Cosmology and the arrow of time : Sean Carroll

  Transcriber: Katarina EricsonReviewer: Denise RQ The Universe is really big. We live in a galaxy, the Milky Way Galaxy. There are about a hundred billion starsin the Milky Way Galaxy, and if you take a camera and you point itat a random part of the sky, and you just keep the shutter open, as long as your camera is attachedto the Hubble Space Telescope it will see something like this. Every one of these little blobsis a galaxy, roughly the size of our Milky Way. A hundred billion starsin each of those blobs, there are approximately a hundred billiongalaxies in the observable Universe. A hundred billion is the only numberyou need to know, the age of the Universebetween now and the Big Bang is a hundred billion in dog years (Laughter) which tells you somethingabout our place in the Universe. One thing you can do with a picturelike this is simply admire it, it's extremely beautiful,and I've often wondered what is the evolutionary pressurethat made our ancestors develop, adapt, and evolve to really enjoy picturesof 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 isthat the Universe is changing with time. If you looked at one of these galaxiesand measured its velocity, it would be moving away from you, and if you look at a galaxy even furtheraway, it will be moving away faster. So we saythat 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 togetherthe temperature goes up.

  That makes sense to us. The thing that doesn't make senseto 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 thingssmooth themselves out." But the conditions near the Big Bangwere very, very different than those of the air in this room. In particular, things were a lot denser, the gravitational pull of thingswas a lot stronger near the Big Bang. What you have to think about is, we had a Universewith a hundred billion galaxies, a hundred billion stars each, at early times,those hundred billion galaxies were squeezed into a regionabout this big, literally at early times; you had to imagine doingthat squeezing without any imperfections, without any little spots where there werea few more atoms than somewhere else, because if there had been,they would've collapsed under the gravitational pullinto a huge black hole. Keeping the Universe very, very smoothat early times is not easy. It's a delicate arrangement. It's a clue that the early Universeis not chosen randomly, there was somethingthat made it that way, and we would like to know what. So part of our understanding of thiswas given to us by Ludwig Boltzmann, an Austrian physicist in the 19th century, and Boltzmann's contribution wasthat 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 sayingthat entropy is the number of ways we can rearrange the constituentsof 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 arrangementsthat look that way. A high entropy arrangement is one that there are many arrangementsthat look that way. This is a crucially important insight, because it helps us explainthe second law of thermodynamics; the law that says that entropyincreases in the Universe, or in some isolated bit of the Universe. The reason why the entropy increasesis 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 entropyincreases, by the way, is what's behind what we call'the arrow of time, ' the difference between the pastand the future. Every difference that there isbetween the past and the future is because entropy is increasing. The fact that you can rememberthe 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 explainedthat if you start with low entropy, it's very natural for it to increase because there are more waysto be high entropy. What he didn't explain was why the entropywas ever low in the first place. 

The fact that the entropyin the Universe was low, is a reflection of the factthat the early Universe was very smooth, we would like to understand that,that's our job as cosmologists. Unfortunately, it's actually not a problemwe've been giving enough attention to. It's not one of the first thingspeople would say if you ask a modern cosmologist what arethe problems we're trying to address. One of the people who did understandthis was a problem was Richard Feynman. 50 years ago, he gavea 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 Universehave 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 becompletely understood until the mystery of the beginningsof the history of the Universe are reduced still furtherfrom 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 truethat we've figured it out by now. In fact, it's morethan a fifty-year old problem, Boltzmann understoodthat this was a problem, and he suggested an answer to it. Before I get to that, I should say that the reason the problemhas gotten worse, rather than better, is because in 1998, we learned somethingcrucial 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 laterand look at it again, it'll be moving away faster. Individual galaxies are speedingaway from us, faster and faster, so we say the Universe is accelerating. Unlike the low entropyof the early Universe, even though we don't know the answerfor this we at least have a good theory, that can explain itif that theory is right, and that's the theory of dark energy. It's just the ideathat 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 pushesgalaxies apart from each other. Because dark energy,unlike matter radiation, does not dilute awayas the Universe expands. The amount of energy in each cubiccentimeter remains the same, even as the Universegets bigger and bigger. This has crucial implicationsfor what the Universe is going to do in the future. For one thing, the Universewill expand forever. Back when I was your age, we didn't know whatthe Universe was going to do, some people thought it wouldrecollapse in the future, Einstein was fond of this idea. But if there's dark energyand the dark energy does not go away, the Universe is just goingto keep expanding for ever and ever. 14 billion years in the past,a hundred billion dog years, but an infinite numberof 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 itwe cannot see and never will see.

 There's a finite region of spacethat 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 Hawkingtold us that a black hole, even though you think it's black,it actually emits radiation when you take into accountquantum mechanics. The curvature of space-timearound the black hole brings to life the quantum mechanicalfluctuation that the black hole radiates. A precisely similar calculationby Hawking and Gary Gibbens shows that if you havedark energy in empty space, then the whole Universe radiates. The energy in empty space bringsto life quantum fluctuations, so even though the Universewill last forever, and ordinary matter radiationwill dilute away, there will always be some radiation,some thermal fluctuations, even in empty space. So what this means is that, the Universeis 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 increasesbecause there are many many more ways for the Universe to be high entropyrather than low entropy.

 But that's a probabilistic statement. It will probably increase, and the probability is enormously huge, it's not somethingyou have to worry about, the air in this room all gathering overone part of the room, and suffocating us,it's very, very unlikely. Except if they lock the doorsand kept us here, literally forever, that would happen. Everything that is allowed, every configuration that is allowed to beattained by the molecules in this room, would eventually be attained. So Boltzmann says, you can startwith a Universe in thermal equilibrium, he didn't know about the Big Bangor the expansion of the Universe, he thought that space and time wereexplained by Isaac Newton, they were absolutely,just stuck there forever. So his idea that natural Universewas 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 lowerenergy, lower entropy configurations. And then of course, in the natural courseof things, they will expand back. So it's not that entropymust always increase, you can get fluctuationsinto lower entropy, more organized situations. Boltzmann then goes on to inventtwo very modern-sounding ideas, the multiverse and the entropic principle. He says, the problem with thermalequilibrium is that we can't live there. Remember, life itselfdepends on the arrow of time.

 We would not be able to processinformation, to metabolize, walk and talk if we lived inthermal equilibrium. So, if you imagine a very big Universe,an infinitely big Universe, with randomly bumping intoeach other particles, there will occasionally besmall fluctuations to lower entropy states and then they would relax back. But there would also belarge fluctuations, occasionally you'll make a planet,or a star, or a galaxy, or a hundred billion galaxies. So Boltzmann says, we will only livein the part of the multiverse, the part that has an infinitely big setof fluctuating particles, where life is possible, that's the regionswhere entropy is low, maybe our Universe is just one of thosethings that happens, from time to time. Now, your homework assignment isto really think about this, to contemplate what it means. Carl Sagan once famously saidthat in order to make an apple pie, you must first invent the Universe. But he was not right. In Boltzmann's scenario, if you wantto make an apple pie you just wait for the random motion of atomsto make you an apple pie. (Laughter) That will happen much more frequently than the random motions of atomsmaking 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 fluctuationsthat make us are minimal.

 Even if you imagine that this roomwe are in now exists and is real, and here we are and we havenot only our memories, but our impression that outside there issomething called Caltech and the United Statesand the Milky Way Galaxy. It's much easier for all those impressionsto randomly fluctuate into your brain than for them to actually randomlyfluctuate 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 bein minimal fluctuation, even if you left our galaxy out, you would not geta hundred billion other galaxies. Feynman also understood this,Feynman says: "From the hypothesisthat the world is a fluctuation, all the predictions arethat 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 concludethe 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, whydid the early Universe have low entropy? And I would love to tell you the answerbut I'm running out of time. (Laughter) Here is the Universethat we tell you about versus the Universe that really exists.

 I just showed you this picture, the Universe is expanding for the lastten billion years or so, it's cooling off. But we now know enough about the futureof the Universe to say a lot more. If the dark energy remains around, the stars around us will use uptheir nuclear fuel, they'll stop burning, they will fall into black holes. We will live in a Universewith nothing in it but black holes. That Universe will last10 to the 100 years, a lot longer thanour little Universe has lived. The future is much longer than the past. But even black holesdon't last forever, they will evaporate, and we will be left with nothingbut empty space. That empty space lastsessentially forever. However, you notice thatsince empty space gives off radiation, there's actually thermal fluctuationsand it cycles around all the different possible combinationsof the degrees of freedom that exist in empty space. So even though the Universe lasts forever, there's only a finite number of thingsthat can possibly happen in it, they all happen over a period of timeequal to 10 to the 10 to the 120 years. So here are two questions for you: number one, if the Universe lastsfor 10 to the 10 to the 120 years, why are we bornin the first 14 billion years of it, in the warm, comfortableafterglow of the Big Bang? Why aren't we in empty space? You might say, there's nothing thereto be living, but that's not right. You could be a random fluctuationout 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 youmy favorite scenario; either it's just like that,there is no explanation, it's a brute fact about the Universethat we should learn to accept and stop asking questions. Or maybe the Big Bang isnot the beginning of the Universe. An unbroken egg isa low entropy configuration and yet when we openour refrigerator we do not go: "How surprising to find this low entropyconfiguration in our refrigerator." That's because an eggis not a closed system. It comes out of a chicken. Maybe the Universecomes 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 oursin low entropy configuration. If that's true it would happenmore than once, we would be partof a much bigger multiverse. That's my favorite scenario. So the organizers asked me to endwith a bold speculation; my bold speculation is that I will beabsolutely vindicated by history, and 50 years from now all of my currentwild ideas will be accepted as truths by the scientific and external communities who will all believethat our little Universe is just a small partof a much larger multiverse, and even better, we will understandwhat happened at the Big Bang in terms of a theory that we will be ableto 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 finallyknow the answer some day. Thank you. (Applause)