CSABA CSAKI: Last [INAUDIBLE] lecture in this series of five. My name is Csaba Csaki. I am one of the faculty members in the physics department, and I'm working on research that is most closely related to Nima's research. So that's why I'm doing the introduction today.
Of course, I don't have an easy job, since [? Saul ?] said all the important things yesterday already. So I tried to come up with some new stuff. So I had to dig a little deeper in my memory.
So Nima was actually born in the US, but he's of Iranian descent. And it actually turns out that they actually did move back briefly to Iran after the revolution in 1979. So if you ever want to hear a real [AUDIO OUT] story, ask him how they have actually escaped afterwards and moved back to North America.
So after that, they [AUDIO OUT] settled in Canada, in Toronto. That's where Nima attended college. And I actually got to know him, I think, in '96, when both of us were about to get their PhDs. He was in Berkeley. I was at MIT.
And already, around that time in '97, he was asking people around him, what do you know about extra-dimensional physics? And I was always wondering, what weird questions [INAUDIBLE]. Everybody knows if there are extra dimensions, they are so small that they could never be relevant for physics.
So then his paper came out on large extra dimensions. And then I said, OK, yeah, he found a loophole. But within two months, it's going to be excluded, and that's certainly not something that I want to be working on.
So guess what I was working on in the last 10 years. Well, [LAUGHING] mostly theories of extra dimensions. So I learned back then that I have to take everything that Nima says very seriously. So I hope that he will tell us more exciting stuff today. Okay, let's welcome Nima.
NIMA ARKANI-HAMED: Thank you, Csaba. Csaba will not modestly say that we first met under circumstances when he was the clear star graduate student of the year. [AUDIO OUT] talks. And we--
CSABA CSAKI: [INAUDIBLE]
NIMA ARKANI-HAMED: Number two. Well, very good. [LAUGHING] But [AUDIO OUT]. The goal of today's lecture--
Whoops. Is that? Do I do something with this, or move something? OK, great.
So yesterday, [AUDIO OUT] basic rubric of special relativity and quantum mechanics that governs all physical laws. And those are just the very general principles that govern all the physical laws that we know.
And today, I want to tell you how those general physical principles are realized in our actual use, OK? Before I do that, I just have a quick coda to some of the things said in yesterday's lecture. So those of you who weren't here yesterday, just ignore me for a few minutes.
First of all, it was pointed out to me by a couple people that I'd said something very confusing about the radioactive decay of particles. The very first example I gave for quantum uncertainty was to say that if you take two radioactive particles and let them decay, we can't predict ahead of time when one will decay-- one could decay after one minute, one could decay after two minutes. And that that's a very vivid illustration of quantum uncertainty.
But I said that we could make a prediction for the average lifetime if we had many, many, many of them. The problem is that I was using the word "lifetime" for something that we in particle physics always are using the word "lifetime." but what you normally say is the phrase "half-life."
So you can make very specific predictions with the half-life. But of course, it's not true that if you take a million particles, all of them will decay, or a big fraction of them will decay at some [INAUDIBLE]. What happens, actually, is if you take this large number of particles, and you just plot when they decay, [INAUDIBLE] just a fraction of them that are left as a function of time.
If there's just two of them, you get some very choppy histograms. But if you have many, many of them, it'll start looking like a smoother and smoother histogram. For any particular collection of them, it won't be perfectly smooth. It'll have little bumps and wiggles [INAUDIBLE].
But then if [INAUDIBLE] an infinitely large number of particles, there is a perfect curve [INAUDIBLE] exponential-- beautiful, smooth curve. So the fraction of particles that's left would be something with 1/2 to the power of the time divided by something that you might call the half-life.
So this is what quantum mechanics predicts. That cruve-- the shape of that curve-- the fact that it's an exponential, is the precise prediction of quantum mechanics. Even though it's not true [INAUDIBLE].
The little graph like this that I drew yesterday refers to what you might talk about as a measurement of the half-life. So if you take the material, and you wait to see, how long does it take for the first half of it to decay? How long does it take for the next half to decay? How long does it take for the next half of it to decay?
You could make a plot of when that time is. And of course, if you have a small number of particles, that plot will be very choppy. But as the number of particles becomes larger and larger, the plot will become more and more sharply [INAUDIBLE] around the answer that we call the half-life. Unfortunately, this is what we call the lifetime. And part of [INAUDIBLE], so [INAUDIBLE].
The second thing that I wanted to say was something I didn't get to last time. But we ended last time by marveling at how incredibly different the quantum rules work from classical physics. And they're so different, and the rug is so pulled under you, from the point of view of the classical physicist, that you might wonder how we ever have a hope of figuring things out.
If whatever we know now can change so radically compared to what we think, it seems like, OK, maybe we got lucky a few times. But this is going to be a very, very, tall order. But as I mentioned in the beginning of the lecture yesterday, that's not how revolutions in physics work.
It's never the case that there's no possible connection to the previous theory. There are always to be a connection to the previous theory. Often, the way of finding it-- and in fact, it's often a good way of finding what the next theory might be-- is to try to understand more deeply, and in as many different ways as you can, the theories that you have already.
And I just wanted to quickly mention that this fact, that quantum mechanics isn't deterministic, but classical mechanics is-- which is the feature, the hallmark of quantum mechanics, and the thing that makes it so radically different from classical mechanics-- that fact, the absence of determinism, really had an avatar in classical physics. There was a clue sitting there in classical physics for 150 years that this might be coming. And that clue was an observation made by people about 100 years after Newton, that there was a completely different way of talking about classical mechanics.
Not in terms of a particle goes from one point to the next, to the next, because some force acts on it. And it goes from one place to another, because some force is telling it where to go next-- that extremely deterministic picture. But people found instead that there was a completely different picture for what might make a particle go from A to B.
That a particle would go from A to B by picking a path that minimizes some quantity from A to B, that minimizes the average value o of the kinetic energy minus potential energy. It's not obvious, but it turns out to be a complete reformulation of classical mechanics. Completely equivalent to Newton's laws, but it's not manifestly deterministic.
In fact, when you say it, it sounds startling. It's like, what, the particle's sniffing out every way to go from here to there, and then choosing the one that minimizes the action? It turns out to be determinist. But it's not hardwired into the formulation.
It's easier that there's [INAUDIBLE] for light. Light goes from A to B just to minimize the time. That's really cool. So for example, if you want to make it bounce off a mirror, then light goes from A to B in such a way that it gets from A to B as quickly as possible while we force it to bounce off the mirror. That force is this famous fact of the angle of incidence is going to equal the angle of reflection.
Or, if you want to go from A to B in-- I don't know, this is glass. So light goes slower in glass than a mirror. Then it turns out that the fastest way to go from A to B is the way that satisfies the famous Snell's law that probably you all learned in high school.
But this is a formulation of physics that's not manifestly deterministic, but turned out to be completely equivalent to the standard classical rules. Those classical physicists might have wondered, why is it true that there's such a reformulation of the theories we have that's so different in philosophy than the clockwork, deterministic Newtonian picture? We now know the answer! This formulation exists, because the world is not deterministic, but is quantum mechanical.
And as [INAUDIBLE] taught us, in a specific sense, the particle actually does make use of all those other paths from A to B. It does sniff out every possible path from A to B. It takes every possible path from A to B, with a particular state vector associated with each one of them. And for big objects, the biggest contribution comes from the classical [INAUDIBLE], which is how classical physics is partially emerging.
So I just wanted to go through this, because it's a beautiful example of this philosophy of radical conservatism. Things never just go haywire. There's always some connection between the old theories and the new ones, and we just have to find out what that connection is. And the way of thinking about the theories we have that makes that connection as transparent as possible.
So even quantum mechanics, which is so incredibly different than classical physics, is not that different. It's not so different that there isn't a hint of it sitting there already in alternate formulations of classical [INAUDIBLE]. All right. That's it for the end of yesterday's [INAUDIBLE].
OK. So let's talk about what's actually in the universe, OK? So there's four basic interactions that we know of. Gravity that keeps the Earth going around the sun, electromagnetism, as well as the less familiar ones-- the weak and the strong nuclear forces.
The weak force is what's responsible for radioactive decay. The strong force, or what we now understand is some very residual relative of the strong force, is what's responsible for keeping the protons together inside a nucleus.
You know, in a helium atom, there's two protons and two neutrons. The two protons are repelling the heck out of each other. Something is keeping them confined to the nucleus.
And that was called, a long time ago, the strong force. And anyways-- there's modern relatives of it. But these are the four basic interactions.
And this is a picture of all the length scales we know of in nature that we probe experimentally. At the biggest distances, around 10 to the 28 centimeters, is the size of the observable universe, which is expanding, as we'll discuss. A million times smaller than that are galaxies.
OK, a whole bunch smaller than that, at 10 to the 13 centimeters, is the size of a solar system. Us. DNA. Atoms.
Around 10 to the minus 8 centimeters. Protons and neutrons, around 10 to the minus 14 centimeters. And bracketing all of these things are two important scales, which are both clearly physically important and happen to represent the frontiers of what we probe so far.
OK, so this largest scale, the size of the universe, is also called the Hubble scale. Down here at 10 to the minus 17 centimeters-- actually, another interesting length scale. It has a name-- it's had a name for 70 years.
And it's called the weak length scale. It didn't have that name for 70 years, but people have known about it for 70 years. And we now call it the weak, or the electroweak length.
So as I said, this represents the frontiers of our experimental probe of nature. At the largest scales, we have a whole variety of experiments probing cosmology at the very largest distances. And at the very, very smaller scales, we probe close distances, using very [INAUDIBLE] accelerators.
The Large Hadron Collider, which is now running, is designed to, and will thoroughly, probe physics at distances around 10 to the minus 17 centimeters. So that's around 10 times smaller than the smallest distances that we've probed so far. Around 1,000 times smaller than the nucleus of the atom, and around a billion times smaller than the atom itself.
So I'm now going to clean this picture up and tell you about the scales that we think about in our subject. So that's the entire previous transparency. And the two scales that we think about are the extremes-- so the very largest scale, the little scale.
There's actually a third length scale that we talked about that's even much much, much tinier than those, called the quant length. It's around 10 to the minus 33 centimeters. And let me tell you a little bit about these scales. These are going to be our friends for the next number of [INAUDIBLE].
Before I do that, I want to make a note on units. I'm not going to crucially use this so much in the rest of the lectures. But I just wanted to say it, because I can't give lectures like this without saying it.
So I'm going to use centimeters and standard units-- and don't worry so much. But you should realize that these are extremely artificial units. When we measure something in meters, every single number that has any meaning in physics doesn't have any units. It's some pure, dimensionless number.
When we say that such and such is 1.8 meters high, what we really mean is that there's some bar sitting in Paris. And if take that bar, and we put 1.8 of those bars up next to the thing, then they'll be commensurate with each other. But these units are completely artificial human units that have to do with some bar sitting there in Paris.
And the fact that we [INAUDIBLE] many different sorts of units. We have kilograms, units for mass, units for length, units for time. In fact, there's only one unit. Really, there's no units, because everything is dimensionless.
But given that we're going to be doing both relativity and quantum mechanics here, it makes a lot of sense to work with units [INAUDIBLE] [INAUDIBLE] are 1, right? Now, that sounds a little bit confusing. [INAUDIBLE] just 1.
But what it really means is that I can trade in distance for a time, using c. I can trade in energy for an inverse time using h bar. And so I can measure everything in one consistent set of units.
Those units could have units of length, they could have units of 1/length, they could have units of mass, energy. Any one of those suffices. And I can get everything else from them. Now, in particle physics, we really like to use a unit which is 1 giga electron volt, a unit of energy. And one reason that's convenient is that that energy is approximately the rest mass of a proton, OK?
So getting practice with these units-- the size of the proton is around 10 to the minus 14 centimeters, and that's around the inverse of its size. That's 1/GED in size. So the proton, you could say, it's an inverse GED, or you could say it's 10 to the minus 14 centimeters. So that tells you a conversaion-- inverse GED is 10 to the minus 14 centimeters.
So for example, I am 10 to the 16 inverse GED tall. Now, you see, that has real physical meaning. If I want to communicate to an alien how tall I was, it would do me no good to say, if you put me up next to 1.72 bars in Paris-- oops, sorry. You haven't been to Paris, you don't know what the bars are-- shoot! How am I going to tell you how tall I am?
But their protons are the same as our protons. So I could say instead, if you'd stack 1 to the 16 protons on top of each other, that's how tall I am. It's physical. These are correct, natural units. That's why they're called natural units.
My mass is 10 to the 29 GED. That has real information. I'm made of around 10 to the 29 atoms-- that's what I weigh.
Because basically all the mass, properly speaking, [INAUDIBLE] proton is [INAUDIBLE] atom. But it tells me something about how many protons I'm made of. This lecture time, if you're lucky, is 10 to the 27 GED inverse.
But these units tell us something actually very deep and fundamental about the kinds of forces we know in nature. For example, do you all know that the electrical forces and gravitational forces are both inverse square law forces? You probably learned all that in school.
So if we talk about the electric force between two electrons, or the gravitational force between two electrons, they both go, like, 1/the distance between them square. The electric force is repulsive, the gravitational force is attractive.
OK. So of course, I'm writing it in terms of the energy, the electric energy, or the gravitational energy, between two electrons. And this is what the electric energy is-- it goes, like, 1/the distance.
And there's something, which, if you have vivid memories from high school, involves the product of charges and something called k. And there's all sorts of terrible things, you measure them in [INAUDIBLE]. I can't give any of that script, OK?
But actually, forget about all of that. If we use natural units, we actually learn something quite important. You see, energy has units of 1/time, which is the same as 1/distance. And this h bar equals c equals one unit.
So that means, whatever this coefficient is, 1/distance already has the same units of energy. So whatever that coefficient is-- it's just some number. Just a number. That number turns out to be around 1/137. Point something, which I don't remember.
That's fascinating! There's an actual, pure number associated with the strength of the electric force. That's a pretty small number. 1/137 is some interesting, pure number in nature.
Let's do the same thing for gravity. For gravity, we say that it's there's G Newton times the product of the masses overall. Now, this is different. Because e and 1/r have the same units, but there are these two masses. So whatever G Newton is has to have units which are inverse of mass square, which is the same as a length square.
So in these natural units, G Newton is 10 to the minus 33 centimeters squared. That was that third length that we talked about, that I said, we haven't gotten anywhere close to probing this tiny scale-- 10 to the minus 33 centimeters. But we know there is something interesting about it. And this is why-- the Newton constant, gravity, is associated with this tiny, tiny number-- 10 to the minus 33 centimeters.
Now, this is really interesting. Because this strength is not a pure, dimensionless number. It has units. So that means that there is no real sense in which you can say gravity is weak or strong.
Gravity is weak at very large distances compared to 10 to the minus 33 centimeters. It's astonishingly weak! But at distances comparable to 10 to the minus 33 centimeters, or even shorter, thereabouts, it should be very strong.
There is nothing else to compare it to. You have to be able to compare it to something to be able to tell if it's strong or weak. In fact, it's not invariantly strong or weak-- it just depends on whether you're at long or short distances.
Of course, most everyday life is at enormous distances compared to 10 to the minus 33 centimeters. And that's why gravity is an enormously weak force. Look, this electric force between two electrons is 10 to the 42 times stronger than the gravitational attraction between them. The only reason why gravity dominates at very large distances is that we're mostly made out of neutral things. But fundamentally, it's an incredibly weak force.
So, back to our back to our pictures. This is just an advertisement for the next couple of lectures. Everything in this picture contains all the central theoretical crises we have in physics today. Hopefully fertile and important crises, revolution features everything we want to know [INAUDIBLE].
But down here at 10 to the minus 33 centimeters, this is where the facts of the quantum mechanics and gravity become important. And as we'll discuss tomorrow, spacetime is gone. And we have to figure out how to replace it with something else.
And there's another extremely salient feature of this picture, which is that there are these gigantic separations, right? There is a [INAUDIBLE], and there's this huge gap until we [INAUDIBLE] scale, [INAUDIBLE] scale. And they have a huger gap until we get to these much, much larger distances [INAUDIBLE] the size of the universe.
So this is simply saying that universe has many very, very separated important length scales from each other. Despite the fact that there's microscopic physics and microscopic laws, there was a big, macroscopic universe. That turns out to be a very major puzzle.
It's also possible to accommodate it in our current understanding of physics. We barely manage to do it, but in such a ridiculous way, that it's clear that we're missing something very, very big. So the answer to that really basic question, why is there a big universe, is also likely to teach us a lot. And is likely [INAUDIBLE] you [INAUDIBLE] understand. So those are the major discontents that I was referring to, and the discontents are going to be discussed at much greater length in the next few lectures.
All right. So let's come back to our story of what's in the universe. Well, one of the big themes of the past 400 years since Newton has been the realization that everything that we can understand-- all the apparently large, dizzyingly diverse array of phenomenon-- as we understand more, seem to be different aspects of the same thing.
It's really actually [INAUDIBLE] who realized that the same force of gravity pulling the apple down to the Earth was exactly the same force that's keeping the moon going around the Earth. That's something that's so seemingly obvious now we teach it in kindergarten-- or whenever we teach it.
But it took Newton's genius to realize that it was true. Far, far from obvious. Amongst other things, the moon goes around in a circle, [INAUDIBLE]. So he had to understand everything else about motion in order to see that this was not obviously ridiculous, either. That it was not just not ridiculous, it was true.
Electricity and magnetism. What the heck could lightning and these funny rocks that attract or repel each other have anything to do with each other, right? But Maxwell realized in the 1800s that they're also different aspects of the same thing. And furthermore, that light, which was the third thing that seemed to have nothing to do with the first two, was just undulations of electric and magnetic fields.
So more and more things come into an underlying common rubric. As we discussed yesterday, relativity in quantum mechanics continued this in a very significant way. Unifying space and time, unifying waves and particles into quantum particles. As we learn more and more, we're seeing that everything that's out there is an underlying reflection of less and less.
There is more and more unity. And we just have to figure out how to crane our necks around and see exactly why it is that everything-- exactly how it works. But often, in subtle ways, in often, shockingly beautiful ways, we find that very different phenomena are different aspects of the same thing.
So this is where we got to yesterday. And now I want to continue by telling you what happens when we try to put quantum mechanics and relativity together. It turns out that putting them together is not easy. One reason that it's not easy is that they use different words.
Well, for one thing, relativity is deterministic, and quantum mechanics isn't. So relativity is just an update of Newton's laws. Quantum mechanics changed everything.
But whenever we [INAUDIBLE] to combine quantum mechanics and something, in the last 100 years, what that's meant is that we take the something else, and we make it consistent with quantum mechanics, OK? Quantum mechanics has never once been modified since it's been written down in 1927. Such an incredibly rigid structure. It's very hard to imagine how we could monkey with it in any way. It's just to say people have tried.
But every success that we've had is by bending theories together in such a way to make them consistent with quantum mechanics. Anyway. But it's possible! It's possible to put them together.
But it's not easy. You might have given up. But it is possible. But the union between them turns out to have really unexpected consequences. And one of these consequences that I'll discuss is that putting quantum mechanics and relativity together--
Perhaps I should have said one more thing. Another major difficulty is that the basic laws of quantum mechanics, as I briefly discussed with you yesterday, does make time very important. You specify the state of the system at some time, and then you evolve to see what happens at some other time. You say the word "time" just as often in quantum mechanics as you do in classical mechanics.
However, relativity says, oh, no-- time, space, they can be mixed into each other. That's the hard part. How do you get a set of laws in quantum mechanics that like to use time, and make it consistent with the fact that you can mix time and space into each other?
That is the challenge. It turns out that you can do it, but it has a number of remarkable general consequences. And one of them is that it forces the existence of anti-particles.
This is a prediction that was so strange and so counterintuitive that even the people whose theory predicted it, Dirac in particular, refused to make this prediction. Anti-particles popped out of Dirac's theory, but it was so weird that he tried to call them something else for a long time.
And it wasn't until actually [INAUDIBLE], who had no stake in whether Dirac's theory was right or wrong, said, look, your theory creates anti-particles. And it does. And of course, dutifully, it was discovered [INAUDIBLE] a number of years later.
But it's remarkable that this unification over an extended notion of spacetime, together with quantum mechanics, doubled the world. Now, I want to tell you roughly why this works. There are some holes in this argument, but it gives you the spirit for what is the right argument. It all has to do with this basic conflict between causality and quantum mechanics.
Let's go back to relativity. Remember in relativity, nothing can go faster than the speed of light. A way of saying that is, let's say you have something at A, and it transmits a signal faster than light to B.
Why is that not allowed? That's not allowed, because in another reference frame, running very fast, relative to this-- remember, we can move along hyperbolas-- and another reference frame-- B would have occurred before A.
So you fire a gun, you kill someone at B faster than the speed of light. In another reference frame, they're dead before the gun was fired, OK? That's complete conflict with causality.
Forget determinism. Remember, quantum mechanics means that you can't predict what happens next. Even more basic than determinism is causality-- that what happens next is at least only a function of what happened before. For heaven's sake.
So something even more basic than determinism is causality. And causality in special relativity forbids signals to go faster than light. However, in a quantum mechanical world, you can't forbid anything.
For example, there's always some tiny chance that you thought you turned it on at A, but by the uncertainty principle, really it turned on over there, maybe from there to there. You just think that it went faster than light from A to B. But one way or another, there is some signal leaking out outside of this [INAUDIBLE]. And it can go to another reference frame, and indeed it happens earlier in time. That's just inevitable if if you have quantum mechanics.
So what do you do? You could give up and say, these things are not compatible with each other. We need a massive revolution that's going to upend both things. Or you would say, no, let's work hard, because there's some possible way it could make sense.
And there is one way out. The one way out is to give this process a causal interpretation. Say ah, how do you know something went from A to B?
What, are you saying there was some flow of e electric charge forward in time from A to B? Great. There was a flow of electric charge forward in time from A to B. You'd think there's a flow of negative charge backwards in time from A to B here.
But here's another way of interpreting it causally. There's a flow of positive charge forward in time from B to A. So your attempt to interpret what's going on that's forced on you by quantum mechanics causally gives you one way out. But it makes it a necessity for there to exist some particles out there of positive charge-- otherwise completely identical to the electron, but with a positive charge.
So you could interpret it as a flow of charge forward in time for the meaning of this process. That's why empty particles must exist. There are particles identical-- everything identical except their charge, with opposite charges.
Now, that's a very basic consequence of putting relativity and quantum mechanics together. And it has a number of remarkable consequences. One of them is that even the vacuum-- empty space--
Remember our march from Newton to now is endowing more and more and more structure to emptiness. Or to what Newton would have just thought as a very static arena. Space and time was a static arena where everything takes place. Relativity mixes up space and time, general relativity curves space and time.
Now, even emptiness has some structure. Even the vacuum is exciting. And the reason is that there's really no sense in which the vacuum-- there is no mutual sense in which you would think of it as empty.
So let's imagine I take a magnifying glass-- that's my sad magnifying glass. And let me try to use it to verify that indeed, this region of space is empty. Doom de doom, I'm looking at the region of space.
Nothing there-- that's great. OK? Nothing there.
But in a quantum mechanical world, in order to probe what's going on at a short distance, by the uncertainty principle, I need a lot of energy. As we'll discuss on Friday, when we discuss this golden hour of experiments, that's also very expensive. You need to build very high-energy accelerators to smash particles into each other at very high energies so we can probe very short distances. That's a direct consequence of the uncertainty principles.
So if I want to probe what's going on in a smaller and smaller region of space, I need to use higher and higher energies. Now, what happens is when that region becomes sufficiently small, I've put so much energy into that region that nothing stops me from producing a particle and an anti-particle. Charge is conserved, energy is conserved. Everything is conserved.
Nothing stops me from producing a particle and an anti-particle. The act of trying to verify that this little region of space is empty produces for me a particle and an anti-particle pair. And every such act will do that.
Of course, the world is quantum mechanical. Every time you look, it'll look different! But one way or another, any act of trying to probe what's going on at short distances will produce particles and anti-particles.
I told you we use accelerators to probe these very short distances, as we'll discuss at greater length on Friday. And people often describe accelerators as the world's most powerful microscopes. But you can ask, what are they looking at?
They're not looking, like, at a piece of hair, or something like that, right? They're looking at the vacuum! They're taking snapshots of the vacuum and figuring out what the vacuum looks like at these very tiny distances. And those snapshots are so interesting that we have to build $10 billion dollar experiments to understand them.
So if you have this boring picture of an electron sitting there-- a point-blank electron sitting there. And with electric field lines going out forever, that's really not correct. Surrounding it all the time are these particle and anti-particle pairs that are popping in and out of the vacuum all the time.
What that means is that's a better mental picture. Now think of it as empty-- that's a mental picture that's closer to telling you what actually happens in an experiment. Any act of measuring what's going on at those distances will, inevitably, produce particle anti-particle pairs.
Now, that's one of the general consequences of putting relativity and quantum mechanics together. There are other consequences. And there is a completely well-defined mathematical framework for how to put the two of these things together.
And really, when I said yesterday that a lot of the development of physics in the 70 years after relativity and quantum mechanics was conservative, it was conservative in the sense of more and more deeply understanding this marvelous structure called quantum field theory. This turned out to have incredible layers of depth, and complexity, and ability and richness-- ability to describe nature in surprisingly subtle ways that took all that time to sort out. And we're still not done understanding, we're still not done fully appreciating all of its problems.
But as far as describing the world is concerned, these developments culminated in the 1970s with the invention of a very specific quantum field theory that does describe all the known interactions that we know, together with the way they interact with all the matter-- everything down to distances of 10 to the minus 16 centimeters. And it's a spectacularly successful theory that's given the highly overly modest name of the standard model of particle physics. That's because, well-- if it was today, this would be the most super-duper awesomest theory of all time, but people hyped things less back then.
But I cannot overemphasize how important it is that this theory exists. I mean, the situation is really, really different than it was 100 years ago. 100 years ago, before relativity and quantum mechanics and quantum field theory, there were basic questions about the world.
Why is this table hard? Why is water wet? We didn't have answers for those questions. You know, forget deep, philosophical questions. But we didn't have answers to basic questions about what the world around us looked like.
Quantum mechanics and relativity in their full glorious generalization into the standard model leaves any question about everyday world completely answered. Of course, it could be complicated systems, it could be hard to work out the equations, but that's it. We know everything we need to know to talk about the physics of the everyday. Where the everyday goes down to nuclear distances, down to subnuclear distances. And not only do we know how to describe that, but we also understand what we don't know very, very well.
So what the actual frontier is is very sharply defined in a way that was simply not true 100 years ago, when there were so many questions left unanswered that it was a really different situation. This is a really-- it's a great achievement. And it's a very quantitatively successful physical theory.
For example, if you take this picture that you have these particles popping in and out of the vacuum all the time around the electron, one consequence that it has-- if you imagine these particles popping in and out, the electrons in the middle have some electric charge, and it will attract a little bit the positrons and repel a little bit these other electrons. And that has the effect that if you're really, really, really far away from the electron, you will remember some value towards effective electric charge.
But as you go closer and closer in, you're sort of penetrating this cloud of electrons and positrons. And you're seeing more and more of this unshielded value of the charge. So this phenomenon is a lot like what happens, well, it's called vacuum polarization.
And it's really something you can calculate precisely that while at very large distances compared to 10 to the minus 11 centimeters, it turns out, the strength of the electric charge is basically constant-- it's this number, 1/137. As you start going to shorter distances, then you start seeing these electron positron pairs. [INAUDIBLE] goes up gradually.
It's very gradual. It goes up logarithmically. But it goes up. It's a measurable effect. People have measured it.
In fact, you can take the effects of these virtual particles into account in a very precise way. And use it to predict all sorts of other things. This is the most famous example, and it's an example that [INAUDIBLE] worked on here at Cornell.
The electron has magnetic properties. It has a little spin. The reason why magnets work is because the electrons are spinning around, and they all have individual little magnetic fields that pile up.
But precisely how magnetic it is is something that you can actually compute. And there is some standard value you might expect in some units-- it doesn't matter what it is, it would be 1 or 2. But there's some deviations that you'd expect from the presence of these clouds of particles.
And this is the number, OK? 0.001159652181 dot dot dot. And you'll notice that I didn't put whether that's an experimental number or a theoretical number, because those numbers actually are the same. Experiment and theory agree to this eleven decimal places.
So this isn't very, very [INAUDIBLE]. There is a whole machinery that tells you how to do this, and it works. I don't think we've ever had a prediction in science that's good to 11 decimal places.
But in a sense, much more important than the fact that we can do these very quantitative predictions, is that for the first time, this theory, this standard model, has allowed us to see that all these different forces that we talked about. While we don't yet see them really, precisely as different aspects of literally the same thing, for the first time, we see that they're described in exactly the same language. Exactly the same rubric, exactly the same words, exactly the same formulas. For the first time, it becomes possible to entertain the idea that they're actually, in a sharp way, different aspects of the same thing.
All of these forces, all of them are associated with little stick figures like this that tell you how particles of matter, electrons, electron neutrinos, quarks, interact with other particles that transmit forces. So electrons interact with photons-- that's where electromagnetism comes from. Electrons and things called neutrinos interact with other kinds of particles called W particles. This is where [INAUDIBLE] interaction comes from.
The protons are thought to be made of things called quarks and gluons, as we'll review in a second. But we find [INAUDIBLE] interactions between quarks and gluons. It turns out that gluons can self-interact with each other. Photons can't.
Electrons and gravitons have the same kind of interactions. Gravitons can interact with each other.
But you'll notice the same thing-- the same three stick figures-- always three, OK? And each one of those things is associated with a very sharp formula. And all you have to do is put these things together in all possible ways. And you get specific rules for how to predict, in principle, anything.
So for example, if you want to collide two electrons, as [INAUDIBLE] had to think about things in this way, then you put this stick figure with another one like that, and get a process that has two electrons coming in and two electrons going out. If you want to have an electron and the anti-electron annihilating and making [INAUDIBLE] and [INAUDIBLE], then you draw these pictures together. And you put them together in other ways.
But that's it! There are these little twiggy stick figures. And you put them together in all possible ways, and that tells you everything that can happen. And gives you a rule for computing it.
This is the really important point-- those forces as I described them couldn't look more different from each other. There was gravity, electromagnetism-- at least both gravity and electromagnetism were associated with the things that looked like they were [INAUDIBLE]. But they looked, in detail, very different.
Then, of course, the weak and the nuclear forces look utterly different, completely, than the other ones, right? But it turns out, that that's just an illusion. It's a long-distance illusion.
At short enough distances, they look identical! Just as you'd be led to expect from this picture. There's nothing really different. Everything is the same-- three stick figures put together all the time. There's nothing really different.
So let's see how it works. So for example, let's see what I mean by long-distance illusion. We know that if I have two-- this stick figure interaction is associated with electromagnetism.
And I know one consequence of that is if I put an electron here in space, there's an electric field that goes out forever, I can measure it far away, it's solved. OK? So that's an immediate consequence of that stick figure. Whatever it means, even if you don't know what it means, one thing it must do is give you electric fields. You can an electron there-- great!
I'm saying that quarks and gluons have the identical stick figure. So how could it possibly be? Because no one has seen such a thing as a quark sitting there with its gluon electric fields coming out.
If you had seen it, we would have studied it in high school. We haven't seen it! How come we haven't seen it?
Actually, it turns out to be for a remarkably malicious reason. Well, it's malicious for some people. For other people, it gets them a Nobel prize.
It turns out that it's actually basically true. It's basically true that if you plop a quark down, it would have some gluon electric fields coming out of it. And you were to look at nature at very short distances, much shorter than 10 to the minus 14 centimeters, which is around the size of a proton, that's more or less what it would look like.
But again, these things are constantly being surrounded by a cloud of virtual particles around them, OK? And it just turns out that because of this funny feature that gluons can self-interact, but photons can't-- that the screening phenomenon I was mentioning to you earlier-- remember, the electric charge gradually gets stronger as you go to shorter and shorter distances? Because you penetrate this cloud, and you see more and more of this sort of [INAUDIBLE] charge of the electron?
It turns out that there is just the opposite sign of this effect. If I could explain it in five minutes, [INAUDIBLE] would not have won the Nobel prize for it, but it's true. And it's basically exactly the same calculation.
It's not all that different. It's basically the same setup, it's basically the same question. You turn the same crank, but you get a different answer.
Just the sign is different. It's still slow. It's still gradual. It's still logarithmic.
At very short distances, OK, it's different. The sign is different, but you don't care all that much. However, as you go to longer distances, the fact that this is anti-screening means that the strength of this interaction grows and grows and grows.
Remember, for electromagnets, it was, like, 1/137. Here, let's say it starts off with 1/10. But it grows and grows and grows, and eventually, it becomes really strong somewhere. You give it long enough, it becomes really strong.
It turns out, it becomes really strong at 10 to the minus 14 centimeters. And that's the reason why protons and neutrons are the size of 10 to the minus 14 centimeters. If you looked inside a proton and a neutron, you would see a proton would be made of two up quarks and a down quark surrounded by a sea of gluons.
We can't pull any of them out of the proton, just because-- I mean, at short distances shorter than 10 to the minus 14 centimeters-- no problem. If you shoot a light beam to see what happens to it, and you shoot it with high enough energy, so it's probing what's going on at 10 to the minus 16 centimeters, what's going on will look exactly as if the light beam came in to hit a happy quark that was wandering along. It bounced off. It looked just like the other quarks sitting there, and it had its gluon electric field, and all that stuff.
But you can't separate them. You can't see them, because it's a long-distance property. Just as this accidental fact about this minus sign means that the quarks and gluons are permanently bound up inside the proton and the neutron.
Similarly, let's draw this stick figure, OK? So the stick figure that we had for electromagnetism had another consequence. There was a long range force, electric force, between two electrons.
If I scatter two electrons off each other, if I go to arbitrarily large distances, some scatter. They repel each other. Doesn't matter how far apart from me.
And that's associated with this picture. You see, you should think of this picture as doing the following thing-- these little stick figure pictures are taking advantage of the quantum uncertainty. What they're really doing is saying, this electron can come along. But because there's this quantum uncertainty, and the quantum fluctutations all the time, there is some chance that it can emit a photon.
It's not a real photon, because I'm borrowing from the uncertainty principle. So if I wait long enough-- if I don't pay attention long enough, I could [INAUDIBLE] the photon, and then it disappears. And I look again at a sufficiently large distance, and there is some scattering that was mediated by that borrowed photon.
But because the photon is massless, I can go to arbitrarily large distances and get some effect from it. Of course, the effect gets weaker and weaker. That's fine.
The force gets weaker and weaker. Goes like [INAUDIBLE]. In fact, it gets just as weak as you would expect from this borrowing picture.
However, it turns out that the W particle-- its only difference from the photon is that it has a mass. It's not massless. It has a mass. And its typical size is around 10 to the minus 16 centimeters.
So it looks exactly the same, but because we happened to have been stuck for 2,000 years at distances large compared to 10 to the minus 16 centimeters, it looks radically different. But at short enough distances, it looks the same. So these apparent huge differences are a long-distance illusion of something that, at short enough distances, is really identical. The structure is identical.
I have to say that this is why we do high-energy physics. This is why we do particle physics. You know, it's hard and expensive. But we do it not capriciously. We do it for this reason.
Often, this part of physics is described as the desire for understanding the fundamental building blocks of matter. That may be the motivation for some people, but I don't think it's the motivation for most of us. After all, it could be Russian dolls all the way down.
That's really not why I'm interested. There's this whole zoo and cacophony of particles. You know, who cares about them when there are all these other interesting things to explain in the world around us?
The reason we do it, the reason we go to short distances, is this hard-earned lesson, that the fundamental beauty, unity, and simplicity of the laws of nature is revealed in short distances. We would never have been able to see the fact that there's really one thing going on here that's mass at long distances. We see it at short distances.
What we're interested in is the laws. We don't care that much about the particles-- the particles are like the alphabet. The laws are the novel.
We're interested that the particles tell us something about the laws. It's the laws that we're interested in. And it's the structure of the laws that are becoming so similar and so unified as we start studying them at shorter distances.
I want to make a final comment-- oops. [INAUDIBLE]
So you don't need to understand anything about this other than just to see that it exists, OK? So I've told you about some of the particles that are out there-- up quarks, down quarks, electrons. I don't want to go through the names of every single one of them. Partially, I'm a little bit embarrassed, because some of them have silly names like charm and strange, because some of these things were invented in the 60s and 70s, OK?
But it's also really not that important. What is important is that there is a very specific menu of particles that we see in nature. Again, it's had the separation between the matter particles and the particles that carry and transmit force.
The things that carry and transmit force are associated with a very specific sort of mathematical structure called [INAUDIBLE]. It doesn't matter, but we know what we're doing. We know how to compute them. We know what the rules are.
So the gluons that I talked before are associated with one factor of the group. The Ws and the photon are associated with another two factors. And these-- we have quarks, we have [INAUDIBLE], like the electrons, [INAUDIBLE], neutrinos, and so on.
And it turns out we have three groups of them. There are three [INAUDIBLE] so-called families. So the ones that are familiar are one of the families, but there are two other ones.
And in any case, this is just a table of how each one of these things interacts with each one of the other guys, right? It looks a little bit complicated, but that's just fine. That's true.
This menu tells you exactly which stick figures to draw. So different possible menus, you would draw different stick figures, and then you would turn on the machinery. You would turn the crank, you would make all sorts of predictions.
But you have to give a menu-- who is the matter? Who are the forces? Who is in a stick figure interaction with who?
Now, I told you that to all these forces-- strong, weak, electromagnetism-- they all look similar. They have the similar sort of laws.
What are the strengths of the interactions? The strengths of the electromagnetic interaction-- remember, that was interesting. It was a pure number. It's around 1/137. The strength of this weak interaction is around 1/60. The strength of a strong interaction is around the 10th.
Remember, these numbers aren't absolute. They change slowly as you go to different distances. But this is at around a distance of 10 to the minus 16 centimeters, where we measured. You see, not only are the mathematical laws very, very similar, the actual numerical values aren't all that different from each other.
This is really a long way to come from Newton, where he said, oh, wouldn't it be great if gravity was a 1/r squared law? But it could've been a 1/r.2.1, and he wouldn't have blinked.
We can't do that! We can't monkey with anything. We have extremely rigid set of rules and very, very few parameters that we can adjust.
Actually, in this theory, there's, depending on how you count, between 19 and 26 parameters-- like these, dimensionless numbers that we can adjust. That's it! That's still a reasonably large number of parameters, but it's way smaller than infinity. And again, there really seems to be some essential unity behind them.
OK. There is one basic problem, which is what? So if this theory is supposed to answer any question you might want to ask about the particles and the forces, and the one basic problem that's left is understanding the origin at least of the masses of some of the particles, like the electron. Or the W particle, why the weak interacts with the short range.
And I wish I could give you a better description of how this physics works. I've thought about it a long time, and I've never managed to come up with a good explanation for a more general audience. This is the best that I, and many other people can do.
But you're going to complain right away. But let me say the words. So the words are, that the way to think about where the mass of the electron comes from is that somehow the universe is filled with a condensate of some sort of field, a kind of substance.
Immediately, you say, aha! Isn't that just like the ether? You idiot!
And the best I can say is, it's a kind of condensate that's not like the ether. It looks the same to every observer, OK? So don't give me a hard time.
But what happens is as the electron moves along, it actually bumps into this condensate at regular intervals. And that's what gives it its mass. Otherwise, it would zip around at the speed of light.
Again, at short enough distances, everything looks basically massless. Because these interactions haven't taken place yet. But at long enough distances, they will look like they appear to have mass.
There are other particles that have a bigger, strong interaction, like those W particles and other things-- things called top quarks and Z particles. They're sort of banging into it all the time. For very good reason, it turns out that the photon doesn't interact with it at all. So it just sails through, which is why it's exactly massless. So that's where mass comes from-- in this constant interaction with this condensate that's everywhere in the universe, but that's not like the ether, OK?
Now, the typical length scale between these collisions is around 10 to the minus 17 centimeters. Remember, I told you that 10 to the minus 17 centimeters number was actually a number in nature. It was a natural number. It's like 10 to the minus 33 centimeters was the strength of gravitational interaction. This 10 to the minus 17 centimeters is a number that tells you how far electrons, and top quarks, and Ws, and so on move before they bang into this condensate that gives them their inertia.
So it's an important length scale. It was an important length scale 3,000 years ago. It'll be an important length scale 10 million years from now. But we happen to be living in the era where we're about to go there. And it's interesting that we're about to do these experiments at the Large Hadron Collider [INAUDIBLE].
Now, one thing that simply must happen is when we excite things at 10 to the minus 17 centimeters-- when we excite them at those scales, no matter what we do, we have to put some ripple in this condensate whose typical size is around 10 to the minus 17 centimeters. Now, a ripple in this condensate is putting some energy in it. And that energy is going to come out in the form of particles.
These ripple excitations of this condensate is what's called the Higgs particle. And this is one thing that's essentially guaranteed to show up at the LHC. The Higgs particle, or something like it, must show up at LHC. I've bet years of salary on this. And unfortunately, I've done it in public enough that at this point, I'm getting weekly emails from people around the world asking to take me up on it.
But it's really an unfair bet, because really, precisely, the stake was, the H the Higgs or something like it must show up. "Something like it" has a very specific meaning. But let me just say that if the Higgs or something like it doesn't show up, then quantum mechanics is wrong.
It isn't something that's in this theory, maybe [INAUDIBLE] theory. It's just that really something like it must, must show. And we'll take about that at greater length on Friday.
All right. Let's see. I've run out of time.
All right. I think I'll keep going [INAUDIBLE].
OK. You can vote with your feet. But I won't go on too much longer. I don't have that many more meaningful [INAUDIBLE].
So the other thing that I wanted to talk about-- it was slightly ambitious to try to talk about both, partly because [INAUDIBLE] lecture. But let me give it a brief go. Actually, we'll be returning to some of these themes tomorrow. So if it goes by a little fast now, we'll do it again later.
So everything that we're talking about now is focused on the physics of the very, very small. I'm now going to switch gears and tell you about the physics of the enormous, the entire universe. As you'll see, in a second, these two kinds of physics are intimately related to each other. And surprisingly, perhaps, they're intimately related to each other because the universe is expanding, which has a [INAUDIBLE], and we'll come to it in a second.
Now, the universe is expanding. It's a fact. And as I mentioned yesterday, the statement the universe is expanding is really the statement that space is being invented all the time at some rate, OK?
So imagine that here's three galaxies-- these three red galaxies. After some time, the universe doubles in size. What that really means is that just more space is invented everywhere. I just put an extra square everywhere between everything, and I doubled it in size.
But you see, this has an interesting consequence. The distance between that distance used to be one unit. Now it's two units. That distance used to be two units. Now it's four units. And this all happened after some fixed amount of time-- let's say, I don't know, after 5 billion years.
So that means that if you're sitting on top of this guy, you would think that that guy is moving away from you. How fast is it moving away from you? Well, it's moving one cell per 5 billion years.
What about this guy? You'd think that guy's also moving away from you. But is now is moved even further away. So its velocity away from you is even bigger.
So there's a very basic prediction of this picture that no matter who you sit on top of, because space is expanding at a uniform rate, you will see everybody else moving away from you. And the further and further away things are, the faster and faster they'll be moving away from you with a linear relationship. There is no center, because anyone would come to this conclusion. And it's a consequence of the fact that it's not [INAUDIBLE], but just that space is being invented at a uniform rate.
OK. So that means that if you plotted the relative velocity as a function of distance, you would find that these more and more distant objects would lie on the straight line. So the velocity would be some constant times d-- times the distance. So this doubling time-- the so-called Hubble time-- it'd be the inverse of that parameter H.
So that's a basic fact about an expanding universe. This is how Hubble deduced that the universe is expanding, by seeing [INAUDIBLE]. And I should say that one of the reasons it gained such immediate acceptance amongst many, many theoretical physicists is that the expanding universe was an instant, immediate consequence of Einstein's theory of gravity.
It's such a natural consequence that Einstein should have predicted himself. It's another instance of theories being smarter than theorists, which happens very often with good theories. And unfortunately, not often enough to bad theorists. But it's a prediction that was so dramatic, Einstein refused to make it. Just like Dirac refused to predict anti-particles, even though it was correct.
So it's so natural that the universe is expanding-- that's great. Oh, thank goodness it's expanding. General relativity is correct-- of course it's expanding. That should have been, and was the attitude.
Now, the rate at which it's expanding, this doubling time, has to do with the actual content of the universe-- what energy and mass there is in the universe. And there is a very simple formula you can derive for it. We won't need it in too much detail, but it says that this parameter that gains the doubling time, where it's inverse of the doubling time squared-- it has to do with gravity, curvature of the universe, so it has to know about G Newton.
And gravity talks to energy, and in this case, we can't be talking about the total energy of the universe. Things are expanding here, so it has to do with the energy per unit volume. Or what you might call the energy density.
But anyway, this is the formula that tells you the rate at which things are expanding as a function of the energy density. Now, we know the universe is expanding now. If we run it backwards in time, that means that the universe was smaller before. Again, smaller doesn't mean that it was a smaller ball, just means there was less of it. There was less of this space had been invented, generated between all these points.
But that means that everything was closer together before, and this density was higher before. So that means that the rate at which it's doubling in size hasn't been constant. In fact, the rate at which it was growing in size was bigger before, and is smaller now.
Just to have the number in mind, the rough energy density of the universe today is around 10 to the minus 3 electron volt per millimeter cubed. It's a miniscule, miniscule, minuscule number. It's, roughly speaking, [INAUDIBLE]. The energy in this radiation that fills the universe that we'll talk about in a second.
So we know that as we go earlier in time, the universe is getting smaller and smaller. Everything that's around us is going to get closer and closer. They're going to start banging into each other more and more. It's all going to start heating up more and more.
And if we extrapolate earlier in time, we come to the realization that if you go somewhere before around the age of the universe now minus 100,000 years, or 100,000 years after the Big Bang-- I haven't said the word Big Bang yet-- that's why I didn't want to say that-- but at early on times, everything is a dense soup of particles. As we go to earlier and earlier times, it just gets hotter and hotter and hotter. Now, if we extrapolate it very, very, very far back in time, then we hit something called the Big Bang that we can't extrapolate beyond.
But what people call the Big Bang theory has really nothing to do with the Big Bang part of it. We have no idea what happened at the Big Bang. That'll be part of the theme of tomorrow. We don't even know if the question is sensible. When we say the Big Bang theory, we really mean the aftermath of the Big Bang theory. We really mean that we're talking about the fact that the universe was once very hot and very dense.
Now, it turns out that we have incredibly good evidence that that was true. And that's because if you imagine the universe gets hot and dense enough, then various nuclear reactions would have taken place early in the universe that would have produced the nuclei of lots of the elements that we see around us. Helium lithium, beryllium.
These nuclei-- I mean, you can actually calculate it. How many helium nuclei? How many beryllium nuclei? How many lithium nuclei?
What you get out of these hot, early nuclear reactions, while the universe was so very, very hot that these reactions were allowed to go. But the universe cooled, and then these reactions stopped, so you're left with some particular prediction for the abundance of helium, lithium, beryllium, and [INAUDIBLE].
Those predictions are all dead right, to a few percent accuracy each. So there are sort of five or six predictions accurate at the few percent accuracy level each that give us very strong evidence that really, the universe was once hot, dense, smaller, and all of this happened. So and of course, it's nice that, again, it's an immediate consequence of general relativity. So it's a good thing that it's true.
So early on, the universe [INAUDIBLE]. This is why the physics of the very small relates to the physics of the very big, because our entire universe earlier on was also very small. And the physics there involved very, very high energies. And because of the fact that we can pop particles in and out of the vacuum if we have high enough energies, as we go to earlier and earlier [INAUDIBLE] things get hotter and hotter, all the particles and forces and everything that are out there are going to play a role. It just gets smaller and smaller and hotter and hotter. Everything [INAUDIBLE].
Now what happened if we run the picture forward in time is that in this hot, dense soup, even photons couldn't move very far before they banged into something else. And so you shouldn't have a picture of the early Big Bang. You couldn't see anything if you were there. The light in your eye would just immediately get absorbed by something else along the way.
But around 100,000 years after the Big Bang, the universe became diluted enough that light could just stream freely. And the rest of the matter became trapped up in atoms. And so you would expect to see, then, some of the remnants from this time, around 100,000 years after the Big Bang, when the light finally streamed freely, what arrived to pin us on the earth. So that's a very direct prediction of this Big Bang idea that we should see-- in every direction of space around us-- we should see that there was some remnant of some photons at some temperature. And you could even predict the temperature ahead of time. This is the famous cosmic microwave background radiation that was indeed due to [INAUDIBLE]. This is another prediction which is correct.
OK. Now just a few more things, and I will stop. One of the really remarkable things about this microwave background radiation is that the temperature-- and you can measure it with [INAUDIBLE] antenna. You point it that way, you point it that way, you point it that way, the temperature is basically the same everywhere. No matter where you point it, the temperature was the same. So it's extremely-- it's very, very uniform.
Actually, people discovered that, with much more precise measurements, that there are tiny, tiny non-uniformities in the temperature. The scale of the non-uniformities was around one part in 100,000. So there's some difference in the temperature here and there and there and there which are around one part in 100,000.
That tells you something very interesting about this early period. It says that, in this early period, mostly everything was very uniform, but there were tiny inhomogeneity in one part in 100,000, here [INAUDIBLE]. Those inhomogeneities is where we came from. Because if the universe was totally, perfectly homogeneous, then there's no reason for anything to clump. We're very clumpy.
But where did this clumpiness come from? It came from this underlying one part in 100,000 difference between here and there. How is that possible? It's because there was this one part in 100,000 difference. The universe eventually cooled. But the fact that there was one part in 100,000 difference meant that there was one part in 100,000 more mass over there than over there. And that's all gravity needed to take over. Even if it's one part in 100,000 more gravity here, it'll gradually start collapsing right around here. There's a little bit more mass here than over there. But they'll attract each other more, and that one part in 100,000 starts amplifying here. And you're left with a little empty space here. Then over there, that part starts [INAUDIBLE].
So this one part in 100,000 grows and grows and grows, and turns into proto-galaxies, which turn into galaxies, turn into solar systems, turn into us. So these one part in 100,000 differences between the temperature there, there, there and everywhere is where all the structure of the universe came from.
Now it turns out that-- forget about this one part in 100,000. In the standard picture of the Big Bang, if we assume that all you had was this hot soup going back earlier and earlier in time, we can run-- we understand Einstein's equations and all the physics perfectly, we could run all the equations. And we find the following paragraphs, or people found the following paragraphs. That it seems very hard to explain why it is that that part and that part and that part of the sky are at the same temperature.
So this is something I'm not telling you why, I'm just telling you the fact that if we imagine again [INAUDIBLE] space-time diagram going all the way back to the Big Bang to represent [INAUDIBLE], the sky over there, and that's [INAUDIBLE] sky over there, you can trace back in time all the places earlier in time that could have possibly affected that region and that region. Now that could be inside these 45-degree lines. But there's definitely no way for these things to overlap each other before the Big Bang was reached. That just turns out be-- again, I'm unfortunately not explaining it. I'm not telling you, deriving it for you. But it turns out to be true.
The standard Big Bang picture, what that means is that that part of the universe and that part of the universe were actually never causally connected to each other. No signal could have possibly transmitted information from one side to the other. You see how different this is than the picture of the Big Bang meaning everything comes out of a point, right? Because if everything came out of a point, obviously everything is talking to everything else. It's not like that. It's the whole universe that's shrinking everywhere, losing space as we go back in time. And it's just doing it at just such a rate that it's impossible for information from over here to go over there. So that just makes it a real puzzle. How come they're all exactly the same temperature? No physical mechanism could communicate between them to say that they're the same temperature.
So everything else I've told you about cosmology is rock solid. This is speculation, but it's as close to-- as we-- it's the closest we have to rock solid speculation in physics today. And that's the idea of inflation, that actually something different happened than just this hot soup going back [INAUDIBLE]. And that, very early in time, there was a period where the universe expanded at a ridiculous the exponential rate, very, very fast exponential rate. You should think of it as taking a really tiny region of space and blowing it up to be the entire universe, essentially.
And it turns out that, in the space-time picture, it effectively gives you way more time for things [INAUDIBLE] completely solves this problem. But it does so by making things expand vastly faster than normal-- than we normally thought. In fact, expand at an exponential rate. Well, we'll talk about this whole phenomenon more tomorrow. But anyway.
So you should think that the even more modern view of the Big Bang is that something in the Big Bang, who knows what that is. I was gonna say God knows what that is, but-- and then there was this period of incredibly rapid, exponential expansion. And then the universe became hot, and we have the standard aftermath of the Big Bang [INAUDIBLE].
This picture has-- the reason I was going through this was just to tell you this truly remarkable punchline, because it's one of the most amazing things in all of science today, which is that this picture gives us-- not only explains why it is that that part of the sky and that part of the sky have basically the same temperature, but it also tells you why they should have slightly different temperatures. And the reason is that, during inflation, just like at every other time, there's quantum fluctuations constantly. Now, normally, there's quantum fluctuations [INAUDIBLE]. But as we've said over and over again, they sort of average out as you go to large enough distances and you don't see them. And even in cosmology, even though the universe is expanding, it's normally expanding at a slow enough rate that those fluctuations cancel out and you don't see them [INAUDIBLE].
But when you make the universe inflate, when you make it expand exponentially, the following remarkable thing happens, that, if early on during inflation there are some fluctuations-- you know, just fluctuations in space, these quantum fluctuations-- inflation takes those fluctuations and it doesn't let them cancel out. It actually blows them up and makes them macroscopic. These underlying quantum fluctuations are amplified by inflation to become these macroscopic fluctuations that are exactly the extent of the minus five difference in the temperature here, there, there, and everywhere.
If inflation is correct, you and I are here because of quantum mechanics. In a very direct sense. And the initial conditions for the universe question-- what determined them, what gave rise to us precisely-- ultimately has the answer of quantum uncertainty and quantum indeterminism. I told you before this indeterminism wasn't just-- wasn't all bad. It gave us stability of matter, it gave us all the way the world is the way it is. It gives the [INAUDIBLE] gives us everything else. This gives us us. The origin of all structure in this picture of the world is quantum fluctuations that are spread out [INAUDIBLE].
OK. There is a variety of other things to discuss, but I won't discuss them now. I will discuss them-- there will be an appropriate place to discuss them later. But let me just end and remind you what we'll be talking about in the next couple of lectures. So that's a snapshot of our pictures of [INAUDIBLE] cosmology. And the two lectures will be developed-- will be devoted to the various discontents. We will talk about the difficulty of quantum gravity, why we have [INAUDIBLE] space-time, when we discuss physics of the [INAUDIBLE]. And we'll talk on Thursday about the mystery [INAUDIBLE]. Thank you very much, and sorry [INAUDIBLE].
CSABA CSAKI: OK. So before I open up the floor for questions, [INAUDIBLE] stick figures that Nima [INAUDIBLE]. Those were actually invented in this building--
NIMA ARKANI-HAMED: Yes they were. Yes they were.
CSABA CSAKI: And inflation [INAUDIBLE].
NIMA ARKANI-HAMED: And yet another thing, perhaps the most-- it won't [INAUDIBLE], but this is the most important thing in this talk. But actually the most important thing-- oh.
CSABA CSAKI: You skipped--
NIMA ARKANI-HAMED: It didn't occur to me--
CSABA CSAKI: I believe I said that.
NIMA ARKANI-HAMED: Ah.
CSABA CSAKI: [INAUDIBLE].
NIMA ARKANI-HAMED: Oh my goodness. I forgot. Yes.
CSABA CSAKI: [INAUDIBLE].
NIMA ARKANI-HAMED: Well actually, let me--
CSABA CSAKI: [INAUDIBLE].
NIMA ARKANI-HAMED: No, no, it turns out truly-- boy, I feel terrible. This is the most important slide in the entire talk.
It's actually extremely important. Those four guys are leaving. They're not gonna hear [INAUDIBLE]. So part of this thing-- remember I told you that these basic things are these stick figures, right? You might ask, why aren't there other, more complicated things? Why can't I have stick figures with four, five, seven [INAUDIBLE] coming out? Right? These are all [INAUDIBLE].
If we could have that, that would be very bad. If all those things were important, then we're not going to be able to explain anything. If you have to know about what all these different stick figures mean, there would be no notion of some simplest, most important set of which everything else is a consequence. But really remarkably, that does not happen. This is maybe the biggest insight into the nature of quantum field theory that people had since its conception. And these were ideas that Ted Wilson and Fisher and friends developed here.
And that's the point that, in fact, at any given energy scale or length scale that you want to talk about physics, there is a fixed number of particles that we could be talking about, and a completely fixed number of interactions you should be talking about. There aren't zillions of interactions. There's only a fixed number. There's a finite, small number of relevant interactions.
And the reason really has to do once again, once again, [INAUDIBLE]. All of these pictures, I told you, have to do with some probability of a quantum fluctuation occurring. Those fluctuations are getting bigger and bigger at shorter at shorter distances, smaller and smaller at longer and longer distances. That means that that is the chance that there's a quantum fluctuation involving three particles, two electrons and one [INAUDIBLE]. [INAUDIBLE] fluctuations [INAUDIBLE].
I thought you that that strength turns out to be a dimensionless number, 1/137. That's an extremely special fact that's only true for these [INAUDIBLE] stick interactions. And it's a little bit intuitive. Let's say I have two electrons and four photons coming up. Well for that to happen, four photons have to fluctuate with the electron in the same spot. That's not [INAUDIBLE] quantum fluctuations to have to all have to occur at the same spot in order to make that interaction happen. Those fluctuations are getting bigger and bigger at shorter distances, but they're getting smaller and smaller at longer distances.
So that means that the strength of that interaction cannot just be a pure number. It actually gets weaker at longer distances. There is some interaction associated with that. [INAUDIBLE] could be there, but it has [INAUDIBLE] associated with it. So whatever it is, it's not important at sufficiently long distances. Long here can mean short compared to anything we care about, but from the point of view of fundamental physics, at any given energy scale, you only have to ever talk about a small number of dimensionless interactions.
And what they are, always the same one. Always the [INAUDIBLE]. You just have to provide the menu. And that's it. You may encounter new things as you go to shorter and shorter distances, but those new things will have their own stick figures. This separation of the possible interactions between the ones that matter and the irrelevant ones that don't is a very big conceptual [INAUDIBLE] very big conceptual breakthroughs. It gave us this idea that all the theories that we're talking about are effective theories. And they can be replaced by other theories as we go to shorter and shorter distances.
But that's very important, because it means that this is why there's only 19 parameters, 19 or 26 parameters. That number comes from a very simple rule. You get the menu, you draw all of the possible stick figures, and you count how many you have. That's it. But as I mentioned, it's shockingly different than Newton, who could have had continuous power you want to with the force law, one over r-squared, one over [INAUDIBLE]. They're all equally good. Now all of our uncertainty about what the next scale of-- what's happening in the next scale of physics is encoded in these very small number of parameters. And that's very, very important.
Thank you so much for allowing me to do that. Hey, any excuse of giving Cornell credit.
SPEAKER 1: Another thing that you could have mentioned that we've done here was the theory behind the [INAUDIBLE].
NIMA ARKANI-HAMED: I did say that. Yes.
SPEAKER 1: OK. So I also wanted to remind you to remind [INAUDIBLE] that the bars are no longer used as the standard of length. They actually have switched [INAUDIBLE].
NIMA ARKANI-HAMED: I know. I know. I know. Meters [INAUDIBLE]. Meters were historically involved. Yes, indeed, indeed, for some reason, people are now [INAUDIBLE]. Yes. [INAUDIBLE].
SPEAKER 1: [INAUDIBLE].
NIMA ARKANI-HAMED: It shows how silly it is, right, because we could just be working with natural units for everything, and not have to define the meter to be some number of wavelengths of some [INAUDIBLE] light, which I [INAUDIBLE]. But yeah, historically it was a bar in a glass jar [INAUDIBLE]. How is that divine knowledge? They don't even know.
SPEAKER 1: [INAUDIBLE] times, standard graphite being 2.9979248-- [INAUDIBLE].
NIMA ARKANI-HAMED: Right, right.
SPEAKER 1: [INAUDIBLE]-- practically just fixed your number.
NIMA ARKANI-HAMED: Right.
SPEAKER 1: Then you define length in terms of the standards of time, which is more effort to measure. So it is an actual complaint they use.
NIMA ARKANI-HAMED: Right.
CSABA CSAKI: And we'll take this next question.
SPEAKER 2: If 7 is the ratio of [INAUDIBLE]?
NIMA ARKANI-HAMED: Yes.
SPEAKER 2: How [INAUDIBLE]?
NIMA ARKANI-HAMED: Yes, that's actually very, very important. That was--
CSABA CSAKI: --a very good question.
NIMA ARKANI-HAMED: Yes. I said that some of these nuclei-- like helium and lithium, and beryllium, and so on-- came out of the Big Bang. But the question was, don't they also come out of supernovae? I mean, This is the story that we all hear, we are made of stardust, stuff like that.
Actually, this is the reason why everything is, in principle, synthesized early in the Big Bang. Because there's a little less and less and less of the heavier and heavier nuclei. And this is why you only make the predictions from things like helium, lithium, beryllium, and so on.
These much lighter nuclei are less likely to come from supernovae. Because they burn through heavier and heavier and heavier nuclei. They get down to the iron. Then everything explodes out.
But it's harder to get these lighter nuclei out of supernovae. Now, it's not impossible. It's now impossible.
I mean, when people were first thinking about this, there was a possibility that the people who liked the Steady State model of the universe, and not the Big Bang, tried as hard as they could to make a sun and supernova, stuff like that, generate the light nuclei. But it's very hard. And of course, the other thing you can do is try to go as far away as you can from obvious places that could have been contaminated by supernovae going on and things like that.
So you can see what the actual primordial [INAUDIBLE] was. And now there's extremely good evidence that there's actually completely different particles-- helium, lithium, and so on. So those are the things that you really make sure that they can't come from supernovas.
CSABA CSAKI: Carl?
SPEAKER 3: If I could go back to what you told us about yesterday, about decoherence, it is scoring how macroscopic world interferes and moves with a [INAUDIBLE]. But I was extremely excited about the problem of a super conductor.
NIMA ARKANI-HAMED: Right.
SPEAKER 3: A big piece of lead--
NIMA ARKANI-HAMED: Absolutely.
SPEAKER 3: --that holds a current.
NIMA ARKANI-HAMED: Right.
SPEAKER 3: Why does that escape your audience?
NIMA ARKANI-HAMED: Because the interactions are small. I mean, that's actually the whole point. That's really the whole point. The whole point is that the distinction between quantum and possible isn't between big and small.
It's between open and closed. And you can have big things that are very quantum mechanical as long as you prevent the interaction with the environment that would cause the loss of coherence. So it makes superconductors cold, superfluids or Bose condensation-- which also helps-- and you have tons and tons of particles in exactly the same state.
This is why coherent states of like-- the classical wave interference is quantum interferences of those coherent states. Classical waves, or the quantum probabilities from the photons, they're not being decoherent. Again, they're in a nice, coherent state. They have weak enough interactions with anything else.
They move coherently. And as you know very well, if you take big buckyballs, you make them cold enough and you shield the interactive environment enough, then you would see the same thing. So it's really the distinction between opened and closed, and not big and small.
Big and small allows the classical world to even be possible, allows those states to be possible. But you need something else. You need the decoherence to knock down all the other [INAUDIBLE] states.
And conversely, without decoherence, even big things seem quantum mechanical.
CSABA CSAKI: Last question.
SPEAKER 3: Correct me if I'm wrong, but the [INAUDIBLE], is it true that [INAUDIBLE] and reaction to up to three elements forever?
NIMA ARKANI-HAMED: Yes.
Well, I mean, you can go up a little.
CSABA CSAKI: OK, so I think we have picked a good time to stop and we will continue tomorrow at five o'clock. Thanks.
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Renowned theoretical physicist Nima Arkani-Hamed delivered the second in his series of five Messenger lectures on "The Future of Fundamental Physics" Oct. 5.
Formerly a professor at Harvard, Arkani-Hamed currently sits on the faculty at the prestigious Institute for Advanced Study in Princeton, New Jersey, where Einstein served from 1933 until his death in 1955.
The Messenger lectures are sponsored by the University Lectures Committee. The lectures were established in 1924 by a gift from Hiram Messenger, who graduated from Cornell in 1880.