SAUL TEUKOLSKY: Good evening. My name is Saul Teukolsky. I'm the Chairman of the Physics Department. It's my pleasure to welcome you to this year's messenger lectures. The messenger lectures were founded 86 years ago to bring distinguished scholars in all fields to the campus. Some of the famous scientists who've been messenger lectures in the past include Millikan, Eddington, Oppenheimer, Feynman, Penrose, Martin Rees, and recently Steven Weinberg.
And so it's a great pleasure for me to welcome Professor Arkani-Hamed from the Institute for Advanced study in Princeton to be this year's messenger lecturer. He got his Ph.D. at Berkeley in 1997. He was a postdoc at SLAC at Stanford and then an assistant professor and associate professor at Berkeley. He then moved to Harvard as a professor and in 2008 took up his current position as professor at the Institute for Advanced Study.
Despite his relative youth, he has already won many honors and awards, including Sloan Fellowship, Packard Fellowship, the Sackler Prize in Physics, and election to the American Academy of Arts and Sciences. He is one of the leading particle theorists of his generation. He is famous for his proposal with Dimopoulos and Dvali that the extreme weakness gravity relative to the other forces might be due to the existence of extra dimensions of space beyond the three that we know of that could be as large as a tenth of a millimeter.
This exciting proposal set off a flurry of activity and experimental efforts in an attempt to either prove or disprove it. And I'm sure we're going to hear more about this. He's also produced many other theoretical ideas to make progress beyond our current understanding of these fundamental physics.
He has set up a very ambitious schedule of lectures. Following the lecture tonight, there are four more in the series. They will all be here at the same place, but at 5 o'clock, from 5:00 to 6:00. The title of tonight's, you can see, is Setting The Stage, Space Time in Quantum Mechanics. Although it says up there Future Fundamental Physics. That's what I've got.
But lecture two, according to me, it says Standard Models of Particle Physics and Cosmology and Their Discontents. Lecture three, Space Time is Doomed, What Replaces It? Lecture four, Why is There a Macroscopic Universe? And finally, A New Golden Age of Experiments, What We Might Know by 2020.
For those of you who are impressed by the effort that will go into giving such a concentrated series of lectures, you may be interested to know that in addition to these, he is giving every morning this week, so that's five, technical lectures on scattering theory. He's also giving the relativity lunch and a talk to the physics club. And for all I know, there are a few others that maybe have been scheduled. But anyway, join me please in welcoming Professor Arkani-Hamed.
ARKANI-HAMED: It's a real-- let me turn this on so I don't get in trouble. Oops. Is that OK, technical person? Yeah, I think that's fine. The button's green, so it looks good.
Well, it's really a tremendous pleasure to be here at Cornell to give this rather modestly titled series of lectures on the future of a subject that has a long and glorious past. Going back over 2,000 years to the ancient Greeks, who first started suspecting that there's a systematic way of understanding the enormous diversity of different phenomenon we see in nature around us in terms of potentially simpler rules.
The modern way we think about fundamental physics traces its origins back to Kepler, Galileo, and especially Newton, who gave us an additional very important insight that the essential simplicity and underlying unity of the physical laws of nature are best expressed in the language of mathematics and in a language of simple mathematical laws.
This makes talking about not just the future, but the current and the past state of the subject to a more general audience a little bit challenging without using this wonderful language. And therefore, in talking about it, one is normally tempted to use metaphors and similes and analogies to try to get the point across. And I will be doing some of that. But I'll do my best to give you a straight story.
Every now and then maybe a little equation up there. It will rarely require knowing anything more than high school algebra. And if it bothers you, just ignore it. It doesn't matter anyway. But if it doesn't bother you, you might get a little something out of it.
This part of physics, fundamental physics, is in an extremely interesting place right now. It's a very exciting period. And to explain why, we can start by remarking that the 20th century began with two very big revolutions in our understanding of the laws of nature given by our understanding of relativity by Einstein and even more remarkable in a revolutionary discovery of quantum mechanics. That took basically from 1900 to 1930 to complete. And it completely overhauled our picture of physics. And indeed, most of today's lecture is going to be talking about what the overall looked like.
You can very broadly summarise the rest of the history of 20th century fundamental physics as grappling with the repercussions of those two revolutions and trying to see how they make sense together. And it turned out that the remaining 70 years were really about just putting these two things together and understanding how they work together and understanding the extremely rich and remarkable consequences that putting them together had in a way that allows us to understand everything that we've actually observed about the physical world so far.
So while the first 30 years were all about revolution, the last 70 were really fundamentally conservative. We're putting together the laws that we knew and loved together, relativity and quantum mechanics, and figuring out what all their consequences were. That's just the way it is in this part of physics. You never know ahead of time if what's needed is a revolution or just to be conservative, to keep going with the theories that you have.
If we knew ahead of time, if the right answer was always to be revolutionary or always be conservative, graduate school be a much more boring place. If it was to be always revolutionary all the time, we'd hand our students berets send them off to mountains in South America. If it was to be conservative all the time, we'd send them to Wall Street or maybe not. But you just never know ahead of time. And in fact, most of the 20th century, the rest of the 20th century, was essentially conservative.
However, there are many reasons to suspect that the period we're in right now is actually going to require something revolutionary. And that's why it's exciting. On the theoretical side, there's clearly something very deeply wrong with these ideas that we have. And what's particularly exciting about this decade is that there's a whole slew of new experiments that are happening that will shed light on at least some of these theoretical puzzles. And we might have, if not the answer, certainly not the answers to all of them, some partial but important progress on subsets of them by 2020.
So the way I've described it seems to have a big divide between conservative and radical thinking. But in fact, in practice, there isn't such a big divide. And the reason is, the nature of revolutions in physics is not like the nature of revolutions in society, which are violent, bloody things that completely up end the previous order. That's never how it's worked in physics.
In fact, what we find, and as we'll see today, is that revolutionary developments tend to involve a much deeper understanding of the things that came before. Not only do they not append them, but they put them in their proper context and they build on them to a much deeper understanding.
This is why, in fact, regardless of whether your temperament is to be that of a conservative or a revolutionary, there is a basic philosophy that all of us in theoretical physics adhere to, which is what you can call a philosophy of radical conservatism.
What that means, I think this is a phrase that was coined by John Wheeler a long time ago, and what it means, what a radical conservative does is take the laws that are known and push them to their absolute limits. See if they make sense, push them to their absolute limits. They don't drop everything, abandon everything at the first sign of trouble. You just take what you have. You push, you push, you push until you actually run into an actual crisis or paradox.
Once you find a crisis or paradox you're incredibly happy. Because a crisis or paradox means that that's where all the effort should be focused and something's got to give. But in practice, we are going to take this philosophy of radical conservativism very seriously in these lectures. I'm going to first describe the theories that we have. So here's an outline for the five lectures.
So today I will remind you of these revolutions at the start of the century, which involved enriching our ideas of space time through relativity and quantum mechanics. Tomorrow I will tell you about our actual current picture of the universe. What's in it, what interactions there are, what sorts of particles there are, how they all fit together. And so that's a recapitulation of the 20th century in the first two lectures.
And the third and the fourth lecture, I will tell you about two very sharp theoretical paradoxes that really seem to push, to give a guide for what's going to come next. One of them has to do with the fact that for many, many separate arguments, all very strong individually, suggests that the very notion of space time is not a fundamental one. Space time is doomed. There is no such thing as space time fundamentally in the actual underlying description of the laws of physics.
That's very startling, because what physics is supposed to be about is describing things as they happen in space and time. So if there's no space time, it's not clear what physics is about. That's why this is a hard problem. And that's a serious comment, as we'll see.
A second problem, and these may be related to each other. But a second problem is that in our current understanding of the laws of physics, it seems almost impossible to accommodate a very basic fact about our universe. Our universe is big. We are big. The universe is big. But the underlying laws that describe nature are micro physical. They operate at small scales. And as we'll see, this might not seem like such a crisis.
But the ubiquitous phenomenon of violent quantum mechanical fluctuations in the vacuum that we'll talk at length about tomorrow and the next day seem to actually make it impossible for there to be a macroscopic universe. So trying to understand how nonetheless a macroscopic universe arises is going to be a really major challenge.
We actually don't have a good understanding for that very, very basic question. Why is the universe big? We can accommodate it in our current theories, but the accommodation, as you'll see, is so absurd that it makes us think we're missing something very, very big as an answer to a very basic question.
It's a wonderful thing about the status of our subject that the two driving questions in it are extremely simple to state and describe. You'll really get a fully accurate and honest appraisal of what these problems are. It's hard to describe the solutions or the potential solutions. But the actual problems are easy to state and understand, and we'll do it.
And I'll end by discussing these wonderful experiments that are happening this decade, everywhere from the Large Hadron Collider to experiments that are designed to look for dark matter, to understanding the dark energy that seems to be driving the expansion of our universe today. There's a whole slew of experiments that will perhaps tell us something about some of these questions, and I'll describe that.
But today it's all about setting the stage. And so tomorrow we'll talk about the detail things that are in the world, this particle, that particle, this interaction, and so on. Today I'm talking about the basic rubric that we think governs all of physics. So we're not going to be talking in great detail about the actual content of the world. We're going to be talking about the very basic laws that govern it, relativity and quantum mechanics.
And as a backdrop, I want to remind you what Newton's picture of the world was. And Newton's picture of the world, imagine here's time going vertically up and here's space, here's a particle just sitting at rest. Doop, doop, doop, doop, doop. Moving up in time. At different snapshots in time, it's sitting there at rest. Here's a particle that's moving at some fixed velocity to the right here.
But here's something else that a particle might do. A particle might move and some curvy fashion. And what Newton told us is that when the particle moves in a curvy fashion, that's because it's being acted on by a force. And that that force causes the velocity to change from one moment to the next. The change in the velocity from one moment in the next is the acceleration. And there's this famous equation, f equals ma, that tells you exactly how that velocity changes from one instant to the next.
So in this Newtonian picture of the world, all you have to do is specify at any given moment where are all the particles, how fast are they moving, and in what direction? Go. What are the forces? Go. And you will be able to predict everything that happens in the universe after that simply by applying these laws of motion.
Furthermore, the nature of the forces were that they were extraordinarily simple and beautiful. The force of gravity, for example, was described by the existence of a force on this particle one by the presence of particle two that was proportional to his famous constant g times a product of the masses divided by the distance between them squared. So there is extremely simple forces acting pairwise between particles, which together with specifying the initial positions and velocities would allow you to predict everything.
Note also that this picture allowed a very interesting notion of an action at a distance. Didn't matter how far away that particle was. It would still exert a force on you. If the particle was 10,000 meters away and you moved it over there, then instantly over here you would feel the force change. It's now pointing in that direction rather than in that direction. So there's a notion of an action at a distance.
This was this clockwork picture of the universe that really allowed you to predict everything. There was no part of the universe that wasn't accessible, no part that couldn't be understood and predicted. All of that's going to change, of course. So let's first review how Einstein changed part of this.
So Einstein's name is famously associated with the principle of relativity. But what's sometimes not appreciated is that actually relativity is not an idea that goes back to Einstein. In fact, even Newton's laws had a form of relativity that even predated Newton himself. It was Galileo who first realized that this notion of relativity existed.
What's the idea behind relativity? The idea is that, let's say I drop a ball. And I just drop it straight down. Then I know that after one second it'll have fallen five meters. After two seconds, it'll fall 20 meters. three seconds, 45 meters and so on. The distance that it falls is proportional to the square of the time as it falls. And that's something that I can just observe about what happens when I drop a ball here.
Now I can ask a different question. What happens if I take the ball and I throw it? I throw it that way with some velocity. I guess I chose that to be seven meters a second here. Now, that's a different question, right? It's not just dropping it. It's a different question. I'm throwing it.
But the idea of a Galilean relativity is you can figure out what happens if you throw it in the following simple way. Imagine you threw it that way in seven meters a second. But imagine that you were someone else who was running along at seven meters a second. That someone else who's running along at seven meters a second wouldn't see that the ball was moving. That person would just see the ball sitting there.
The idea is that what that person sees is exactly what you saw when you just dropped the ball. That person moving along also sees the ball fall and fall five meters after one second, 20 meters after two seconds, 45 meters after three seconds, and so on. In other words, the nature of the laws and what the motion looks like-- the nature of the law is it's completely independent of the frame of reference if you're moving at constant velocities relative to each other.
And you see it's actually a powerful principle, because it allows you to predict something. It allows you to predict what the shape is going to be if you threw the ball. It's very simple. You just imagine that first you're running along with it. So we know what would happen then. It's just falling. And then now you just go back and say, ah, if I was running along with it, it would fall straight. If I'm not running along with it, that just means that every second it's moving forward in this direction by seven meters. Another seven meters.
So the shape here is a parabola. So it's quite powerful. Knowing that when you drop it straight, it falls in a straight line, you can deduce from this principle of Galilean relativity, which is a consequence of Newton's laws, that you'll fall on the parabola otherwise.
Another consequence of this is that if you're sitting on a spaceship. And please forgive my terrible drawings throughout these lectures. They're only going to get worse. So if you're sitting here on a spaceship and you throw a ball with some velocity v, then imagine that also the spaceship is moving. If the spaceship is moving with some bigger, other velocity capital V, then the ball appears to move at a velocity that's just the sum of the two of them.
That's just the completely intuitive fact. If you're running along and you throw something, then it's going to be moving with the velocity given by the sum of those two things. That's another consequence of Galilean relativity. And Galilean relativity, in due course, was understood as a simple consequence of Newton's laws.
But it has a disturbing consequence. The disturbing consequence-- oh, maybe I should before going here. The disturbing consequence is that because of this, it's possible to send signals between here and there as fast as you like. It's really easy. If you want to send it from here to there and your ball's going slow, just hop on a spaceship and make it go faster. If that's not fast enough, hop on another spaceship. It will make it go even faster.
There's no limit to how fast you can throw something from here to there. And that means there's absolutely no limit on how far you can extend your reach of influence. Arbitrarily distant regions of the universe, incredibly distant regions of the universe, can nonetheless have an effect on what's going on here because of this very basic fact that these velocities add. You can always make something go faster.
Now, this is a disturbing idea. It may bother you, as it bothered Newton's contemporaries, that things arbitrarily far away can have an impact on what's going on here. You may wish to change that. You may wish to say, no, that shouldn't be the case. There should be some limitation on the range over which things can affect each other.
But you see, if there is such a limitation, that must mean that there is a maximum speed at which any signal can possibly be transmitted. And that maximum speed must be exactly the same for everybody, no matter how they're moving. If it wasn't, then you can always go faster than it. And that's the whole point. That's what got us into this puzzle to begin with.
So that means that there's got to be a maximum speed-- let's call it c-- for any single transmission. But which must have the peculiar feature that every single observer agrees that when you're sending something that maximum speed, it's going at that speed c. So it doesn't matter if you're standing on a rocket ship or not. If you throw something with this maximum speed, everyone will always agree that it's going at the same velocity.
Now, this quote unquote c, of course, turns out to be the speed of light around 300,000 kilometers a second, which is a gigantic speed compared to anything we're used to in our everyday life. But nonetheless, there is such an upper limit. And that basic fact, that very basic fact, you see, we demanded something that seems innocuous. We don't want arbitrarily distant regions of the universe be able to affect us. But that basic fact has startling consequences for the relationship of space and time.
For example, imagine that there's a little box here that emits at some time a beam of red light and a beam of green light that go in opposite directions in a box. I'll draw pictures like this often in this lecture. This is just a picture of a position in this direction and time in that direction. So sitting here at the origin here is when the green beam went off in one direction, the red in the other direction. And these x's are the splat that occurs here and the splat that occurs there.
And you might be tempted to say that the red light hits one end of the box at the same time as the green light hits the same other end of the box. The word simultaneously makes an appearance. They're happening at the same time. But if it's true that there's a maximum speed and that speed is the same for all observers, that is a fake notion.
Because imagine the box was moving that way. Well, that speed is always the same. It's always 200,000 kilometers a second. And that end of the box is running towards. That end is running away from it. So the red light hits that end before the green light hits that end.
Or imagine the box was going the other way. Then you reverse the order in which the events happened. Depending on your state of motion, depending on whether you're at rest relative to the box, running relative to the box, you will come to a different conclusion about whether these events happened at the same time or not.
So this was one of the first thought experiments that Einstein did that really bugged him. Because it seemed to suggest that the notion of time wasn't absolute, that you couldn't say in some absolute sense that these two things occurred at the same time.
This is a bedrock piece of Newtonian thinking, that there was such a thing this time that sits there ticking along at uniform rates for everything in the universe. But this seems to make that a possible. The word simultaneously is meaningless. There's no such thing as simultaneity. That's a simple consequence of this fact that there's an upper speed limit.
Now, that's just the beginning of a remarkable fact. You see, what we just saw there is that, depending on how fast you're running, you can either have things happen at the same time or slightly earlier times or slightly later times. There's no such thing as simultaneity. And that seems to imply that there's some sort of strange mixture between time and space going on.
In fact, there is a strange mixture between time space. And to prepare us for the idea, I'm going to talk about something much more prosaic, what you're all used to, which is a not strange mixing between space and space.
So imagine you have, I don't know, a red arrow lying on the ground. There it is. It exists. There is such a thing as the red arrow in the world. But two different people, person one and person two, want to decide to describe the position of the arrow. They want to describe the tip of one end and the other end of the arrow.
Person one might come along and say, aha, this arrow, I can describe what it is by saying there's two coordinates, an x-axis and y-axis, they're orthogonal to each other like I learned in school. And so I can say that one end, well, there's one end and in the x direction there's amount x1 and in the y direction there's an amount x2. And that's it. I've given the coordinates of the tip of the arrow. If I walk x1 meters in this direction and y1 meters in the orthogonal direction from one end of the arrow, I arrive at the other end.
OK, but someone else, person two, can come along and without knowing at all what person one did, just do it differently. Here person two could set up a completely different way of giving you exactly the same information. They're going to walk this way and then walk in the orthogonal direction. And the directions in which they walk are rotated relative to each other. That's all. They have no idea. One that has no idea what the other did.
They then compare notes. They say hey, I saw a red arrow. Did you see a red arrow? Yeah, I saw a red arrow too. Oh really? Did we see the same red arrow? Tell me, what are the coordinates of your red arrow? And one of them will say, oh, my coordinates are 10 meters for x and 3 meters for y. And the other one would give two different numbers for x and y. And they'd say, gee, it doesn't seem like we're talking about the same red arrow.
Until they realize, wait a minute, maybe you were walking in a different angle than I was. Let's see. Let's see if it's possible. Well, there's a simple check we can do to see if we're discussing the red arrow, there's something we should both agree on, which is the length of the arrow.
And you all learned in high school how to compute the length of a right angle triangle like this. You just take the sums of the squares of the two legs. So there's x1 squared plus y1 squared is what person one would call the length squared of that arrow. And x2 squared plus y2 squared is what person two would call the length of that arrow.
And while x1 and x2 and y1 and y2 may not agree, if they're talking about the same arrow, they had damn well better agree on the length squared. That's a check they could do. And to see if they're equal, they're probably talking about the same arrow.
The arrow has some independent meaning all by itself. The coordinates with which it's described do not. They can depend on who you are. They can depend on various random things. But the actual length doesn't.
So we can make a plot of all the possible x and y values that random different people could assign this arrow. And what we find is that person one is here, person two is there, there's some other person there, some other person there, some other person there.
But we find that all the different xy values that they could measure would all lie a circle. And in that circle, the radius of that circle, the length squared of that circle, would be elsewhere. So x and y can change, but there's something that's invariant, something that everybody agrees on, which is x squared plus y squared.
We could say this more poetically by saying that position in the x direction and position in the y direction don't have independent meaning, only a mixture between the two of them has an independent meaning. We can rotate x into y, y into x. There is there such a thing as the plane itself, the xy plane.
All right, this is very familiar. But it gets more interesting in the context if we go back and now think about relativity. Because in fact, exactly the same thing is happening in relativity. There's some minus signs here and there.
So let's go back to this a picture where there's a light bulb going off and sending two beams of light in two directions. One seen by the eye of this blue line, and one seen by this purple line. And let's now draw, once again, here's the picture.
Here's how one observer would describe what happened. They'd say, OK, here one went that way and it was seen by this guy. The other went there and was seen there. Another observer that's running relative to the first one at some fixed velocity would make a different conclusion. We just said, you could even say which one had hit first can depend. One can happen before the other. The word simultaneously doesn't make sense and so on. So the second person would say, OK, that one's there and that one hits there. So they will not agree on what the values of x and t are.
By the way, always when I write these things, I multiply the times by the speed of light. That's just because of the speed of light times time has the same units as distance. So it's a simple way of going back and forth between distance and time.
But the thing that they all agree on is that light is always travelling at the same speed c. That's a thing that they all agree on. And that means that no matter what that coordinate is, that its magnitude, its length, and x2 is the same as c times t2. It's moving on 45 degree lines here. And similarly, that one. Its magnitude is equal to c times t2.
A nicer way of summarizing that statement is if you square the value of x, the square of the value of x is always equal to the square of the value of ct. That's just reflecting the fact that both observers agree that the light is moving at the same speed c. So the first observer says x1 squared minus ct 1 squared equals 0. The second observer says x2 squared minus ct 2 squared equals 0.
But that immediately tells us something rather remarkable. That there is an invariant that everybody agrees on, even though the actual x and t coordinates may disagree. And that invariant is not x squared plus y squared, like it was for the length of the little red arrow. But is x squared minus c squared t squared. Everybody agrees that the values of x squared minus c squared t squared are the same.
So if we do the same exercise as we did before, imagine all possible observers. Imagine all possible x and t values that they might be able to assign to give an event. Then instead of lying on a circle, they will lie on lines on curves where x squared minus c squared t squared is the same.
So let's say we're talking about some event that took place here at the origin near x equals 0 but sometime later. OK, another observer might see it there. Another observer might see it there. But all observers would agree that it lies not on a circle, but on a hyperbola. That hyperbola.
See, observers moving really really, really fast might see that it happens out there. But it's going to lie on the same hyperbola. And that's how they can all agree that they're talking about the same event. They're talking about exactly the same event if this x squared minus c squared t squared is the same for everybody.
If instead you have an event that happens over here, then all possible observations of that event would yield these possible values of x and ct that lie on this hyperbola. But apart from that minus sign, it's exactly like our x and y story. And we've mixed up space and time. So we can rotate space and time into each other.
This fact had a number of remarkable consequences. For instance, let's imagine that an event here is the birth of something and the death of something later. That takes some amount of time, let's say 80 years if you're lucky.
But another observer moving very, very fast relative to that one will see the birth of the same place with the death happening very, very far away. That means that to this observer, it seemed like the time span between birth and death talk a lot, lot longer. So it just seems that by running really, really fast, so if something is moving very, very fast relative to you and if it lives 80 years, you might think that it lives a lot longer.
That's called time dilation and it's a real effect. We see it all the time. It's a commonplace phenomenon in our part of physics. One dramatic example is that the Earth is bombarded by very high energy particles that hit the upper atmosphere and produce, amongst other things, a particle what we call the muon.
Now if the muon was just sitting here in my hand it would decay and disintegrate in 2.2 microseconds. So it disappears really, really fast. If I just took it and I threw it really fast and ignore this time dilation fact, there's no way that it would make it from the upper atmosphere down to the Earth. It would just disintegrate too quickly. But precisely because it's moving really fast, this effect stretches out its lifespan. And that's how it manages to make it to the ground. This is real.
Another effect, which I won't have time to explain, is length contraction. So things that move very fast shrink. And again, it's not in your head. It's meaningful. If you take a steel cable, you attach it between two spaceships, you start off the two spaceships accelerating at the same rate, so they're moving faster and faster, the spaceships always keeping the same distance between each other, this rod actually contracts in size.
Eventually it'll snap. Despite the fact that at all times the distance between the spaceships is the same. They're accelerating at the same rate. But the rod is moving faster and faster. It contracts and it really snaps. It would really snap.
Now, how big is this effect in everyday life? Let's say I wanted to make sure, I mean, I will not survive more than 80 years. But if I ran really, really fast and then stopped, I might get to see what the world looks like in 3,000 years. But as fast as I could possibly run, and I don't think I can run at 30 kilometers an hour for my entire life, but if I could, this would give me 10 seconds over my entire lifespan. So you need to be going really close to the speed of light in order for this to be important, which is, again, why people manage to go for so long without noticing it.
Another remarkable consequence is that mass, energy, and momentum got unified. So time and space got unified. But many other things, which were apparently unrelated, became unified in this way. So famously, E equals mc squared says that mass can spontaneously change into energy. Other notions. Electricity and magnetism were seem to be different aspects of the same thing and could be mixed up with each other in the same way that space and time could be.
So this notion of relativity enriched a notion of space and time to something new, space time. And Einstein went further to show that even this wasn't some static arena, but that space time could be curved. And that the curvature of space and time was associated with gravity. So the Earth goes around the sun because it's taking the shortest possible path it can in this curved space time.
And again, this notion that space time had some internal dynamics of its own and wasn't just static led to a number of dramatic consequences. For example, you've all heard that the universe is expanding. But it's not expanding into anything. When we say that the universe is expanding, we really mean that at a steady rate, space is being invented all the time, between all the particles that are out there.
If you have these two galaxies, two red galaxies, here what's going on when we say the universe is expanding is a few million years later, the universe has doubled in size. That means that there's space being invented constantly at a fixed between all these points. That's why it looks like they've separated. Not because they're moving into anything, but because the space is being generated and created between them at a steady rate.
That's a remarkable notion you couldn't even have thought of, you couldn't have even conceived of, if you didn't understand that not only were space time unified, but that they weren't some fixed mesh in which everything else happened. They responded to the presence of masses and particles. And that response had to do with gravity and other things.
Another dramatic consequence of this extension of our notion of space time is the idea of a black hole. You know that if you're on the surface of the Earth and you throw a ball at five kilometers a second, that's pretty fast. But the ball will still land on the Earth somewhere. But if you throw the ball at 11 kilometers a second, it'll escape the gravitational field of the Earth and just go as far away from the Earth as you like.
So there's a simple formula that tells you how fast you have to throw something in order for it to escape from so much mass and such region of space. And you can ask what happens when that speed approaches the speed of light. If you put so much mass into such a small region of space, then it can simply become impossible even for light to escape from that region.
When that happens, simply nothing can get out. Absolutely nothing can get out. And that means that something very peculiar and new happens. That there are regions. It's possible to make regions of space and time completely inaccessible to us. You just put enough mass in there, you can collapse a region into a black hole.
If you fall into it before you cross this so-called event horizon, before you get too close, you can send signals to your friends. Everything's great, life is fine, everything's OK. Then you cross over that event horizon and no signal you ever send will ever make it out after that. This is, again, a consequence of extreme bending of space and time that's allowed and made possible by these enriched notions of what space and time are.
A better way of drawing this is that really you imagine there's this throat that you can get sucked down. And if you're far enough away, you can send a light beam and have it get out. But right at the event horizon, if you just try to flash a beam of light out, you'll find there is no out. It'll just go zip around the horizon. It doesn't even go one millimeter out. Zips around the outside of the horizon.
And if you are a little bit inside it, just simply nothing you do will ever get signals out. And in fact, deep inside is a place that has a very unpleasant end for you. There's absolutely nothing you can do to run into this so-called singularity and nothing you can do will avoid it. In fact, any amount of struggling will just make your demise take place more quickly. So again, this is remarkable. As I said, there could be regions of space that we'll never access because space and time are now dynamical things.
Let's move on to discuss quantum mechanics. Quantum mechanics is, in many ways, as I mentioned, much more radical than relativity is. A reason for that is that as phenomenal as Einstein's achievements were, they're largely involved taking existing concepts, time and space were existing concepts that people talked about for hundreds of years. And he just figured out the right way of thinking about them.
But when we came to quantum mechanics, we had to invent entirely new concepts and entirely new ideas that had no classical antecedents whatsoever. And that's why it was a much harder slog. A lone genius in a patent office could figure out relativity. But it took the German and English academic hierarchy with roughly 10 or 15 people working over 20 or 30 years to figure out quantum mechanics. It was not a lone genius working in a patent office. It was these guys wearing ties. It really worked, but it took this great collective effort.
All right, here too quantum mechanics unified seemingly very disparate parts of physics before. So before quantum mechanics, there were phenomenon that seemed to have a particle like character, like baseballs moving around, and things like a light that seemed to have a wave like character. So that was the situation in the 1800s. There were particles in the world, there were waves in the world. And that was that.
In our modern understanding, there's no such things as waves. Everything is a particle. But they're not classical particles. They're particles that move according to quantum mechanical rules. Sometimes large macroscopic collections of quantum mechanical particles behave as classical waves. And sometimes these large macroscopic collections of quantum particles behave as classical particles. But it's really the underlying quantum particles that manifest themselves in a certain limit in two different ways, wave like or particle like.
The most remarkable thing about quantum mechanics is that it signaled the end of this dream that began with Newton that there was a clockwork universe where we could predict. If we knew everything, at least if we knew everything about was going on at a given time, we could predict everything everywhere in the universe later. There's this picture of determinism. And this picture was completely smashed by quantum mechanics.
So there's a variety of slogans that go with it that you've probably heard of. For instance, there's the uncertainty principle. This is just one big blow to this idea of determinism. Remember, Newton tells you that to predict what goes next, you have to give me at a given time where the particle is and how fast it's moving in what direction. The uncertainty principle says that's impossible, I'm sorry.
You might be able to ask the question in the English language, where is the particle and how fast is it moving? But it's a meaningless question that just does not have an answer. You can know that the particle, you can know where it is within some precision. But that's inevitably associated with some spread in the direction in which it's moving. And there's no way that you can know both of them perfectly.
These are encoded in these famous uncertainty principles that say the product and the uncertainty of the position and the momentum, the momentum you remember is the mass times the velocity of a particle. But this product can never become 0 the way you could in a Newtonian world, but is always bounded by this number, known as Planck's constant. Written here as H with a little slash through it. Something similar is true for energy and time.
And another slogan is that the world is not deterministic. The only thing we can predict is probabilities for certain events to take place. And this is really, honest to goodness, true. It's completely nuts, but it's true. You can take two radioactive atoms. Atom one, atom two. They're completely identical. They're produced in identical ways. They're in every possible way identical. Radioactive one will sit there and disintegrate in one minute. Particle two will sit there and disintegrate in two minutes. It just actually happens. It's a true fact about the world.
That means that there's just nothing you can do. If you hand me one of them, I just can't tell you when it's going to disintegrate. That's a tremendous loss of productivity for a physicist who thought they could predict everything. We can't even do something as dumb as tell you when some radioactive particle is going to decay. Tough luck. That's just the way the world is.
What we can do, however, is if you give me a very large collection of these radioactive atoms, I can tell you on average when they will decay. What happens if you put a big vat of them in a box and you measure them, every single one of them decays. And you just plot the fraction of the decay at any given time. You'll find as you put more and more atoms in this box, this fraction will become more and more sharply peaked around some particular number. Let's say 86 seconds.
So you can say that on average, they decay in 86 seconds. And that really means something. It means that if you give me 17 gajillion of them, then by far the vast majority of them will decay in 86 seconds. And the fraction of in that will decay in 86 seconds gets closer and closer to 1 the more and more clothes that I have. So we can predict things on average we can predict probabilities. But we can't make predictions for individual events, for individual occurrences.
Now once again, all of these uncertainties are very small for typical objects. So here's a typical object. Me. And just so you have an idea, if the uncertainty in my position is the size of an atom, then the uncertainty in my velocity due to the uncertainty principle is 10 to the minus 35 centimeters a second. That's not very big. That's not very important.
So large macroscopic bodies will move around in a way where these effects are not important. But they become important on very small scales. And actually there's a very important proviso to that, which I hope I have time to explain, but we'll see if I get there.
All right, so here's a variety of-- now, it seems really depressing. There's so many fewer things we can predict. The world is not deterministic. But far from being depressing, quantum mechanics is the most successful physical theory we have ever had. And all of these things, the uncertainty principle, this indeterminacy in everything, plays a crucial part.
There's an awful lot of nonsense said about quantum mechanics and people relate it to new age things and eastern mysticism and stuff like that. And it's all complete load of crap. There's nothing sharper and more well defined and harder, with a harder core in it than quantum mechanics. The reason why matter is stable is because of quantum mechanics. Atoms exist and are stable and make sense because of quantum mechanics.
In a classical picture of the world, and this really caused people lots of consternation, you might imagine electrons spinning around the proton. But nothing stops the electron from just running into the proton and just banging into it. There's no reason you would have stable atoms. That's because the energy of the electron can be made smaller and smaller and smaller by getting closer and closer to the proton. That's the effect of the attraction, the electrical attraction the proton has on the electron.
Not so in a quantum world. In a quantum world, what happens is that you see here the lowest possible energy, what the electron wants to do is to be on top of the proton and not moving. But the uncertainty principle says that's impossible. If I know it's right on top of the proton, I have no idea how fast it's moving. It could be moving so fast that it's actually escaping out of the proton and vice versa.
So instead, if you were to try to visualize it, you would have to-- and this isn't very precise, but it'll do for now. You should think of it as a cloud that's surrounding the proton. And what happens is that as you start getting too close, just there's some inevitable energy due to the fact that you have some momentum.
You're moving and that extra bit of energy due to the uncertainty principle actually makes the energy go back around and increase. You can't get too close. So there's a nice, stable place. And if you work it out, that gives you actually the size of the atom. That's what Bohr did. That's why Bohr is famous.
So quantum mechanics, this uncertainty, this indeterminacy, goes into making matter stable. If it wasn't for that, atoms wouldn't be stable. And more than that, the fact that an atom there and an atom there and an atom there all more or less look the same is also because of this. So the stability of matter is a direct consequence of quantum mechanics.
There are other strange features. You might imagine that there's a poor ball stuck here at the bottom of this well. And it's just sitting there at rest. And that's it. Its permanent future is to explore the vicinity of its little bottom here.
But in a quantum mechanical world, that's not true. In a quantum mechanical world, there's always some tiny chance that it has, I don't know exactly where it is, I don't know it's exactly at the bottom. There's always some tiny chance that it could have some momentum that could kick it over and make it go to the other side. That's a phenomenon known as tunneling. This is impossible in a classical picture of the world but becomes possible quantum mechanically.
You see again this uncertainty allows a richer diversity a phenomenon to happen. Nothing would stop you. This conserves energy. Everything would be the same. Just taking the ball here, moving it over there, nothing bad has happened. The energy is the same. Everything is fine. But it just can't happen in the classical world. But it can in a quantum world. The quantum world allows more things to take place. It unifies things that otherwise couldn't talk to each other in a classical world.
This is also a very important phenomenon, which is, however, only important for small objects. There is some tiny chance that me sitting here will tunnel through that wall and spontaneously appear on the other side. Let me do the calculation for you to tell you what that probability is. The probability is around 10 to the minus 10 to the 30.
Let's say that number again, shall we? It's not one. It's not 10 to the 30. It's not 30 one's followed by 0. That would be 10 to the minus 30. It's 10 to the 30 0's followed by a one. This is an unimaginably small number, literally unimaginable. In fact, if I waited around long enough to see whether this happened, before that there'd be some fluctuation in my brain that would make me think that something else happened. So it's completely unreasonable to even talk about probabilities that are this small.
On the other hand, imagine that you're an electron sitting in the middle of a hunk of metal. And in this hunk of metal, there's a bunch of positively charged particles. And there's some well of energy. There's a well of energy just like the little well we drew before. And in the classical world, the electron would be perfectly happy to sit here or sit there or sit there or sit there. And it would just sit there for all time. It wouldn't move.
But in a quantum mechanical world, that's not true. As we said, there's some probability for the tunnel. And for electrons and metals that probability is not small. In fact, it's very close to one. This is where currents come from. Currents are a consequence of this quantum mechanical fact that electrons are actually tunneling from place to place to place as we move along a piece of metal. For small things, this is an important and interesting effect. For me, it's not very important, which is why people didn't notice it for 2,000 minus 100 years.
Another very important consequence of quantum mechanics is that the states of minimum energy, whatever they are, the minimum energy is never 0. This is going to be a fact that's going to come back and haunt us in the third lecture.
Imagine you have something as prosaic as a ball hanging on a string. In a classical world, what's the smallest possible energy it could have? 0. It could just be hanging and not moving. It has no potential energy, it is no kinetic energy, nothing.
In a quantum world that can never happen. Because I can never know exactly that it's actually hanging. There's always some uncertainty in this position. And associated with that, there's some uncertainty in its momentum and there's some jiggling. There's constantly some quantum jiggling.
You can do a very simple estimate that tells you that the minimum amount of energy is actually that Planck constant we talked about times the frequency of the motion of this pendulum. So for anything that oscillates, there's a tiny minimal amount of energy associated with it, given by this number h times frequency.
This is historically where the quantum in quantum mechanics came from. Because it suggests that lumps of energy couldn't be made is fine and be divided up as finely as you like, but came in little packets. And the size of the packet, as Planck first enunciated, had this sort of behavior.
Now when did I start? I have 10 minutes? OK. All right. All right, let try to see how much of this I can do. I want to just quickly try to give you-- this may go a little too quickly, but I'll be very happy to discuss in more detail if anyone's interested in coming down right after the lecture.
Often in discussions of quantum mechanics, we are very qualitative. And it leaves you, if you're not in the subject, it leaves you wondering whether we're just sort of BSing all the time. It's all uncertain. You don't know exactly what you're doing. What the heck are you doing? On the other hand, you say no, this is the most spectacular physical theory we've had of all time. Trust us.
So I just want to give you a taste of what quantum mechanics is really like. This is an honest description of the quantum dynamics of what you might think of as a particle moving around a circle. We're going to make our life easier and imagine that the particle can only live in certain bins that are placed around this circle. Let's start off imagining that it could live in three bins, one, two, and three.
And the rules of quantum mechanics. The underlying rules, there's no uncertainty principle and determinism and all that. Those are words. Those are consequences of an underlying, very sharp set of laws. And the sharp set of laws tell us to talk about the state of the system in a very particular way. So let's start talking about this notion of a state of a system.
Let's imagine that we have the particle living there in position one. OK, it's really sitting there in position one. We definitely know it's sitting there in position one. And we describe that by writing a little vector. It's called a wave function or a state vector. But it's really simple here.
You see, I'm just writing 1, 0, 0. The first entry is supposed to refer to bin one, the second to bin two, the second to bin three. So this would be, I told you that no matter what state the system is in, it's associated with some wave function or a state vector. This is the state vector associated with the ball definitely being in one. That's the state vector associated definitely being in two, that's the state vector associated with being definitely in three. So far so good?
OK, now the magic begins. And the magic is that we're allowed to talk about other states. We're allowed to talk about completely general states that have not just 1, 0, 0, 0, 1, 0, 0, 0, 1, but actually any entries. A, B, C, or psi one, psi two, psi three if you want to be a little fancier.
So you can really think of this as having a three dimensional space as being a little vector. Being a little three dimensional vector in this three dimensional space. And its first entry is psi one, the second entry is psi two, the third entry is psi three. Slight deviation from normal vectors is that the entries of this vector aren't normal numbers, but are so-called complex numbers.
If you don't know what complex numbers are, it's really simple. I'll tell you how to think about it. Each one of these numbers, think of it itself as being a little vector in a two dimensional space. This is some other two dimensional space. Each one of those numbers, each one of these little entries is actually a little arrow. There is a little arrow for one, there's a little arrow for two, there's another little arrow for three. I'm done. If I give you these three little pictures of the arrows, I've completely specify the state of the system.
Now, you can ask what happens if I measure one of the particles in one, in bin one or in bin two or in bin three. This is where the strangeness of quantum mechanics comes in. We can only predict probabilities. But quantum mechanics tells you that the probability to measure that you're in one is given by you just look, there it is, psi one. You look at that little vector, you take its length, and you square its length. So the probability for finding the particle in one is a square of the length of the associated vector. Similarly for two, similarly for three.
Now, that's how I describe the state of the system at any given time. What happens as, let's say I give you at some time, at some later time, it's going to move around. This state is going to move around. There's something important about it. The total length of this little vector is always one.
That's because the ball is either in one or in two or in three. The sum of all the probabilities has got to add up to one. So as the state moves in time, this state vector also moves around. But it moves around in such a way that the length of this vector is always one.
And a final thing I have to tell you is that if I have two state vectors, A and B. And here's what they are at 0 seconds and at one second they evolve into these new vectors. But I might imagine a third state vector, which would be just adding A and B together.
Then if I saw what happened to that guy later, later would just turn to adding A and B at this time. So if I have A and B here, A goes there, B goes there. Then A plus B would just go to this A at later time plus B at the later time. So this is technically known as the fact that the evolution in time is linear.
Believe it or not, I've given you all of the postulates of quantum mechanics. These are the central tenets of quantum mechanics.
So how does life become interesting? Let's now imagine that I have many, many, many bins. So let's say there's 20 bins here. To specify the state, I'll have to give you 20 of these little arrows. So there's 20 of these little arrows. I'll get tired of drawing in the vector, so sometimes I'll just draw them around a circle like this.
So again, that little arrow is psi one, that little arrow is psi two. If I want to know the probability that this funny state will be found in three, I just look. There's three. I take the length of that little vector and I square it. Four, I take the length of a much smaller vector and I square it.
So evidently it's much more likely to find this particle in three than to find it four even though there's some small chance it will be found in four. So this is just some random state. Any old state is going to look like this. But now I'm going to show you the picture of some very special states.
So consider this special state. So remember, these are just the values of those little vectors. So imagine this special state where that little vector whose length gives you the probability, remember. As I go around the circle, it actually just sort of tracks the movement around the circle. That's a rather pretty looking state. Notice that the length of all these vectors is the same.
Oh, I don't know what happened there. Sorry about that. The dangers of Microsoft Journal. Anyway, all these vectors have the same length. That means that if you measured to see is the particle in location 13, is it in location 17, is it location three, there'd be equal probabilities to find them anywhere. All those lengths are exactly the same.
But this is not just some uncertainty, is it here or is it there, is it there, did I flip a coin or flip a 20 sided coin to decide where I found the particle. It's not like that. In fact, this state has a very interesting property. It has a definite value not of position of the particle, but of its momentum. This state turns out to correspond to the particle actually moving around the circle with a very definite momentum. It's the momentum being Planck's [INAUDIBLE] divided by the radius of the circle.
That's what a state of definite momentum looks like. You see, it looks nothing like the state of definite position. The state of definite position would just have one of these arrows in one slot and 0's everywhere else. The state of definite momentum has equal length arrows everywhere. But what tells you what momentum it has is the fact that the arrows are cycling around the circle and coming back to the starting point.
You might imagine other things. Maybe as the arrow goes around, it cycles around twice before it comes back to the starting point. That's what I've schematically represented here where I got tired of drawing all the rest of them. Well, that correspond to a particle moving with the momentum two times h bar over r. To the value of the momentum is encoded in this interesting way the angles of these little arrows move as you move around the circle.
What if the arrows moved around the other way as you went around the circle? Well that corresponds to the particle moving in the opposite direction. So the states of definite momentum, these are them. There are not the states of definite position. But there isn't some gibberish.
There is one states that are definite positions, the other states are definite momentum. This is the meat of the uncertainty principle in action. But now you're seeing much more sharply what it actually looks like. This is a completely honest description of what, as I said, of the description of the quantum mechanics of a particle moving around the circle. This is actually how we do it and how we teach it in courses.
A final comment. I told you that for large objects, these quantum uncertainty effects were irrelevant. But that's only part of the story. For large objects it's true that there are certain states, like me, roughly speaking, sitting here with small uncertainty in positions, small uncertainty in velocity. Those states exist. That's very nice. There are sort of approximately classical like states.
But you might wonder why we don't see other crazy states of nature. For example, nowhere in the previous example did I say that that little ball was small. That little ball could be me. Nowhere in this example. So how come we don't see me in these crazy states? Why don't I walk in the room and see me in a state where you don't know exactly where I am, but I'm definitely moving that way?
By the way, it's really meaningful. If you put little turnstiles in the way, they'd all be spinning. You would see that I'm moving that way even though we had no idea where I was. But how come we don't see that? How come before when you walk into this room, this state of horrible and utter chaos isn't what confronted us and instead you find people roughly well localized, sitting in seats and so on?
These other things are also perfectly decent states. They're there. Why don't we see them in nature? So the statement that quantum is small and classical is big is only part of what's going on. There's actually something deeper. The really correct slogan is not that quantum of small and classical is big, but that quantum is open and classical. Quantum is closed and classical is open.
By which I mean simply the following. The reason why we don't see these crazy states is because of something that so far in this entire discussion I've neglected. In this whole discussion we pretended that all that was going on was this ball moving around the circle and everything else.
But there's something else going on. There's air molecules in the room. There's all sorts of other things out there. They're also part of the system. Even if they're some measuring apparatus that's going to be measuring what's going on, that's also part of physics. There isn't some separate, weird part of physics which is measurement and the conscious mind of the experimenter that's wondering what's going on. It's all part of physics. We can describe all of it in one gigantic, large system.
And in fact, if we imagine here all the air molecules in the room at some initial time, here's the state. The particles in one, the air molecules all over the place here. What would happen after a very short time? Oh, the particle would still be a location one.
Now, the air molecules will be in some different location. And the precise location where they will be will depend on the fact that the particle was there. Some of the air molecules bounced off of it there and I'm moving in a different direction because it was there. Many of them will bounce off of it and move in different directions because it's there.
So if I wanted to specify the state, I'd have to not only specify the state of the ball, but also the state of all the air molecules. And a short time later, that state of all the air molecules is something different, but is a something different that's correlated with the fact that the particle sitting there in one. There's something else that would happen correlated with the particle sitting there and two and correlated with the particle sitting there in three.
Now let's say I took one of these crazy states, which was a sort of uniform amount of all of them. By this principle of linearity that I told you earlier, I can make a precise prediction for what the state of everything is later. The state of everything later is, again, the particle one is sitting there. But now there's a state of the air molecules correlated with the fact that one was there. Similarly for two, similarly for three. That happens very rapidly.
But now let's say I just want to study what's going with the ball. I have no idea what the air molecules are doing. I'm not keeping track of all the details of what the air molecules are doing. I'm just looking at what's going on in particle one. That fact of not paying attention to the air molecules, ignoring the air molecules and just studying the system itself, completely destroys this remarkable quantum coherence.
Remember I told you the precise momentum, for example, that we had the state which were these particles going around in the circle. And I said this was a magical state. The precise value of the momentum, for example. This is not just some random state where you don't know, you throw a 20 sided die to decide whether the particle's here or there. It's a very special state where there's extra information. The extra information, it has some momentum.
And that momentum is encoded in the very special relationship between the arrow in this direction and the next direction and the next direction and so on. But the second there's any tiny interaction with this environment, that information becomes lost. That information is there, but to recover it you also have to keep track of what happened to all the other air molecules out there. And we don't do that.
In a technical sense, the overlap between the state of the air molecules one and the state two. In other words, those states that were correlated with the particle being in position one and being in position two, is some absurdly small number.
Another one of these absurdly small numbers. That's because a huge number of air molecules interacted. Even if any one of them changed by a tiny amount, there's so many of them that the net change is inevitably gigantic. And those states have nothing to do with each other. They're essentially completely independent separate states.
That fact, so this number is 0 for all practical purposes. And a little bit more detailed analysis tells you this completely destroys those delicate relationships between these arrows from one place to another that allow for that very interesting quantum state to exist.
So the bottom line is the reason when you walk into the room you don't see these crazy quantum states all over the place is because long before you walk into the room, everything was interacting with the air molecules. The problems of air molecules measured already where everyone was sitting. And unless you look in extreme fine detail at what those particles are doing, these very peculiar quantum mechanical states don't make an appearance in everyday life.
But they're there. They could really be there. And if you make things cold enough and protect them enough from the environment, it's possible to make even macroscopic objects really have that property that I said. You walk into the room, you have no idea where they are, but you definitely know they're moving that way.
And the bottom line of this is that it is possible to make exact predictions in quantum mechanics. But it's predictions for peculiar sorts of observations. To make exact predictions in quantum mechanics requires two kinds of infinity. You have to take some system and study it with some measuring device. You have to do the experiment an infinite number of times. Because you don't know what's going to happen every time. We can only predict the probabilities. But furthermore, we have to do the experiment with an infinitely large apparatus.
Again, if you don't make the apparatus infinitely large, there's always some chance that the apparatus itself suffers a quantum fluctuation and does the measurement wrong or thinks something else or something worse happens to it. So it is possible to make exact predictions in quantum mechanics. But it involves two idealizations, two infinities. An infinite number of experiments and an infinitely large apparatus.
I go through these points in quite some detail because they're going to play a crucial role in the doom in space time and the trouble with the microscopic universe that we're going to get to in a couple of lectures. OK, let me skip that.
OK, so let me end. So I told you the story of quantum mechanics and relativity. And I hope you're struck by something, something that always strikes when I think about it, which is that these big revolutions, which are so celebrated, are actually associated with a dramatic decrease in the amount and number of things we thought we could predict about nature.
Before quantum mechanics and relativity, remember in this Newtonian picture of the world, we can, in principle, predict everything about everything. There was no part of the universe that was beyond our reach. There was nothing that we couldn't in principle predict with arbitrary precision. It's an enormously powerful conception of what the power of the physicists might be.
But we discovered something very important. That there are limitations to what we can talk about, even in relativity. We can't understand what we can't access what's going on inside a black hole. In quantum mechanics, even worse, there's no determinism. We have to do these experiments infinitely often to measure probabilities with big apparatuses. We have to have the separation between big apparatus and small systems that we look at.
So it's very peculiar that we seem to be finding out that we can predict fewer and fewer things about the world. But there is a strange paradoxical flip side to that, that the more we understand these things, the more we see that relativity and quantum mechanics unified seemingly completely different phenomenon and made them turn out to be different aspects of the same underlying thing. Space and time became unified. Energy and mass. Waves and particles.
So it's strange. On the one hand, we seem to have fewer and fewer things to predict. On the other hand, the things that are left seem to be more and more closely related to each other. This is probably not an accident. You see, the fact that there's fewer and fewer things to predict is actually, there's a deep reason for it.
It's because there are fewer and fewer things because what seemed to be very, very different things in the classical world precisely turned out to be different aspects of the same thing. There are few of your things we can predict is related to the fact that the things that are left are really all the same thing. So these are two important flip sides of each other.
Again, I stress this fact because in the third and the fourth lectures, we're going to see big generalizations of this. There are even fewer things that we can predict when we push the limits in this philosophy of radical conservatism the theories that we currently have. There's even fewer things that we predict, and yet as we'll see, even more and more things are going to seem to be unified with each other. Well, we can all extrapolate what the endpoint of this might be. But I don't know if we're going to get there anytime soon.
Let me just end by giving the advertisement for next time. The marriage of space time in quantum mechanics. So we talked about relativity, we talked about quantum mechanics. As I said, much of the rest of the 20th century was about putting these two concepts together. What's turned out to be a remarkably constrained, difficult, but ultimately successful thing to do. And the marriage brought a whole variety of further surprises that tomorrow is going to be about.
For example, the fact that anti matter has got to exist. That for every particle in nature, there's some anti particle. If they met they would annihilate into energy. There's electrons and anti electrons. They really exist. We make anti electrons routinely in high energy physics experiments. There could be an anti me out there somewhere. Who would finish lectures on time.
And associated with that are really radically new picture of what we conventionally think of as empty space. In fact, as we'll understand, empty space is not only not really empty, but almost everything that we do in fundamental physics is about trying to more and more deeply understand the properties of the vacuum of empty space. But that's for next time. So that's where we'll pick it up tomorrow. Thanks a lot.
Let's take a few questions.
ARKANI-HAMED: Absolutely. Absolutely. Well, no.
ARKANI-HAMED: Yeah, so this phenomenon, which I described briefly, which really deserves a whole talk on its own. But the phenomenon that the reason we don't see these funny quantum states is because things are interacting with an environment around them. That phenomenon is called decoherence.
And the question was whether this phenomenon of decoherence explains the famous Schrodinger cat paradox or gives an explanation for why we don't see cats that are both alive and dead in Schrodinger's famous paradox. Absolutely. It's because the cat's being bombarded with air molecules all the time. A very, very cold cat would. An exceedingly cold, well it'd be dead for other reasons. But right.
ARKANI-HAMED: We can go through this in detail. Maybe we can go through this in detail offline. It's a wonderful true fact. And it's really because this phenomena of actually real. The explanation, again, has to do with the failure of simultaneity. The explanation to your question, again, has to do with the failure of simultaneity. Because when I said that I'm starting them off like this and then at the same time they start accelerating, then right. So that that breaks the symmetry you're talking about.
AUDIENCE: You seem have said that quantum mechanics is a limit for us [INAUDIBLE].
ARKANI-HAMED: It has nothing to do with us.
ARKANI-HAMED: No, I meant we in the royal, very royal, we sense.
AUDIENCE: [INAUDIBLE]. Does the universe know what it's doing?
ARKANI-HAMED: Apparently. I really want to stress this, that really an awful lot of nonsense is said about quantum mechanics. And it's true. There are mysterious things about it. It's true, it's strange that the world isn't deterministic.
The real mysteries, there are mysteries involved with measurement and the sorts of problems that come up. But all of them have to do with the words gravity and cosmology. If the words gravity and cosmology don't make an appearance and someone says there's something mysterious about quantum mechanics, they're selling you something.
In particular, when we do measurements down a lab, when normal things happen, these are completely beautifully described by the standard laws of quantum mechanics. And there's no difficulty whatsoever. This basic phenomenon of decoherence solves almost all the old paradoxes.
I should say that this was a point very well appreciated by Bohr and Heisenberg and their friends. Bohr was such a horrible writer and explainer of this sort of thing that it didn't really penetrate. But it was really revived in the 1980s and is really a perfectly well understood thing. The process of measurement is not some different thing. It's part of nature.
It's insane to say otherwise. It's actually part of nature. Measuring devices made out of the same stuff, everything else is made out of. There's is no mysterious consciousness involved with the process of measurement. There's no such thing as wave function collapse. Words for [INAUDIBLE], who at least might worry about some of these things. Everything's just good, old fashioned quantum mechanics.
But there is something important about the fact that when you have interactions of small systems with very, very, very big systems, then these quantum coherences can very quickly become lost. That's the reason why classical physics emerges. It's the reason why measurements yield well defined answers.
But it does mean that if you want to make arbitrarily sharp predictions, you have to get these two idealizations to happen. You have to do the experiment infinitely often and you have to do it with an infinitely large apparatus. And it sounds like a complete technicality until we get to the doom of space time, lecture three, which turns out to be a direct consequence of these facts combined with gravity.
SAUL TEUKOLSKY: One more question back there.
ARKANI-HAMED: Yeah, I'm sorry. So I didn't put any units pause, I'm sure you appreciate. Because the units are irrelevant when the number's that small. So you could call it per second or per age of the universe and it won't make that much of a difference.
But you're right. It should have some units. He's absolutely right. Of course, if I just know for a fact that I'm here, then 10 to the minus bajillion seconds later, I'm still here. So there's some probability per unit time for tunneling across the wall. And I didn't give the appropriate units. But the number was so tiny that it doesn't make any difference.
For the electron, when I say the probability is one, it does make a difference. And there are some typical characteristic velocities with which electrons will move around from one well to the next. There I really should have responsibly put in a per second. I just didn't know the number off the top of my head.
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Renowned theoretical physicist Nima Arkani-Hamed delivered the first in his series of five Messenger lectures on "The Future of Fundamental Physics" Oct. 4.
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.