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The universe

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is really big.

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We live in a galaxy, the Milky Way Galaxy.

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

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And if you take a camera

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

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and you just keep the shutter open,

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

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it will see something like this.

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Every one of these little blobs

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is a galaxy roughly the size of our Milky Way --

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a hundred billion stars in each of those blobs.

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There are approximately a hundred billion galaxies

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in the observable universe.

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100 billion is the only number you need to know.

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The age of the universe, between now and the Big Bang,

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is a hundred billion in dog years.

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(Laughter)

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Which tells you something about our place in the universe.

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

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It's extremely beautiful.

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I've often wondered, what is the evolutionary pressure

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that made our ancestors in the Veldt adapt and evolve

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to really enjoy pictures of galaxies

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when they didn't have any.

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But we would also like to understand it.

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As a cosmologist, I want to ask, why is the universe like this?

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

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

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it would be moving away from you.

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And if you look at a galaxy even farther away,

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it would be moving away faster.

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So we say the universe is expanding.

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

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things were closer together.

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In the past, the universe was more dense,

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and it was also hotter.

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If you squeeze things together, the temperature goes up.

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That kind of makes sense to us.

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

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is that the universe, at early times, near the Big Bang,

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was also very, very smooth.

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You might think that that's not a surprise.

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The air in this room is very smooth.

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You might say, "Well, maybe things just smoothed themselves out."

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

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than the conditions of the air in this room.

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In particular, things were a lot denser.

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The gravitational pull of things

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was a lot stronger near the Big Bang.

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What you have to think about

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is we have a universe with a hundred billion galaxies,

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a hundred billion stars each.

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At early times, those hundred billion galaxies

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were squeezed into a region about this big --

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literally -- at early times.

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And you have to imagine doing that squeezing

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without any imperfections,

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without any little spots

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where there were a few more atoms than somewhere else.

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Because if there had been, they would have collapsed under the gravitational pull

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into a huge black hole.

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Keeping the universe very, very smooth at early times

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is not easy; it's a delicate arrangement.

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It's a clue

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that the early universe is not chosen randomly.

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There is something that made it that way.

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We would like to know what.

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

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an Austrian physicist in the 19th century.

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

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You've heard of entropy.

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

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Boltzmann gave us a formula --

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engraved on his tombstone now --

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that really quantifies what entropy is.

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And it's basically just saying

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that entropy is the number of ways

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

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so that macroscopically it looks the same.

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If you have the air in this room,

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you don't notice each individual atom.

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A low entropy configuration

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is one in which there's only a few arrangements that look that way.

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A high entropy arrangement

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is one that there are many arrangements that look that way.

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This is a crucially important insight

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because it helps us explain

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the second law of thermodynamics --

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the law that says that entropy increases in the universe,

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or in some isolated bit of the universe.

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The reason why entropy increases

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is simply because there are many more ways

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to be high entropy than to be low entropy.

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That's a wonderful insight,

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but it leaves something out.

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This insight that entropy increases, by the way,

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

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the difference between the past and the future.

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Every difference that there is

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between the past and the future

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is because entropy is increasing --

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

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

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always in that order,

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that's because entropy is increasing.

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Boltzmann explained that if you start with low entropy,

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it's very natural for it to increase

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because there's more ways to be high entropy.

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What he didn't explain

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was why the entropy was ever low in the first place.

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The fact that the entropy of the universe was low

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was a reflection of the fact

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that the early universe was very, very smooth.

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We'd like to understand that.

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That's our job as cosmologists.

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Unfortunately, it's actually not a problem

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that we've been giving enough attention to.

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It's not one of the first things people would say,

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if you asked a modern cosmologist,

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"What are the problems we're trying to address?"

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One of the people who did understand that this was a problem

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was Richard Feynman.

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50 years ago, he gave a series of a bunch of different lectures.

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He gave the popular lectures

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that became "The Character of Physical Law."

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He gave lectures to Caltech undergrads

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that became "The Feynman Lectures on Physics."

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He gave lectures to Caltech graduate students

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that became "The Feynman Lectures on Gravitation."

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

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he emphasized this puzzle:

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Why did the early universe have such a small entropy?

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

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he says, "For some reason, the universe, at one time,

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had a very low entropy for its energy content,

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and since then the entropy has increased.

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The arrow of time cannot be completely understood

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until the mystery of the beginnings of the history of the universe

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are reduced still further

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from speculation to understanding."

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So that's our job.

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We want to know -- this is 50 years ago, "Surely," you're thinking,

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"we've figured it out by now."

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

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The reason the problem has gotten worse,

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rather than better,

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is because in 1998

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we learned something crucial about the universe that we didn't know before.

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We learned that it's accelerating.

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The universe is not only expanding.

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If you look at the galaxy, it's moving away.

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

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it will be moving away faster.

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Individual galaxies are speeding away from us faster and faster

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so we say the universe is accelerating.

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Unlike the low entropy of the early universe,

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even though we don't know the answer for this,

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we at least have a good theory that can explain it,

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if that theory is right,

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and that's the theory of dark energy.

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

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In every little cubic centimeter of space,

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whether or not there's stuff,

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whether or not there's particles, matter, radiation or whatever,

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

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And this energy, according to Einstein,

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exerts a push on the universe.

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It is a perpetual impulse

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that pushes galaxies apart from each other.

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Because dark energy, unlike matter or radiation,

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does not dilute away as the universe expands.

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The amount of energy in each cubic centimeter

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remains the same,

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even as the universe gets bigger and bigger.

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This has crucial implications

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for what the universe is going to do in the future.

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For one thing, the universe will expand forever.

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Back when I was your age,

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we didn't know what the universe was going to do.

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Some people thought that the universe would recollapse in the future.

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Einstein was fond of this idea.

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

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the universe is just going to keep expanding forever and ever and ever.

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14 billion years in the past,

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100 billion dog years,

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but an infinite number of years into the future.

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Meanwhile, for all intents and purposes,

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space looks finite to us.

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Space may be finite or infinite,

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but because the universe is accelerating,

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there are parts of it we cannot see

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and never will see.

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

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surrounded by a horizon.

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So even though time goes on forever,

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space is limited to us.

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Finally, empty space has a temperature.

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In the 1970s, Stephen Hawking told us

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that a black hole, even though you think it's black,

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it actually emits radiation

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when you take into account quantum mechanics.

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The curvature of space-time around the black hole

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brings to life the quantum mechanical fluctuation,

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and the black hole radiates.

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A precisely similar calculation by Hawking and Gary Gibbons

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showed that if you have dark energy in empty space,

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then the whole universe radiates.

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The energy of empty space

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brings to life quantum fluctuations.

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And so even though the universe will last forever,

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and ordinary matter and radiation will dilute away,

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there will always be some radiation,

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some thermal fluctuations,

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even in empty space.

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So what this means

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is that the universe is like a box of gas

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that lasts forever.

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Well what is the implication of that?

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

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He said, well, entropy increases

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because there are many, many more ways

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for the universe to be high entropy, rather than low entropy.

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But that's a probabilistic statement.

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It will probably increase,

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and the probability is enormously huge.

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It's not something you have to worry about --

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the air in this room all gathering over one part of the room and suffocating us.

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It's very, very unlikely.

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Except if they locked the doors

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and kept us here literally forever,

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that would happen.

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Everything that is allowed,

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

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would eventually be obtained.

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So Boltzmann says, look, you could start with a universe

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that was in thermal equilibrium.

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He didn't know about the Big Bang. He didn't know about the expansion of the universe.

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He thought that space and time were explained by Isaac Newton --

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they were absolute; they just stuck there forever.

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So his idea of a natural universe

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was one in which the air molecules were just spread out evenly everywhere --

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the everything molecules.

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

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the random fluctuations of those molecules

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will occasionally bring them

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into lower entropy configurations.

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And then, of course, in the natural course of things,

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they will expand back.

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So it's not that entropy must always increase --

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you can get fluctuations into lower entropy,

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more organized situations.

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Well if that's true,

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Boltzmann then goes onto invent

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two very modern-sounding ideas --

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the multiverse and the anthropic principle.

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He says, the problem with thermal equilibrium

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is that we can't live there.

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Remember, life itself depends on the arrow of time.

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We would not be able to process information,

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metabolize, walk and talk,

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if we lived in thermal equilibrium.

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So if you imagine a very, very big universe,

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an infinitely big universe,

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with randomly bumping into each other particles,

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there will occasionally be small fluctuations in the lower entropy states,

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and then they relax back.

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But there will also be large fluctuations.

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Occasionally, you will make a planet

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or a star or a galaxy

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or a hundred billion galaxies.

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So Boltzmann says,

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we will only live in the part of the multiverse,

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in the part of this infinitely big set of fluctuating particles,

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where life is possible.

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That's the region where entropy is low.

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Maybe our universe is just one of those things

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that happens from time to time.

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Now your homework assignment

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is to really think about this, to contemplate what it means.

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Carl Sagan once famously said

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that "in order to make an apple pie,

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you must first invent the universe."

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But he was not right.

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

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you just wait for the random motion of atoms

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to make you an apple pie.

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That will happen much more frequently

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than the random motions of atoms

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making you an apple orchard

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and some sugar and an oven,

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and then making you an apple pie.

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So this scenario makes predictions.

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And the predictions are

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that the fluctuations that make us are minimal.

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Even if you imagine that this room we are in now

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exists and is real and here we are,

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and we have, not only our memories,

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but our impression that outside there's something

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called Caltech and the United States and the Milky Way Galaxy,

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

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than for them actually to randomly fluctuate

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into Caltech, the United States and the galaxy.

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The good news is that,

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therefore, this scenario does not work; it is not right.

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This scenario predicts that we should be a minimal fluctuation.

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Even if you left our galaxy out,

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you would not get a hundred billion other galaxies.

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And Feynman also understood this.

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Feynman says, "From the hypothesis that the world is a fluctuation,

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all the predictions are that

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if we look at a part of the world we've never seen before,

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we will find it mixed up, and not like the piece we've just looked at --

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high entropy.

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If our order were due to a fluctuation,

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we would not expect order anywhere but where we have just noticed it.

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We therefore conclude the universe is not a fluctuation."

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

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If the universe is not a fluctuation,

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why did the early universe have a low entropy?

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

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(Laughter)

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Here is the universe that we tell you about,

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versus the universe that really exists.

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I just showed you this picture.

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The universe is expanding for the last 10 billion years or so.

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It's cooling off.

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But we now know enough about the future of the universe

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to say a lot more.

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If the dark energy remains around,

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

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They will fall into black holes.

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We will live in a universe

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with nothing in it but black holes.

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That universe will last 10 to the 100 years --

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a lot longer than our little universe has lived.

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The future is much longer than the past.

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But even black holes don't last forever.

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They will evaporate,

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and we will be left with nothing but empty space.

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That empty space lasts essentially forever.

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

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there's actually thermal fluctuations,

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and it cycles around

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all the different possible combinations

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of the degrees of freedom that exist in empty space.

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So even though the universe lasts forever,

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there's only a finite number of things

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that can possibly happen in the universe.

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They all happen over a period of time

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equal to 10 to the 10 to the 120 years.

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So here's two questions for you.

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Number one: If the universe lasts for 10 to the 10 to the 120 years,

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why are we born

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in the first 14 billion years of it,

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in the warm, comfortable afterglow of the Big Bang?

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Why aren't we in empty space?

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You might say, "Well there's nothing there to be living,"

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but that's not right.

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You could be a random fluctuation out of the nothingness.

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Why aren't you?

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More homework assignment for you.

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

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I'm going to give you my favorite scenario.

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Either it's just like that. There is no explanation.

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This is a brute fact about the universe

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that you should learn to accept and stop asking questions.

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Or maybe the Big Bang

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is not the beginning of the universe.

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An egg, an unbroken egg, is a low entropy configuration,

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and yet, when we open our refrigerator,

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we do not go, "Hah, how surprising to find

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this low entropy configuration in our refrigerator."

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

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it comes out of a chicken.

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Maybe the universe comes out of a universal chicken.

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Maybe there is something that naturally,

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through the growth of the laws of physics,

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gives rise to universe like ours

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in low entropy configurations.

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

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we would be part of a much bigger multiverse.

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That's my favorite scenario.

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

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My bold speculation

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is that I will be absolutely vindicated by history.

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And 50 years from now,

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all of my current wild ideas will be accepted as truths

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by the scientific and external communities.

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We will all believe that our little universe

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is just a small part of a much larger multiverse.

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

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in terms of a theory

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that we will be able to compare to observations.

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This is a prediction. I might be wrong.

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But we've been thinking as a human race

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about what the universe was like,

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

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It's exciting to think we may finally know the answer someday.

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Thank you.

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(Applause)