously argue for the
adequacy of theories that make no falsifiable
predictions. Can we do better by going back and
taking the relational approach more seriously?
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My main theme We should believe
relationalism, in the sense I will define it, not
just because there are good philosophical
arguments for it (Leibniz, Mach, etc...) but
because it leads to theories that are more
tightly constrained, and hence more
falsifiable. I will describe two (3, if time)
contemporary examples of this 1) Quantum
gravity 2) The search for a complete theory of
nature. 3) Is there a quantum theory for
systems like the universe that contain their
own observers?
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My main theme We should believe
relationalism, in the sense I will define it, not
just because there are good philosophical
arguments for it (Leibniz, Mach, etc...) but
because it leads to theories that are more
tightly constrained, and hence more
falsifiable. I will describe two (3, if time)
contemporary examples of this 1) Quantum
gravity 2) The search for a complete theory of
nature. 3) Is there a quantum theory for
systems like the universe that contain their
own observers? But first, we need a more precise
definition of relationalism.
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• What do physicists mean by relationalism?
• The world is made of a large number of entities
  or events
• How do they get their properties?

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• What do physicists mean by relationalism?
• The world is made of a large number of entities
  or events
• How do they get their properties?
• In an absolute scenario, there is an external and
  static entity, such as Newtons absolute space,
  and properties of elementary particles are
  defined individually in terms of their relations
  to the absolute entity.
• Hence, a particle in Newtons absolute space has
  the same properties whether it is one of many or
  the only thing in the universe.
• The absolute entities make up the background.

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• What do physicists mean by relationalism?
• The world is made of a large number of entities
  or events
• How do they get their properties?
• In an absolute scenario, there is an external and
  static entity, such as Newtons absolute space,
  and properties of elementary particles are
  defined individually in terms of their relations
  to the absolute entity.
• Hence, a particle in Newtons absolute space has
  the same properties whether it is one of many or
  the only thing in the universe.
• The absolute entities make up the background.
• The most basic statement of relationalism is
• R1 There is no background

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How then do we understand the properties of
elementary particles? The relational view
posits that R2 The fundamental properties of the
elementary entities consist entirely in
relationships between those elementary
entities.
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How then do we understand the properties of
elementary particles? The relational view
posits that R2 The fundamental properties of the
elementary entities consist entirely in
relationships between those elementary
entities. Examples of purely relational
systems Graph
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How then do we understand the properties of
elementary particles? The relational view
posits that R2 The fundamental properties of the
elementary entities consist entirely in
relationships between those elementary
entities. Examples of purely relational
systems Graph Partially ordered set
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How then do we understand the properties of
elementary particles? The relational view
posits that R2 The fundamental properties of the
elementary entities consist entirely in
relationships between those elementary
entities. Examples of purely relational
systems Graph Partially ordered
set Example of a partly relational system
knots and links
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What is time in a relational theory? R3 The
relationships are not fixed, but evolve according
to law. Time is nothing but changes in the
relationships, and consists of nothing but their
ordering. Relationalism is also a research
strategy Relational strategy Seek to make
progress by identifying the background
structures in our theories and removing them,
replacing them with relations between physical
entities which evolve subject to dynamical law.
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Summary relationalism according to
physicists R1 There is no
background. R2 The fundamental properties of the
elementary entities consist entirely in
relationships between those entities. R3 The
relationships are not fixed, but evolve according
to law. Time is nothing but changes in the
relationships, and consists of nothing but
their ordering. Relational strategy Seek
to make progress by identifying the background
structures in our theories and removing them,
replacing them with relations which evolve
subject to dynamical law. absolute vrs
relational background dependent
vrs background independennt
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General relativity is a partly relational theory
Layers of structure Dimension Topology
M Differential structure Metric and
fields gab, f In GR M is fixed.
gab and f describe relational
information. KEY POINT A physical spacetime is
NOT modeled by a manifold, metric, and fields,
but by an equivalence class of manifolds and
metrics, which are equivalent under any
diffeomorphism !! A diffeomorphism is a smooth
map from M to itself that takes differential
functions to differential functions.
q
f
p
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• What information is coded inside an
• equivalence class?
• Not fields at points. because physical points are
• only identified by what happens there.
• The causal structure. i.e. which events are
  causally related to which?
• The measure. i.e. what is the volume of each set
  defined by the causal structure?
• It can be shown that the information in a
  spacetime
• M, gab, f is completely characterized by the
  causal structure and the measure.
• Hence, once the dimension, topology and diff
  structure are fixed,
• the physical content of GR is about the causal
  relations among physical events.

q
f
p
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3. Relational space and time in quantum
gravity Conventional quantum mechanics and
quantum field theory (QFT) are background
dependent theories. Background structures
background geometry, inner product, external
clocks and observers Hence there are two
options Background dependent give up
relationalism, and quantize gravitational waves
on fixed backgrounds, using conventional QFT
methods. perturbative quantum GR, string
theory... Background independent Find a way to
define a quantum theory which is relational and
applies to relational theories. causal sets,
loop quantum gravity, dynamical triangulations
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• A purely relational approach to quantum
  spacetime causal sets
• Def A causal set is a finite partial order
• a --gt b means a causally precedes b.
• Postulates
• A quantum spacetime history, h, is nothing but a
• causal set.
• The dynamics is given by a rule that assigns a
  quantum
• amplitude Ah, a complex number, to each
  history.
• The amplitude to go from initial to final state
  is given by the
• sum over amplitudes for each history that does
  so.

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• The motivation for the causal set approach
• The physical information in GR (apart from M) is
  coded in the causal relations amongst events.
• But quantum spacetimes should be discrete.
• A classical spacetime can be approximated by a
  causal set.
• Def A causal set C approximates a spacetime
  M,gab when
• there is an embedding C --gt M,gab that
  preserves the causal structure, with one event in
  the image per Planck volume.
• But there is a problem

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The inverse problem Every classical spacetime
M,gab can be approximated by a causal set,
and in many ways.
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The inverse problem Every classical spacetime
M,gab can be approximated by a causal set,
and in many ways.
But for almost no causal set C is there a
spacetime M,gab of low dimension, that it
approximates.
?
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This is an example of a more general inverse
problem facing any discrete approach to quantum
gravity
Its easy to approximate smooth fields with
discrete structures.
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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,
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• Loop quantum gravity provides a robust method
  for the
• quantization of diffeomorphism invariant
  theories.
• Consider a classical gravitational theory, T,
  whose histories are
• described as diffeomorphism equivalence class of
  metrics and fields,
• (M, gab, f), .
• Assume that
• The topology and dimension of spacelike surfaces,
  ?, are fixed.
• The metric and fields have dynamics given by the
  Einstein
• equations or some natural extension.

Note that the dynamics can be expressed in an
equivalent formulation in which the configuration
space is that of a gauge field Aa on a spatial
manifold and the metric information is in the
electric field.
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The fundamental theorem Consider a background
independent gauge theory, compact Lie group G on
a spatial manifold S of dim gt1. No metric!!
(GSU(2) for 31 gravity) There is a unique
cyclic representation of the algebra generated
by Wilson loops and electric flux in which the
Hilbert space carries a unitary rep of the
diffeomorphism group. Lewandowski, Okolo,
Sahlmann, Thiemann Fleishhack (LOST
theorem)
This means that there is a unique diffeomorphism
invariant quantum quantum theory for each G.
Ashtekar GR is a diffeomorphism invariant
gauge theory!! Hence this class of theories
includes loop quantum gravity and spin foam models
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• This gives rise to causal spin network theories
  
• Pick an algebra G
• Def G-spin network is a graph G with edges
  labeled by representations of G and vertices
  labeled by invariants.
• Pick a differential manifold S.
• G an embedding of G in S, up to
  diffeomorphisms
• Define a Hilbert space H
• G gt Orthonormal basis element for each G
• Define a set of local moves and give each an
  amplitude
• A history is a sequence of moves from an in state
  to an out state
• Each history has a causal structure

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• Basic results of loop quantum gravity
• 1) The quantum spacetime is discrete in that each
  node of the graph
• corresponds to a finite quanta of spatial
  volume. The operators
• that correspond to volumes, areas and lengths
  are finite, and
• have discrete spectra with finite non-zero
  minimal values.
• Hence a graph with a finite number of nodes and
  edges defines
• a region of space with finite volume and area.

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• 3) Any history of the quantum theory is defined
  by a series of
• local moves on graphs that take the initial
  state to the final
• state. The set of local moves in each history
  define a causal set.
• 4) The amplitudes for local moves that follow
• from the quantization of the Einstein equations
• are known in closed form. The sums over those
• amplitudes are known to be ultraviolet finite.

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• 5) Similarly, the quantum Einstein equations in
  the Hamiltonian
• form have been implemented by exact operator
  equations on
• the states. Many exact solutions are known.
• The entropy of black holes is understood exactly
  in terms of
• the quantum geometry of horizons.

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• It has recently been proven that cosmological
  singularities
• bounce, so the evolution of the universe
  continues through
• apparent classical cosmological singularities.
  This has led
• to a prediction for an effect, observable with
  current CMB
• data.
• 8) These theories have generically
• excitations whose coherence is
• maintained by topological
• conservation laws. These are
• candidates for elementary particles.
• 9) There are known explicit candidate ground
  states, whose
• excitations reproduce the physics of quantum
  fields and
• linearized gravitational waves on fixed
  backgrounds.

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Open problems of loop quantum gravity Classical
limit Find the quantum state which is in fact
the ground state of the theory and show that it
reproduces quantum field theory and classical GR
from its excitations. Do science Make
predictions for doable experiments that can test
the theory up or down. Remove the remaining
background dependence The results so far
defined depend on the fact that the dimension and
topology, ? of the spatial manifold is fixed, so
that the graphs are embedded in ?. This helps by
lessoning the inverse problem. Can this be
removed-and the inverse problem solved-so that
all the structure that was background for
previous theories, including dimension and
topology, is explained as following from
solutions to a relational theory?
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The most important news It is possible to probe
the Planck scale experimentally, to search for
genuine quantum gravity effects. The reason The
discrete structure of space and time leads to
corrections to energy momentum relations and
(possibly) to the actions of the Loretz
transformations at short distances E2 p2
m2 a lp E3 These are observable, and a is
expected to be measured or bounded in experiments
now in progress AUGER ultra high energy cosmic
rays GLAST Gamma ray busts (because of a
resulting energy dependence of the speed of
photons.) Loop quantum gravity may provide
robust predictions for these effects. It does in
21 dimensions, and there are recent calculations
that give predictions for them in 31
dimensions, that depend on the choice of ground
state.
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• Lessons for the absolute/relational debate
• Loop quantum gravity is the most successful
  background
• independent quantum theory of gravity. It works
  by being
• conservative and sticking to the principles of GR
  and QM.
• ?Thus LQG is partly relational, in exactly the
  same way that GR
• is partly relational the dimension, topology and
  matter fields are
• fixed, the metric of spacetime is described
  quantum mechanically
• in purely relational terms, in terms of evolving
  labeled graphs
• embedded in the spatial topology.
• ?The main barrier to making an entirely
  relational theory of
• quantum spacetime appears to be the inverse
  problem.
• But even so, loop quantum gravity, as a partly
  relational theory is
• more tightly constrained, and more testable than
  non-relational
• alternatives.

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• Reductionism vrs relationalism
• Common sense reductionism When a system has
  parts, it makes sense to base an understanding of
  it on the laws that the parts satisfy, as well as
  on patterns that emerge from the exchanges of
  energy and information among the parts.
• But this has a built in limit What do we do
  when we get to
• elementary entities that have no parts?
• How do we explain the properties of the
  elementary particles?
• Two options
• In a background dependent theory the properties
  of the elementary particles are given by their
  relations to the background.
• In a background independent theory the
  properties of the elementary particles can arise
  only from their relations to each other.

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A relational complete theory must proceed
differently. Its guiding principle must be
asymmetry rather than symmetry. WHY? Leibnizs
principle of the identity of the indiscernible
If two entities have the same relations to the
rest, they are to be identified. Each individual
entity must then have a unique set of relations
to the rest. The fundamental entities in
spacetime are the events. The relation of an
event to the others is coded in the information
that arrives to it from the past. We may call
this the view of the event. Spacetime must be so
asymmetric that there are no two events with
identical views. The universe cannot have any
symmetries The universe cannot be in thermal
equilibrium
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Hence, a relational complete theory must have
mechanisms that drive the universe away from
symmetry and equilibrium. Interestingly,
gravity does both these things. (This is
interesting because by Einstein gravity is the
force that exists because space and time are
relational.) Are there others?
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Hence, a relational complete theory must have
mechanisms that drive the universe away from
symmetry and equilibrium. Interestingly,
gravity does both these things. (This is
interesting because by Einstein gravity is the
force that exists because space and time are
relational.) Are there others? Natural
selection.
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• Hence, a relational complete theory must have
  mechanisms that drive
• the universe away from symmetry and equilibrium.
• Natural selection is in some senses relational
  theory
• The properties natural selection acts on, such as
  fitness, are relational
• quantities, they are meaningless for a world with
  a single species.
• Natural selection follows the relational
  strategy. Properties such as
• species were believed to be eternal, and a
  priori become
• relational and historical.
• Could natural selection or something like it
  account for the
• choice of physical laws and their parameters?
• Could it account for the anthropic observation?
  Our universe is
• much more complex (in for example its
  astrophysics and chemistry)
• than most universes with the same laws but
  different values of the
• parameters of those laws (including masses,
  charges, etc.)

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• To apply natural selection to a system it must
  have
• A space of parameters for each entity, such as
  the genes.
• ?A mechanism of reproduction.
• ?A mechanism for those parameters to change, but
  slightly,
• from parent to child.
• ?Reproductive success depends strongly on the
  parameters.
• This can be applied to cosmology
• The space of parameters is the space of
  parameters of the standard
• models of physics and cosmology. This leads to
  the term the string
• theory landscape.
• ?The mechanism of reproduction is the formation
  of black holes.
• ?We may conjecture that the low energy parameters
  do change in
• such a bounce.
• The mechanism of differentiation is that
  universes with
• different parameters will have different numbers
  of black holes.

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• These lead to genuine falsifiable physical
  predictions
• Most ways to change the parameters of the
  standard models of particle
• physics and cosmology should have fewer black
  holes.
• There can be no neutron stars with masses larger
  than 1.6 times the
• mass of the sun.

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In these instances, the relational theory turns
out to be more predictive, and more falsifiable
than background dependent theories. WHY? The
difference is between 1) Explanations that
refer ultimately to a network of relationships
amongst equally physical entities, which evolve
dynamically. vrs 2) Explanations that refer to
relationships between dynamical entities and an a
priori, non-dynamical, background. The former
are more constrained, hence harder to construct.
More of what is observed is subject to law, as
there is no background to be freely chosen.
Hence, relational, background independent
theories are more testable, and more
explanatory.
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Relationalism and quantum theory
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The problem of quantum cosmology

• The measurement problem is still unsolved after
  80 years.
• It gets worse when the observer is inside the
  system
• Attempts to make sense of quantum cosmology
• Many worlds
• Fails because of the preferred basis problem.
• Decoherent histories
• But, almost no decohering sets of histories are
• semiclassical (Dowker and Kent)
• Is there an alternative?
• Can relatonalism help?

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• Relational quantum theory
• (Crane, Rovelli, Markopoulou)
• Formalize Bohrs flexible boundary between system
  and
• observer.
• Basic postulate There are as many Hilbert spaces
  and
• observables algebras as there are possible
  divisions of the
• universe into system and observer. Each
  describes the
• information availabel to an observer about the
  system
• outside of their boundary.
• Slogan Not one quantum state for many
  universes, but one
• universe described by many quantum states.

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• The most developed formalism
• Markopoulous quantum causal histories
• Ties the structure of the many Hilbert spaces to
  causal structure.
• Each observer has an incomplete view of the
  system because
• of the causal structure.
• Hence there is a Hilbert space for each event.
• To each event in a causal structure is a density
  matrix
• describing information available at that event.
• To each causal relation is a (CP) map,
  incorporating
• the dynamics, between the Hilbert spaces
• Problem In GR, the causal structure is
  dynamical.
• But here the quantum structure is tied to a
  single causal structure.

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• There are two ways to resolve this
• The causal structure of the emergent classical
  spacetime is
• different from that of the fundamental theory
  (Markopoulou).
• 2) The quantum theory is an approximation to
  something else,
• valid only for small subsystems of the
  universe.
• The global theory must then be a hidden variables
  theory.
• New idea Relational hidden variables the hidden
  variables are
• not more complete descriptions of an individual
  particle, they
• are so far unknown relations between each pair of
  particles.
• As we cannot control them we must average over
  them
• Hence, quantum theory.

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Hence, we have seen in two significant examples
that We should believe relationalism, in the
sense of background independence, not just
because there are good philosophical arguments
for it (Leibniz, Mach, etc...) but because it
leads to theories that are more tightly
constrained, and hence more falsifiable. And
we have seen that relationalism offers hope
for the still unresolved problems in the
foundations of quantum mechanics, by giving rise
to alternatives not yet discredited.
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Leibnizian
Platonic
Space absolute, eternal emergent,
relational, background
evolving Properties defined with respect
all defined relationally to the
background Dynamics background
background dependent independent Symmetr
ies maximal none Classical
Newtonian general relativity theory
dynamics Present string theory loop
quantum gravity, Incarnation causal sets,
dynamical triangulations, NCG etc.
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Plank scale phenomenology
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Plank scale phenomenology What is the symmetry
of the ground state of quantum gravity?
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Plank scale phenomenology What is the symmetry
of the ground state of quantum gravity? What is
the fate of Lorentz and Poincare invariance in
the limits of low energies, large universe,
small cosmological constant?
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• What is the fate of Lorentz and Poincare
  invariance in the limits of low energies, large
  universe, small cosmological constant?
• There are three possibilities
• 1 brokenthere is a preferred frame
• 2 nothing new realized linearly as in ordinary
  QFT
• 3 realized non-linearly, i.e there is relativity
  of inertial
• frames, but the lorentz transformations
  become
• non-linear at the Planck scale

61

• What is the fate of Lorentz and Poincare
  invariance in the limits of low energies, large
  universe, small cosmological constant?
• There are three possibilities
• 1 brokenthere is a preferred frame
• 2 nothing new realized linearly as in ordinary
  QFT
• 3 realized non-linearly, i.e there is relativity
  of inertial
• frames, but the lorentz transformations
  become
• non-linear at the Planck scale
• 1 and 3 lead to modifications of dispersion
  relations
• E2 p2 m2 a lp E3 b lp2 E4
• 3 leads also to non-linear conservation laws
• These are experimentally distinguishable!!!

62

• What is the fate of Lorentz and Poincare
  invariance in the limits of low energies, large
  universe, small cosmological constant?
• There are three possibilities
• 1 brokenthere is a preferred frame
• 2 nothing new realized linearly as in ordinary
  QFT
• 3 realized non-linearly, i.e there is relativity
  of inertial
• frames, but the lorentz transformations
  become
• non-linear at the Planck scale
• 1 and 3 lead to modifications of dispersion
  relations
• E2 p2 m2 a lp E3 b lp2 E4
• 3 leads also to non-linear conservation laws
• These are experimentally distinguishable!!!

63

• Could lorentz invariance be broken in quantum
  gravity?
• The hamiltonian constraint enforces invariances
  under
• Local changes of slicing ? relativity of inertial
  frames
• So there can be no explicit preferred frame in
  LQG...
• (There could be spontaneous breaking as in
  Jacobson et al)

64

• Could lorentz invariance be broken in quantum
  gravity?
• The hamiltonian constraint enforces invariances
  under
• Local changes of slicing ? relativity of inertial
  frames
• So there can be no explicit preferred frame in
  LQG...
• (There could be spontaneous breaking as in
  Jacobson et al)
• But there is a discreteness scale Ep

65

• Could lorentz invariance be broken in quantum
  gravity?
• The hamiltonian constraint enforces invariances
  under
• Local changes of slicing ? relativity of inertial
  frames
• So there can be no explicit preferred frame in
  LQG...
• (There could be spontaneous breaking as in
  Jacobson et al)
• But there is a discreteness scale Ep
• Do all observers agree on it?
• Doesnt this violate Lorentz invariance?

66
The lorentz transformations preserve a velocity,
c, but not an energy.
67
The lorentz transformations preserve a velocity,
c, but not an energy. Could we modify them so
that they preserve a single energy as well?
68
The lorentz transformations preserve a velocity,
c, but not an energy. Could we modify them so
that they preserve a single energy as
well? Thus, the Plank energy could be observer
independent.
69

• This leads to doubly special relativity (DSR)
• (Amelino-Camelia,Magueijo,ls...)
• Principles
• Relativity of inertial frames
• There is an invariant speed c and an invariant
  energy Ep
• For E ltlt Ep c is the speed of light.
• This implies the lorentz transformations are
  realized non-linearly, so as to preserve the
  energy scale Ep
• Momentum space is curved
• spacetime geometry is non-commutative.
• Energy-momentum conservation non-linear
• Modified energy-momentum relations

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Conjecture DSR is realized in the low energy
limit of LQG
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• Conjecture DSR is realized in the low energy
  limit of LQG
• Evidence for Double Special Relativity in Loop
  Quantum Gravity
• Realized precisely in 21 gravity with matter
  hep-th/0307085
• Occurs naturally as L ?0 limit hep-th/0306134
• Algebra of observables quantum deformed for
  finite L with
• k6p/G L
• Limit L ?0 is deformed, k-Poincare algebra
• This is explicitly realized in the behavior of
  perturbations
• around the Kodama state. hep-th/0209079

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• Some results on the low energy limit
• Candidate ground states exist
• Approximate flat space or slowly varying (on
  Planck scale) spatial geometry
• Eigenstates of geometrical observables (weaves)
• Coherent sates
• Kodama state (dS or AdS)
• Excitations of them which satisfy the constraints
• to leading order in lp are gravitons for l
  gtgt lp,
• When coupled to matter QFT on background
  recovered
• (finite due to Planck scale discreteness)
• Energy-momentum relations get corrections
• E2 p2 m2 a lp E3 b lp2 E4
• Pullin Gambini, Alfaro, Morales-Técotl
  Urrutia, Thiemann and Sahlman, ls

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• Planck scale modified dispersion relations are
  experimentally observable
• E2 p2 m2 a lp E3 b lp2 E4
• One effect of a modified energy momentum relation
  
• can be to raise the threshold for pion
  production from protons
• scattering from microwave photons. The
  threshold is predicted to be at
• 3 1019 ev. There is evidence from AGASA the
  cutoff is not seen.

AGASA
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Some experiments see anomalous events AGASA,
Sugar Some dont HIRES We wait for AUGER.
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• More Planck scale experimental probes
• Energy dependent speed of light. vc(1 a lp
  E b lp2 E2 )
• Accumulates for long distances
• Observable in Gamma Ray bursts.
• present limits have a lt 1000
• next satellite, GLAST will put limits a lt 1 in
  2005-7
• Tev photons from blazars, controversial whether
  anomalies exist.
• Rotation of plane of polarization, predicted by
  Gambini-Pullin
• The effect is energy dependent, so polarization
  washes out
• Radio galaxies Not seen!!!
• Polarization observed in Gamma Ray Burst 021206
• Colburn,W. Boggs, S. E. Nature 423,
  415417 (2003).
• This implies a - a- ltlt 1
• Mitrofanov, Nature, VOL 426 13 Nov 2003
• HENCE, Gambini-Pullin ansatz is ruled out
  experimentally!!!

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Beginning last year, one reads papers in
Nature in which experimental results are used to
rule out predictions which follow from ansatzs
for the ground state of quantum gravity. Hence
quantum gravity has become experimental science.
Note Gambini Pullin ansatz is ruled out, but
not the theory itself.
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• Conclusions
• There are obstructions to recovering smooth, low
  dimensional manifolds as approximations to
  combinatorial structures such as spinnets and
  spinfoams.
• Can we get some physics from them?
• In particular locality is unstable. Hard to get
  low energy and microscopic notions of locality to
  coincide.
• Can we use these for non-local hidden variables
  and recover quantum mechanics of subsystems from
  statistical mechanics of spin nets or foams?
• If we can, we can resolve the foundational
  problems of quantum cosmology, by making use of
  an obstacle to spin foams having a good low
  energy limit.
• The first indications are positive, but much to
  do.