CSABA CSAKI: Welcome everybody to today's public talk. My name is Csaba Csaki. I'm a professor here in the physics department. And I have the pleasure of introducing our speaker, Professor Nima Arkani-Hamed, for the IAS in Princeton.
Nima is the most influential particle theorist of his generation. He's working on particle phenomenology, LHC physics, inflation, cosmology, scattering amplitudes, the fundamentals of field theories, so basically everything in particle theory. He was an undergraduate at the University of Toronto and he got his PhD at UC Berkeley in 1997, after which he was a post-doc at SLAC, then a junior faculty back at UC Berkeley. He became a professor, a full professor, at Harvard in 2001. And he joined the Institute for Advanced Study in Princeton in 2007.
He's renowned for his work on large extra dimensions, dimensional deconstruction, little Higgs theories, supersymmetry, supersymmetry breaking, dark matter, gravity, modified gravity, scattering amplitudes. And the list just goes on, and on, and on. He had numerous awards, including the Gribov Medal of the European Physical Society, the Sackler Prize in Tel Aviv, and most importantly the Fundamental Physics Prize of Yuri Milner, which makes him not only one of the smartest people in the room, but also the richest person in the room most likely.
He's a fellow of the American Academy of Arts and Sciences. And if you saw the Particle Fever movie, you must have seen him. He was one of the main characters there. And if you haven't seen Particle Fever, you should watch it. It's really good.
And most importantly, he was a Messenger lecturer here in 2010. And we taped his videos. And his videos are the most viewed non-sports events on CornellCast.
NIMA ARKANI-HAMED: [INAUDIBLE] yourself a lot better.
CSABA CSAKI: So you should watch it. And even more importantly, he is a professor-at-large here, an A.D. White Professor-at-Large at Cornell. And this is his second visit. So we are really happy to welcome him tonight. Let's welcome Nima.
NIMA ARKANI-HAMED: Back at Cornell, as always. And I'm going to talk about perhaps an unusual topic for a public lecture by a physicist. I've given many lectures, when I come here and elsewhere, on the state of fundamental physics or important things about the actual physics. But in the spirit of being a professor, even if a professor-at-large at a university that is supposed to value a wide liberal arts education, I decided to spend today talking about some sort of broader, more structural things about our field and how we think about things.
Now, in this part of science we have had for a long time a sense that there is some objective world out there and we're trying better to understand it. So there's clearly a sense in which there is a notion of right and wrong. And that notion of right and wrong, which is there in science and is also there in mathematics, obviously is going to give some rough moral character to what we talk about. So that's part of what I will talk about. That's a relatively trivial part of what I want to talk about.
But there is something, I think, a little bit more interesting. I should say part of my motivation for giving this talk is that like many physicists, many scientists, I'm an atheist. But unlike some atheists, I'm certainly not a militant atheist. And I dislike a lot a certain strand of militant atheism.
Part of the reason for it is that there is an experience you get that there are many very negative things associated with religion. As someone who spent a good fraction of my childhood in post-revolutionary Islamic Iran, I can tell you that I've experienced firsthand what some of the horrible aspects of extreme religious fanaticism can be like. But on the other hand, there are amazing things about some aspects of religion. When you go to these incredible cathedrals in Europe, you're absolutely filled with a feeling of awe and sort of a transcendent experience. That's available to everybody. It's available to absolutely everybody. And it's extremely important. And it feels important to have a contact with something much, much larger than yourself.
So it's often said that if we take that away, if we take away some large thing out there that cares about us, that has some relationship to us, then there is less meaning in the world. And often, some secular humanists will say, well, there is no invariant meaning. There is a big impersonal universe out there. There is no invariant meaning. And we have to decide for ourselves how to behave, what good behavior is, what bad behavior is, and so on.
But it's ultimately a social construct and a decision between ourselves about how to go about doing things. And that's always struck me as a little hollow and it doesn't feel right. A part of the reason that it doesn't feel right is that we actually get in our business, just in the day-to-day part of doing it, not just in gaping in awe at the mysteries of nature, but actually in the business of going about doing physics and business of going about doing science, we get a lot of this kind of experience. We have the feeling that we're interacting with something much vaster than ourselves, that knows much more than us what's going on. And that if we interact with it properly, it tells us what to do next and sort of improves us and makes us better.
We get that experience day-to-day as a routine part of our lives. And that's what I want to tell you about today and make an argument that there's something in the structure of the laws of nature that actually gives some invariant basis for a certain way to behave. That it's not a social construct, but it's something about the structure of the laws, not in and of themselves, but in how they interact with us, that's associated with a certain moral code.
Now, I very, very much doubt that anything I'm saying in this talk is actually original. Certainly, almost everything I'm saying about the structure of science will be perfectly familiar and obvious to all the people who work in this business, in the audience. But nonetheless, I thought aspects of it might be of a wider interest. So I think it will be fun to talk about.
So just repeating some of the things I said right at the start, in science and math we have an objective notion of right and wrong. In science, there is a world outside. And we think we're learning more about the world. And ultimately, the agreements of our theories and explanations for what's going on with experiments we do decides who is right and who's wrong. It's not a social construct.
Perhaps more obviously, in mathematics there's a notion of right and wrong. And it's a fascinating thing, especially about the structure of physical laws, that they're expressed in fundamentally mathematical language so that these two notions of right and wrong meld with each other in an interesting way. And our central obsession, again unstated, so implicit, so in the air we breathe that we don't rhapsodize about it all the time, is that we think there is a Truth out there with a capital T and we want to find it. So that Truth with a capital T is going to be appearing everywhere else in the rest of the talk.
Now the interesting point is that over a period of centuries, we have found that the most successful way for human beings to discover these truths is associated with certain patterns of behavior, a right way of doing things and a kind of intellectual moral code. So this is not a moral code about how human beings should treat each other, how to be good people, or anything like that. It's a very sort of mercenary, selfish thing.
As scientists, as physicists, and mathematicians, we want to get after this truth. There is various strategies for going about doing it. And some of those strategies prove more successful than others. And just as a mercenary fact, our desire to get to the answers more quickly, to understand them more deeply, it turns out-- the most successful ways of doing this turns out to be associated with a certain sort of intellectual moral code.
So while it's true that this truth that we're talking about, this truth in natural law ultimately, is something that could care less about other human beings, it's out there. It's a property of the universe. Its invariant and human independent and impersonal. There is an aspect of it which is related to human beings, which is our struggle to understand it. So it's out there. But we are struggling to unveil this truth.
And the act of this struggle, on the one hand, is associated with certain successful strategies for just how to go about doing it. And, as I'll argue, these strategies require sort of a morally good behavior, a right way of going about doing things. Now, this part of the story is relatively trivial. We'll talk about what this morally good behavior is.
I think you'll all agree that it's obvious that this morally good behavior-- now, again, not in relation to trying to learn more things about the truth of the natural law. It's all fairly clear why the morally good behavior is good. So that's a relatively trivial part of the story. But a more interesting part of the story is that not only do we have to behave morally well, but that as we learn about things more and more deeply, we find that the best kind of explanations there are, the explanations themselves, not how we're behaving, but the explanations themselves, have a sense of being morally correct. And part of the talk will be trying to explain what we mean by morally correct explanations.
The fact that the best explanations turn out to be morally correct ones is not obvious at all ahead of time. Had the laws of nature had some sort of crappy, random quality to them, this would not be true. Had they been like some elaborate game that was invented by a bored teenager, this would very likely not be true, that the correct explanations have this morally correct character.
The fact that the best explanations have this morally correct character is reflecting a deep and still quite mysterious aspect of the truth itself. It's related to a greater and greater unity in the things that come under the umbrella of aspects of nature we understand, as well as a even more mysterious deeper relationship between those truths and the truths that mathematicians, for separate reasons, find interesting and important.
So again, there are two things that I want to talk about. I'm going to talk about these two aspects in more detail. But the sort of summary of what I want to say is that this intellectual moral code exists. It's a property, not of the laws, but of how we go about finding the laws.
There's a good way of going about them and a good, morally correct sort of thing to be looking for. And it derives its authority from nature. It's an invariant thing. It's an invariant in its relationship of us and it.
But this moral code has striking similarities to what we think of as good moral behavior more generally. Now, I'm not at all claiming that in every difficult, complicated ethical situation, thinking along these lines is going to tell you what to do. This is at best a sort of a coarse first approximation to a kind of morality. Nonetheless, it is interesting that this thing that derives its authority from nature has similarities to what we think of as good moral behavior more generally.
But it is invariant. It's not dependent on gods or other human social constructs. It's a property of us interacting with the laws of nature and trying to understand them. All right. So first, let's talk about what this morally good behavior is. How we should behave in order to most successfully extract truths about nature.
So a few slogans for what you should do. Number one, it's obvious that you have to be honest. You have to be honest with yourself most importantly of all, and with others. Now that's the complete no-brainer. We're all trying to understand something about this world out there. And many of us are studying it.
It's good for all of us if more people know the things that we know are true so far. We share information. We don't hide or squirrel things away. And part of the very openness, centuries-long openness of the culture of science, is, again, not because we're fundamentally good people. But because from a ultimately selfish desire that we're all trying to get there, being honest with ourselves and with others is an absolute necessity.
So everything I'm going to say in the next few slides is just totally obvious. But I want you to keep in mind they're totally obvious to us. They're totally obvious in most of academic life. They're not completely obvious in most of the rest of human life. So be honest to yourself and others.
Secondly, it doesn't matter who you are. Only the content of your ideas are relevant, again completely obvious. One aspect of this is you can be a young 20-year-old grad student. If you have a fantastic idea, people will pay attention. That's because we have an agreed-upon notion of what it is that we're after. We have a sense of what it makes to make progress.
It doesn't matter if you're famous or not. It doesn't matter who your advisor was. It doesn't matter whether you're in a social clique of people who have worked on the subject before or not. If you have a good idea, it will eventually penetrate. I'm not saying-- we're not perfect people. There are sociological problems sometimes. But they almost never get in the way of the ideas being recognized.
In the other direction, it doesn't matter if you've had five Nobel Prize winning worth ideas and you've won two of them, or one of them, already. If you're saying bullshit, no one will care. And that's good because we care about whatever's going to push us forward, independent of who's saying it, in either direction.
Steven Weinberg, one of the greatest living theoretical physicists, a Cornell graduate, says this very nicely. That in science, we have heroes, not prophets. So people do incredible things. They make huge progress. They are heroes. We remember them. We're grateful to them.
But nothing they say is set in stone. And we certainly don't keep referring back to what people said 30 years ago, never mind 2,000 years ago, in order to decide what we do next. So we have heroes and not prophets, another very basic, important aspect of this moral code.
Yet another completely obvious thing, we never deal in certainties in science. We're never in the possession of the whole truth and we know it. We never pretend to be in the possession of the whole truth. We don't pretend to have certainty.
We always talk about degrees of confidence. That's just life. But the fact that we're not certain is not an excuse for laziness or timidity. You do the best you can at any time. You take the ideas that you're the most certain of and you boldly extrapolate them. The ones that you're the most confident in, you boldly extrapolate.
If we had to stop at every moment in time and say, look, we haven't checked this fact from experiment-- I don't know for a fact that the atoms on Pluto are the same as the atoms here. Maybe we shouldn't assume that. Maybe if we send a spacecraft out there, it's made out of anti-atoms. And when it lands, it will annihilate, right? That's crazy.
So we have to have some degree of confidence. We have to take the ideas that we're confident in and we extrapolate them. But we always have to remember that there's a chance that we're wrong and always remember the degrees of confidence that we're talking about.
Related to all of this is that it's extremely important in science to be tolerant of other people's ideas and to keep an open mind because we don't have the whole truth. Someone else might have a piece of it. Even if they're mostly wrong, they might have a piece of it which is right. We have to listen to other people. And we have to keep an open mind.
So that sounds great and very kumbaya. We'll all get along. But it's a double-edged sword because we are only tolerant and keep an open mind provided that the people we're listening to are being as honest, scrupulously honest, working as hard as they can, as committed as we are, for this joint quest that we're on. If they're not doing that, it's actually extremely important to be intolerant. And there's a great quote by Robert Oppenheimer, who said, it's important to keep an open mind, but not so open that your brains fall out.
What that means is that if someone comes along with a crazy idea and you start listening to them, and you realize they haven't done the first check on them, the most trivial things that you would check in the first 30 seconds, then they're just full of crap. Then there's no reason to listen to them. And, in fact, given the finite amount of time and resources that we have to think about things, it's actually very important to be intolerant, actually harshly judgmental, of ideas that are not perfectly honest or are intellectually lazy.
Now, I say this because the most important person to be harshly judgmental and intolerant about is yourself. That's one of the most difficult things to do in the subject, is you have an idea. It's not immediately obviously wrong. You've worked so hard and nothing has been working. And it's just so delicious to sit there for awhile, before you know the idea is wrong, and not just get off your butt and check as quickly as possible that it's wrong.
Many people have said that the greatest skill that a theoretical physicist can have is to prove their ideas wrong as quickly as possible. So you have to do this to yourself. But the tolerance that I'm talking about is tolerance amongst a group of equally committed people, who are working hard and have the same large goals in mind. There's no need to have random tolerance for anybody who says anything.
So those are a number of extremely simple and I hope quite obvious features of morally correct behavior, that helps us to better understand and uncover of the structure of these laws of nature. Now, I want to transition to the more interesting part of the story that has to do with this notion of morally correct understanding. So what do we mean by a morally correct understanding?
If you were to drop in on a random group of theoretical physicists having a conversation about some topic, these morality-laced words keep making an appearance. There's no a priori reason for them to. But people will say, that's morally the right reason. Morally this is true because of x, or the moral reason for this is y, or that's not the right way of thinking about things.
They say that's not the right way of thinking about things, not because someone has given them a wrong answer to something. They've given a perfectly correct answer, a perfectly correct method to arrive at some result. But they say, no, that's not the right way of thinking about things. So what are we talking about? What we're talking about is what I want to spend some time explaining.
So this part is more non-trivial. First of all, even the provisional understanding of the truth that we have at any given time-- so we don't have the whole story, of course. But what we have has a surprising element to it. Even the provisional understanding of the truth we have at any given time has a large degree of what you would call local perfection to it. In other words, the laws that we have at any given moment are essentially almost perfect.
What I mean by perfect is that it's hard to add bells and whistles to them. It's hard to modify them. It's hard to continuously to form them to something else. They're sort of locally sitting there and are perfect.
The deepest principles of physics, once uncovered, have a feeling of inevitability to them. And that's true for the more modern ideas. But it's also true for the ideas that were developed three centuries ago. Locally, at any given point in time, this has always been the case.
Now, this thesis that the laws of nature have this amazing feeling of inevitability to them I think has been most beautifully talked about by Steve Weinberg in this book that I think I'm advertised in every public talk I've every given problem probably. If you haven't read this book, Dreams of a Final Theory by Steven Weinberg, you should. I think it's the best the popular physics book out there, but the deepest one certainly.
And in it, he talks at length about this notion that there's something amazing about the laws. They're hidden for a long time. But once you know the principles, one thing follows after another. You don't have to make seemingly random strange choices. They have a feeling of inevitability about them, which is associated with this local perfection.
Now, that makes something somewhat mysterious because we eventually learn deeper truths. And often the deeper truths involve radical changes from the past. For example, we have the transition from classical physics to quantum physics in the early part of the 20th century. And you couldn't ask for a bigger radical change in what seemed like the basic principles of physics.
There was the Newtonian clockwork universe, where everything was determined, where the future was determined if you gave initial conditions in the present. And we went to this fundamentally probabilistic picture of the world given to us by quantum mechanics. The entire rubric changed. Everything changed.
So how can that be? How can it be that if at any given moment-- how can it be that the new laws, if the old ones worked so well and they have this sense of perfection to them, how can it be that the new ones can look so radically different? And that, at least to me, is the most miraculous aspect and the strangest and most mysterious and wonderful thing about the structure of the laws of nature.
Is that what happens is that you discover new perfect things. They're not sort of smoothly, continuously connected to the old ones. You discover entirely new perfect things. But once you see the new perfect ones, you get a much deeper understanding of the old perfect things, without changing the fact that the old ones had a local perfection to them.
So here is a rough picture, a very rough picture. If you imagine our knowledge of the universe sort of increasing as we go forward in time, you might have thought that we knew about classical physics and we gradually learned more and we learned about quantum mechanics. And that somehow the transition from classical to quantum laws is somehow smooth. Once you know this, well, you sort of changed it a little bit. And gradually, you learned better, and better, and better. And it turns into quantum. And it's not like that at all.
It's, rather, something like this. The classical picture of the world is the top of a local mountain in the space of ideas. And you go up to the top and it looks amazing up there and absolutely incredible. And you learn that there is a taller mountain out there. Find it, Mount Quantum.
And they're not smoothly connected like this. In fact, you've got to make a jump to go from classical to a quantum. But once you get up there, it's taller. It's taller. And look at that beautiful Mount Classical. OK. It's just sitting there. We're not changing the fact there is a beautiful peak sitting there.
So it's local perfection. The fact that you can't make little modifications around it is it's preserved. But you see something larger. You see something bigger.
This also tells you why we have such major challenges in trying to extend our understanding of physics. We don't have these knobs, and little wheels, and twiddles that we can turn. We have to learn how to make these jumps. And it is a tall order. And that's why things are difficult.
As I said, we have the transition from classical to quantum a hundred years ago. Today, the analog of that transition is that many, many of us suspect that the notion of spacetime can't be fundamental and it has to be replaced by something else. But what could that possibly mean? Space and time are the most-- physics for 400 years, if nothing else, is about telling us how things change in time as you move through space. What could it possibly mean that there is no such thing fundamentally as space and time? There's got to be some other principles and ingredients underneath it.
Well, we don't know. There's going to have to be a jump of a comparable magnitude, in the jump that people have to make in going from classical to quantum. So that's one of these other mountains in the distance. But what I want you to take away from this is, first, an appreciation for the magnitude of the challenge. But second, the fact that even though our understanding can be provisional, the things we understand have an internal quality to them.
That peak isn't going anywhere. Even if we understand many, many more things, and that recedes into a distance, and that recedes into something bigger, these things are always there. They have an eternal perfection to them. And even though you might be working at a given moment in time, long before where the rest of them are, there's a job you can do, which is to find what your local peak is and get there and try to stake out as many routes to the top as you can.
The last comment I made is associated with the final big surprise, at least to me, about the structure of these laws, about these truths that we've seen. Which is that quite stunningly, exactly the same truths, exactly the same laws, turn out to be describable in seemingly radically different ways. This is a big surprise. You might have thought that you find these perfect things. It's so rare to find something that's so totally perfect that there's just a right way of looking at it in order to understand it. But it's never the case.
We've actually seen that always the laws have multiple ways of being looked at, again from seemingly radically different starting points. That's actually very important because different paths to the top of these local peaks can give us different views of the next horizon. So different ways of understanding the truths you have now can suggest different paths for trying to make the jump to what happens next.
Depending on the path you take, different aspects of the next peak over might be obvious. An easy route might be obvious from the way you took up, while it might be completely hidden from some other path. So that means that not only are there these truths, with this crystalline, perfect quality to them. But we have to learn to understand all the different ways of thinking about what they are.
So, so much about the sort of structure of the general laws. At any given time, we're working within some broad framework of laws. And then we're trying to use the laws to explain things; understand things; find regularities, maybe in the structure of the laws themselves; regularities in nature that we can explain from the laws. So we're trying to use these laws to come up with explanations for what we see, either in our exploration of the structure of the laws or in nature itself.
And so now in talking about explanations, this notion of a morally correct explanation are explanations that seem as close as possible to the fundamental principles and where the explanations have a similar sense of inevitability about them. And that once you start thinking about what's going on from a particular point of view, one thing follows after another. And everything is simple and straightforward.
The idea here is that a morally correct explanation, that has this sense of inevitability about it, is probably reflecting this perfection of the underlying laws. And it's also true, in the same way, that the laws have a local perfection. That the morally correct explanations also have a local perfection and are eternal. So when you find a morally correct explanation of some phenomenon, even if we understand a zillion other things about the way the world works, those explanations will always be there, and will never change, and will always be the correct way of thinking about things within the local framework that they were found in.
So one contrast in just the sort of character of explanations that we're talking about is a contrast between these two sets of words. So you might think that these words would cause joy when uttered to a theoretical physicist or a mathematician. Oh, that's a really ingenious argument, that's a really clever idea. OK. The word "clever" and "ingenious" is damming with the faintest praise, if you use it to characterize what someone has done.
Because we know that when something is clever and ingenious, it's about you as a human being, you as an individual. It's your cleverness and your ingenuity, which might be great and you might even be a genius. But your cleverness and your ingenuity has got nothing on the depth and grandeur of the structure of the laws themselves. That's vastly bigger than all of us, knows vastly more than all of us what's going on.
Now, this is something that we often have to do when we're struggling to understand things. There is no shame in being clever and ingenious. But if someone says you're being clever and ingenious, they're trying to goad you into finding the right explanation. And the words that are used when you find a right explanation is, that's a deep explanation, that's a simple explanation. So it's this contrast between ingenious and clever versus simple and deep.
So morally correct explanations are supposed to reflect this perfection of the underlying laws. They're supposed to have the same sense of inevitability that the laws have. And you know when you find them because they are simple and deep, rather than clever and ingenious.
Now, this is all very abstract. So I want to give you a number of examples. And let's really crash all the way down to Earth by looking at a little physics problem. Those of you who are undergraduate physics majors have probably seen this problem. Maybe many of you have seen this problem in high school. And so, yes, we have gone from morality to asking the following question.
You have a helium balloon. You have a helium balloon in a bus. I haven't drawn the wheels. So you have a helium balloon and it's hanging up. And now you accelerate the bus forward. You accelerate the bus in this direction.
What do you think happens? What do you think the helium balloon does? That's the question, what happened to the helium balloon?
How many people think that the helium balloon-- you're going this way. How many people think the helium balloon does that? OK. How many people think the helium balloon stays like that, does nothing? How many people think it goes forward? OK.
All right. The helium balloon goes forward. It actually goes forward. Why does it go forward?
Well, if you think about it a little bit, you can begin coming up with a mechanical explanation why it goes forward. You see, as the bus rushes forward, more air is collecting in the back. The air was just sitting there. And now the bus is accelerating forward. So more of the air molecules are smushed up towards the back of the bus and there's fewer at the front of the bus.
So you have this helium balloon sitting there. There's more air molecules over here now, jiggling around and banging into it, compared to the ones on this side. So there's going to be more force on it from this side compared to that one. And so the helium balloon will move over, like that.
So that at least tells you that it's going to go forward. But you can go ahead now and do a calculation with air molecules and how they go backwards. You can build little toy models for what's going on. And actually, out of a lot of work, you find a rather sort of amazingly simple answer for the angle the helium balloon makes when it's moving forward with an acceleration a.
And that's because while that explanation is perfectly correct, it's exactly what's going on-- that's in fact, even mechanically what's going on. It is that there is more air on one side than the other and it's pushing the balloon forward, and all of that. It's not the deep understanding for why it goes forward.
The deep understanding for why it goes forward is related to Einstein. We're celebrating the 100th anniversary of general relativity. And something that Albert Einstein taught us is that acceleration is the same as gravity. So if you're in the this bus that's accelerating forward, Einstein tells you that you feel as if there is an additional component of gravity that's pushing in the opposite direction, with the same magnitude of acceleration.
So there's the usual acceleration due to gravity that's going down. But there is this extra acceleration that Einstein tells you to imagine is there, because acceleration is the same as gravity. So when you're in the bus, it looks like there's a net gravitational field that's pointing in that direction. The acceleration goes backward and the g goes down. So there's a net gravitational acceleration that's going in that direction.
And so what do helium balloons do? They float. So the helium balloon is going to go and float, but in that gravitational field, which is pointing in this direction. So that's why the helium balloon moves forward. But also, we predict exactly the angle that it moves to.
That is a morally correct explanation. There is a deep general principle. Of course, that's reflected in the fact that the air molecules have got to adjust themselves and do all of it. But when you understand deeply why something is true, then you understand why that's true. And actually, you can also do many other things.
If you're doing more complicated kinds of acceleration, different parts of the bus were accelerating at different rates, and so on, then you can use this deeper explanation to come up with the right answer for those more complicated situations.
NIMA ARKANI-HAMED: Sorry? Sorry? The model would not work in a vacuum.
AUDIENCE: Do morals?
NIMA ARKANI-HAMED: Sorry? Sorry?
AUDIENCE: Do morals?
NIMA ARKANI-HAMED: Do morals work in a vacuum? No, they don't. Because, as I said, as I said, the morals are not a property of just the world. They're a property of how humans understand the world.
OK. So those of you who haven't seen this example before, I hope you enjoyed it. And this is the sort of thing that happens to us every day when we do calculations in theoretical physics. It's not every four years. It's every day. Because that's one of the joys of this subject, is that the deep underlying principles are never far away. And, in fact, if you're doing things right, they're never far away. And the giant things that we know are reflected in the little concrete things that you're doing.
So now I want to move to some lighter examples. Let's talk about something else that probably many of you learned about in high school, the law of conservation of energy. So the first thing that you learned in school is that particles move around and they move in straight lines, unless they're acted on by a force. And if they're acted on by a force, they have an acceleration given by Newton's law.
So the way to figure out where a particle goes next is you figure out where it is now, the velocity with which it's moving. And if you know the force, you know the acceleration. So you can figure out where it goes next. OK. So we have F equals ma.
Now, those in principle are the entire laws. And that's all you need to know. You can predict where everything goes next. But people, shortly after Newton-- maybe even Newton himself, I don't know-- discovered that there are certain quantities that were conserved, no matter what the force was.
You chose some force. But no matter what the force was, there was some quantity that you associated with the force, some integral of the force that you called the potential, by this formula. And you notice that the x dot is just the velocity. You notice that the energy is 1/2 mv squared. You might remember that from my high school, plus the potential energy. This quantity is conserved.
And you can check that. If someone tells you, look, I claim that 1/2 mv squared plus the potential energy at conserved, you can go check. You say, gosh, what is the time-- how does energy change with time? And using the fact that F equals ma, you notice that, huh, yeah, it's actually true. That thing doesn't change in time.
So that's an observation. So someone hands you the laws. And that's the clever, ingenious part. You're mucking around with the laws. You've trying to solve them. You're playing with the equation.
Nothing wrong with this, OK. I stress again, there's nothing wrong with the cleverness and ingenuity part. But you discover that, gosh, it's true. There is such a thing. Energy is conserved.
Now, it's clearly true. It's a clever observation. But you have no idea why it's true. And you might think, come on, give me a break, why it's true? I mean, it's true. OK. So what are you complaining about?
Well-- but it gets more complicated. Because when you go to more and more interesting situations, you find that energy isn't conserved anymore. Oh, well.
OK. For example, you have the electron. You have an electron, a charged particle. And it's spinning around some-- it's spinning around on a string, let's say. You have an electron spinning around on a string.
So there's the 1/2 mv squared. There's the kinetic energy of the electron plus whatever potential energy it might have. That's the energy that we're talking about. And that energy is conserved. The electron slows down, slows down, and slows down.
OK. And that's what we discover when we know something about the laws of how electrons interact with electromagnetic radiation. But if you look at the energy of the electron, the energy of the electron is most certainly not conserved. But what's going on when it spins around is it's giving off some electromagnetic radiation. So when charges accelerate, they give off radiation.
Then some even more clever person comes around and say, wait a minute, I can invent a new notion of energy, and not just potential-- kinetic plus potential. It's kinetic force potential, plus there's a kind of energy that I can attribute to having electric and magnetic fields. So there's some energy that electric and magnetic fields have.
Now, you ask him what it looks like? He says, well, you have to integrate over space, 1 over 8 pi, E squared plus B squared. OK. So how did you get that?
But anyway, they got it. And you say, OK, you're very smart. Let me check that it's true. You go, you check the equation of motion. Like, holy crap, it's true. This energy is conserved, amazing.
And it happens over and over again. You discover more laws, more things. Every time you keep finding, yeah, the old energy isn't conserved anymore. But there was some new thing. And you keep being able to keep defining some new piece of the energy, new piece of the energy, that you always add up so that all the time, it's conserved.
So when this starts happening, you wonder if there's something up, right? Maybe the first time, just with kinetic plus potential, you say-- you're complaining. It doesn't look so complicated. But why is it that every time we find something new? It's always possible to define some additional notion of energy so that the total is conserved. So why is that?
Ever since Newton wrote down his laws, till a hundred years ago, we didn't have a good answer to this question. But a hundred years ago, we found the morally correct, simple, and deep answer to this question. And the path by which we found this answer is rather interesting because it illustrates some of the other things that I was telling you about the structure of the laws.
One of them is that I told you that it turns out that you can think about the laws in radically different ways. You can think about exactly the same laws in radically different ways. And already, by the late 1700s and early 1800s, theoretical physicists had figured out that there was a way of recasting Newton's laws in what seemed like a sort of a radically different language. Even though the end result ended up being exactly the same, the sort of philosophy underlying the ideas seemed radically different.
So Newton tells you that the way the particle moves from A to B is that once you know where it is and how fast it's going, you just tell it where to go next. So it's completely local. What's going on here, tells you what's going on there. And you just keep on going.
But de Maupertuis, and Euler, and Lagrange, and other people, in the 1700s and 1800s, found a completely different picture for what determines the path a particle takes from A to B. They said, imagine the path. The particle takes every path it could between A and B, every possible one. And then imagine that it just sort of sniffs them all out; and looks around; and says, I'm going to take the one that makes the following quantity as small as possible. And that quantity is the average value of the kinetic energy minus the potential energy along that path. So that's called the action, the average value of the kinetic minus potential energy along that path.
Now, you see this feels completely different. It looks like the particle is thinking about what's coming next. It doesn't at all look deterministic. And yet, when you set up-- when you ask what path is chosen by these rules, you discover it's exactly the paths that satisfy Newton's laws.
So it's completely equivalent. That's a feature that I was telling you about. The same truth, the same ultimate equations, can be thought about from these two radically different points of view.
And this was already known, as I said, in the 1800s. But it took another 100 years for people to realize that it's the second point of view that furnishes us the morally correct understanding for the existence of conservation laws. And this is something whose 100th anniversary we're also celebrating this year. One of the truly great mathematicians of the early part of the 20th century, who did amazing work in all kinds of areas of pure mathematics, but wrote this one paper in 1916, that we celebrate today, and I guarantee you will also celebrate in a thousand years, if we're still around, was Emmy Noether.
And I don't have time to explain. It's a relatively simple explanation. But what she noticed is that when you think about physics in terms of equations of motion, like Newton tells you, the existence of these conservation laws is mysterious. You keep finding them. But you don't know why they're there.
On the other hand, when you think about physics in terms of the action, then there are various completely obvious features of the action. For example, if things are just moving around in space-- obviously if I'm using a clock to measure where everything is, it doesn't matter what I set the zero of the clock to be. You could set the zero of the clock to be noon. Someone else could set it to be 1:00. But all that matters is the time differences between when one thing happens and another thing happens. There is no meaning at all to what you call the zero of the clock.
So that simple fact, that there is no meaning to the zero of the clock, Emmy Noether showed when you think in terms of the action, immediately leads you to understand that energy is conserved. And, in fact, all the other famous conservation laws that you learned about in school-- translations in space are associated with momentum conservation. The fact that it doesn't matter how you rotate your head to look at what's going on, only the relative angles between things matters, is associated with the conservation of angular momentum.
This explanation is simple, and deep, and eternally correct. It was come up with in the context of classical physics. But the world has changed since then. We know quantum mechanics is correct. We know we may learn other things afterwards. But this explanation is simple, and deep, and will always be the right way of thinking about these things.
Now, we can pursue the story a little more because another thing I told you is when you have a morally correct explanation, it has more of a chance-- even though it's developed in the context of the provisional theory you have now, it has more of a chance of surviving and being the right explanation, even when you understand things better later. And in this case, we can go back to highlighting this big difference in apparent philosophical starting points between Newton's law, a way of thinking about things, and this principle of least action way of thinking about things.
This picture is manifestly deterministic. This picture, as I've stressed, is not manifestly deterministic. It looks like you're imagining what might come next and deciding what to do in between.
Now, people wondered back then, people wondered why it was that there were these radically different ways of thinking about things. Why was it that even though determinism seemed like a key crucial feature of the clockwork universe of Newton, why was it that there's this other way of thinking about things, where determinism doesn't seem to be so important? Somehow it comes out that determinism doesn't seem to be important. Why, indeed?
The reason why the second way of thinking about classical physics exists is because of quantum mechanics. The world is not classical. The world is quantum mechanical.
And as another Cornell, I guess not alumnus, but former professor, Richard Feynman, famously taught us, actually while he was here, you can think about quantum mechanics most beautifully, and in some sense most deeply, starting about thinking about the principle of least action. Instead of saying that the particle just sniffs out every way that it could go from A to B, and it just randomly chooses the one that minimizes the action, Feynman taught us that, in a very precise sense, the particle takes every possible path that it can between A and B. But it's a quantum mechanical particle, and not a classical one.
There is some probability amplitude for the particle to go from A to B. You have to add up all the amplitudes for every way it can go. And only in the limit, where Planck's constant, the important key feature of quantum mechanics-- only in the limit where you send that constant to zero, does it turn out that the contribution from all the paths, other than the one that minimizes the action, cancel out. So the particle has only the choice to take the classical path from A to B.
But, more generally, it doesn't. And the world isn't deterministic. And this picture actually tells you the various probabilities for going from A to B.
So this is an illustration of why it's so important to have at your disposal all the different ways there are of thinking about what your provisional truth is at any given time. Because some of them could be better suited to making the jump to the next level than others. Newton's laws, even though they were the first way we leaned how to think about classical physics, were not the right way to make the jump to quantum mechanics. Only by exploring, being obsessed with the truth, not being content to find one way of loving it, but trying to find as many different ways as possible of knowing what it is, might you find the one that tells you the right way to take the next step.
And you see in this example, because the underlying ideas of the action-- and everything just really ports beautifully through, from classical to quantum physics, only the interpretation changes in a fundamental way-- all of Noether's arguments, all of Emmy Noether's arguments about conservation laws go through completely unscathed. It's absolutely amazing. All these arguments about conservation laws, many other things change, tons of other things changed when we went from classical to quantum. But our understanding of the conservation laws, even though they're come up with by this classical physicist a hundred years ago, are equally true in quantum mechanics today.
That's the importance of finding morally correct explanations. That they're not only perfect and will last forever, they are also most likely to continue to be correct, even when you understand more about the way the world works.
I want to give a third example of morally correct understanding, that also has an important connection with Cornell. Going back to Feynman, something that Feynman famously taught us is how to visualize the interactions between elementary particles. And he gave us these beautiful diagrammatic pictures for how to think about particles coming in and out, from very far distances, smashing into each other, going back out.
The kinds of experiments we like to do in particle physics look like this. And, for example, if I have two electrons, electrons of some charge q, if they're interacting with each other, well, there's some probability amplitude of them to interact with each other that's related to the electric charge of the electrons, proportional to the square of the electric charge of the electrons. And you associate it with a picture, that these two electrons are exchanging, we say, a virtual photon.
But that photon can pop out of the vacuum in an electron and positron pair. And that modifies what that probability is. So there is some correction to it. And details, roughly, the sort of energies involved in this process are E. There is something that goes like-- there's a correction that's the charge squared time some function, a logarithm of the energy divided by the mass of the electron.
All right. But something that people noticed by staring at these diagrams is something rather remarkable, that you could have incredibly complicated processes, most any complicated process you like. And that all of these processes, at least some leading piece of all of these processes, no matter what they all were, could all be reabsorbed into thinking about just that going on, but replacing the value of this charge with some sort of effective charge that depended on the energy of the process.
So what's extremely interesting about that is that it's true for any process that you might want to consider. That no matter what you do, the sort of leading effect of this royal mess of virtual particles and anti-particles, and all these complicated diagrams, is all absorbed into just thinking about some effective strength of the interaction between electrons and photons.
This was a result that many people contributed to understanding, Feynman and Julian Schwinger, very early on, Freeman Dyson, many other people, through to the '60s. And it was a sort of a tour de force in technical development of quantum field theory for people to prove this fact. If you are unfortunate enough to be a graduate student in the 1960s learning this basic fact, you see its very profound and simple end results. But if you really wanted to dig in to see where it came from, you would have to go to the back of dusty textbooks; extremely complicated proofs; very detailed, delicate, combinatorial graphical arguments.
Nobody read any of these proofs. Maybe five people in the world understood them. And it sort of sat there, like the stone in the middle of the-- in the heart of our understanding of the interaction of electrons and light.
So, again, it's strange. It's strange when something profound and simple has a technical, weird, complicated explanation. But that was the state of the art for 20 years. Feynman couldn't do it better. Nobody could do better. OK. That was life.
You thought, well, that's what it is. No. We're not going to do much better. There's all sorts of other things to do. Let's do that.
And the vast majority of people in the '60s were not obsessed with this problem. There's a few people obsessed with it. And one of them was a young professor here at Cornell, named Ken Wilson. Wilson thought about this problem solid for seven years. He had many reasons to think that there had to be a simpler way of thinking about things. He thought about it solid for seven years.
When he started thinking about it, it was a backwater of the subject. No one else much was paying attention to it. But in thinking about it, he realized the right way of thinking about things. The basic fact that he realized is that the correct way to think about physics is locally.
Physics is local. And we shouldn't organize our thinking by these diagrams of Feynman. Those diagrams of Feynman were good for some things, but not good for others.
And, in fact, the deepest way of organizing our understanding of physics wasn't diagram by diagram for these processes, but scale by scale. That we should try to think about what the laws of nature look like at some resolution. And when we understand what they look like at some resolution, we should learn mathematically how to gradually zoom out, gradually zoom out and get a picture at larger and larger scales. So starting at very small scales, we could zoom out and find a picture at larger and larger scales.
That is, indeed, simple and deep. When you begin to read these papers, you say that sounds right. That sounds good. But can there possibly be any beef here?
Something so simple, where does all that complication go? And, you see, nothing ever goes anywhere. But that complication from before is just dealt with in a fantastically interesting and sort of remarkable way from this very simple and deep picture. It's explained.
This picture revolutionized our understanding of fundamental physics. It not only explained these things about electrons and photons, it explained countless other phenomenon that we'd seen in nature. When you boil water, when we have all sorts of phase transitions between different phases, there are certain universal aspects about how those phase transitions work. And those questions, on the face of it, have nothing to do with the interactions of electrons and photons, nothing to do with these questions that I started talking about. But this general way of thinking about things dealt with all these problems at the same time.
And this Wilsonian way of thinking about what physics really is has stayed with us ever since. It's not going to go anywhere, no matter what we learn. Even when someday we'll know that spacetime is doomed and it's all gone, this picture is eternal. It's always going to be right. It's locally right. And it's the best way of thinking about the phenomenon that it talks about.
So those were the examples of morally correct explanations. And I want to end with a few final comments about how it is that interacting with these perfect structures out there actually makes us better. This truth is ennobling. As I've described them to you, the laws are perfect. There are these perfect, crystalline, simple, deep things.
So why is it they're so hard to find? The reason they're hard to find, in almost every case I can think of, is that the laws are perfect, but humans are imperfect. And when we think about what the laws might be, when we think about anything, when we are confronted with any situation, we bring to the situation a whole bunch of unconscious assumptions and prejudices that obstruct our path to the right answer, obstruct our path to the truth, even the local truth.
That's inevitable. That's just life. I mean not only are we not infinitely smart, very far from it. But on top of that, there's all sorts of hidden things that we don't know, that we're carrying around, that make it difficult to orient ourselves in the right frame of mind in order to see the right answer.
This is why the relatively trivial things that I was telling you about in the beginning, about acting morally, is useful. Because if you just go about acting morally, you try to be honest. You're honest to yourself. You're honest to others.
You try to attack the questions. You don't fool yourself. If things don't work, you admit it. If someone else is doing better than you are, you go see what they're doing. You're not jealous.
You do all these things. Why do you do these things? Because it's not we who are great, it's the laws that are great. It's the laws that are perfect. But our interaction with them makes us better. And everyone in physics, and mathematics certainly, who has even done a small, good thing in their career will tell you that you have this feeling that you're being led by the nose by the right answer.
You do this. You do that. This is wrong. That's wrong.
You keep casting them off. And you're dragged in, slowly, but surely, kicking and screaming, to the right answer by the thing that's out there. By the thing that is out there, which is true.
It's a really remarkable thing that interacting with the truth enhance as your abilities. It makes you better. And finally, ultimately, whether you're extraordinarily talented or less talented, none of these things matter all that much in the grand scheme of things. If you're in the rough vicinity of the truth, it will reel you in, to find it.
All of us in this business have had this experience at some level. And it's an absolutely magical and remarkable feeling. Even at the smallest levels, in the middle of a little calculation, this thing can happen to you. So this interaction with this large truth is ennobling in this sense.
Now, a final set of comments that I want to make are that, of course, at the most exciting moments in the development of science, there seems to be mutually contradictory truths. So what are you supposed to do in that period? There's this truth. There's that truth. They seem to be completely at odds with each other.
In different spheres of human life, if there are people who strongly believe these mutually contradictory things, it doesn't always end well. But we had situations like this, we had situations like this a hundred years ago. Light is a wave. Light is a particle. These are mutually contradictory truths.
But what do we have to do when we're faced with these mutually contradictory truths? Here it is especially important, in this context, to bend over backwards in an effort to understand the opposing point of view. Because what we've seen over and over again is that they will all be necessary to find the deeper truth that supersedes them.
You see, if you're a light as a wave guy, or a light as a particle guy, and that was your camp-- oh, screw you particle guys, screw you, wave guys-- then you're not going to get the whole story. The whole story isn't either of them. The whole story is this larger thing behind them. But you need to know everything about them.
And even if you start in one camp-- again, not all the time. It's not kumbaya and not everything goes. Presuming that everyone is doing things honestly, there is no crap going on. But if you really think that you're seeing honestly contradictory aspects of the truth, then even if you don't like it, even if you hate it, you have to go learn the other thing.
This is true at a very grand level. The examples that I told you about lights-- waves and particles-- was an example. But it's also true in everyday life of a researcher.
Here is yet another Cornell alumnus, Steve Shenker, who is a famous professor of physics at Stanford. There's something called Shenker's theorem. And Shenker's theorem is that that subject you most hate, will be the one that you next need to master for your research. And it's really true. It's been true for me many, many times.
And so even if you really hate something, you have to put it aside and start thinking about the world from the point of view of that thing that you hate. And if there is something to it, then it will eventually be important. And you might end up loving at least aspects of it. But we can't be prejudiced. And especially in the moments where we have the largest stakes, where we have to resolve these big contradictions.
So finally, after all this long intellectual sermon about morally good behavior and morally correct explanations, why is it hard to be morally good? It sounds easy. The first part is pretty easy. Be honest, et cetera, et cetera. That's pretty easy.
But the second part sounds trivial. Just think about simple and deep explanations. Don't be ingenious and clever.
So why? Why is it hard?
The reason it's hard is that when we're confronted with some problems, some things we don't know how to solve, our first instinct is to just jump in and start doing something randomly. We start doing something. So something's going to work.
Why do we do that? Whereas we see always, in the end, in the end, that things have this deep inevitable sense to them. But we never start that way. We just never feel like we have a luxury to start that way. Nobody-- I certainly don't do it. I know very, very few people-- we'll see two of them in a moment-- who do.
But we sort of jump right in. So why? Well, the ultimate reason for this is fear. The practical aspect of it is that we fear that we're wasting our time. So if there is some set of questions-- if we're not just doing something. Something is going somewhere. We're doing calculations. Then maybe, if we're sitting around thinking about the basic structure, we'll just be going around in circles forever.
We're wasting time. We're not getting anywhere. We're nervous about not getting anywhere.
So that's the practical reason. And if you ask people, why are you doing that way? They say, well, I want to do something. Totally defensible.
But, of course, underneath it is the fear of death. That's why we're worried about wasting time because we have a finite amount of time to do this stuff. If we had an infinite amount of time, I guarantee you I would be morally good every day of the week.
We don't. And so you say, well, maybe this time I'll cheat. And I'll run to the answer. Oh, no one will notice. I'll come back and give a deep explanation later. But it's the fear of death which is underneath it, like a lot of immoral behavior.
It's very, very hard-- it's very, very hard to try to do things right all the time. And there are very few people who have managed to do it for long periods of time. Two examples, maybe the sort of two greatest examples from the 20th century, of some of our heroes in physics and mathematics, who are great at doing this, were Albert Einstein in physics and one of the greatest mathematicians of the 20th century, Alexander Grothendieck in mathematics. And both of them have this character that the way they approached problems was not the way other people approached them. They didn't mind if it took a long time.
So Einstein struggled for eight years to find general relativity. And you think it sounds easy. You just sit there, you struggle for eight years. You just do things right. You struggle. You struggle.
But I tell you, when you try to mimic Einstein, even a little bit, at the six-month mark, you're getting very, very nervous. At the two-year mark, you're like, holy crap. It's all going to hell. I have no idea, the superhuman sort of moral strength that it took for him to pursue these ideas for such a long period of time without giving up.
And how did he describe it? He described it, these beautiful words. "The years of anxious searching in the dark, with their intense longing, their intense alternations of confidence and exhaustion and the final emergence into the light-- only those who have experienced it can understand it."
But very much a sense that it's not him inventing it. There is something out there. And the something out there is calling to him. And he is following it, following it, following it, until it finally emerges.
Grothendieck, in a sense, was more extreme even. Very famously, he never solved problems concretely. He always invented larger and larger abstract structures, into which finally, when things were defined properly and thought about correctly, everything became trivial.
And he had this description of how to go about solving difficult problems in mathematics. There is an earlier part of this paragraph, which is a little more famous. But I like this part more. "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration. The sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it-- yet it finally surrounds the resistant substance."
So that's his mental image of clearly something out there. Something out there that's advancing on him, advancing on the problems that he's grappling with, until finally, when done in this correct way, things fall apart in the right way.
So what can the rest of us do? So the rest of us, who don't have this sort of fortitude to be able to take it-- so Grothendieck worked in this style for around 12 years. And then famously sort of left active mathematics and had an interesting life after that. He died, I think, last year.
The rest of us, I think, can take great comfort from this other very famous, I think, beautiful phrase of Steve Weinberg, which is that even doing whatever we're doing in our much smaller ways, that there are these ultimate fears driving our immoral behavior. But "the effort to understand the universe is one of the very few things which lifts human life a little bit above the level of farce and gives it some of the grace of tragedy."
Now, everything that I've been telling you in this talk is about the moral structure of natural laws as they relate to human beings. Of course, much of the language that I've used clearly has striking similarities with how we think about moral behavior more generally.
But you might think, very justifiably, this is a pretty coarse, sort of basic aspect of morality, perhaps just one thin slice through it. And that the real world is much messier. It's much more complicated. And these sort of simple odes to the pursuit of Truth, with a capital T, will not cut it. There's just something much, much more difficult and complicated going on.
And I don't know. I'm not a very sophisticated person about these things. But there are people that I know who've spent their lives, essentially obsessed with these much more complicated and difficult moral dilemmas and difficulties in the world.
This is one of the people I admire tremendously, I'm sure many of you know, one of the greatest documentary filmmakers of our time, Errol Morris, who has many fantastic documentaries, like The Thin Blue Line, the documentary about Abu Ghraib, The Fog of War, and so on. So he knows something about moral complication. He knows something about the messiness of the real world.
And here is what he has to say, as the most important thing that he's learned in the course of all the things that he's done over the years. "There is such a thing as truth, but we often have a vested interested in ignoring it or outright denying it. It's not just thinking something that makes it true.
Truth is not relative. It's not subjective. It may be elusive or hidden. People may wish to disregard it. But there is such a thing as truth and the pursuit of truth-- trying to figure out what really has happened, trying to figure out how things really are."
So, so much for the messiness and complication of the real world. Another aspect of what I talked about is how this scientific pursuit of truth has this element of touching something transcendent in it. And, of course, there are other walks of life, there are other things in life, that gives us that experience, more widely shared, more viscerally, by many more people. And a lot of the arts are about exactly having such experiences.
So is there any indication there for something like this, something like it, an underlying truth being responsible for the depth and the importance? And here, I can just tell you about a phenomenal series of lectures that Leonard Bernstein gave. Well, he gave many phenomenal lectures like this. But a particularly amazing set of lectures that you can find on YouTube. Actually they're, I guess, a TV program where he talked about all sorts of aspects of music.
Some of them were from the 1950s. I'll show you a little clip in a second. In the very first one, he actually talks about Beethoven's Fifth Symphony. And he begins talking about the da, da, da, dah. And that's an amazing start.
But what makes it amazing he says, is not so much the da, da, da, dah, but all the notes that come after it, that complete it. I mean it's a sort of well-known fact about Beethoven that his music does have this feeling of inevitability. One note follows after another, like it's this perfect thing. You couldn't change anything without ruining it.
What Bernstein does in this TV program is he shows what an incredible, painful journey it was for Beethoven to find that perfect structure. He goes and he finds all kinds of passages that Beethoven had put in and then decided to remove.
But he goes and he puts them back in. He has an orchestra sitting there. He goes and puts them back in so he can listen to what it would have sounded like if they were in. And it sucks.
In almost all cases, it's just terrible. And why is it terrible? Not because we're used to the right one. But in some objective sense, you look at it and say, no, that's just wrong. It's just wrong.
But that's what he did. It's not like he invented this thing that was perfect in one go. He was in the neighborhood of something fantastic. And he was imperfect. But he kept going back and removing, and removing, removing the imperfect things, until the perfect things emerged out of it.
That's the thesis. That's what Bernstein explains. And what absolutely blew me away when I first saw this video was the language that Bernstein used in describing what Beethoven was doing.
It's identical. I mean, not roughly analogous to. It's identical to the language that I was using earlier in this lecture about logical inevitability, coherence, and faithfulness to its own logical structure.
So I want to just play you a little clip, if I can, of the last thing that he has to say about this. Whoops. Sorry. This might take-- I need to find the right spot. I lost it. Sorry.
NIMA ARKANI-HAMED: So he's going through all the things that suck. OK.
-And so he tried to do a third ending.
NIMA ARKANI-HAMED: Oops.
-And this one worked. But the odd thing is that as it turned out, this third ending is even more abrupt than the first ending was. So you see Beethoven had to struggle and agonize for all this time in order to arrive at what is apparently so simple a thing, that his first ending didn't have the trouble of being too abrupt, but rather not abrupt enough. And so out came finally this third ending, which is as right as rain.
[MUSIC - LUDWIG VON BEETHOVEN, "SYMPHONY NO. 5"]
And so Beethoven came to the end of this long symphonic journey, at least for one movement. Imagine a lifetime of this struggle, movement after movement, symphony after symphony, quartet after concerto, after sonata. Always probing and rejecting, and this constant dedication to perfection, to the principle of inevitability.
Somehow this is the key, the only key we can have, to the mystery of a great artist. That for reasons unknown to him, or to anybody else for that matter, he will give away his life and his energies just to make sure that one note follows another, with complete inevitability. It seems rather an odd way to spend one's life. But it isn't so odd when we think that the composer, by doing this, leaves us at the finish with a feeling that something is right in the world, that checks throughout. Something that follows its own law consistently. Something we can trust, that will never let us down.
NIMA ARKANI-HAMED: So I hope you're struck as much as I was by the explicitly overtly moral character of what he was talking about. As well, of course, as the very striking similarity with some of the broad themes that I was talking about earlier.
So I really should stop there since it's hard to talk after Bernstein. But let me just say a few final comments.
So I'm ending. But I began, in the beginning, by telling you that I wasn't a militant atheist. But I don't believe in God. I do, however, think that instead of worshipping a vast and unknowable god, we can devote ourselves to this slow unveiling of the vastness of truth in all of its glory.
It's not unknowable. It's gradually more and more knowable. And even the parts of it that we might know within our lifetimes will have this perfection to them, have this eternal quality to them, and can give a deep sense of meaning to our lives.
This pursuit of truth, there is the scientific truth that we talked about. But the last few things that we just touched on, the Errol Morris quote and what Bernstein was talking about, I think strongly show that there was some larger notion of truth that can guide almost everything that we find worthwhile in life.
But at least what I was telling you about, I believe, provides some invariant rough sort of moral code. The perfection of the truth that we're looking for, we, interacting with it, makes us better. And doing this allows us to transcend our mortality and touch something eternal. Thank you very much.
CSABA CSAKI: Thank you very much, Nima, for this very nice lecture. Now, it's time for questions. Yes?
You raised the question at the end of the inevitability and unknowability of things. And it's fantastic [INAUDIBLE]. But I think there are some things that are unknowable [INAUDIBLE]?
NIMA ARKANI-HAMED: Well, I guess that there are some differences between historical sciences and other sciences. There are some things that are always unknowable about the past, potentially. Although, at some level, we hope that it might be extremely hard, but that we might be able to know all of them.
I think actually it's sort of pointless to have a discussion about the ultimate limits of knowledge since we're nowhere near saturating it. And once we get close to the point of saturating it, if we ever get there, in 20,000 generations, or whatever it is, then I suspect that our language for thinking about things will be so different than it is now that the words will mean something else then.
I really doubt that-- what I was stressing, that our provisional understanding-- you know, whatever we learn next about biology, whatever big revolution we learn about biology, Darwinian natural selection is going to be the right way of understanding the things about the world we see now, even if we learn more things. This idea of local perfection is, I think, very important. Because it means that we can simultaneously expect progress, as well as having things that have a non-ephemeral significance.
And whether or not eventually there are limits to everything-- you know, some of the most abstruse, esoteric questions in trying to apply quantum mechanics to the entire universe right now, which are just beginning to be questions that we can think about properly in theoretical physics, start touching on this question of the fundamental limitations of knowledge. But I think, at the moment, our language is so poor for being able to articulate those questions well. But it's not really responsible to what we're working on.
CSABA CSAKI: Next question. Yes, back there?
AUDIENCE: I'm curious. With your morality, do you consider some of the questions, the fundamentals of physics, to be immoral themself?
NIMA ARKANI-HAMED: No. You see, that's part of the beauty of the construct that I'm suggesting. I'm not saying this is the only moral code. You can invent any moral code you like.
What I am saying is that if you don't think that there is something out there telling you what to do, OK, if you think that there is just a impersonal world and nothing else, that it's rather interesting that the act of trying to learn something about it forces certain patterns of behavior and thought on you that are broadly good. That's interesting. It didn't have to be that way.
So there is a notion of morality, which is not purely a human construct, but derives its existence from the external world. Of course, the external world could give a crap about us. But that's fine. This notion of morality is about our relationship to the external world.
You can do anything you want. You can have a nudist colony in San Francisco. You can do anything you want. People can do anything they want. And I suppose from this moral code that I'm talking about, if it doesn't impinge on my way-- on our desire to learn more about the laws of nature, we won't have a problem. But if it does, we might.
CSABA CSAKI: OK. Right there.
AUDIENCE: Do you have any practical advice or [INAUDIBLE] certain problems when you have, like, very limited knowledge from years ago? And you just don't have enough. And as you have finite time, you're trying to pick a topic, like, yes, it's working for you.
NIMA ARKANI-HAMED: The practical advice is the following. Pick a question. And pick a question and a topic which you're absolutely crazy about.
What I mean is you have to find the ultimate underlying questions really compelling. And if you don't know it already-- I don't know what stage of grad school you're in. But things are not easy. So there's a lot of extra difficulty and complication.
So if on top of all that difficulty and complication, you're just not that sure that what's going on is all that important, all that great, then that's going to just suck. So just choose things based on the science, based on the level of excitement and interest of the science.
But you have to be practical as well. And it's part of the general moral code that I was talking about. I celebrated Einstein, and Grothendieck, and these people, who managed to work solid on a problem for eight years. Trust me, you don't get up in the morning able to do that. The way you're able to work on a problem for eight years is you first manage to work on a problem for two months, three months, four months, a year.
You have to exercise these muscles. You have to get good at it. You have to bite off as much as you can chew.
And it's a hard balance. But you will know. You will know, if you're honest with yourself, if what you're doing is just really easy and is not challenging you at all. Or if what you're doing is so hard, that it's also not challenging you at all because you're not doing it.
You have to find the perfect intermediate stage, where you're in pain all the time. OK.
You're in pain all the time. But it's a good kind of pain because you're making a little bit of progress. But it has to be about questions that you actually care about. If you don't care about them, there's problem.
AUDIENCE: Thank you.
CSABA CSAKI: OK.
AUDIENCE: What comes after spacetime?
NIMA ARKANI-HAMED: There is none.
AUDIENCE: [INAUDIBLE]. On the other hand, [INAUDIBLE] dependent. But in the real world, when people can have more authority, [INAUDIBLE] always. [INAUDIBLE]. How great are [INAUDIBLE]?
NIMA ARKANI-HAMED: Well, I think the example of the Errol Morris quote is very important. I encourage you to watch his documentaries. This is not some tweed jacket academic.
You're dealing with complicated situations, with people killing each other. It's not obvious who killed who. We're torturing people in Guantanamo. Why are we torturing them?
So the really most dirty, god-awful complicate difficult aspects of life, all we offer-- what I'm saying is that there is this truth out there. Interacting with the truth out there, doing it properly-- because there's a way of doing it that isn't just agreed upon-- internally agreed upon as a social convention among a bunch of us.
I think that's sort of a remarkable fact. And that if more people in the world cared about and believed that there was such thing as an objective truth-- it's difficult to find. But that it's worth fighting to find it. I think the world would just be a uniformly better place.
It certainly won't solve all of our problems. But if we had that under control, I would love to live in the world where we're dealing with the next level of subtle difficulties after that.
CSABA CSAKI: OK, in the back?
AUDIENCE: A question and comment. Another good book by Steven Weinberg is titled The First Three Minutes.
NIMA ARKANI-HAMED: Yes.
AUDIENCE: My question is [INAUDIBLE] You might want to take them serious because the [INAUDIBLE] aether-like substance [INAUDIBLE] universe [INAUDIBLE].
NIMA ARKANI-HAMED: I'm glad you brought up the aether because this is-- if I had another hour for this talk, I would have spent much of it talking about the aether.
The aether is often held up as a-- and actually, a lot of our folk history of science, even the way we teach kids in high school, undergraduates and so on-- it's filled with stories that are roughly-- we're not quite as mean as this-- but roughly is, how could those people have been so dumb back then?
OK. It's unbelievable. These people thought everything went around the Earth. How stupid, right? Because they wanted the Earth to be the center of everything.
Or these morons, everything thought was filled with an aether. What a dumb idea, right? How could they possibly think that? And then this genius Einstein comes along and say you idiots are all wrong.
Actually the aether was a fantastic idea. The aether was an amazingly good idea. And it's a great illustration of the power of the scientific method. It's very much along the lines of what I was saying, that you take the things that you know and you push them and you extrapolate them.
Absolutely no reason to think that there wasn't a medium filling things. Every other wave that people had seen, involved a medium. No problem. But it's important to be concrete and to do something about it. That's the point.
So what was great about the idea of the aether is that people had a concrete problem they had to work on. They had to try to build some material that filled the universe, that gave you waves. But they discovered something very important about electromagnetic radiation, that it was polarized. They discovered the phenomenon of polarization.
This was the key to get people on the correct path to understand electricity and magnetism. Because it meant that you had to find some kind of material that propagated waves, but that didn't have any compressional part of the wave. The waves only oscillated transverse to the direction they were moving.
Then various people tried to build actual aethers that made this happen. And James Clerk Maxwell is one of the people who actually built the mechanical model. So there is an actual model, with cogs-- little cogs, and gears, and wheels touching each other. And when the cogs were all rotating, that corresponded to having a magnetic field, for example.
So he built this explicit concrete mechanical model. And then he noticed in his model, when he kicked his model, that it propagated waves. But the waves only oscillated transverse to the direction of motion.
So the idea of the aether that was not only not a bad idea, it was science working as it should. You push the ideas you have. But you try to make them concrete.
You're not lazy. You try to make them concrete. You try to make them work. You try to make predictions. You try to compare it to experiment. And by building this mechanical model, Maxwell discovered the correct equations, what we now call Maxwell's equations.
Now, irony of ironies, that these very equations that the aether helped discover were what were used by Einstein decades later to overthrow the idea of the aether itself. That's a wonderful irony.
But there's no way the equations would have been come up with if people hadn't had this underlying mechanical model of an aether in mind. They're too complicated. There's no way you would just, out of the blue, guess equations like this. This is a fantastic example of how science works.
The aether was a wonderful idea. It was concrete. It gave people something to do. And because the truth is out there, it doesn't even matter if you're not seeing all of it. If you're seeing part of it, then you will eventually get dragged to the right answer, even if, by the time you're done, you have to throw out some of the key concepts that got you in to begin with.
So there's nothing stupid about the idea of the aether at all. It just seems to be wrong for light. There was no such thing as aether for light or for any of the other excitations that we know of.
There is some sense in which the universe is filled with an aether. This cosmic microwave background that fills the universe does give us a preferred frame of reference. And it's true, that at sufficiently long distances, where cosmology is important, the laws of special relativity are wrong. So in that sense, there is an aether. It's only properties of the vacuum, and light, and gravity, and all the elementary particles we know. None of them, as far as we know, can be thought of as excitations of an aether.
CSABA CSAKI: Last question?
AUDIENCE: Is there something today that [INAUDIBLE] the aether in the 1800s?
NIMA ARKANI-HAMED: There might be. So one of the biggest puzzles that we have in physics today, which I devoted a solid hour and a half on, talking about, when I was giving the Messenger lectures here back in 2010, is the very simple question of why the universe is large.
The universe is large. It's one of the most basic facts about the world. It's made out of small things. The laws are defined and are given to us at very short distances. But the universe is enormous. So why is the universe enormous?
We don't have a good understanding of it. And on the contrary, because there are violent quantum mechanical fluctuations in the vacuum, at least as far as we understand things, it looks completely insane that the universe should be large. Because the fluctuations are enormous, more and more enormous at smaller and smaller distances. So we have no good understanding for why there is some kind of macroscopic coherence to the world at very large distances.
We don't know why there's a macroscopic universe. And that question has driven part of the field of theoretical physics in a very specific set of directions for 30 years. One avatar of this problem is closely related to mysteries about the Higgs particle. And thinking about that aspect of the problem suggested to many of us that when the Large Hadron Collider turned on, there had to be a bonanza zoo of new particles coming out. And that hasn't happened yet.
It might happen, starting in three weeks, when we start colliding particles at the LHC again. We still don't know that this idea is wrong. It may well be right, that the things that we're thinking about for 30 years is basically right. And we'll see what particular version of it is right.
But it might be that we eventually find out that it's wrong. And that's what's really at stake with this next round of experiments at the LHC. If it turns out to be wrong, then I think, in 50 years, it will be called the aether of the 21st century. But it's not like the aether-- it's not a question about a substance. It's a question about a particular approach to trying to understand the question of why there's a macroscopic universe.
CSABA CSAKI: All right. Let's thank Nima again.
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A.D. White Professor-at-Large Nima Arkani-Hamed examines values and principles of conduct in the study of physical science phenomena, April 21, 2016.