>> 
CHRIS: Hello, everybody. Welcome. I'm pleased
to introduce to you today Dr. Sean Carroll
here to talk to you a little bit about the
nature of time. And as today is about astronomy,
I thought I wanted to just do a little plug,
we were talking earlier that today is actually
a semi-important day, kind of a local maxim
of importance for astronomy in that this morning
was released the U.S. Decadal Survey, which
kind of focuses what astronomers will do for
the next 10 years. And so, one of the things
that came out of that survey was that, new
experiments about dark energy and about looking
back further in time at the early universe,
were at the top of the list. So this is kind
of a very appropriate talk for today. Just
a little bit about Sean before we get started.
Sean started out with a Ph.D. at Harvard in
astronomy. He spent a little more time in
Boston MIT then he came out to California
to UCSB and then went back to the other side
of the Mississippi up to the coast of Chicago
and then has landed for the last four years
back in the sunlight here in California at
Caltech. Besides all these credentials, these
nice universities and his great publications,
one of the reasons that I've--I ask Sean to
come here today is that he's a great science
communicator. And I even verified this on
his Wikipedia page this morning, that is a
direct--so you have to know it's true. He's
recently made appearances on the Colbert Report,
as we're just talking so you may have seen
him there. And a few of you may have been
at the Comic-Con a few weeks ago, where he
was at the booth roundtable about science
and science fiction movies. And, you know,
as people become famous these are the things
that they do and now they're here at Google,
giving a tech talk to you all. So with that,
I'd like to present Dr. Sean Carroll to talk
about the Origin of the Universe and the Arrow
of Time. Here you go.
>> CARROLL: Thanks. Thank you, Chris. I never
really love it when the introduction says
that you're such a great speaker or communicator
or things like that. It sets up a little standard
that I don't know if I can reach. But it's
great to be here at Google, it's--especially
because without you guys, I would not have
any of the images that I'm showing in this
talk. And it's a great topic, I think, to
talk about to almost any audience because
what I'm going to try to do is to connect
things that happen in your everyday life,
the sense of time. You know, we all know what
time is, we use it all the time, you were
smart enough to get here at 11 A.M. for this
talk. But there are deep mysteries about how
it works and those deep mysteries, thinking
hard about them, leads you to think about
the Multiverse. So I really want try to convince
you to just trying to sort out what happens
in your everyday life in terms of the difference
between the past and the future ends up with
you thinking about these grand ideas, that
we are then trying to bring back to experiments
that we can actually test somehow. So, the
first question everyone asks is, "What is
time, what do you mean by time?" And there's
a famous quote by St. Agustin back in 450
A.D. or something like that, were he says,
"I know what time is until you ask me." I
can use it, you know, you can get here on
time, you know what it means if someone says
a certain TV show lasts an hour or something
like that. But then you start thinking about
it and you get confused. And the reason is
actually not because the concept of time is
all that confusing it's just that we use the
word "time" in different notions, different
senses, and so those get mixed up. But the
simplest notion is actually a very easy one.
Time is kind of like space. And this was something
that was really made very formal by Albert
Einstein in Theory of Relativity, but it was
true even for Isaac Newton or for Galileo.
Time helps us locate things in the universe.
If you want to get here to this lecture, you
say where it is, which particular room it's
in at Google in California, et cetera. You
say where it is in space and you say when
it is in time. So just like we had the three
dimension of space were you use to locate
objects, we have the one dimension of time.
It's a number. It helps us find things in
the universe. You had the train moving through
the station, you want to get on the train,
you need to know what station you're at and
you need to know what time the train is leaving.
So one way to think about time is it's just
a coordinate. It labels different moments
in the universe. We happen to live in a universe
that has a very, very nice property that things
don't completely rearrange themselves from
moment to moment in time. There's some smoothness,
there's some continuity. The world is not
exactly the same from moment to moments in
time but it's not completely different either.
So you have a moment 10:01, 10:02, et cetera.
There's you and there's your cat. Your cat
is walking away from you, but the cat does
not turn into a dog or just, you know, scatter
across the universe from moment to moments
in time, there's some continuity there. That's
one of the things that makes it a little bit
different, time versus space, and as you go
from point to points in space, things can
change dramatically. Here is the table, here
is not the table. From moment to moments in
time, things change smoothly as the result
of the Laws of Physics. Now what you want
to do, if you believe that, is say, "Well,
how do we measure time?" We measure space
by metersticks or odometers, which are basically
things whose length we know. The nice thing
about metersticks is that every meterstick
is the same length as every other meterstick.
It was a difficulty back in the day when people
literally measured length in feet, by which
they meant the length of the foot of the boss
on the project, then every project would have
a different notion of feet. These days, we're
smarter than that, we say, "We have a universal
notion of distance, one meter is this much
size." So likewise for time, we measure time
using clocks. And what a clock is, is simply
something that does something repetitively
in a predictable way compared to other clocks.
And now you say that sounds like a little
bit of a circular definition but you look
at the actual clock here, the thing about
a wristwatch or a conventional clock is that
every time the little hand goes around, the
big hand goes around 12 times. That is absolutely
predictable. The earliest clocks were in the
sky. They were astronomical events. We know
that every time the Earth revolves around
the Sun it rotates around its axis 365 and
one quarter times. It is a fact about the
universe that clocks exist. We could imagine
different laws of physics that didn't have
clocks in them. We could image that you could
setup one little wristwatch, but for no other
wristwatches in the world was that--was there
a relationship between them. We live in a
world full of clocks, a world where things
happen repetitively, synchronously over and
over again in predictable ways. That is what
allows us to tell time and to measure it and
to use it as an important part of how we get
around the world. So the next question people
ask is, "But I experience time to move faster
or slower sometimes." And I'm here to tell
you that is your fault, that is not the fault
of the Laws of Physics. And the reason why
you experienced time differently is because
your body is full of clocks. You are implicitly
telling time, there are things about your
person that repeats in a predictable way.
Your heartbeat, your breathing, the rhythms
and pulses of your central nervous system,
all act as clocks. But they're not very good
clocks. If you've had too much coffee or you're
tired, or you're bored or whatever, the perception
of time tends to differ because those clocks
are not keeping very good time. One example
of a successful application of this idea was
Galileo. This is a story which I suspect is
true, I can't actually verify whether the
story is true, but I will tell it to you anyway
because it's such a good story. Galileo grew
up in Pisa. He went to church at the cathedral
in Pisa which is right next to the Leaning
Tower and this is an image, on the left, from
that church. Some days, the sermon was not
as interesting as other days, as you might
expect and so you or I, our minds would wander
and we would think about what we're having
for dinner that night or whatever. Galileo,
being Galileo, thought about the nature of
time. And he was looking at this chandelier,
this precise chandelier in the cathedral in
Pisa and he saw that it rocks back and forth.
And again, we would go, "Oh, that's a pretty
chandelier," but Galileo said, "You know,
some days it's rocking back and forth quite
a bit, other days it's only a little bit,
but it looks like when it's moving far, it's
also moving faster. I wonder if there is some
uniformity there and the time that it takes
that chandelier to rock back and forth is
always the same, no matter how far it's actually
rocking back and forth." Again, if we had
that idea, we would think that's a cool idea,
but Galileo did the experiment. He said, "I'm
going to test whether or not the time it takes
the chandelier to rock back and forth is in
fact uniform." So, he timed the oscillations
of the chandelier using his own pulse. Using
his heartbeat as a clock, he timed the number
of oscillations of the chandelier versus the
number of beats of his heart and he found
out, by doing this on successive Sundays,
that indeed, the time it took that chandelier
to go back and forth was always the same.
This is the beginning of what physicists now
call the simple harmonic oscillator, the foundational
idea, for anyone who's ever taken a physics
course, and the idea behind the pendulum being
a good timekeeper for a grandfather clock
or for other kinds of timepieces. The existence
of oscillators like this, that are predictable,
lets us tell time. These days we would use
a little quartz crystal that is even more
accurate but it's the same basic concept.
Our bodies are not as good, that's why time
seems to move faster or slower for us. So
those are the similarities between time and
space, just to get your grounding here, but
what I really want to talk about is the most
important difference between time and space.
And that is, that time has a direction and
space does not. There's a little bit of an
exaggeration because here on Earth, space
does have a direction. You can tell the difference
between up and down, down is the direction
in which things fall when you drop them. But
if you're in your spacesuit far away from
the influence of the Earth, if you are sort
of experiencing space all by itself, not under
the influence of this giant gravitating mass
beneath us, all directions of space would
look equal to you. There'll be no difference
between up and down, left, right, forward,
backwards. The Laws of Physics don't know
any difference between different orientations
in space. But contrast that with time, there's
two directions, there's forward and backward,
the past and the future, but they're very,
very different. You might walk around an unknown
city and make a wrong turn, turn left instead
of turning right, no one ever makes a wrong
turn into yesterday. No one ever confuses
the past with the future. They're very, very
different. You remember what happened in the
past, you do not remember, most of us, what
happen in the future. You can influence the
future, you think that you can make a choice
right now that changes what happens in the
future but you can't make a choice right now
that changes what did happen in the past.
So, what is the origin of this difference
between past and future? That's really what
this talk is going to be about. The way that
we talk about this difference between the
past and future is in terms of the arrow of
time. Unlike space, time has a direction pointing
from the past to the future. Here are a bunch
of pictures comparing two similar kinds of
objects and under each of them I've--I have
a big blue arrow saying the direction of time.
But the point is I didn't need to put that
arrow there. Whether it's the car, the King
of Rock and Roll or the evolution of a species,
if I just showed you these pictures, it's
perfectly obvious to you which is one--which
ones are in the past, which ones are in the
future. That's because we all experienced
time to move from past to the future in a
consistent way. We might someday imagine discovering
alien life, based on different chemistry with
different laws of society and so forth, but
we cannot imagine discovering an alien species
that remembers tomorrow and tries to predict
yesterday. The arrow of time is completely
consistent within our observable universe.
We grow older, we're born, we grow older and
then we die, it's never the other way around
no matter what Benjamin Button movies you
might be seeing. Now the reason why this is
a mystery is because just like with space
the Laws of Physics don't pick out this arrow
of time. The deep down Laws of Physics, whether
we're talking about Isaac Newton or Einstein
or Schoedinger or Superstring Theory, all
have the property that they treat the past
and future completely identically. There is
no arrow of time to be located in the Fundamental
Laws of Physics. If you look at billiard balls
knocking to each other over there, you can
do the experiment, there's a pool table right
over there. If you imagine physicist billiards
were there's no friction, there's no noise
or anything like that, and you just have two
billiard balls bump into each other and scatter
off, I could make a movie of that and I could
play the movie backwards and you would not
notice anything funny going on. The Laws of
Physics that describe just two particles bumping
into each other and going their own way are
completely reversible. Any trajectory, any
solution to those equations works equally
well played backwards in time. But then you
find a messy circumstance with lots of particles
in them, like we have in the macroscopic world,
like a cue ball and a bunch of billiard balls
that are racked together nice and neatly,
you will see very often in the world, smacking
that cue ball into the rack balls and they
scatter across the table. That's going from
the past, where the balls are nicely arranged,
to the future. You will never see, starting
with balls scattered randomly across the table,
someone smacked the cue ball and they all
arrange themselves into a nicely racked orderly
configuration. In other words, if I took the
movie of the original thing, the rack balls
scattering across the table and I played it
to you, you would instantly know that it was
being--if it was being played backwards or
forwards. The arrow of time comes into existence
when we go from just a couple of particles
to a large number of particles. And this is
actually not a mystery in any way. It's the
beginning of a mystery where we understand
the basic mechanics of why the arrow of time
moves in one direction. We attribute it to
something called entropy. Entropy is basically
a measure of how messy or disorderly things
are. So here is the natural progression of
time, from neatness on the left to messiness
on the right. Now we have to emphasize, you
can clean up your room, there's no Law of
Physics that says you cannot take a messy
configuration then make it nice and more organized.
But the Law of Nature is that left to their
own devices, in other words, a closed system,
a system that is not influenced by the outside
world only ever becomes messier, only ever
has an increase of entropy. That's the Second
Law of Thermodynamics. So, if you leave the
left-hand side room all by itself, people
walk around, they bump into it and so forth,
it becomes the right-hand side, it's never
the other way around. The disorder of the
universe increase with time and that is the
thing, that is the single unique foundational
thing that separates the past from the future.
So to quantify it, we invent entropy and here
we go from the bottom left, you have a low
entropy configuration organized and in the
past, so you have an unbroken egg. As time
goes on, it's easy enough to break the egg;
it's easy enough to scramble the egg and disorder
increases all along the way. That is the Second
Law of Thermodynamics. If I made a movie of
that, played it backwards, you would know
that I were playing it backwards. Now I want
to emphasize, I can't go into all of the details
here, but I want to emphasize this claim that
the increase of entropy is really underlying
all of the different ways in which the past
is somehow different from the future. So the
fact that we are first born and then we live
and then we die, that's ultimately because
of the increase of entropy. The fact that
biological evolution goes from what we have--exhibit
in the early atmosphere and biosphere of the
Earth was just a few unicellular organisms
to all of the complexity we have today, that's
also because of entropy. The fact that you
remember the past but not the future is also
because of entropy. The fact that you can
think that we can cause things to happen tomorrow
but we cannot cause things to happen in the
past, it's also because of entropy. It's not
because of the Rules of Logic or the Fundamental
Laws of Physics. The fact that we feel time
to be passing in our personal lives, again,
that's because of entropy. So here is an image,
due to Roger Penrose, that shows you exactly
how this is working here on Earth. If entropy
were at its maximum point with all that thermodynamic
equilibrium, so the gas in this room where
it's smoothly spread all across the room,
that's an equilibrium, entropy is as high
as it can go; there is no change in the gas
in this room. There is no flow of time, it's
just sitting there. The reason why here on
Earth there is any notion of time passing
is because we are very far from equilibrium.
And the reason we're far from equilibrium
is because the Sun is a very hot spot in an
otherwise cold sky. So, if you could actually
count up the amount of energy that the Earth
gets from the Sun, its equal, modulo a little
bit of global warming, to the amount of energy
we give back to the universe. We get light
from the Sun and we re-radiate radiation back
into the sky. But for every one photon that
we get from the Sun we give back 20 photons,
each with on average 1/20th of the energy.
So we get mostly visible light from the Sun,
we radiate mostly infrared light. And for
photons, the entropy is just proportional
to the number of photons. So in other words,
we take the same amount of energy from the
Sun that we give back to the universe but
we've increased its entropy by a factor 20.
That is what allows stuff to happen here on
Earth. That is why we are not in equilibrium.
We are little machines, whether it's photosynthesizing
or chewing plants and metabolizing, or thinking
and computing, as you guys do, it's all increasing
the entropy of the universe, which is allowed
because we are so far away from equilibrium.
We are nowhere near a maximum entropy state.
There's a long way to go before we reach maximum
equilibrium. So this was more or less put
on a quantitative footing by this guy, Ludwig
Boltzmann, in the 19th century. And this is
Boltzmann's gravestone in Vienna, and I like
to tell my students that, you know, there's
an equation on top of Boltzmann's gravestone,
so they should all be thinking throughout
their graduate school careers, "What is the
equation that would be on my tombstone after
I die?" If you can do as well as Boltzmann,
you're doing very, very well. So the situation
for Boltzmann in the 1870's was that physicists
didn't really believe in the existence of
atoms for the most part. There were a few
pioneers, Boltzmann, Maxwell, Thompson, who
thought that atoms where the way to go, but
a lot of physicists said, "You keep talking
about these things but we can't observe them,
science shouldn't deal with unobservable things."
These might be familiar arguments, if any
of you who are fans of cosmology and particle
physics today. But Boltzmann and Maxwell and
Thompson said, "The reason why we should think
about atoms"--by the way, the chemists had
already caught on, chemists were all believers
in atoms because they helped them understand
chemical reactions. So Boltzmann and his friends
tried to make the same argument for physicists.
They said, "We can understand thermodynamics
and the properties of gases and fluids if
you believe in atoms. We can understand them
in a better way and make predictions and ultimately
maybe we'll even see these atoms someday."
So, what Boltzmann said is that, "What I can
understand is entropy. If you grant me the
existence of atoms, I can tell you why entropy
tends to increase." And basically, he said
that entropy just counts the number of ways
that I can rearrange the atoms of a system
without changing its observable macroscopic
properties. So here at the bottom you see
another example of the arrow of time, if these
were all the same collection of milk and coffee
you would know that the one on the left was
in the past, the one in the right was in the
future. It's easy to mix things together;
it is hard to unmix them. So Boltzmann says,
"I know why that's true," it's because over
on the left, I could change two coffee atoms
with each other, we would now call them molecules,
but two coffee particles without changing
any--the overall observance, the macroscopic
appearance of that cup of coffee. I could
also exchange different milk atoms with each
other. But if I started mixing the milk atoms
with the coffee atoms then things would begin
to look different, I would disturb the macroscopic
appearance. So there's a small number of ways
that I could do the rearrangements. On the
right-hand side, when the milk and the coffee
are all mixed together, there's many ways
that I can do the rearrangements. There's
just a lot more freedom to arrange the constituents
of that system without changing its macroscopic
appearance. So what Boltzmann said is that,
"The reason why entropy tends to go up is
simply because there are a lot more ways to
be high entropy than to be low entropy." If
we get a little abstract here for a second
here is just a plot of all the different ways
that you could have a collection of atoms
and they're divided up by what you can observe
about them, the individual atoms you don't
observe. When you look at the cup of coffee
you don't see the position and the velocity
of every single atom you only see some macroscopic
features. So what Boltzmann says is there
a lot more high entropy states, a lot more
ways to arrange the atoms of something with
high entropy than with low entropy. So if
you start a system in a low entropy configuration,
you're starting it very delicately arranged,
very, very precise. And if you just let it
go, if you don't disturb it from the outside
world by cleaning it up as it were, it will
naturally wander into a higher entropy part
of the configuration space. There are more
ways to be high entropy than low entropy,
that's why entropy tends to increase. This
is Boltzmann's great contribution and this
formula on his tombstone is the formula that
says that the entropy is the logarithm, to
be technical about it, of the number of arrangements
that you can do to a system without changing
its macroscopic appearance. So that's a pretty
good explanation for why entropy tends to
go up. There are more ways for it to be high
entropy than to be low entropy. But if you're
thinking about it, you realize that there
is yet something that is not quite answered
and this has been controversial since the
time of Boltzmann to today and that is, "If
there are a lot more ways to be high entropy
than to be low entropy, why did you ever start
out with low entropy?" Why is it, in other
words, that the entropy was lower yesterday?
So, what Boltzmann is able to do is explain
why starting with today entropy will tend
to go up. There's a lot more ways that our
universe today can evolve into a higher entropy
universe tomorrow. What he can't explain is
why the entropy was lower yesterday. Given
everything we know about the universe today,
there are a lot more higher entropy pasts
from which we could have come than lower entropy
past, but nevertheless we believe that the
universe really did have a lower entropy yesterday.
Why is that? Well, the reason why the universe
had a lower entropy yesterday than today is
because it had an even lower entropy the day
before yesterday. The reason why it had an
even lower entropy the day before yesterday
is because it had an even lower entropy the
day before that. And this is not, I'm not
going to reveal the true underlying real explanation,
that is the real explanation for why entropy
was lower in the past and it keeps going.
Many, many days, 13.7 billion years to the
Big Bang. The reason why entropy has been
increasing during your lifetime is because
we live in the universe that started at the
Big Bang when our observable universe came
into existence, with an incredibly low entropy,
an incredibly tiny entropy compared to what
it could have been, and the entropy has been
increasing ever since. There's no explanation
for that in terms of anything that Boltzmann
ever taught us. There's no dynamical explanation.
There's no statistical mechanics argument,
particle physics argument, general activity
argument or anything like that that explains
why the entropy of the universe was low near
the Big Bang. This is something that we can
assert is true. We start in a little tiny
region of that graph and everything we know
follows from that, all the business about
thermodynamics, memory causality, free will,
we can explain all that if you tell me that
the universe started with a low entropy. If
you ask why, I can say, "I don't know." This
is our job as cosmologists. So, it's kind
of again like space. Remember when we said
that there's no arrow of space, except of
course that we're here on Earth so there is
an arrow of up and down. There's an arrow
of space in our local vicinity because we
live close to a very influential object, namely
the Earth, that influences our notion of up
and down. The arrow of time is the same way
is what I'm trying to say. The reason we observe
an arrow of time around us in the universe
is not because it's there in the deep down
Laws of Physics, it's because we live in the
aftermath of an influential event, the Big
Bang. The Big Bang started with a much, much,
much lower entropy than it needed to everything
else follows from there. So we want to understand
why was the Big Bang like that. So to do that,
let's think about the universe. And the universe
when people try to--when cosmologists give
talks to large audiences, they usually start
talking about rubber sheets and raisin bread
and things like that. My favorite thing to
do is to actually think about the universe,
because we're not standing outside looking
at the universe, we're embedded inside. This
is a picture that you would get if you took
a really good camera and pointed it at a region
of empty space and just kept the shutter open
for quite awhile, that what they did with
the Hubble's Space Telescope and this is the
Hubble Ultra Deep Field. It just shows us
that even what you think looks like an empty
region of space is in fact full of galaxies.
In the 1920's, Edwin Hubble pinned down what
these little blobs were. They knew that they
existed, but there was an argument, "Are they
just clouds of gas and dust here within our
Milky Way Galaxy or are they outside?" Hubble
showed that every one of these blobs, for
the most part, is a galaxy just like our own.
So we live in the Milky Way Galaxy with about
a hundred billion stars roughly speaking.
We live in a universe, the observable part
of the universe has roughly a hundred billion
galaxies, each one of them roughly a hundred
billion stars. So the universe is big, that's
the first important thing to know. The second
important thing, you know, is the universe
is getting bigger, it's expanding. This was
also discovered by Edwin Hubble in the 1920's.
If you look at a galaxy and you look at it,
not only its distance but measure its velocity,
if--all faraway galaxies are moving away from
us. That's not because we're special in any
way, if you sat on one of those galaxies we
would be moving away from them. Every galaxy
sees most of the galaxies around it to be
moving apart, the further away a galaxy is,
the faster it is moving. So what this really
mean is that the whole universe is expanding,
the space in between the galaxies is growing.
If you play that movie backwards, in the past,
everything is closer together, the density
is higher, you keep pushing it into the past,
the density becomes very high and the temperature
becomes high. So in the early parts of the
universe's history, the universe was a hot
dense plasma and it was opaque. About 380,000
years after the Big Bang, it cooled down enough
so that the universe became transparent and
we can observe the relic radiation from that
moment when the universe became transparent.
That is the cosmic microwave background. This
is an image of the microwave background from
a NASA satellite called WMAP. And the tiny
little fluctuations here in color, are enormously
amplified from the actual tiny fluctuations
in temperature that you see when you look
at the microwave background from point to
point. The early universe was incredibly smooth,
and that's a reflection of the fact that it
was incredibly low entropy. I said that the
air in this room is high entropy and smooth
but the difference is that the early universe
had an incredible density, there's a tremendous
amount of stuff there. When the density is
that high, smooth does not equal high entropy.
Smooth equals low entropy because it wants
to collapse under the force of gravity. It
wants to be wildly in homogeneous with black
holes and empty regions and so forth but instead,
the early universe was incredibly smooth.
We can go all the way back to 13.7 billion
years ago, everything is at the same place
in the universe, the density is infinite,
the curvature is infinite, that's the Big
Bang. That's what our equations tell us, we
don't know whether that's true or not, we're
trying to put it all together. So that's the
past of the universe, in the future what's
going to happen, well this used to be a great
thing to debate. When I was in graduate school,
we use to wonder whether or not the universe
would eventually re-collapse or not. Now we
more or less know, at least we have a very,
very sensible theory that makes a prediction
which is that the universe is going to expand
forever. The reason we think that is because
in 1998, astronomers measured the velocity
of receding galaxies to unprecedented precision.
And what they realize is that not only is
the universe expanding, it's accelerating.
If you look at a galaxy right now and measure
its velocity away from you, go away and then
come back a billion years later and measure
its velocity again, that velocity will be
faster. That's a surprise because if you think
about an expanding universe, it should expand
but evermore slowly because the different
galaxies are pulling on each other through
their force of gravity. Instead, it's expanding
and now it's sped up. So, what is going on?
We don't know for sure what's going on, let
me admit that. But we do have a theory that
works very, very well and is probably right.
And that theory is that there is energy in
empty space, what we called Dark Energy or
Vacuum Energy or the Cosmological Constant.
So if you have a little cubic centimeter of
space and you emptied it out so there's nothing
there, it's completely empty, and you ask,
"How much energy is there in that little cubic
centimeter of space?" You might be tempted
to say, "Well, there's zero energy because
it's empty." The truth is there is some energy
even in empty space, not very much, 10 to
the minus 8 ergs, but there are many cubic
centimeters in the universe. And right now,
there's more of this Dark Energy than any
other form of energy. About 73% of the universe
is dark energy by energy. And the effect of
this dark energy is in part an impulse, a
perpetual push to the expansion of the universe.
That's why we've now begun to accelerate away
and that's why we're not going to re-collapse.
The universe is not being pulled by the matter
inside anywhere near substantially enough
to ever make it come back. Our best theory
right now is that the universe is 13.7 billion
years to the past to the Big Bang but the
future goes on forever, literally, to infinity.
That is the best guess we have right now,
it will not end. So here's my very brief overview
of the history of the universe, one second
after the Big Bang, is the earliest time when
we have any data from Big Bang nucleosynthesis.
This is an image from my imaginary telescope,
it was hot. It was giving off gas. It's white
here. 380,000 years after the Big Bang and
it cooled off enough to become transparent,
we see the microwave background and now we
can perceive these subtle ripples in density
from place to place. Ten to the ten years
later, approximately today, we're dominated
by stars and galaxies. This is the stellar
ephorus epoch in the history of the universe,
when you can actually see pretty pictures
by taking images. Now if you wait until ten
to the fifteen years after the Big Bang, those
stars will die out. You'll be left with a
few rocks, a few Brown Dwarfs and a lot of
Black Holes. We have a Black Hole at the center
of our galaxy which is pretty big a few times
a million solar masses. That's nothing compared
to the galaxy. The galaxy has a hundred billion
solar masses, but if you wait long enough,
those stars are going to die out and they
will all fall into that Black Hole. So after
ten to the fifteen years after the Big Bang,
we have a Dark Universe, nothing but Black
Holes and a few stray rocks. However, Black
Holes don't last forever. In the 1970s, Stephen
Hawking showed that even Black Holes give
off radiation; they evaporate due to the effects
of Quantum Field Theory. They lose mass. So,
these Black Holes turn into a thin rule of
particles moving apart in this accelerating,
expanding universe. And then that will die
out after, I have to say this, one Google
Years in the good old fashioned sense of the
word of Google before you guys messed it up
with your search engine stuff. Ten to the
one hundred years after the Big Bang, all
of the Black Holes will have evaporated away
into particles and those particles will all
have separated from all the other particles
and we will be left with nothing but empty
space. And that will last forever, so 13.7
billion years is a long time, a Google Year's
is an even longer time, but this last forever.
That's a very long time. And it should emphasize
how weird it is that we live in this year--era
of the universe's history where it's sort
of warm and comfortable. Almost all of the
history of the universe is dark and forbidding.
We live in a very unusual time and that is
a reflection of the fact that the Big Bang
began with an exceptionally low entropy. This
is a high entropy state of the universe. Nothing.
Nothingness is disorderly high entropy and
stable. It just sits there. That is what equilibrium
is really like. So this is the evolution of
entropy in the universe. It starts out low.
Things are orderly because you have to delicately
arrange the density of stuff in the universe
to keep it smooth. Once it expands, the force
of gravity acts as the contrast knob on the
universe, it makes stars and galaxies. But
those stars and galaxies will eventually evaporate
into nothingness in the future. Entropy is
going up the entire way. So our task as cosmologists
is to explain why that is the case. Given
that there's a Big Bang, why did it start
in such an exquisitely ordered configuration
with such low entropy? If you randomly picked
a configuration of all the particles in the
universe, it would not look anything like
the Big Bang. So one thing is for sure, the
Big Bang was not randomly chosen. We need
some answer to why the Big Bang looked like
it did. And we don't know the answers. Some
people will tell you that they know but they
don't. This is an open question right now.
We're working on it, so when I went to sort
of explore some of the possibilities. One
possibility was actually broached by Boltzmann
himself, he appreciated that this was a problem.
There was a long time when Boltzmann and others
thought that they could prove that the entropy
needed to be smaller in the past, but eventually
they realized that you can't do that because
the ultimate laws of Physics are time-symmetric.
You can't prove that the past must be different
from the future. You need to put it in there.
So Boltzmann did the--a sensible thing. He
said, "Well, if the low entropy of the past
is unusual, what would be usual? What should
the universe look like?" Now remember in the
1870's, physicists thought that the Second
Law of Thermodynamics was a law, not just
a good idea. It was absolute. But Boltzmann
said, "Look, if you believe my statiscal understanding
that the reason why entropy goes up is because
there are more ways to be high entropy than
to be low entropy." As a consequence of that,
occasionally the entropy can go down. There's
a standard exercise that you learn when you
do--and as an undergraduate physics major
when he learned stat-mech, take all the gas
molecules in this room, compute how long you
will have to wait on average before they all
move to one half of the room. It's a long
time. It's much, much longer than the age
of the universe, but if you're Boltzmann,
you know about the Big Bang, you don't know
about general relativity. You think that Newton
was right; space and time were absolute and
time will last forever. He thinks the universe
is not going to end nor did it have a beginning
so he imagines that even very, very improbable
things will occasionally occur. You can start
with the collection of particles that is high
entropy spread out through the room. Eventually
they will just, through the random motions
of the molecules, come into low entropy configurations
and then relax back. So here's a plot of that
actual simulation in a computer of a box of
gas with maximum entropy. We've normalized
it so that the entropy is equal to one when
it's maximum. And it can't go up. It's at
its maximum but it can through random fluctuations
go down and then relax back up again. And
that's exactly what it does. So Boltzmann
says, "Maybe we live here." The point is that
if you wait long enough, you will get fluctuations
that are relatively large. Maybe we live in
the aftermath of a random fluctuation of the
particles spread throughout the universe.
We would remember the past as being the point
of low entropy here. Remember, the arrow of
time is not fundamental; it's not there in
the Laws of Physics. It's a reflection of
the fact that entropy is increasing. So, on
the right-hand side of this graph, people
who live there remember that minimum as the
past and this right-hand side is the future.
If you lived on the left-hand side, you would
remember this as the past, where the entropy
was lowest, and you would call this direction,
the future. What you label the past and the
future merely reflects the local growth of
entropy in your surroundings. So Boltzmann
said, "The entropic principle and the multiverse,"
he used ideas--he didn't have the words, he
used the same ideas that string theorists
used today to try to explain our universe.
He said, "Look, if my theory predicts that
the universe should spend almost all of its
time in thermal equilibrium, the problem is
that you can't live in thermal equilibrium."
He says, "There must be then there in the
universe which is in thermal equilibrium as
a whole and therefore dead." That's the entropic
principle. Here and there, relatively small
regions, the size of our galaxy, which we
call worlds, which during the relatively short
time of eons, that's a little physicist's
joke, deviates significantly from thermal
equilibrium. So, both of them says, "Look,
okay, maybe most of the universe is in thermal
equilibrium but we can't live there." As a
selection effect, living beings will only
arise in regions of space and time where the
entropy is changing according to Penrose's
picture. So, most of the universe is unobserved
by people like us, but occasionally there
are fluctuations into lower entropy states.
Very occasionally, there are large fluctuations
into very low entropy states like our galaxy.
Maybe that's who we are. Maybe we are seeing
the aftermath of a fluctuation into our galaxy.
If you read Boltzmann's papers back then,
it was--he was slightly embarrassed by this
idea but he thought it was kind of cool and
it's interesting to read. This is not, however,
an original idea. If you do to the literature
search, you can find that there are precursors
to Boltzmann's idea, the earliest one I found
was from 50 B.C. This is Lucretius, a Roman
poet writing in dactylic hexameter but like
Boltzmann, Lucretius was an atomist at the
time when being atomist was not the conventional
thing to be. Lucretius was a follower of Epicurus
and Democritus, the Greek philosophers and
he was stuck with the same problem that Boltzmann
had. Mainly, if the universe is just made
of atoms and the atoms have no purpose or
a theology, they are just randomly bumping
into each other. How do you explain all the
structure and complexity and order that we
see around us? And so Lucretius says and you
have to imagine he's speaking sarcastically
at the beginning of this quote. "Surely, the
atoms did not hold council, assigning order
to each, flexing their keen minds with questions
of place and motion and who goes where. Rather
they shuffled and jumbled in many ways, and
in the course of the endless time they are
buffeted, driven along, chancing upon all
motions and combinations. At last they fall
into such an arrangement as would create this
universeů" So it's exactly Boltzmann's scenario;
it's just chaos, particles are randomly moving
around but if you wait long enough, you'll
get a universe just like ours. So this is
a venerable idea and it's a good idea in the
sense that yes, it would lead to universes
like ours without assuming an arrow of time.
There's no intrinsic direction to time in
this plot here. There's no overall trend,
right or left. We're just looking at a really
tiny piece of the overall plot. The problem
is the idea doesn't work. Boltzmann unlike
Lucretius had recourse to equations. He could
make predictions and this was actually done
by Arthur Eddington in the 1930's and he realized
that Boltzmann's scenario made an extremely
strong prediction that is very vividly falsified.
This is a good scientific theory, it's just
wrong. And what Eddington realized was that
if you are most of the time in thermal equilibrium
and you're waiting for a fluctuation to decrease
the entropy, then it is overwhelmingly more
likely that you would get a small fluctuation
than a large one. In fact, they're exponentially
more small fluctuations than large fluctuations.
So, if this is true, the prediction you make
is that given whatever you need for entropic
reasons, let's say, you want a person to exist
or you want a planet to exist or you want
the galaxy to exist, no matter what it is
that you choose, that you're going to wait
around until it fluctuates into existence,
this theory predicts with overwhelming likelihood,
that everything else in the universe is still
in thermal equilibrium. So, if we wait long
enough for our galaxy to fluctuate into existence,
we don't need a 100 billion other galaxies,
we would just have empty space outside our
galaxy, but that's not true. I mean you can
sort of focus in and then you realize, you
know, I don't need the galaxy; I can just
do with the solar system. It's much smaller
and then you predicted the rest of the galaxy
shouldn't exist. Then you realize, actually,
I don't need this room. I don't need the rest
of the universe. I could fluctuate into, out
of the surrounding chaos; I could fluctuate
into exactly the configuration of stuff in
this room right now, including all of you,
including all of me, including our brains
and the state of our brains that really is
convinced that outside there is a Google and
there is a California and there is the Earth.
These are just in our brains. It's a much
easier configuration to get your brain with
the thought that Google exists than to actually
get Google or the Earth or whatever. So, if
you like the prediction of this model that
as soon as you walk outside it's thermal equilibrium.
This is the model that is falsified everyday
all the time. So, it is not true. The--all
the way that you can take it [INDISTINCT]
says, "You know, I don't even need you guys.
I can just have myself. In fact I don't need
my body, I can just have my brain with the
thoughts that you were all here." So what
this scenario really predicts is that the
overwhelming majority of intelligent observers
are disembodied brains that fluctuate out
of the chaos into a configuration that lives
long enough to look around and go, "Ha, thermal
equilibrium," and then dissolves back into
the surrounding chaos. So, we don't live like
that, this is not true. This is ruled out
by the data. These brains are known as Boltzmann
brains. This is an image from a story about
them in the New York Times. They mislabeled
them. It's not Boltzmann's brain. Boltzmann's
brain is under the tombstone, in Vienna. These
are Boltzmann brains that are the prediction
of this false model. However, not only--not
everyone really likes this idea. So, after
this story was written in the New York Times,
those of us who are quoted in the story, all
received a letter from someone who didn't
really like the idea and I will read the letter
to you. I have to translate it a little bit.
This is from George Wing, who is 10 years
old. He says, "I don't know if you exist but
I do. I do not agree with your article and
I do not believe that mumbo jumbo. If you
do, well, it's a disturbing thought but I
know how to deal with it. I will not let the
world disappear under my nose but if you do,
I can't say I'm sorry. Sincerely, a 10-year-old
who knows a little more than some people,
George Wing. P.S. Some people have a little
too much time." So I appreciate the criticism
from George and from people who are much older
than George and should know better, but there's
that fundamental misunderstanding here. We're
not saying that we are Boltzmann brains. We're
saying that this a theory that predicts that
we are but we're not, therefore this theory
is wrong. This is the standard way that science
gets done. Okay. So that was a possible theory,
in the sense that it made predictions. I did
not put in an arrow of time by hand but it's
not right. We need to do better. But we have
a lot of things that Boltzmann didn't have.
We have quantum mechanics, general relativity,
cosmology, the Big Bang. So, the context of
our problem is a little bit different. What
Boltzmann knew was that at that some moment
in the far past, the entropy was very small.
What we know is very specific. We know that
we started with something like the Big Bang.
It had that low entropy but we know more than
that. It had a very specific arrangement of
particles that we need to explain. So as cosmologists,
it's our job to explain why the Big Bang was
like that. My own personal--and again, we
don't know for sure, it might be that there
is no explanation other than that's the universe
in which we live. Stephen Hawking said, "It's
like that and, therefore, it is." We are--have
a boundary condition. It's just put like that
and we need to live with it rather than try
to explain it. I think we can be more ambitious.
I think that when we have something in the
universe that is so unlikely, in terms of
conventional counting, that's a clue. That
is a hint that there's something going on
and we should uncover what it is. And my own
guess is that what is going on is that the
Big Bang is not the beginning of the universe.
In other words, an egg, an unbroken egg is
much lower entropy than scrambled eggs are.
And yet when you open your refrigerator, you're
not surprised to find an egg. You will not
go, "Huh, that's a very low entropy configuration.
This is a puzzle." Why, because the egg is
not a closed system. The egg is not all by
itself. It's not the whole universe. So maybe
the egg came out of a chicken, right? Maybe
the universe came out of the universal chicken.
Maybe the universe is not a closed system.
Maybe it's not all by itself. Maybe it's part
of a bigger system where we can find some
dynamical explanation for the arrow of time.
Now, you may get a little uncomfortable about
the idea that there exists something before
the Big Bang. That's because people like me,
cosmologists go around telling you that the
Big Bang is the beginning. There is no before
the Big Bang, talking about what happened
before the Big Bang is like talking about
what is north of the North Pole, it's a nonsensical
idea. All that is not true. I'm here to confess
to you. It maybe the way that reality is arranged
but we have no basis in what we currently
understand about the universe, for saying
with confidence that there was nothing before
the Big Bang. It's just a guess. What we have
is Einstein's Theory of General Relativity.
That's our best understanding right now of
how space and time works. This is the picture
that you should keep in mind of Einstein.
Most pictures of Einstein were taken in--when
he was 70 years old and the hair was all going
off and he was wearing the sweaters and so
forth, but back when he was actually inventing
our current notions of space and time, someone
was combing his hair and he was a very well-dressed
young man. He looked very sharp and he was
and what he was doing was understanding how
gravity worked. He says that gravity is the
manifestation of the curvature of space and
time. He wrote equations which are still the
right equations as far as we know for understanding
how the curvature of space-time responds to
stuff in the universe. Those equations tell
us that at the Big Bang, things were singular.
The curvature of space was infinite. The density
of stuff was infinite. The right way to think
about that is not to say that the Big Bang
is the boundary to time and space, the moment
in which everything came into existence. The
right way to think of it is to say that we
don't know what happens. That is the position--that
is the place, the moment where our understanding
gives out, the equations blowup and it's not
that we sense--say it--we can say from those
equations what happened, it's just that we
need better equations. Einstein's General
Theory of Relativity is not good enough to
tell us what happened at the Big Bang. And
this is not a surprise because general relativity
is not compatible with quantum mechanics,
the other great triumphant theory of 20th
Century Physics. We know general relativity
is not the final answer. We need to do better.
So the best thing we can do about the Big
Bang right now is to say, "We don't know what
happened." We should be open-minded. Maybe
it's the beginning. Maybe it's just a phase
that the universe goes through. Maybe the
Big Bang happens every once in a while. So,
the--my strategy would be to do the same thing
that Boltzmann did. Instead of taking the
universe as we see it, let's ask what the
universe should look like. If we really buy
into this picture of entropy as counting the
number of states, the things look like and
you say that high entropy states are more
likely than low entropy states, then what
should the universe look like? Well, the answer
is, our actual universe is increasing in entropy,
it's going up toward the future, so we should
just say, "What will the future look like."
The future looks like empty space. Nothing
there. So, the strong prediction of a sensible
model, if you take the entropy arguments seriously,
is that we should live in empty space. And
you might say like Boltzmann did, "Well, but
we can't." There's an entropic reason why
we don't live in an empty space, mainly there's
nothing there to do the living. It's empty.
But even that argument turns out not to quite
be right and the reason why is again because
of Dark Energy. If the Dark Energy is truly
persistent and constant as we think it probably
is. It doesn't go away. It lasts forever.
But in the 1970's, Gary Gibbons and Stephen
Hawking said that, "If you have Dark Energy,
even empty space isn't really completely empty."
In the following sense, if you go to empty
space, Google Years in the future from now
and you bring along a thermometer or a particle
detector and you say, "Well, just put it there
and wait to see what it measures." You might
say, "Well, it's empty space, it doesn't measure
anything." But in fact, there are fluctuations
due to quantum mechanics and all the fields
of which the universe is made. The electromagnetic
field, the electron field, the neutrino fields,
the gravitational field, these all fluctuate.
If there were no dark energy, if space were
truly zero energy then those fluctuations
would be undetectable. But when there is dark
energy, they bring to life those fluctuations.
There is a non-zero temperature to empty space.
I can tell you what the temperature is, it's
about 10 to the minus 30 degrees Kelvin. It's
very cold. Actual empty space right now has
the cosmic microwave background in it which
is three degrees Kelvin, that's a lot warmer
and more comfortable but even empty space
has a non-zero temperature. And what that
means is there are fluctuations, particles
can come and bump into your thermometer and
it lasts forever. So it in fact is Boltzmann's
scenario. What we said was a ridiculous scenario
that is not right, turns out to be the real
world. It's the favorite scenario of modern
cosmologists. The universe will last forever
and there will be these thermal fluctuations
inside. This will include atoms. You will
fluctuate into molecules. You will fluctuate
into DNA. You will fluctuate into brains and
planets and galaxies. But you're still stuck
with the fact that that's not the world we
live in. This is a problem. This is what is
called the Boltzmann brain problem. Why do
we live in this warm comfortable part of the
universe when there's an infinite amount of
time stretching out in the future? And a very
small probability per year that things like
us will fluctuate into existence. So you multiply
a small probability by an infinite amount
of years and almost all the people in our
real universe should be disembodied brains
living in empty space. We are not, that is
a puzzle. Furthermore, most planets should
be otherwise in empty space, et cetera. However,
unlike Boltzmann we have a loophole. We have
something that Boltzmann didn't have and that
is relativity, general relativity. The idea
that space and time are not absolute, not
fixed, just sitting there. They are actors
in the game. They're not just the stage. They
can change. So, in fact, you can get fluctuations,
not only in particles but in space-time itself.
So it's possible, although this is again,
not established physics by any means, it is
possible that if you wait long enough you
will fluctuate into not only a brain but a
whole new universe. In other words, you can
imagine, because space and time are flexible,
you can imagine there's a fluctuation in which
not only do you get a bunch of energy to make
some object but space-time itself bends and
pinches off. So you start a little bump, but
then it becomes a little pinched-off region
of space and then it becomes a completely
disconnected region of space. It separates
from the universe around it and it's almost
egg-shaped, just to keep the entropy argument
going there. It's almost like the universe
is giving birth to another little egg. We
call this a baby universe. And the thing is
that the baby universes are easier to make
if they're small. So you make small universes
rather than big ones, but most universes that
you make, most baby universes don't last very
long. They will just collapse very, very quickly
and you will not notice that they were ever
there. Occasionally, however, you will fluctuate
into not only a baby universe, but a baby
universe with a huge amount of dark energy
and you might worry and you might say, "Well,
where does energy come from?" This is the
miracle of general relativity that if you
have a closed part of the universe, if you
have a self-contained region of space, the
total energy is always exactly zero. It caused
no energy to make a new universe. You can
make as many of them as you want. If it's
an empty universe, it will just re-collapse,
but if it contains a huge amount of dark energy,
that will make that universe expand and accelerate.
And the dark energy will fill it with the
tremendous amount of energy density which
will eventually then decay into a hot plasma
that is very smoothly spread out throughout
the universe because of the stretching influence
of the Dark Energy. In other words, the natural
future of this baby universe is just like
what we perceive as the Big Bang. So the idea
is that, unlike in Boltzmann's scenario, here,
we have a way to increase the entropy. In
Boltzmann's scenario, we said we were in thermal
equilibrium. We are at the maximum entropy
we could possibly get, but the hypothesis
that we're now considering is that there is
no such thing as maximum entropy. There is
no state of the universe in which it just
sits there, stably forever. The entropy can
always increase by making new universes. This
universe costs zero energy. You can make them.
One could come into existence in this room
right now. They're very small. From our point
of view, what it would like is a little Black
Hole fluctuating into existence then evaporated
away almost as quickly you would not even
notice. You might have just given birth right
here to a whole new universe. This is very
rare, unlikely it has happened even once in
the last 13.7 billion years, but we have an
infinite number of years to wait. It will
happen in infinite number of times. So, the
universe is a bubble-making machine. The bubbles
mostly collapse and go away but occasionally,
they grow into universes like ours. The explanation,
in other words, is that the reason why we
live in a warm universe where entropy is increasing
is because we are a spin-off of the bigger
universe's attempts to increase its entropy
forever. And the nice thing about this scenario
is that it could work both directions in time.
So here is the map of the universe in space
and time, time is going vertically and in
the middle of this map, you're in empty space.
Nothing but dark energy. Nothing else going
on. There's no arrow of time. There's time
but there's no difference between the past
and future in this empty region of the universe.
So you evolve it forward in time and you ask,
"What happens?" And what happens is it gives
birth to a new universe, here and there. So
these little funnels are new universes, baby
universes that come into existence, are warm
and happy for a while and then become empty
space themselves and last forever. This happens
many times and in that little period between
the birth and the baby universe and when it
cools off, there is an arrow of time. We live
in one of these regions. Just one of these
tiny little regions of space-time is our entire
observable universe. However, if you go to
the past, the same thing should happen, because
the Laws of Physics work the same forwards
and backwards. So there should be the birth
of baby universes, they will expand and cool
toward our past. So these guys, if we--if
they live here observe an arrow of time, but
it's pointing toward what we would call the
past. To them, we are in the far past, to
us, they are in the far past. Locally, everyone
sees everything normal. There's no universe
in which there's a Benjamin Button scenario
and people are born old and grow younger.
Everyone to them--to their own point of view
is born young and grows older, observes eggs
turning into scrambled eggs, remembers the
past and not the future. It's just that the
overall orientation is different between these
two different sets of universes which are
completely disconnected and can never talk
to each other. The nice thing about this is
you didn't put it in the arrow of time. You
didn't assume it from the start. You started
in empty space with no arrow of time and it
developed out of the creation of baby universes.
Of course, we have no right to say this is
what happens. This is attractive scenario
for the reasons I just explained, but there's
a lot of unknown physics lurking here. So
the question you should be asking is, "How
would you ever know?" You should be asking
the same question that Ernst Mach was asking
Boltzmann back in the late 19th century; "How
you see these things? How will you ever know
that they are actually real?" Well, unlike
atoms, improved technology will not allow
us to see baby universes if they are truly
disconnected. But we don't know if that is
true. There are some people who are looking
into the possibility that other universes
literally bumped into our universe and leaves
signals in the cosmic microwave background.
You might say, "Well, it should be obvious
if another universe bumped into us." But in
fact it's not. There's many scenarios in which
the influence of another universe in our past
is actually fairly subtle and you have to
look very hard to try to observe it. The more
promising idea, I think, is that we need to
understand better the Fundamental Laws of
Physics. If we understand how gravity, particle
physics and quantum mechanics all play together,
we'll be able to say whether it is naturally
true that empty space predicts that baby universes
are created or not. So what we need to do
is improve our knowledge of particle physics
and gravity. One obvious example is the Large
Hadron Collider at CERN in Geneva. The new
particle accelerator that just turned on and
is now collecting data, smashing protons together
at unprecedented energies, trying to discover
new laws of physics, new ways that particles
interact with each other. Another example
as Chris mentioned at the beginning of my
talk is, observations of the universe. The
astronomical decadal survey recently came
out and is saying that we should look to understand
better Dark Energy and Fundamental Physics
throughout the universe. So I think it's these
kinds of observations which will eventually
help us figure out not only what our universe
looks like but what maybe the multiverse looks
like. All right, so the last slide, just to
put you back in firm grounding here, here
are three things we know for sure. First,
we know that this it is entropy that is responsible
for the arrow of time, even things that don't
feel especially entropic, like the fact that
you remember the past but not the future are
all ultimately due to the fact that you live
in an environment where entropy is consistently
going up. The second thing is that the reason
why entropy is going up is because we live
in the aftermath of the Big Bang. It's the
special, initial conditions 13.7 billion years
ago that setup the universe like a little
wind-up toy. It's been clicking along ever
since and eventually it will just die out.
The third thing we know is that we don't know
why. We don't have the final answer to why
the Big Bang had such a low entropy. This
is an incredibly important pressing problem
for modern cosmology if we are going to claim
to be understanding in making predictions
about the early universe; this is the puzzle
we really have to solve. So when it comes
about what we don't know, we don't know what
the right answer is. We don't know. Is it
just initial conditions? Are we supposed to
be satisfied with knowing what the early universe
is like and not trying to explain it? Or is
there something else going on? Is our universe
part of a bigger picture? I love the fact
that you are led to these speculations by
thinking about stuff that happens in your
kitchen and your everyday lives. And if you
want to learn more, people are writing books
about this stuff or you can just wait to see
what the experiments and the theories tells
us. I hope that I can come back, you know,
in a year or two and explain all the answers
to these pressing questions. Thank you.
>> 
CHRIS: All right. Thank you very much. I think
we might have time for a couple of questions.
It doesn't look like we're getting kicked
out that right away. So if you want to ask
a question, feel free to step up to the microphone.
>> So you had a picture of what the world
looked like, the one second after the Big
Bang.
>> CARROLL: Yes.
>> How do you take that photograph? Were you
there?
>> CARROLL: This is a--yeah, so this is an
image one second after the Big Bang. This
is--to be honest, it's a false color image.
But it is based on data in the following way.
We, you know, we see the cosmic microwave
background. That is the earliest epoch in
the history of the universe we can actually
see with a telescope. However, one second
after the Big Bang, the universe was a nuclear
reactor. It was turning protons and neutrons
into helium, deuterium and lithium. We can
make a prediction based on our theories of
the universe right now that says if the universe
was behaving in such and such a way, how much
helium should you get, et cetera. Those predictions
turned out to be right. So the point is that
one second after the Big Bang is that moment
about which we have empirical information.
Before that, we don't. We can extrapolate
our theories back to ten to the minus 35 seconds
after the Big Bang, but here we actually have
constraints. You can't come up with the new
theory of cosmology that says the universe
was doing something radically different one
second after the Big Bang.
>> Thanks.
>> How do baby universes solve the Boltzmann
brain problem? Wouldn't you be much more likely
to create a little baby universe big enough
just for one Boltzmann brain?
>> CARROLL: Now, that's a very good question.
I mean, the honest answer is, we don't know.
So the question is fine, you make baby universes,
but why don't you make small low entropy baby
or high entropy baby universes? Tiny fluctuations,
rather than big fluctuations that have a hundred
billion galaxies in them. So, I can't tell
you, for honest, that we know that you do,
but if it is true that it solves the Boltzmann
brain problem, it's because of inflation.
It's because the universes that survived,
that there are basically two categories of
baby universes. There's baby universes that
just re-collapse or baby universes that start
exponentially expanding under the influence
of inflationary cosmology. And if that's true,
it's easy to get a hundred billion galaxies;
no problem. So the fundamental answer for
how you solve the Boltzmann brain problem
is that it's easier to make a universe than
to make a brain.
>> 
Since your talk is about entropies, going
on a little bit of dance in here, but are
you familiar with the Erik Verlinde's new
theory about gravity being--can be explained
as entropic force on the holographic universe
and would it come...
>> CARROLL: A little bit, yes.
>> Okay.
>> CARROLL: So do you want to know something
about it?
>> Yeah. Well, my question is--I mean, do
you think that is a credible theory? And if
so--first of all--I mean, how does it actually
interact with the arrow of time, because we
think of gravity as something that happens
in time, right?
>> CARROLL: So this physicist named Erik Verlinde
caused a raucous recently by being quoted
in the New York Times saying, "Gravity does
not exist." That's not true. Gravity exists.
He does admit that things fall, but what he
means when he says gravity does not exist
is really that space and time, the curvature
of which we see as gravity are not fundamental.
That just like air is not some air fluid.
It's actually just made of atoms interacting
in different ways. He thinks that there's
a fundamental deeper constituent that makes
up space and time and just like sound waves
can actually be explained in terms of atoms,
gravity can be explained in terms of the thermodynamics
or the statistical mechanics of these underlying
degrees of freedom. It's a--it's an interesting
idea. It's very promising. We'd--we honestly
don't know yet whether it is absolutely revolutionary
and true; completely false or not even able
to be turned into a sensible theory. So, the
jury is still out on that. I think it's going
to be interesting to see what happens to it
over the next few years.
>> There are a lot of theories about the universe
is expanding and there's some major change
coming along in 2012. Do you have any point
of view on that?
>> CARROLL: Wait, I'm sorry. I couldn't hear
you. Say that again.
>> There are a lot of theories about the expansion
of universe and the frequency of Earth changing
in the near future like 2012. There are a
lot of theories along that.
>> CARROLL: Oh, 2012, right, yes.
>> Yeah.
>> CARROLL: Complete craziness unfortunately,
yes.
>> Do you have any major--something to say
about that?
>> CARROLL: Yes. What happens in 2012 is much
more like the Y2K problem than the end of
the universe. It's really just the date in
the Mayan Calendar, when you flip over to
the next page; it's not the end of anything
even according to the Mayans. And certainly
according to modern cosmology, there's nothing
dramatic that is going to happen in 2012 except
the possibility that Sarah Palin becomes President
or something like that. But certainly from
the cosmology and fundamental physics point
of view, nothing bad is scheduled.
>> How do you know you're not a Boltzmann
brain? Is that disprovable?
>> CARROLL: Now, that's a very good question.
How do I know that I didn't just imagine you
making that question? I mean, frankly, my
imagination could do better in terms of questions
that--but it remains true, that if I say the
following question, given that my brain exists
and given that in my brain there are the perceptions
that you all exist and there's the memory
that I just gave the talk and the memories
of you asking these questions, et cetera,
and nothing else; no other information. What
would I predict about the rest of the universe
and the answer is, "Yeah, you're all thermal
equilibrium and it's all just a fluctuation
into my brain." How do you know that's not
true? And I said that you know that's not
true because you make a prediction and the
prediction comes false. You walk outside and
it should be thermal equilibrium. That's a
little bit quick. That's not a very rigorous
answer because if I walk outside and I see
that it is not thermal equilibrium but then
I re-ask the question and I say, "Well, given
that I saw it's not thermal equilibrium outside,
what do I predict," and the answer is still,
that you guys are all in thermal equilibrium.
So, the better answer is that it's cognitively
unstable. In other words, I cannot get through
life consistently and coherently imagining
that I am a Boltzmann brain. And you can ask
the same questions about being a brain in
a vat or a simulation on a computer. I cannot
make sense of the world around me assuming
that I am a Boltzmann brain. You can always
be a radical or epistemological skeptic. You
can always believe that I have no right to
believe that gravity exists, et cetera, but
you don't walk out tall buildings from the
top floor; likewise to live in the world you
have to make some sense on what you see around
you. And to do that, the only intellectually
respectable thing is to imagine that you're
not a Boltzmann brain.
>> Okay. Thanks.
>> What difference do you think it will make
ten to the fifteen or ten to the one hundred
or ten to the tenth to the one hundred years
from now whether or not any of us lived or
what we did with our lives and is there anything
we can do to change that?
>> CARROLL: Well, I guess I think the difference
that is made is made now. And I kind of believe--I'm
not 100% sure about this, but I kind of believe
that if we wait ten to the one hundred years
in the future, I can't see any possible way
in which there's any record of anything that
we have done now that will remain no matter--is
it just for--it seems to me to be in principle
impossibility, not just a practical problem.
But I could be wrong, it just--I could just
not be especially imaginative about it. Some
people like Freeman Dyson have claimed that
we can organize things that we do in infinite
number of CPU cycles between here and the
end of the universe. But I think these are
open questions and honestly, it does not keep
me awake at night. Even if everything that
I do is forgotten Google Years from now, I
am still motivated to do things today.
>> So you think then if--that for those of
us who are concerned about what happens ten
to the tenth of a hundred years from now that
the solution is to be more imaginative and
to read up on this Dyson guy?
>> CARROLL: That'll be one--I can't give you
advice. Sorry. You could do that.
>> My question is a little more technical
and less sort of morally philosophically oriented.
Okay. So the theory as I understand it is
that the universe will expand forever because
of the nature of dark energy. But I also understand
that the current inflationary theory posits
that dark energy underwent a phase transition
where its behavior changed. What is--what
leads us to believe that won't happen again?
>> CARROLL: Well, that's a very good question.
Dark Energy, I said that it is persistent
and it's constant, ten to minus eight ergs
per cubic centimeter and it will last forever.
That's not necessarily true. In fact, we believe
that the amount of dark energy per cubic centimeter
was higher in the past. There can certainly
be phase transitions in which things change.
The best argument that it won't happen in
the future is that it hasn't happened in the
past. The universe is already old enough that
if the dark energy we observe now were truly
unstable it probably would've decayed already.
That's not airtight though, we can certainly
get around that. And it's a very viable theory
to imagine that the dark energy is very, very
slowly changing. I just think from experience
personally writing papers about these other
possibilities, the possibility that it holds
together the best seems the most robust and
easy is the one that says that dark energy
is constant and it's not going to change.
So that's where I based these ideas on. If
the universe--if the dark energy really does
go away, we don't have a Boltzmann brain problem
for the future; we still have the problem
of the low entropy past and now I don't know
how to solve it, so I actually don't think
that's an improvement. Yes?
>> Yeah, so you talked about like Google Years
from now when the universe is cold and there
could be an--there's a possibility of fluctuations
which could lead to baby universes. I mean,
is this leading this direction that the fluctuations
are big enough to clear a single Big Bang
or it's just a single universe? Like you gave
an example that, how much time do we have
to wait so that are all the gas particles,
gas atoms or molecules in this room are in
that one corner of the room, right?
>> CARROLL: Uh-huh.
>> So is there a possibility that, I mean,
all the matter that--it is--you may have to
wait for infinite time but they collapse together
to one part of the universe and again a new
Big Bang start?
>> CARROLL: I think that's not a very big
worry because you can calculate the time these
things take; so there's matter in the universe--it's
doing--it is subjects to a lot of random fluctuations.
But the--even though the universe is old,
13.7 billion years, that's a very short time
compared to any of these fluctuation time
scales. Once you get more than about a hundred
particles, the time scale for fluctuations
like we're talking about becomes larger than
the age of the universe. So these kinds of
thermal fluctuations into--or entropy states
are just not relevant for the universe over
the time scales of a Google Years over the
actual amount of time that it will take for
the universe to expand and do things and evaporate
away. So first, all the matter in the universe
will disperse into nothingness long before
we have to worry about thermal fluctuations.
The baby universe kinds of fluctuations are
really quantum mechanical fluctuations to
space and time itself. That's a little bit
different.
>> When I tried to describe your book to my
friends and parents and I tried to make the
connection between the Second Law of Thermodynamics
being the only thing we have that gives direction
to time, which is kind of an abstract notion,
especially for non-scientists and the idea
that we believe we can influence the future
but not the past...
>> CARROLL: Right.
>> ...which is a very concrete thing, it's
hard to make that intuitive connection.
>> CARROLL: Yes.
>> Can you please flesh that out a little
bit?
>> CARROLL: Well, I tried in the books, my
best; although I'll admit that I didn't do
a great job, so you're right. That is something
that is--it's something you can say. It's
something that is true. It is hard to make
it quite vivid. The example that I use is--so
the question just to make sure everyone is
clear, the reason why there's an arrow of
time is because entropy is increasing. One
of the manifestations of the arrow of time
is the fact that we can influence the future
by making decisions, we cannot influence the
past. We can, you know, the--what I think
I say in the book is, if your friend says,
"I've changed my mind. Instead of having Chinese
food for dinner tonight, let's have Italian
food." You would say, "Okay", then you make
a decision. If your friend says, "I've changed
my mind. Instead of having had Vietnamese
food last night, let's have had French food
last night." You'll go, "You're nuts." Ultimately,
that's because of entropy, but it's hard to
say exactly why. But let me give you a little
example that I think is the best that I can
do right now. Imagine you're walking down
the street and on the sidewalk you find a
broken egg, okay? And you ask yourself, "Well,
what are the possible futures over the next
24 hours of that broken egg?" And there's
lots of possibilities. Someone could clean
it up. Dog could come by and eat it. It could
just sit there and get moldy or it could be
washed-away by a rainstorm. There's many open
things. If you say, "What was the possible
past 24 hours of that egg?" You'll like, "Well,
24 hours ago it was an unbroken egg." You're
much more certain in your reconstruction of
the past than of the future. And why, because
you know the past is subject to a low entropy
boundary condition. So you know something
about today and you know something about the
past, but you know nothing about the future
in terms of macroscopic boundary conditions.
So because of that, the set of possible interpolations
between the past and today is much more small,
much more restricted than the set of possible
futures. If you believe in Deterministic Evolution,
if you knew everything about the universe,
you could predict the future just as well
as you could predict the past but we have
much less information about the future than
we have about the past. So that's why the
past seems fixed to us, because there's fewer
things that are compatible with what we know,
when it comes to the past than comes to the
future. The best I can do, yes.
>> CHRIS: That's it, one last question. We
can take one last question.
>> Quick question. If one universe spuns off
two baby universes that are both the same
size as the parent, doesn't that break the
Law of Conservation of Mass Energy?
>> CARROLL: No, it doesn't because every new
universe has a total of zero energy. That's
the great thing about general relativity.
Roughly intuitively the way to think about
that is that there's stuff in that universe
but there's also space-time curvature and
the curvature of space-time accounts for a
negative amount of energy always exactly equal
to the positive energy of the stuff inside,
that's just an implication of Einstein's theory.
So, you can make universes forever and that's
the escape hatch that lets you to escape the
Boltzmann brain dilemma and hopefully try
to explain the arrow of time.
>> CHRIS: Thanks for answering these questions.
Let's thank Dr. Carroll again.
