Here is the full transcript of cosmologist Sean Carroll‘s TEDx Talk on Cosmology and the Arrow of Time at TEDxCaltech conference.
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 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 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 Gibbons 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. 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. 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. 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.