Cosmology and the arrow of time | Sean Carroll | TEDxCaltech

This talk was given at a local TEDx event, produced independently of the TED Conferences.
Sean Carroll research ranges over a number of topics in theoretical physics, focusing on cosmology, particle physics, and general relativity, with special emphasis on dark matter, dark energy, and the origin of the universe.

The Universe is really big.

We live in a galaxy, the Milky Way Galaxy.

There are about a hundred billion stars
in the Milky Way Galaxy,

and if you take a camera and you point it
at a random part of the sky,

and you just keep the shutter open,

as long as your camera is attached
to the Hubble Space Telescope

it will see something like this.

Every one of these little blobs
is a galaxy,

roughly the size of our Milky Way.

A hundred billion stars
in each of those blobs,

there are approximately a hundred billion
galaxies in the observable Universe.

A hundred billion is the only number
you need to know,

the age of the Universe
between now and the Big Bang

is a hundred billion in dog years

(Laughter)

which tells you something
about our place in the Universe.

One thing you can do with a picture
like this is simply admire it,

it's extremely beautiful,
and I've often wondered

what is the evolutionary pressure
that made our ancestors develop,

adapt, and evolve to really enjoy pictures
of galaxies, when they didn't have any.

But we would also like to understand it,

as a cosmologist I want to ask,
"Why is the Universe like this?"

One big clue we have is
that the Universe is changing with time.

If you looked at one of these galaxies
and measured its velocity,

it would be moving away from you,

and if you look at a galaxy even further
away, it will be moving away faster.

So we say
that the Universe is expanding.

What that means, of course,
is that in the past,

things were closer together.

In the past, the Universe
was more dense, and it was also hotter,

if you squeeze things together
the temperature goes up.

That makes sense to us.

The thing that doesn't make sense
to us as much is

that the Universe at early times,
near the Big Bang,

was also very, very smooth.

You might think that's not a surprise;
the air in this room is very smooth,

you might say: "Well, these things
smooth themselves out."

But the conditions near the Big Bang
were very, very different

than those of the air in this room.

In particular, things were a lot denser,

the gravitational pull of things
was a lot stronger near the Big Bang.

What you have to think about is,

we had a Universe
with a hundred billion galaxies,

a hundred billion stars each,

at early times,
those hundred billion galaxies

were squeezed into a region
about this big, literally at early times;

you had to imagine doing
that squeezing without any imperfections,

without any little spots where there were
a few more atoms than somewhere else,

because if there had been,
they would've collapsed

under the gravitational pull
into a huge black hole.

Keeping the Universe very, very smooth
at early times is not easy.

It's a delicate arrangement.

It's a clue that the early Universe
is not chosen randomly,

there was something
that made it that way,

and we would like to know what.

So part of our understanding of this
was given to us by Ludwig Boltzmann,

an Austrian physicist in the 19th century,

and Boltzmann's contribution was
that he helped us understand entropy.

You've heard of entropy,

it's the randomness, the disorder,
the chaoticness of some systems.

Boltzmann gave us a formula,
engraved on his tombstone now,

that really quantifies what entropy is.

It's basically just saying
that entropy is the number of ways

we can rearrange the constituents
of a system so that you don't notice.

So that macroscopically,
it looks the same.

In the air in this room,
you don't notice each individual atom.

A low entropy configuration is one

where there are only a few arrangements
that look that way.

A high entropy arrangement is one

that there are many arrangements
that look that way.

This is a crucially important insight,

because it helps us explain
the second law of thermodynamics;

the law that says that entropy
increases in the Universe,

or in some isolated bit of the Universe.

The reason why the entropy increases
is simply because there are many more ways

to be high entropy than to be low entropy.

That's a wonderful insight,
but it leaves something out.

This insight that entropy
increases, by the way,

is what's behind what we call
'the arrow of time, '

the difference between the past
and the future.

Every difference that there is
between the past and the future

is because entropy is increasing.

The fact that you can remember
the past but not the future.

The fact that you are born,
and then you live,

and then you die, always in that order,

that's because entropy is increasing.

Boltzmann explained
that if you start with low entropy,

it's very natural for it to increase

because there are more ways
to be high entropy.

What he didn't explain was why the entropy
was ever low in the first place.

The fact that the entropy
in the Universe was low,

is a reflection of the fact
that the early Universe was very smooth,

we would like to understand that,
that's our job as cosmologists.

Unfortunately, it's actually not a problem
we've been giving enough attention to.

It's not one of the first things
people would say if you ask

a modern cosmologist what are
the problems we're trying to address.

One of the people who did understand
this was a problem was Richard Feynman.

50 years ago, he gave
a series of different lectures

- you've heard about them already -

popular lectures that became
"The Character of physical law,"

he gave lectures to Caltech undergrads

that became
"The Feynman lectures on physics,"

to Caltech graduate students,
"The Feynman lectures on gravitation."

In every one of these books,
every one of these sets of lectures,

he emphasized this puzzle:

why did the early Universe
have such a small entropy?

So he says:
- and I'm not going to do the accent -

"For some reason, the Universe,
at one time, had a very low entropy

for its energy content,
and since then, the entropy has increased.

The arrow of time cannot be
completely understood

until the mystery of the beginnings
of the history of the Universe

are reduced still further
from speculation to understanding."

So that's our job, we want to know.

This is 50 years ago,
surely, you're thinking,

we've figured it out by now.

It's not true
that we've figured it out by now.

In fact, it's more
than a fifty-year old problem,

Boltzmann understood
that this was a problem,

and he suggested an answer to it.

Before I get to that,

I should say that the reason the problem
has gotten worse, rather than better,

is because in 1998, we learned something
crucial about the Universe,

that we didn't know before.

We learned that it's accelerating.

The Universe is not only expanding,

if you look at that galaxy,
it's moving away,

you come back a billion years later
and look at it again,

it'll be moving away faster.

Individual galaxies are speeding
away from us, faster and faster,

so we say the Universe is accelerating.

Unlike the low entropy
of the early Universe,

even though we don't know the answer
for this we at least have a good theory,

that can explain it
if that theory is right,

and that's the theory of dark energy.

It's just the idea
that empty space itself has energy,

and every little cubic centimeter of space

whether or not there's stuff,

whether there's particles,
matter, radiation, or whatever,

there's still energy,
even in the space itself.

This energy, according to Einstein,
exerts a push on the Universe,

it's a perpetual impulse that pushes
galaxies apart from each other.

Because dark energy,
unlike matter radiation,

does not dilute away
as the Universe expands.

The amount of energy in each cubic
centimeter remains the same,

even as the Universe
gets bigger and bigger.

This has crucial implications
for what the Universe is going to do

in the future.

For one thing, the Universe
will expand forever.

Back when I was your age,

we didn't know what
the Universe was going to do,

some people thought it would
recollapse in the future,

Einstein was fond of this idea.

But if there's dark energy
and the dark energy does not go away,

the Universe is just going
to keep expanding for ever and ever.

14 billion years in the past,
a hundred billion dog years,

but an infinite number
of years into the future.

Meanwhile, for all intents and purposes,
space looks finite to us.

Space may be finite or infinite,

but because the Universe is accelerating

there are parts of it
we cannot see and never will see.

There's a finite region of space
that we have access to,

surrounded by a horizon,

so even though time goes on forever,
space is limited to us.

Finally, empty space has a temperature.

In the 1970s, Stephen Hawking
told us that a black hole,

even though you think it's black,
it actually emits radiation

when you take into account
quantum mechanics.

The curvature of space-time
around the black hole

brings to life the quantum mechanical
fluctuation that the black hole radiates.

A precisely similar calculation
by Hawking and Gary Gibbens

shows that if you have
dark energy in empty space,

then the whole Universe radiates.

The energy in empty space brings
to life quantum fluctuations,

so even though the Universe
will last forever,

and ordinary matter radiation
will dilute away,

there will always be some radiation,
some thermal fluctuations,

even in empty space.

So what this means is that, the Universe
is like a box of gas that lasts forever.

What are the implications of that?

That implication was studied by Boltzmann,
back in the 19th century.

He said, well, entropy increases
because there are many many more ways

for the Universe to be high entropy
rather than low entropy.

But that's a probabilistic statement.

It will probably increase,

and the probability is enormously huge,

it's not something
you have to worry about,

the air in this room all gathering over
one part of the room,

and suffocating us,
it's very, very unlikely.

Except if they lock the doors
and kept us here, literally forever,

that would happen.

Everything that is allowed,

every configuration that is allowed to be
attained by the molecules in this room,

would eventually be attained.

So Boltzmann says, you can start
with a Universe in thermal equilibrium,

he didn't know about the Big Bang
or the expansion of the Universe,

he thought that space and time were
explained by Isaac Newton,

they were absolutely,
just stuck there forever.

So his idea that natural Universe
was one in which the air molecules

were just spread out evenly everywhere,
everything molecules.

But if you're Boltzmann,
you know that if you wait long enough,

the random fluctuations of those molecules

will occasionally bring them into lower
energy, lower entropy configurations.

And then of course, in the natural course
of things, they will expand back.

So it's not that entropy
must always increase,

you can get fluctuations
into lower entropy,

more organized situations.

Boltzmann then goes on to invent
two very modern-sounding ideas,

the multiverse and the entropic principle.

He says, the problem with thermal
equilibrium is that we can't live there.

Remember, life itself
depends on the arrow of time.

We would not be able to process
information, to metabolize,

walk and talk if we lived in
thermal equilibrium.

So, if you imagine a very big Universe,
an infinitely big Universe,

with randomly bumping into
each other particles,

there will occasionally be
small fluctuations to lower entropy states

and then they would relax back.

But there would also be
large fluctuations,

occasionally you'll make a planet,
or a star, or a galaxy,

or a hundred billion galaxies.

So Boltzmann says, we will only live
in the part of the multiverse,

the part that has an infinitely big set
of fluctuating particles,

where life is possible, that's the regions
where entropy is low,

maybe our Universe is just one of those
things that happens, from time to time.

Now, your homework assignment is
to really think about this,

to contemplate what it means.

Carl Sagan once famously said
that in order to make an apple pie,

you must first invent the Universe.

But he was not right.

In Boltzmann's scenario, if you want
to make an apple pie you just wait

for the random motion of atoms
to make you an apple pie.

(Laughter)

That will happen much more frequently

than the random motions of atoms
making you an apple orchard,

and some sugar, and an oven,
and then making you an apple pie.

So this scenario makes predictions,
and the predictions are

that the fluctuations
that make us are minimal.

Even if you imagine that this room
we are in now exists and is real,

and here we are and we have
not only our memories,

but our impression that outside there is
something called Caltech

and the United States
and the Milky Way Galaxy.

It's much easier for all those impressions
to randomly fluctuate into your brain

than for them to actually randomly
fluctuate into Caltech,

the United States and the galaxy.

The good news is that, therefore,
this scenario does not work,

it is not right.

This scenario predicts that we should be
in minimal fluctuation,

even if you left our galaxy out,

you would not get
a hundred billion other galaxies.

Feynman also understood this,
Feynman says:

"From the hypothesis
that the world is a fluctuation,

all the predictions are
that if we look at a part of the world

we have never seen before,
we will find it mixed up,

not like the piece we just looked at."
High entropy.

"If our order were due to a fluctuation,
we would not expect order anywhere,

but where we have just noticed it.

We therefore conclude
the Universe is not a fluctuation."

So that's good, the question is then,
what is the right answer?

If the Universe is not a fluctuation, why
did the early Universe have low entropy?

And I would love to tell you the answer
but I'm running out of time.

(Laughter)

Here is the Universe
that we tell you about

versus the Universe that really exists.

I just showed you this picture,

the Universe is expanding for the last
ten billion years or so, it's cooling off.

But we now know enough about the future
of the Universe to say a lot more.

If the dark energy remains around,

the stars around us will use up
their nuclear fuel, they'll stop burning,

they will fall into black holes.

We will live in a Universe
with nothing in it but black holes.

That Universe will last
10 to the 100 years,

a lot longer than
our little Universe has lived.

The future is much longer than the past.

But even black holes
don't last forever, they will evaporate,

and we will be left with nothing
but empty space.

That empty space lasts
essentially forever.

However, you notice that
since empty space gives off radiation,

there's actually thermal fluctuations
and it cycles around

all the different possible combinations
of the degrees of freedom

that exist in empty space.

So even though the Universe lasts forever,

there's only a finite number of things
that can possibly happen in it,

they all happen over a period of time
equal to 10 to the 10 to the 120 years.

So here are two questions for you:

number one, if the Universe lasts
for 10 to the 10 to the 120 years,

why are we born
in the first 14 billion years of it,

in the warm, comfortable
afterglow of the Big Bang?

Why aren't we in empty space?

You might say, there's nothing there
to be living, but that's not right.

You could be a random fluctuation
out of the nothingness.

Why aren't you?

More homework assignments for you.

So, like I said,
I don't actually know the answer,

I'm going to give you
my favorite scenario;

either it's just like that,
there is no explanation,

it's a brute fact about the Universe
that we should learn to accept

and stop asking questions.

Or maybe the Big Bang is
not the beginning of the Universe.

An unbroken egg is
a low entropy configuration

and yet when we open
our refrigerator we do not go:

"How surprising to find this low entropy
configuration in our refrigerator."

That's because an egg
is not a closed system.

It comes out of a chicken.

Maybe the Universe
comes out of a Universal chicken.

(Laughter)

Maybe there is something that naturally,

through the growth of the laws of physics,

gives rise to a Universe like ours
in low entropy configuration.

If that's true it would happen
more than once,

we would be part
of a much bigger multiverse.

That's my favorite scenario.

So the organizers asked me to end
with a bold speculation;

my bold speculation is that I will be
absolutely vindicated by history,

and 50 years from now all of my current
wild ideas will be accepted as truths

by the scientific and external communities

who will all believe
that our little Universe

is just a small part
of a much larger multiverse,

and even better, we will understand
what happened at the Big Bang

in terms of a theory that we will be able
to compare to observations.

It's a prediction, I might be wrong,
but we've been thinking,

as a human race,
about what the Universe was like,

why it came to be the way it did,
for many many years.

It's exciting to think, we may finally
know the answer some day.

Thank you.

(Applause)