God is Outsourced: Leonard Susskind & Lee Smolin

[Jack Sarfatti]

Lecture 9

What about God? As Lenny Susskind, in the footsteps of Darwin and the
French Rationalists says "I have no need of that hypothesis." The
incredible fine-tuning of the universe is evidence for an infinity of
parallel pocket universes - an actual ensemble not a virtual one. Thus
the Copernican Principle is married to the Weak Anthropic Principle.
What about a time traveling Star Trek Q "Skinwalker" from Michio Kaku's
"Level 4" Civilization able to Dyson metric engineer the fabric of space
time - including escape routes to other parallel pocket universes next
door? Yes, that's the evidence provided by the UFOs.

Smolin wrote:

“Hence we see explicitly that in these theories the properties of
particles are determined by their relationship to the background.
However, notice that something new is happening here, which is quite
important for the relational/absolute debate. The point of spontaneous
symmetry breaking is that the choice of background is a consequence of
the dynamics and can also reflect the history of the system. Hence
theories that incorporate spontaneous symmetry breaking take a step in
the direction of relational theories in which the properties of
elementary particles are determined by their relationships with a
dynamically chosen vacuum state. But if the choice of vacuum state is to
be determined dynamically, the fundamental dynamics must be formulated
in a way that is independent of a choice of background. That is, the
more spontaneous symmetry breaking is used to explain distinctions
between particles and interactions, the more the fundamental theory must
be background independent.

In conventional quantum field theories this is realized to some extent.
But the background of spacetime is generally not part of the dynamics.
But in string theory the choice of solution can involve the geometry and
topology of space and time. Hence, we arrive again at the necessity to
ground string theory on a background independent theory.

6.1 The challenge of the string theory landscape
Before we turn to see how to approach the problem of unification from a
background independent theory, we should try to draw some lessons from
the status of the search based on background dependent methods.

We can begin by asking what tools have string theorists used to study
the problem of unification? A principle tool invoked in much recent work
in string theory is effective field theory. An effective field theory is
a semiclassical field theory which is constructed to represent the
behavior of the excitations of a vacuum state of a more fundamental
theory below some specified energy scale. They have the great advantage
that one can study a theory expanded around a particular solution,
treating that solution as a fixed background. This lets us use many of
the intuitions and tools developed in the study of background dependent
theories. But there are also disadvantages to the use of effective field
theory. One is that the threshold of evidence required to establish as
likely a string background is weakened. Whereas it was at first thought
necessary to prove perturbative •finiteness around the background to all
orders, it is now thought sufficient to display a classical solution to
an effective field theory, which is some version of supergravity coupled
to branes. But no effective field theory can stand on its own, for these
are not consistent microscopic theories. The reliability of effective
field theory must always be justified by an appeal to its derivation
from that more fundamental theory. In the applications where it was
first developed, effective field theory is derived as an approximation
to a more fundamental theory. This is true in QCD and the standard
model, as well as in its applications to nuclear physics and condensed
matter physics. We can see this easily by considering cases in which we
believe there is no good fundamental theory, such as interacting quantum
field theories in 5 or more dimensions. We can construct effective field
theories to our heart’s content to describe the low energy physics in
such contexts. These may be approximations to cutoff quantum field
theories, for example, based on lattices. But they are unlikely to be
approximations to any Poincare invariant theories. This is because there
is strong evidence that the only Poincare invariant quantum field
theories in more than 4 spacetime dimensions are free.

However, in string theory, effective field theory is being used in a
context where we do not know that there is a more fundamental theory.
That more fundamental theory, if it exists, is the conjectured
background independent unification of the different string theories. But
since we do not have this theory, either in the form of a set of
equations or principles, we cannot be assured that it exists. Hence, by
relying on effective field theory we may get ourselves in the situation
in which we are studying semiclassical theories which are not
approximations to anymore fundamental theory. But, nevertheless, if one
insists on confining investigations to background dependent methods,
there is little alternative to reliance on effective field theory. In
the absence of a derivation from a full quantum theory, one can still
posit that the existence of a consistent effective field theory is
sufficient to justify belief in a string background, and see where this
takes us. One requires a weak form of consistency, which is that
excitations of the solution, were they to exist, would be weakly
coupled. Not surprisingly, perhaps, this approach leads to evidence for
a landscape consisting of an infinite number of discrete string
backgrounds [4]. Even restricting the counting to backgrounds that have
positive vacuum energy and broken supersymmetry leads to estimates of
10^500 or more discrete vacua [5]. It is interesting to note that the
term “landscape” implies the existence of a function, h, the height,
such that the discrete vacua are at local minima of h. In the recent
literature, the height h is a potential or free energy. While it is
clear what is meant by this, it is perhaps worrying that the concept of
energy is problematic in a cosmological or quantum gravity context. This
is because, once the gravitational degrees of freedom are included, the
energy of cosmological spacetimes is constrained to vanish. All
cosmological solutions to diffeomorphism invariant theories have the
same energy: zero. There is in cosmology no ground state with zero
energy, solutions with different potential energies are no more or less
likely to exist, they just expand at different rates. Even if the
background geometry is assumed •fixed, energy and free energy are only
defined on a background that has a timelike Killing field. But what
could the height be, if not energy? The context which inspired the
original use of the term landscape in string theory[17], was
mathematical models of natural selection, in which the height h measures
the fitness, which is the number of viable (24) progeny of a state. The
term was introduced in [17] to evoke the methodologies by which fitness
landscapes are studied. However, in the recent string theory literature
on landscapes, the analogy to natural selection is not invoked. What
then is the height? If it is energy, then that implies the existence of
a fixed background, with a timelike Killing field. But what is the
background, when the space we are considering is a space of different
vacua, with different geometries and topologies? There seems to be a
confusion in which reference to a structure that depends on a fixed
background is being invoked in the description of the space of possible
backgrounds. Another way to see that the notion of a fixed background is
sneaking back into the theory is to consider the assumptions behind the
probabilistic studies of the landscape. There are, broadly speaking, two
kinds of methods that might be brought to bear to the study of
probability distributions on such landscapes of states. One may study
distributions that are in equilibrium, and hence static, or one may
study non-equilibrium and hence time dependent distributions. Almost all
the recent work on probability distributions in the string theory
landscape have taken the first kind of approach. Some, but not all, of
this work evokes what we may call 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 few predictions except those
that follow from requiring our own existence. The reliance on the
anthropic principle is unfortunate, because it can be shown that the use
of the anthropic principle cannot lead to any falsifiable predictions.
This is argued in detail in [6], to which the reader is referred. As a
result, one has to suspect that a search for a unified theory of physics
that in the end invokes the anthropic principle has reached a reducto ad
absurdum. Somewhere along the line, in the search for a unified string
theory, a wrong turn has been taken. It could be that the wrong turn is
that string theory is based on physical hypotheses that have nothing to
do with nature. But if this is not the case, some wrong direction must
have been taken in the path that led from the conjecture of a unique
unification within string theory to the present invocations of the
anthropic principle. We can see from the survey of the situation we just
made that the dilemma we have meaning they will have their own progeny
arrived at seems to involve trying to use background dependent notions,
like energy, to do physics in a setting that must be background
independent. For if there is a space of possible backgrounds, on which
we are to do dynamics, it is obvious that the form of dynamics we employ
cannot make reference to any given fixed background. Hence, it seems
reasonable to suggest that the wrong turn is the failure to search for a
background independent foundation for the theory. It is then interesting
to note that the invocation of static probability distributions harkens
back to the absolute perspective. To see this we can ask, what is the
time with respect to which the probability distribution is considered to
be static? It cannot be the time within a given spacetime background,
because the probability distribution lives on the space of possible
backgrounds. Single universes may evolve, and may come and go, but there
is hypothesized to be nevertheless a static and eternal distribution of
universes with different properties. It is this distribution, that
exists absolutely and for all time, that we must go for an explanation
of any properties of our universe. Thus, at the level of multiverses,
static distributions on landscapes have more in common with Aristotle’s
way of thinking about cosmology than it does with general relativity.

Is there then an alternative methodology for treating the landscape,
which would naturally arise from a background independent theory? I
would like to claim there is. The next sections are devoted to its
motivation and description.


7 A relational approach to the problems of unification and determination
of the standard model parameters

Let us then assume we agree on the need to formulate a unified theory in
a background independent framework. Even without having a complete
formulation of this kind in hand, it may be of interest to ask what
would a background independent approach to the problem of unification
look like? How would it address the problems raised in the last section?
To approach these questions we return to the question of how we are to
explain the properties of the elementary particles? In a relational
theory, as I explained earlier, the properties of the elementary
entities can have only to do with relations they have to other
elementary entities. Let us explore the implications of this. The first
implication is that any relational system with a large number of parts
must be complex, in the sense of having no symmetries. The reason is
Leibniz’s 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 elementary entities in general relativity are the events. An
event is characterized by the information coming to it, from the past.
We may call the information received by an event in spacetime, the view
of that event. It literally consists of what an observer at that event
would see looking out their backwards lightcone. It follows that any two
events in a spacetime must have different views. This implies that

1. There are no symmetries.

2. The spacetime is not completely in thermal equilibrium.

These are in fact true of our universe. The universe may be
homogeneous above the enormous scale of 300Mpc, but on every smaller
scale there is structure. Similarly, while the microwave background is
in thermal equilibrium, numerous bodies and regions are out of
equilibrium with each other. Julian Barbour and I call a spacetime in
which the view of each event is distinct a Leibniz spacetime. We note,
with some wonder, that the fact that our universe is not completely in
thermal equilibrium is due to the fact that gravitationally bound
systems have negative specific heat, and therefore cannot evolve to
unique equilibrium configurations. Furthermore, gravity causes small
fluctuations to grow that would otherwise be damped. This is why the
universe is filled with galaxies and stars. Thus, gravity, which as
Einstein taught us is the force that necessarily exists due to the
relational character of space and time, is at the same time the agent
that keeps the world out of equilibrium and causes fluctuations to grow
rather than to dissipate, which is a necessary condition for it to have
a completely relational description. There is a further consequence of
taking the relational view seriously. In a relational theory, the
relations that define the properties of elementary entities are not
static, they evolve in time according to some law. This means that the
properties by which we characterize the interaction of an elementary
particle with the rest of the universe are likely to include some which
are not fixed a priori by the theory, but depend on solutions to
dynamical equations. We can expect that this applies to all of the basic
properties that characterize particles such as masses and charges.

8 Relationalism and natural selection
How far can we go to a relational explanation of the properties of the
elementary particles in the standard model? While the anthropic
principle itself is not explanatory, it is useful to go back to its
starting point, which is an apparently true observation, which we may
call 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.) This requires explanation.
Unfortunately no principle has been found that explains the values of
the physical parameters (which can be taken to be the parameters of the
standard models of particle physics and cosmology.) Given recent
progress in string theory, there is no reason to expect such a principle
to exist. Instead, as the relational argument suggests, those parameters
are environmental, and can differ in different solutions of the
fundamental theory. We then require a dynamical explanation for the
anthropic observation. For it to be science, the explanation must make
falsifiable predictions that are testable by real experiments. There is
only one mode of explanation I know of, developed by science, to explain
why a system has parameters that lead to much more complexity than
typical values of those parameters. This is natural selection. It may be
observed that natural selection is to some extent part of the movement
from absolute to relational modes of explanation. There are several
reasons to characterize it as such.
•
Natural selection follows the relational strategy. Before it, properties
that characterize species were believed to be eternal, and to have a
priori explanations. These are replaced by a characterization of species
that is relational and evolves in time as a resultof interactions
between it and other species.

The properties natural selection acts on, such as fitness, are
relational quantities, in that they summarize consequences of relations
between the properties of a species and other species.

These properties are not fixed in advance, they evolve lawfully.

A relational system requires a dynamical mechanism of individuation,
leading to enough complexity that each element can be individuated by
its relations to the rest. Natural selection acts in this way, for
example, it inhibits two species from occupying exactly the same niche.
By doing so it increases the complexity, measured in terms of the
relations between the different species.

This suggests the application of the mode of explanation of natural
selection to cosmology. This has been developed in [17], and it is
successful in that it does lead to predictions that are falsifiable, but
so far not falsified. The idea, briefly, is the following. To apply
natural selection to a population, there must be:
•
A space of parameters for each entity, such as the genes or the phenotypes.

•
A mechanism of reproduction.

•
A mechanism for those parameters to change, but slightly, from parent to
child.

•
Differentiation, in that reproductive success strongly depends on the
parameters.


By simple statistical reasoning, the population will evolve so that it
occupies places in the parameter space leading to a typically large
reproductive success, compared to typical parameter values. (Note that
creatures with randomly chosen genes are dead.)

This can be applied to cosmology:
•
The space of parameters is the space of parameters of the standard
models of physics and cosmology. This is the analogue of phenotype. At a
deeper level, this is to be explained by a space analogous to genotypes
such as the space of possible string theories. This leads to the term
the string theory landscape.

The mechanism of reproduction is the formation of black holes. It is
long conjectured that black hole singularities bounce, leading to the
formation of new universes through new big bangs. There is increasing
evidence that this is true in loop quantum gravity. We may conjecture
that the low energy parameters do change in such a bounce. There are a
few calculations that support this[6]. The mechanism of differentiation
is that universes with different parameters will have different numbers
of black holes. This leads to a simple prediction: our universe has many
more black holes than universes with random values of the parameters.
This implies that most ways to change the parameters of the standard
models of particle physics and cosmology should have fewer black holes.
This leads to testable predictions. I’ll mention one here: there can be
no neutron stars with masses larger than 1.6 times the mass of the sun.
I will not explain here how this prediction follows, but simply note
that it is falsifiable (25). So far all neutron stars observed have
masses less than 1.45 solar masses, but new ones are discovered regularly.

9 What about the cosmological constant problem?
It is becoming clearer and clearer that the hardest problem faced by
theoretical physics is the problem of accounting for the small value of
the cosmological constant problem. The problem is so hard that it
constitutes the strongest arguments yet given for an anthropic
explanation, following an argument of Weinberg[42](26)

Given that background dependent theories have failed to resolve it, it
is important to ask whether background dependent approaches have done
any better? We mention several interesting results here: (25) Details of
the argument can be found in [17] and[6]. (26) See [6] for a summary,
references and critique.
•
There is an argument for the relaxation of the cosmological constant in
LQG, analogous to the Pecci-Quinn mechanism [43]. This relies on a
connection between the cosmological constant and parity breaking, which
is natural within LQG.
•
Volovik has argued, in a particular example, that if spacetime is
emergent from more fundamental quantum degrees of freedom, then there is
a dynamical mechanism which relaxes the ground state energy [44]. This
mechanism is missed if one formulates the theory in terms of an
effective field theory that describes only the low energy collective
excitations on a fixed background.

•
Dreyer argues that the cosmological constant problem is in fact an
artifact of background dependent approaches [22]. He proposes that the
problem arises from the unphysical splitting of the degrees of freedom
of a fundamental, background dependent theory into a background, which
has only classical dynamics, and quantum excitations of it. He presents
an example from condensed matter physics in which exactly this occurs.
In his model, one can calculate the ground state energy two ways: in
terms of the fundamental hamiltonian, which is a function of the
elementary degrees of freedom, and in terms of an effective low energy
hamiltonian which describes collective, emergent low energy degrees of
freedom. The zero point energy in the latter overestimates the ground
state energy computed in the fundamental theory.

•
The only approach to quantum gravity that predicted the correct
magnitude of the observed cosmological constant is the causal set theory
[45]. There it naturally comes out that a universe with many events has
a small cosmological constant. Whether the mechanism that works there
extends to other background independent approaches is an interesting
open question.


While all these results are preliminary, what is remarkable is that new
possibilities for resolving the cosmological constant problem appear
when the problem is posed in a background independent theory.

10 The issue of extending quantum theory to cosmology
Let us now turn to the third issue raised in the introduction, whether a
cosmological theory can be formulated in the same language as theories
of small parts of the universe, or requires a new formulation. As aspect
of this is the problem of quantum cosmology. In recent years new
proposals to resolve this stubborn problem have been formulated in the
context of background independent approaches to quantum gravity.

10.1 Relational approaches to quantum cosmology
In the last ten years several new proposals have been made concerning
the foundational issues in quantum cosmology, which have gone under the
name of relational quantum theories 27. These have been inspired by the
general philosophy of relationalism.
These approaches have been put forward, in slightly different ways, by
Crane, Rovelli and Markopoulou [46, 47, 51]. The mathematical apparatus
needed to formalize this view has been studied by Butterfieldand
Isham[49]. While they differ as to details, they agree that a quantum
theory of cosmology is not to be formulated in the language of ordinary
quantum mechanics. One way to state the problem is to ask how we
understand the quantum state: Is it a complete and objective description
of a physical system, in which case, how do we account for the
measurement problem? Or is it a description of the information or
knowledge that an observer has about a system they have isolated and
studied? If this is the case, can we apply quantum theory to
cosmology-or indeed to any system that contains its observers?

There is a hint of relationalism in Bohr, who argued for a view
something like the latter. Bohr always insisted that while there must be
a line between the system and observer, that line is flexible, it may be
drawn anywhere. This is frustrating for those who want to believe in a
realist interpretation of the quantum state. A realist would argue that
the observer and her instruments are physical systems. Consequently
there must be a description in which they are included in the system
being studied. Bohr replies there is no contradiction, because now we
are speaking of the knowledge a second observer has of a system
containing the first observer. According to Bohr then, each observer has
a different wave function, that describes the system they observe.
Relational approaches to quantum theory formalize this point of view.
Rather than taking the Everett/manyworlds view, and describing many
universes in terms of a single quantum state, they posit that it
requires many quantum states to describe a single universe. Each of
these quantum states corresponds to a way of dividing the universe into
two subsystems, such that one includes an observer. A relational
approach to quantum theory was proposed by Crane [46], in a paper that
anticipated some aspects of the holographic principle[48]. In that
paper, Crane proposed that there is no quantum state associated with the
universe as a whole. Instead, there is a quantum state associated with
every way of introducing an imaginary spatial boundary, splitting the
universe into two. By analogy with topological field theory, he proposed
that the Hilbert spaces on boundaries of 3+1 dimensional spacetime
should be built up out of state spaces of Chern-Simons theory. When
fully developed, this proposal became the very fruitful isolated horizon
approach to the quantum geometry and entropy of horizons. Rovelli then
developed a general framework for relational quantum theory [47]. The
approaches of Rovelli, however, left open the precise structure that is
to tie together network of Hilbert spaces and algebras necessary to
describe a whole universe. A template for such structure was given in
the work of Butterfield and Isham, who showed now the consistent
histories formulation could be interpreted in terms of a sheaf of
Hilbert spaces[49]. Markopoulou proposed that the structure tying
together the different Hilbert spaces is the causal structure of
spacetime[51]. In this formulation there is a Hilbert space for every
event in a quantum spacetime. The state at each event is a density
matrix that describes the quantum information available to an observer
at that event. There are consistency conditions that proscribe how the
flow of quantum information in a spacetime follows the causal structure
of that spacetime. This is a generalization of quantum theory, for there
need not be a quantum state associated with the whole system. (Indeed,
it is related to a large class of such generalizations studied by
Butterfield and Isham.) This leads to a relational formulation of the
holographic principle, sketched in [52]. The basic idea is that the
events are associated with elements of surface. Each corresponds to a
quantum channel, by which information •flows through from its causal
past to its causal future. The area of such a channel is defined to be a
measure of its channel capacity.

10.2 Relational approaches to going beyond quantum theory
Relational quantum theory gets us out of the paradoxes that arise from
trying to describe the universe with a single quantum state. Still,
there is, unfortunately, a problem with these approaches. This stems
from the fact that the system of quantum states depends on the causal
structure of spacetime being fixed. But in a quantum theory of gravity
one is supposed to take a quantum sum over all possible histories of the
universe, each with a different causal structure. This is to say that
relational quantum theories appear to be as background dependent as
ordinary quantum theory it is just that they differ in how they are
background dependent. Can there be a fully background independent
approach to quantum theory? I believe that the answer is only if we are
willing to go beyond quantum theory, to a hidden variables theory. I
would like in closing then to briefly mention work in progress in this
direction.

We know from the experimental disproof of the Bell inequalities that any
viable hidden variables theory must be non-local. This suggests the
possibility that the hidden variables are relational. That is, rather
than giving a more detailed description of the state of an electron,
relative to a background, the hidden variables may give a description of
relations between that electron and the others in the universe. The
possibility of a relational hidden variables theory is suggested by a
simple counting argument: In classical mechanics of N point particles,
in 3 dimensional space there are 6N phase space degrees of freedom. In
quantum theory this is described by a complex function on the 3N
dimensional configuration space-the wavefunction. But a relational
theory has in principle N^2 degrees of freedom, at least one for every
pair of particles. Most of these are unobservable, by any local
observer, because they involve relations between particles near to us
and those very far away. Thus, any working out of a relational theory
will have to treat them probabilistically. This will require a
probability distribution, which is a real function on N^2 variables. A
real function on N^2variables has much more information in it than a
complex function on 3N variables. Thus, one can imagine deriving quantum
mechanics for 3N variables from statistical mechanics for N^2 variables.
Such a theory would be a non-local hidden variables theory. This leads
to a simple conjecture
Perhaps all the extra information, N^2 as compared to N, necessary for a
completely relational theory, are the non-local hidden variables? In the
last few years two such relational hidden variables theories have been
written down. Markopoulou and I have proposed one [53], and Stephen
Adler [54], proposes another. In our theory the non-local hidden
variables are coded in a graph on N nodes, which is argued to arise from
the low energy limit of a relational theory like loop quantum gravity.
It is too soon to see if these theories will be successful. But they
offer hope that by taking relational ideas seriously may lead to a
successful attack on all five of the problems mentioned in the introduction.


11 Conclusions
In this talk I have described several partly relational, or background
independent, theories:
•
General relativity

•
Relational approaches to quantum gravity, including loop quantum
gravity, causal set models, causal dynamical triangulation models and
relational approaches to string/M theory.

•
Relational approaches to extending quantum theory to cosmology.


Each is partly successful. Several are more successful than less
relational alternatives. But none is completely successful and none is
completely relational. They are not completely relational because each
still has background structure, which is non-dynamical and must be
specified in advance.
However, I believe we do learn something very important from these
examples: In several instances, the relational theory turns out to be
more predictive, and more falsifiable than background dependent
theories. In particular, cosmological natural selection leads to
falsifiable predictions, which anthropic approaches to the landscape so
far do not. Furthermore, there is the very real possibility that the
Planck scale will be probed in upcoming experiments, such as GLAST and
AUGER[7]. Background independent theories appear to give predictions for
these experiments [41]. String theory cannot, because it takes the
symmetry of the background as input. Why is this the case? I only can
make some brief remarks here. The difference between relational and
non-relational theories is between:

1) Explanations that refer ultimately to a network of relationships
amongst equally physical entities, which evolve dynamically.
2)
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, it appears that relational, background independent
theories are more testable, and more explanatory.

This is the reason for my provocative hypothesis. If it is true than the
reason that string theory finds itself in the situation described in the
introduction is that no background dependent theory could successfully
solve the five key problems mentioned there. If this is true, then the
only thing to do is to go back and work on the less studied road of
relational theories. At the same time, I have tried here to explain the
key problems still faced by the relational road. Some of these have to
do with the problem of time. Others have to do with the inverse problem.
We saw it in the discussion of causal set models, which are the only
purely relational theories I discussed. The inverse problem is that
there are many more discrete relational structures than those that
approximate local, continuous structures such as classical spacetimes.
So a purely relational theory that explains the fact that the world, at
least on scales larger than the Planck scale, appears to be continuous
and low dimensional, must explain why those local and low dimensional
structures dominate in an ensemble of histories most of whom don’t
remotely resemble local, low dimensional structures. Let me close by
recalling the extent to which the last three decades of theoretical
physics are anomalous, compared with the previous history of physics.
Many ideas have been studied, but few have been subject to the only kind
of test that really matters, which is experiment. The hope behind this
paper and the work it represents is that by following the relational
strategy we may be led to invent theories that are more falsifiable,
whose study will lead us back to the normal practice of science where
theory and experiment evolve hand in hand.


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