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Cosmologists can trace the evolution of our universe
back 13.8 billion years to the Big Bang.
"Before the Big Bang"
Episode 5
But the Big Bang itself is an event
still shrouded in mystery.
"The No Boundary Proposal"
In this series we explore competing
models of the early universe.
While cosmologists may disagree
as to the true nature of the Big Bang,
what they do tend to agree on is that when the entire
observable universe is far smaller than an atom,
the strange world of Quantum Mechanics
surely becomes relevant.
At Cambridge University, one of the first attempts
to build a cosmology based on Quantum Theory
was pioneered by Stephen Hawking,
Thomas Hertog and James Hartle.
Their theory is known as
the "No Boundary Proposal".
In this episode, they'll explain how
their No Boundary Proposal
may be able to tackle some of the
deepest mysteries of our existence.
From why is there an arrow of time?,
or, is there a multiverse?
And how do we resolve
the Big Bang singularity itself?
Roger Penrose and I showed on theoretical grounds
that if Einstein's General Theory of Relativity is correct,
there must have been a singularity in the past,
a point of infinite density in space-time curvature,
where time has a beginning,
However, although our singularity theorem
predicted that the universe had a beginning,
it didn't say how it had begun.
The singularity theorems Penrose, Hawking,
and others showed
gravity would become so strong in the beginning
that the classical physics would break down.
That meant that Quantum Physics
was inevitably going to be important.
The idea to use Quantum Cosmology
to understand the origin of the universe
goes back way before Penrose and Hawking.
In fact, it came along with the discovery
of the expansion of the universe.
So even in the 30s, people began to ask the question,
well, what happens at the origin of the universe?
And the suggestion was made, back in the 30s,
that at a very early phase of cosmology,
in the very early phase of cosmological evolution,
Quantum Theory would come into play.
But of course, in the 30s, the--
In the 30s the tools were not available
to say anything about the origin.
This was just 'an idea for an idea',
as John Wheeler would have said.
The initial singularity theorems developed
in the 1920s by Friedman and Lemaître,
had the unreasonable assumption that
the universe was perfectly symmetrical.
In the 1960s, Penrose and Hawking developed new
singularity theorems that did not require this premise.
So, in the early days you could have said,
well, the initial singularity--
the initial Big Bang singularity,
is a feature of very specific universes.
But Penrose and Hawking showed that, in fact,
this initial Big Bang singularity is a generic feature.
The real lesson of the singularity theorems
is therefore that we need to combine
the General Theory of Relativity
with Quantum Theory in order to
understand the origin of the universe.
In the 1970s, Stephen Hawking discovered that
when Quantum Theory is applied to black holes,
it causes them to evaporate giving off
what is now known as Hawking Radiation.
[Hertog] Stephen and Jim both realized that if Quantum Theory
has such a big effect on the singularity inside black holes,
presumably it also has something to
say about the cosmological singularity.
[Hawking] It was at a  conference in the Vatican
in 1981 that I first put forward the suggestion
that maybe time and space together
formed a surface that was finite in size,
but did not have any bounday or edge.
Together with James Hartle
from the University of California,
I worked out what physical conditions the early universe
must satisfy if space-time had no boundary in the past.
Our model became known as
"The No Boundary Proposal".
It says that when we go back towards
the beginning of our universe,
space and time become fuzzy and cap off,
somewhat like the North Pole on the
surface of the Earth.
In the singularity the Big Bang is a
moment of infinite density and curvature,
but in the No Boundary state there's a
smooth surface, which although finite,
does not have a single point of origin.
[Hartle] The key concept is the idea of
a wave function,
that sometimes a particle can act
sometimes like a wave,
and sometimes like a particle.
A photon, say.
When it's acting like a wave,
it's described by a wave function.
The No Boundary proposal treats
the universe quantum mechanically,
and therefore the mathematics needed
to describe this strange quantum world
will be needed for the universe as a whole.
And the starting point to do this is Richard Feynman's
sum-over-histories formulation of Quantum Theory.
So, unlike the Copenhagen Interpretation of Quantum Theory,
where you have an external classical world,
in Feynman's sum-over-histories formulation
everything is part of the system.
It says essentially that if a particle goes from A to B,
it doesn't follow a single history,
but it follows all possible paths connecting A to B,
just like in the famous two-slit
experiment of Quantum Theory,
where you have a particle that goes through
both slits and a superposition of paths.
A path integral assigns a "weighting",
or relative probabilities,
to different possible histories
of the universe.
The No Boundary Proposal is a selection principle that selects
the subset of histories of the universe that closed off in the past,
and so allows us to determine which histories of
the universe have the most significant contribution.
The most significant contribution
will come from a geometry
that is Euclidian on the bottom of the shuttlecock and an
expanding De Sitter universe on the top of the shuttlecock.
What I mean when I say the geometry is Euclidean is
that has four space dimensions and no time dimensions.
What I mean when I say that the geometry is Lorentzian
is that has three space dimensions and one time dimension,
just like the geometry we experience
every day in this room.
The No Boundary Proposal is a model of the
Big Bang that is based on Quantum Gravity,
that is given by the path integral over all
Euclidean metrics without boundary.
By contrast the Hawking-Penrose theorems
are about Lorentzian space-time,
which has a boundary at the singularity.
To describe the wave function and its superposition,
physicists use imaginary numbers.
But what are these imaginary numbers, and why are they
so important for the No Boundary Proposal?
[Hertog] Well, imaginary numbers are numbers
which square to something negative.
"i" is an example, and "i" squared is minus 1.
The No Boundary wave function describes
or assigns different probabilities
to different histories of the universe,
and it does so by associating each
history to a geometric construction,
the famous shuttlecock construction,
in which a history is, in fact,
"rounded off" in imaginary time.
In this context, when we say imaginary time
in the No Boundary Proposal,
we're really talking about geometries
in which time behaves as a space direction.
The No Boundary proposal does not describe
a single history for the universe,
but it describes an ensemble
of different histories.
The past is probabilistic just like the future,
it's symmetric.
So in that sense it is similar to a wavefunction of an
ordinary quantum mechanical system,
which describes an ensemble of different histories
or paths just like in the two-slit experiment.
So, if that's true, then there must be
a wavefunction for the universe.
And the question is what is it?
[Hertog] So this is the formula for the
No Boundary wave function.
What does this mean?
The No Boundary wave function prescribes--
The No Boundary wave function
gives you an amplitude,
a weighting for different configurations
at some moment of time,
different kind of universes.
You could think of each "h" and "ϕ" as a universe.
The amplitude of each universe,
according to the No Boundary wave function,
is given by a Euclidean parth integral
There is no notion of time at this level,
time does not appear in this formula.
Now, there's a special condition,
the No Boundary condition,
which asserts that those histories
contribute to the path integral
which have no other boundary except the one
at which you're evaluating the wave function.
And that's what leads to that shuttlecock picture.
How am I going to write, to draw,
a geometry which has no other boundary
than the boundary at which
I'm evaluating the wave function?
I'll naturally draw something like this, right?
So, these shuttlecock geometries.
They are geometries, complex geometries,
which start out with all dimensions
behaving as a space dimension.
This region, which is Euclidian, and where
all dimensions behave as space, changes.
The spatial dimension remains a circle,
but the time dimension opens up,
and becomes distinct from the space dimension,
and describes a universe in which
a spatial circle grows, and grows,
and grows--
I can no longer interchange
time and space here.
This is the way time, Laurentian time evolution,
emerges when the universe gets larger
from what is initially a quantum fuzz.
Classical Physics is not fundamental,
it's an emergent phenomenon, we believe,
from a quantum mechanical theory.
The notion of classical evolution emerges from the No Boundary
wave function when the universe gets sufficiently large.
According to the No Boundary Proposal, the only way to get
a classical universe with a deterministic notion of time
is via a period of inflation.
Inflation is a period of incredibly rapid cosmic expansion
believed to have occurred in the early universe.
Inflation is thought to solve a number of problems
with standard Big Bang cosmology,
and it's driven by a form of matter
known as a "false vacuum",
which causes the expansion to accelerate
instead of slowing it down.
When this form of matter decays inflation ends,
creating a hot soup of particles.
[Hawking] The No Boundary Proposal
explains how inflation started in the first place.
Inflation produces a very large and uniform universe,
just as we observe.
However, that would not be completely uniform
because in the Euclidean path integral
histories that are very slightly irregular have almost as
high probabilities as the completely uniform history.
The theory therefore predicts that the early universe
is likely to be slightly non-uniform.
This produces small variations in the intensity of
the microwave background from different directions.
Some regions will expand slower than others,
which eventually leads to the formation of galaxies.
Detailed observations have confirmed there are
indeed changes in the intensity of the radiation,
at the level of about one part in 100,000.
Moreover the observed pattern is in excellent
agreement with the predictions of inflation,
combined with the No Boundary Proposal.
The standard theory of inflation predicts the
generic features of the primordial  fluctuations,
but it doesn't predict the details.
There are all kinds of inflationary universes.
You need the No Boundary wave function,
and in particular the probabilities that
it predicts for different inflationary universes,
in order to complete the theory and
make specific sharp predictions.
The predictions of the No Boundary Proposal will be a combination
of the probabilities given by the No Boundary wave function
and the possibilities coming out of the
dynamical model of the earlier.
It's the two combined which lead to
very specific predictions.
Now, of course, we don't have a complete
theory of the dynamical model,
so we are not sure yet
what are the possibilities.
But in a specific corner of the string landscape,
the corner described by "D-brane inflation",
that is a model of inflation in String Theory
in which the accelerated expansion
is driven by the motion of a membrane
through an extra dimension;
Within the context of that dynamical model,
the No Boundary wave function will make a
very specific prediction for things like the tilt,
so for the spectral features of the pattern
of microwave background fluctuations,
such as the contribution from gravitational waves
and the tilt, and so forth.
But I don't like to stress those predictions precisely
because of the uncertainty on the dynamical model.
What the point of our program on the
No Boundary wave function is to demonstrate
that if you have a dynamical model for the early universe
and you have a theory of its quantum state,
the two combined yield a predictive
framework for Cosmology.
In other words, the two combined turn Multiverse Cosmology
into a proper verifiable scientific framework.
[Hawking] The goal of Cosmology is to construct a
model of the universe that makes falsifiable predictions
that can be tested by observations.
To falsify the No Boundary wave function you would have
to identify correlations that are impossible within the theory,
such as, for instance, spectral features of the primordial
perturbations which are incompatible with inflation.
So, for a long time it was thought that a
No Boundary Proposal predicted essentially
an empty universe with just a little bit of inflation.
However, that prediction is what we now call a
"bottom-up" probability of the No Boundary wave function.
It's a probability which you derive
straight from the wavefunction,
and which does not take into account the condition
that we actually exist in the universe.
When it comes to testing the
No Boundary Proposal against our observations,
we first must include the condition that
we are part of the universe,
that we are part as a physical system
of the universe.
So, in other words we have to
calculate a conditional probability,
in order to compare the predictions of the
No Boundary Proposal with our observations.
It turns out that this condition has a large effect on the
probabilities predicted by the No Boundary Proposal.
Without this condition the No Boundary Proposal
predicts just a short period of inflation and an empty universe.
But when our observational situation is
taken into account as part of the universe,
in fact, the most probable histories of the universe
that are predicted by the No Boundary Proposal
are histories with a long period of inflation, and
when extrapolated backwards in time,
in fact, with a phase of eternal inflation.
And the reason for that is simple:
In this first class of histories,
which has just a little bit of inflation,
they're smaller, they don't have many
places for us to be,
whereas the histories with a long
period of inflation, they're much bigger!
They have lots of places for us to be.
And since we are a physical system within the universe,
with a certain probability to be anywhere,
we are much more likely to be in one of these
in large histories than in the small histories.
So, in other words, what's most probable to be
it's not necessarily what's most probable to be observed,
precisely because there are more places
for us to be.
"What temperature we'll observe for
the microwave background?"
That question doesn't make any sense,
because it doesn't say what time we'll look at it.
So, you need to distinguish between predictions for
whole histories of the four-dimensional histories of the universe,
and predictions for our observations of it,
which are typically at the moment of time.
That difference between the
two kinds of probabilities,
probabilities for observation and probabilities
for the whole history of the universe,
I think, capture a large part of the difference
of what's meant by "top-down" and "bottom-up".
It turns out that a top-down probabilities
given by the No Boundary Proposal
predict that we have a
long period of inflation in our past,
and therefore we predict a flat universe--
In fact, we predict a universe with so much inflation
that it has a period of eternal inflation.
In our previous film, Alan Guth,
the father of Inflationary Theory,
claimed that inflation is generically eternal.
In other words, almost all models in Inflation
lead to a multiverse.
[Hawking] The multiverse arises in Inflation
from the same quantum mechanical effect
that leads to the irregularities in the early universe,
seen in the microwave background.
This is because if one traces the
universe's history backwards in time,
deep into the face of inflation one can
encounter a regime of eternal inflation.
In eternal inflation, the quantum fluctuations
in the energy density of the matter are large.
It is usually thought and this can keep inflation
going forever in some regions of the universe
Our observable universe would then
become a local "pocket universe",
a region in which inflation has ended.
Globally, the universe would have
a highly complicated structure,
and would consist of infinitely many
such pocket universes,
separated from each other by
inflating regions.
The local laws of Physics and Chemistry can differ
from one pocket universe to another,
which together form a multiverse.
[Hartle] In general, in Quantum Mechanics
there's always a multiverse,
because Quantum Mechanics
doesn't predict one thing,
it predicts probabilities for things.
And the conventional way of handling
eternal inflation has led to paradoxes.
Eternal inflation seems to be produced an infinite
number of each kind of pocket universe.
So, what should we tell the observers
as to in which pocket we are?
That problem clearly shows that the conventional
theory of eternal inflation is incomplete.
The reason the No Boundary wavefunction is
a completion of the theory of eternal inflation
is that it predicts an ensemble of eternally
inflating universes with a probability measure,
with a probability distribution over that ensemble.
That probability distribution allows you
to extract probabilities, relative probabilities,
for one pocket universe versus another.
And it's those relative probabilities which are the key
quantum mechanical prediction for what we should observe.
A number of scientists have claimed that many
features of the universe are delicately fine-tuned.
One example is the initial conditions for inflation.
So, the No Boundary wave function is a solution
for the problem of initial conditions for inflation.
It's often thought that an inflationary universe
requires very special initial conditions.
But the No Boundary wavefunction selects
those universes which have a period of inflation.
So the initial conditions for inflation are not
fine-tuned in the No Boundary wavefunction.
In fact, inflation is precisely what the
No Boundary wave function predicts.
In 1998, scientists discovered the universe
is accelerating in its expansion,
perhaps being driven by a repulsive
gravity term invented by Einstein,
known as the cosmological constant.
This too has been claimed as a case
of delicate fine-tuning.
We need to deal with it from this top-down
or first-person point of view,
in which we're asked not what is the most
probable value of the cosmological constant,
but what's the most probable value of the
cosmological constant that we can see.
The reason is, because as we explained
by Barrow, Tipler, Weinberg, and others,
if the cosmological constant is too big,
the universe expands too rapidly
and then based on calculations by
Tegmark, Reiss, and others,
galaxies wouldn't form and we wouldn't be here
to see what's going on.
In a multiverse, you will naturally have different values
for constants of nature in different universes.
A famous example is the cosmological constant,
which can take different values.
We could, for example, have a universe that
eternally inflates by a cosmological constant,
and within that universe that "false vacuum",
as it's called,
would decay by "bubble nucleation",
and we live in one of the bubbles, right?
That's already a multiverse.
Quantum Mechanics generally predicts probabilities
for ensembles of histories, that's a multiverse.
If the dynamics permits the cosmological constant
to differ from one of those histories to another,
we predict probabilities for the value of
the cosmological constant.
So, those constants of nature in Classical Cosmology,
they're just numbers without any explanation.
In Quantum Cosmology you can
hope to explain those numbers,
or to explain at least certain correlations between
those numbers from a deeper underlying theory.
Let's come back to this universe that has
a false vacuum that's expanding,
but also decaying by nucleation of
bubbles of true vacuum.
If you run that forward for any amount of time
you get a very complex structure,
a roaring sea, so to speak, of bubbles
that's very difficult to calculate.
In fact, it's so difficult that people
assume for the minute that
there's only a finite number of them,
and then try to let the number go to infinity.
That's called a "measure".
Calculating probabilities in an
infinite multiverse is no easy task.
It requires a counting procedure
known in Mathematics as a "measure".
But there's no agreement among
physicists as to what measure to choose.
Is there another way out of
this measure problem?
There's a simpler way of doing it,
which is this first-person, top-down idea that
you should focus on just what it is you observe.
One bubble, right?
And ignore all the other bubbles,
and there is a way of doing that in
Quantum Mechanics called "coarse-graining".
To me fine-tuning is a top-down question.
It doesn't mean very much to say,
well, the theory is wrong
because it predicts some universe
which we can't observe.
To me the real question is whether
the constants of nature that we observe,
given we exist within a universe,
are likely or not.
So, 10 years before the cosmological constant
was discovered
Steven Weinberg pretty much predicted
its value based on this kind of reasoning.
That reasoning is pretty much automatic
in Quantum Cosmology,
because we are very much physical systems
within the universe in this theory.
We're part of this final configuration.
So the real question is whether the No Boundary
wavefunction predicts correct correlations
between our existence and the observed
values of the constants of nature.
And if we do this for the cosmological constant,
for instance, in the No Boundary wavefunction
we're actually able to sharpen
Weinberg's predictions,
precisely because we have a more
definite theory of initial conditions.
That's the way the No Boundary wave function
can be tested against observations, and so forth.
Of course, this may not work,
or agree for all constants of nature.
We're not even sure that all constants of nature can really
vary from one universe to another in the multiverse.
but those constants of nature which can vary
can be predicted using this kind of method.
For the other constants, I don't really know.
Some of them might be determined
by the theory.
So in a way they might be necessary.
[Hartle] It's easy to get the cosmological constant
to vary with an appropriate dynamical theory.
I think we don't know whether other
constants are put in or vary.
In other words, to say that there's
anthropic fine-tuning
you have to have a mechanism for the constants to vary,
and not simply be fixed by the fundamental theory.
Critics of the multiverse have said that as
other bubble universes are not observable,
the multiverse is not science.
Well, I think that's rubbish.
Physics always involves concepts and
ingredients which are not directly observable.
An example is the Higgs boson.
We don't observe it directly,
we observe its decay products.
All theories of Physics have ingredients
and concepts which don't directly--
are not directly observable,
but play a role in deriving predictions
for features which are observable.
Similarly so for the multiverse.
My goal, or the goal of the program
of the No Boundary proposal,
is to turn the multiverse into a verifiable,
falsifiable, predictive framework.
How do we do that?
Well, we use this multiverse
to derive predictions for
observations in our universe.
So, of course, it's true that we're not gonna be able
to observe wildly different universes from ours,
but we use the entire framework,
we use the entire multiverse,
we use the ensemble of histories
to extract predictions for our universe.
So, in that sense,
it's not fundamentally different, I think,
from what is happening in
other branches of Physics.
The Second Law of Thermodynamics tells us that
a random fluctuation of something very ordered
is incredibly unlikely.
But it isn't impossible.
Ludwig Boltzmann,
one of the fathers of Thermodynamics,
wondered if our entire universe
might be just such a rare fluctuation.
The problem is a brain would seem more likely
to fluctuate than an entire universe.
So some have argued that these "Boltzmann brains"
would dominate the multiverse,
and hence disprove its existence.
Well, Boltzmann brains would be a
problem even in a single universe.
If a history continues to expand, for instance,
because there's a cosmological constant,
you create infinite volume and eventually
Boltzmann brains will appear.
Therefore Boltzmann brains are not directly
associated with theories of the multiverse.
One issue is whether those fluctuating brains,
in the far future, in an otherwise cold and empty universe,
represent in fact fluctuations that decohere.
In other words, represent branches,
histories, branches of the wave function
to which we can assign meaningfully a probability.
We have to be able to assign meaningfully
a probability in order to draw any conclusions
about whether or not we are more
likely to be a Boltzmann brain.
I think it's far from clear that those
kind of fluctuations, in fact, decohere.
Jim, Thomas, and I have recently studied
eternal inflation from a different viewpoint.
Our approach has based on the concept of
Holography in String Theory.
Holography says that Einstein's Theory of Gravity
in space-time is equivalent, or dual,
to a theory without gravity that is defined
on the boundary of space-time.
We have used Holography to excise
the phase of eternal inflation in our past
and replace it by a dual theory defined on
the global exit surface from eternal inflation.
One can use a dual theory to calculate more
reliably the global structure of the universe
produced by eternal inflation.
We find that the probabilities for
highly complicated universes
are much lower than what the old
theory of eternal inflation indicated.
This raises doubts about the widely accepted idea that
eternal inflation gives rise to an infinitely large multiverse.
Instead, we conjecture that the end of
eternal inflation is reasonably smooth,
leading to a much simpler universe,
which is globally finite.
What we find is that even though
there can be a phase of eternal inflation,
the late-time universe is smoother than
what the traditional calculations suggest.
So now you might say,
well, where is the multiverse then?
If my universe is smooth, then it seems
to be pretty much the same everywhere.
But remember that the No Boundary wave function
is a function of the late-time configuration.
Therefore the multiverse is still in there.
The No Boundary wave function describes or assigns
probabilities to different kinds of universes.
It's a multiverse not consisting of
pocket universes in a single space-time,
but it's a multiverse consisting of an
ensemble of different universes, okay?
More quantum, if you like.
All theories are approximations.
In order to move from interesting proposal
to something widely accepted,
a theory must be precise enough to
allow for unambiguous predictions
So, what must quantum cosmologists
do to achieve this?
We must find a better way to define
that particle.
This shuttlecock construction is
really an approximate construction.
It's an approximation of this path integral which
has never been defined mathematically precisely.
So that's where Holography comes in.
Holography provides a new route to
specify the No Boundary wave function,
which in the long term might give us a more
precise formulation of the wave function,
perhaps not even based on
traditional notions of space and time.
We are most interested now in learning
how to compute quantum mechanically
what goes on in the early universe,
irrespective of what the particular proposal is.
How do we get between the wave function
of the universe which is a fundamental theory,
part of the fundamental theory,
and predictions for observations,
and that’s a fairly hard thing to do.
We can do that in a sector, if you like, of the wave
function of the universe that's close to classicality,
and there we think we know what we're doing.
Susskind, Paige and other people speculate
that if we look for big quantum fluctuations
then we would predict more probable
things that are not like what we see.
We don't know yet.
They might be right,
but we have to develop our
techniques of computation.
In the meantime, we're making progress
on how to compare things.
The Aurora Borealis is caused by
electrons in the upper atmosphere
being excited to higher energy levels.
As they fall back down to their lowest energy level,
known as the ground state, they give off light.
This notion of a ground state is helpful to understanding how the
No Boundary Proposal explains many mysteries of Physics.
The universe as we see it today was
simpler earlier than it is now:
More homogeneous, more isotropic,
more nearly in thermal equilibrium.
So you would expect it to be described, if there was a
wave function, by the simplest possible wave function.
In ordinary Quantum Mechanics,
that's the notion of the ground state,
the simplest possible state.
Most ordered, most simple.
The No Boundary wave function is the cosmological
analogue of the ground state for closed universes,
and it seems to work.
When it comes to the arrow of time,
the dynamical laws of physics are typically
invariant under the reversal of the arrow of time.
So the observed arrow of time must have
something to do with the initial conditions.
[Hartle] The fluctuation
started out small and grew.
Complexity--
The universe started out simple
and became more complex.
Those are the basic features
of arrows in time.
Complexity is increasing
and that can be quantified
by appropriate entropies
that also increase.
The regularity of the shuttlecock geometry
implies that all fields are initially in their ground state.
So the No Boundary Proposal implies that
when a classical universe emerges,
this will be in a very much in its
ground state.
No structure.
So it implies that the structures develop away
from the Big Bang towards the future.
In one of our previous films,
Sir Roger Penrose argued for a cyclic cosmology
to explain the deep mystery of why
the entropy was so low at the Big Bang.
The No Boundary Proposal predicts that,
so it may be a mystery, I think, to Roger
why the No Boundary Proposal,
but once you accept that
then I think you have the arrows of time.
Interesting enough, the No Boundary Proposal
predicts bouncing universes as well,
then it predicts arrows of time that are
in one direction one side of the bounce,
and the other direction on the
other side of the bounce.
Now, if you have a bouncing universe
that collapses,
reaches a minimum, and then grows,
you might ask, where the fluctuations are small?
It's not at one end, not the other end.
It's in the middle.
Aron Wall, a former student of Jim Hartle,
has argued that the No Boundary Proposal
is not really a universe with a beginning,
because the beginning only occurs in imaginary time.
In real time, the No Boundary Proposal implies
the universe that is eternal to the past and future.
First of all it's important to stress that
what one means by 'real'
is not imaginary, in the sense of fictitious.
But imaginary in the sense of complex numbers.
It's a closure of the universe.
So, it's very much like a beginning of time.
It happens in imaginary time,
as Aron says.
You might wonder
how--
How that shuttlecock construction is connected
to the histories of the universe in real time.
You will typically find that the classical
extrapolation of the history backwards in time
exhibits a kind of hourglass structure.
It's as sort of you have a contracting
phase going backwards in time,
and then you have a kind of bounce,
and you have another expanding phase
on the other side of the bounce.
So, you might think, well, this is very
different from the No Boundary Proposal,
but in fact it's not.
Because the No Boundary Proposal
predicts that near that bounce
all fields are in their quantum mechanical ground state,
their minimum energy state.
There's no structure near the bounce.
The structure in those histories develops
away from the bounce in both directions.
That means that there is an
effective arrow of time,
which goes away from the bounce
towards the future.
But on the other side of the bounce,
the effective arrow of time goes the other way.
That means that in those histories there is
absolutely no communication between both sides.
Many models for the early universe, whether they be derived from
String Theory, Loop Quantum Gravity, or Inflationary Cosmology,
seem to be converging on the idea that our
expanding universe has a mirror image of itself,
creating an hourglass-like structure for the cosmos.
I agree that this hourglass
kind of picture of the universe
is emerging from various angles now,
but the natural initial condition will
evidently make the early universe
rather simple.
And that automatically leads you to
that hourglass kind of evolution,
with the arrow of time pointing in
opposite ways of the bounce.
Having said this, there are other
proposals for Cosmology:
Cyclic cosmologies, or ekpyrotic cosmologies,
in which there is clearly a distinction.
Those proposals also invoke a sort-of
bouncing phase,
but the arrow of time does not reverse,
the arrow of time always goes forward.
In other words, there is communication from
the pre-bounce phase, or the pre-Big Bang phase,
to the post-Big Bang phase.
And eventually, I would imagine that--
Both kind of proposals will lead to
observationally distinct predictions
and will be able to rule one of them out.
Alex Vilenkin has proposed a different
quantum origin for the universe,
where space and time tunnel into existence
from a state of no space and time,
similar to the way that virtual particles
fluctuate from the vacuum.
He claims this has a number of
advantages over the No Boundary state.
Alex Vilenkin, who I know quite well,
is a brilliant scientist,
and we have to take seriously
that we're not going to have a
slam-dunk theory of the
wave function of the universe.
The No Boundary Proposal will predict that
we come from a regime of eternal inflation
at a rather low value of the potential.
Alex's wavefunction will predict
that our universe emerges
from a regime of eternal inflation that
occurs at a high value of the potential.
In the simplest dynamical models,
I believe Alex's propose is ruled out.
Because regimes of eternal inflation
at a high value of the potential
will naturally occur when the
potential has a polynomial behavior.
When the potential goes like the
fourth power of the scalar field, for instance.
But those kind of inflationary histories
predict a large tensor-to-scalar ratio,
which we don't seem to be observing.
So, I think Alex's proposal for
that reason alone is under pressure.
So, I would rather regard them as two separate
approaches to the wave function of the universe,
and we'll compete them on their predictions
for such things as the large-scale structure.
The No Boundary Proposal is a theory of Cosmology
developed before modern quantum gravity theories,
like String Theory or Loop Quantum Gravity
were formulated.
The String Theory is a dynamical theory
and the No Boundary wavefunction is
a very general idea that should apply
to any theory of dynamics.
At least most of them, we hope.
So, probably you can put String Theory
into the No Boundary wave function,
and then check what it says about predictions,
they're not separate.
In fact, one of the beauties of the
No Boundary wavefunction is, I mentioned earlier,
that contemporary final theory
appears to have two parts:
A theory of the quantum state
and a theory of the dynamics.
They're unified in the No Boundary Proposal,
in the sense, given a theory of dynamics,
you probably have something like a no boundary idea.
In a way the No Boundary wavefunction
combines or unifies
the theory of dynamics and the theory of initial conditions,
and you can see this from this formula.
Here's the theory of dynamics,
summarized by its action,
and here are the initial conditions,
in one single formula.
Together they define a wave function,
and from the wave function
you derive both the probabilities
of different universes,
as well as their dynamical evolution.
The multiverse implied by the No Boundary Proposal
and Inflationary Cosmology
may seem like a modern idea.
But George Lemaître,
the father of the Big Bang,
may have hinted at the basic concept
as early as the 1930s in this quote:
«Clearly the initial quantum could not conceal
in itself the whole course of evolution.
The story of the world need not have
been written down in the first quantum,
like the song on a disk of a phonograph.
Instead, from the same beginning ,
widely different universes could have evolved.»
The No Boundary Proposal is the model
of the physical conditions at the beginning.
It describes how our familiar notions of space and time
can emerge from a quantum state of the universe.
[Hertog] There are certain questions that you simply
cannot ask in the context of Classical Cosmology.
An obvious question is,
where does classical space-time come from?
Classical space-time is assumed, obviously,
in Classical Cosmology.
But by deriving, so-to-speak, Classical Cosmology
from an underlying quantum theory of the universe,
you can ask in what regime and how
classical evolution emerges?
So you get a deeper layer of understanding of the
basic building blocks, ultimately, of our universe.
[Hawking] In the No Boundary Proposal
the same laws of nature hold at the beginning,
as in other places.
The beginning of the universe would
be governed by the laws of science.
This removes the need for an intelligent creator.
[Hawking] Ever since the dawn of civilization,
people have craved for an understanding
of the underlying order of the world.
Why is it as it is, and why it exists at all?
There ought to be something very special
about the boundary conditions of the universe,
and what can be more special than
that there is no boundary,
There should be no boundary to human endeavor.
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