YUVAL GROSSMAN: Good afternoon, everybody. My name is Yuval Grossman. And I am a physics professor here. And I'm going to introduce Nima for his fourth lecture. And when Nima came here and he looked at the-- we sent him a very nice program and every day who is set for introduce. He said, why you need to introduce me five times? Once is enough.
And I said, I know you very well. After all, we spent some time together. So I have some stories. He said, oh my god-- no, no, no. OK, so I'm not going to tell all I know about Nima. But I thought I'd share a little bit-- just half a minute, so he has more time.
And I was really lucky enough to share a room with Nima for two years as post-docs. So we were both at Slack, sitting in a room-- I don't know. At Slack, the rooms are much smaller. Here, you feel-- and when we both leaned backwards, we'd start hitting each other. And it's very hard for me to imagine how much he influenced my career and the way I think about physics.
So I learned so much of having this guy sitting in your office. And it's really nice to say, oh, Nima, by the way, how do you do this? And-- op-- here you go. Oh, thank you. And so-- whatever-- it's really a nice way. So these two years were very impressive. I learned quite a lot from Nima. And I keep learning a lot. So I keep it short. And let's have Nima come and give us his fourth lecture.
NIMA ARKANI-HAMED: Thank you so much, Yuval. Yuval's not only a wonderful office-mate, [INAUDIBLE] amazingly patient with a relatively loud voice on the phone all the time. Relatively being a mild term for it. But it really was a really, really small office.
OK, so one of the really delightful things about this subject, which I hope you've been getting a sense for in the past number of lectures, is that some of our very, very biggest questions are about incredibly basic things. They're really simple to state. That's a hallmark of very, very good questions in our part of physics. If they're really simple to state, of course, they're not often simple to understand and come up with a solution for. But they often involve incredibly basic properties about our universe.
And today, we're going to address one of, perhaps, the most basic properties of the universe, which is that it's big. Our universe is big. We are big. The planet's bigger. Galaxies are bigger. Atoms are small. The nucleus of the atom is smaller. The fundamental laws operate on very short distances.
So it's an interesting question why there is, nonetheless, a macroscopic universe. Now, you might think this is not-- so this is coming back to the picture of the scales that we've seen a number of times. We're going to try to understand why it is that, even though it seems there's something fundamental going on down at length scales of order-- 10 to the minus 33 centimeters, the Planck length, or some other incredibly short distance scale-- that nonetheless we have lots of huge scales relative to that.
We have this weak length scale. And we have this gargantuan scale, which is the size of the universe. By the way, there's only about-- I can't do the addition in my head-- but not so many orders of magnitude between those scales. It's remarkable that all we know about the world actually fits between there and there. Nonetheless, it's going to turn out that it's a really major puzzle why these scales are so far separated from each other.
Now, you might think that we understand why something like an elephant is big or we're big. It's just made out of lots and lots of atoms. So it's not so confusing after all. But if you trace that question back and further and further back and ask, why are there a lot of atoms?-- why-- why, why, why, why?-- you end up hitting a number of brick walls. So we're actually going to start from the brick walls and just explain why it is that it's almost impossible to imagine that there is a macroscopic universe, given what we know about the laws of physics.
And that fact suggests a number of radical modification of what physics should look like, in order to explain that extremely basic fact about the world. This all goes back, as everything in this series of lectures has done, to quantum mechanics and relativity, the uncertainty principle, anti-particles, and the whole picture that the vacuum is an exciting place. So we've seen this a number of times.
If I take my magnifying glass and look at a little region of space and time to see if it's empty. I pop out an electron and a positron pair, if I do the magnification powerfully enough. And so everywhere in space, we have this picture of particles and antiparticles popping out-- in and out all the time. So the vacuum, far from being an empty boring place, in this picture, when we combine quantum mechanics and relativity, is a very exciting place-- is a rich place.
And I should say that, even though we keep drawing these qualitative pictures of particles popping in and out and so on, there's a hard machinery behind all of this. We can actually figure out what all these things mean precisely. It's exactly this picture of the particles popping in and out of the vacuum that allows us to make these 12 decimal place accurate predictions for specific questions-- for example, about the magnetic properties of the electron.
So it isn't all pictures. We're going to be talking about a lot of pictures. But it isn't all pictures. And so there is a piece of this story-- there's a piece of these fluctuations coming in and out, that it's not only qualitatively correct. It's amazingly quantitatively correct. So we understand it very, very well.
However, there is a big problem riding underneath it. The vacuum isn't just exciting. It's way too exciting. And one aspect of this problem, which we'll begin with, is the fact that even the vacuum has energy. Now, again, this is another basic consequence of quantum mechanics that we remarked on when we were talking about it.
If we imagined having a ball hanging from a string-- a pendulum-- then in a classical physics, it's minimal energy would be 0. It could be sitting there and sitting at the bottom and standing still. So it would have zero energy, zero potential, zero kinetic energy-- zero energy. But in a quantum mechanical world, it's constantly fluctuating. And it actually has a minimum amount of energy of order Planck's constant times the frequency with which the pendulum would swing.
So that tells you that these quantum fluctuations have energy in them. Let's try to make an estimate for how much energy there is, therefore, in the vacuum. So let's make the estimate by looking at-- now, since the vacuum looks the same here and there and there and there, whatever kind of energy we're talking about should be the same everywhere. So it's an energy per unit volume.
So we can ask about the energy of the vacuum per unit volume here or the energy of the vacuum per unit volume there. And we should get some number for that, right? So that's really what we're asking about, not the total energy, but the energy per unit volume of space.
All right, let's do an estimate. So imagine I make my volume some nice big volume. There are some quantum mechanical fluctuation, by the uncertainty principle again, that lives in that volume. So OK, there's some energy there. Now, let's make a more refined measurement. Let's make the volume smaller. Well, the quantum fluctuation in that smaller volume are bigger, right?
They're associated with much shorter scales, much shorter times, much higher frequencies. And by this basic rule, that the amount of energy gets higher as the frequency gets higher, just the energy in those fluctuations is bigger. OK, so let's make the box even smaller. It gets even bigger. So we have a big problem that, as we make the box smaller and smaller, the energy of the fluctuations is getting bigger.
The box is getting smaller, so the energy per unit volume is just blowing up like mad. In fact, naively, the energy per unit volume would be infinity. I would make the box arbitrarily tiny. And the energy per unit volume would be infinity.
Now, of course, I can't make the box arbitrarily small. We spent all of yesterday talking about how space-time is doomed, we can't talk about arbitrarily short distances-- blah-blah-blah, right? So that means that, surely, it doesn't make any sense to talk about this box when it gets smaller than the Planck length. So definitely, whatever this estimate we're doing is wrong when the box gets close to the Planck length. But it sounds like it should be pretty good somewhere in that neighborhood.
So let's just, to get an idea-- oh-- this quantity, in previous lectures, I called rho, the vacuum energy density. I'm giving it a new name for this lecture, which is the name people normally give it. It's called Lambda. That's a capital Lambda. And its name is the cosmological constant. So I'll interchangeably say vacuum energy, cosmological constant, big Lambda. It's all referring to the same thing, which is the energy density of the vacuum.
So we're now trying to make a good estimate for the energy density of the vacuum. Good theoretical physicists can estimate anything under the sun to a factor of 10. So we are good theoretical physicists, or in the neighborhood of some, so let's do it. All right, so we just got a good estimate for it. It's an energy per volume.
The energy, if the box is of [INAUDIBLE] of a Planck length, is-- now, it doesn't even matter. We don't need to use units or anything. All the words here are Planck. So it's a Planck energy, a Planck volume. The energy density is Planckian. That's actually a technically-accurate statement. It's a Planckian energy density-- very good.
OK, so what would that energy density do? Remember, we said yesterday as well that, if there was a positive energy density in the vacuum, that it would make the universe double in size at some uniform rate. So it would make the universe accelerate. And we can come up with an estimate for the rate of that acceleration. Except we don't even have to remember the formula now, because we know it has to do with gravity.
Gravity is associated with the word Planck. The energy density is Planck. So what's the doubling time for the doubling rate of the universe? It's the Planck time. It can't be anything else. Every word in this discussion is Planck.
Great! So we get a great estimate. We get an energy density of the vacuum. It has a great prediction. The universe would be doubling size every 10 to the minus 43 seconds.
Well, that seems very, very wrong. Now, I've mentioned it already yesterday. But I'll emphasize it again today, because it's the biggest experimental discovery in our subject in the last 20 years. The universe is accelerating. It is accelerating. We discovered that in 1998.
But the rate at which it's doubling is every 10 billion years. It's pretty far from every 10 to the minus 43 seconds. So you see, often when people talk about the accelerating university, [INAUDIBLE] there's some mysterious dark energy that is driving the expansion of the universe. We don't know what it is.
Actually, it's not true. We've known for ages and ages that we can make the universe accelerate. You fall out of bed, you make the universe accelerate. The problem is that we make this back-of-the-envelope estimate of how fast it should be accelerating. And it should be doubling in size every 10 to the minus 43 seconds, not every 10 to the 10 years.
So why did people say that it was such a surprise that the universe is accelerating? That prediction that I just told you, that it's doubling in size every 10 to the minus 43 seconds, was so absurd, so obviously wrong, that all theorists thought that-- even though, normally, theorists are good at doing back-of-the-envelope estimates-- this was a time when there was something just very big missing.
And clearly, if it's off by so humongously much, there must be some very deep principle we have yet to uncover that tells us that, in fact, this vacuum energy is 0-- exactly 0. You can't get it so far off. So we all expected that it would be exactly 0. That's what was so shocking about the accelerating universe, not that it was accelerating, but that it was accelerating but at such an incredibly tiny rate.
That meant that this value of the vacuum energy wasn't going to be declared to be 0 by some angels who'd save theoretical physicists. It was really non-0. And we'd have to come up with an understanding for why it had the specific value that it has. The specific value that it has, which is around 10 to the minus 3 electron volt per millimeter cubed-- that specific value is 120 orders of magnitude smaller than what we get from this back-of-the-envelope estimate.
I used to say, when I gave talks, that that was the biggest error in the history of physics. Then I realized, there's no reason to smear any other science. I don't think anyone else has screwed up so bad. So I think it's the biggest error in the history of science. By error, I mean, the biggest disagreement between a reasonable back-of-the-envelope estimate and the right answer.
I assure you, we do not screw up this bad in physics ever anywhere else. We're used to predicting things to 12 decimal places. So that's why this is such a shocking problem, not to even get to within a factor of 10 or 100-- to be off by 120 orders of magnitude.
Now, I told you we have this spectacularly successful theory. We predict all these things. It's so awesome. So what do we do about this? What do we actually do? Before predicting these detailed properties of the magnetic properties of the electron, we should surely understand why the universe isn't doubling in size every 10 to the minus 43 seconds, right?
Well this is what we actually do. What we do-- we say, no. It's fine. Don't worry about it. It's fine. Well, we do worry about it. But this is the calculation we do. We say, that was indeed some quantum correction to the energy density of the vacuum. We just estimated it. We're very good. We pat ourselves on the back. Great job. We estimated that.
Imagine that you do the calculation and it's in Planck units. So you get some specific number-- 2.6493781... It goes on forever. You work very hard. So this is a quantum correction. That's this quantum mechanical origin of this vacuum energy. But we say, ah! It just so happened that there was a classical contribution that was sitting there already.
What was the size of that classical contribution?-- you ask. Well, it just happened to be negative 2.6493781... And they happen to agree to 120 decimal places and begin to disagree in the 121st decimal place. That's what we actually do. We're allowed to do it. No one will stop us from doing it.
And once we do it-- I want to emphasize this. Once we do this, everything else works. It's not like this thing feeds in everywhere else and is screwing up every other calculation. It's a "said it and forget it" thing. You fix it at the start. And then everything's fine. But it's really weird. It's very deeply weird.
For obvious reasons, this is called fine-tuning. It's really like taking your finger on a dial and just adjusting things to part and 120 to get something to work. This situation we're in is like walking into a room and seeing a pencil standing on its tip in the middle of a table. And it's vertical to an accuracy of 10 to the minus 120 degrees.
Now, it could be. It's a consistent way the pencil could be. It's consistent with what we know about physics for the pencil to be within 10 to the minus 120 degrees of vertical. But if you saw something like that, you would probably wonder that something's up. You might look for a string hanging from the ceiling, something that explains why it's vertical.
You would find very dissatisfying the explanation that, oh, that's just the way it was. It just accidentally happens to be 10 to the minus 120. That's the explanation we give now. It just accidentally happened to be 10 to the minus 120. And this is our current answer to the question, why is the universe big?
Since these lectures are being videoed, I'm not sure I should make this remark. But maybe, I'll make it anyway. I think it's great that the intelligent designers don't know about this. This is a much, much better argument for intelligent design than anything to do with evolution. Those things are all true. This is a situation where we, ourselves, don't have an incredibly compelling answer yet.
I'm going to tell you about the answers we do have. And we take the problem seriously. And we think about it. And we proposed scientific approaches to it. But it's really a major puzzle. This is not one of those things we understand amazingly well. We don't. It's something we're speculating about.
I think it just goes to show, the intelligent designers actually don't care about the Big Bang. They don't care about cosmology. They just don't want to be monkeys-- funnily enough.
Now, that's the biggest problem. That's the biggest one of these fine-tuning problems. But there is another one. And for this, we have to go back to remembering something I told you about-- where mass comes from, in our understanding of the standard model of particle physics. Remember, we had this picture where we said, the electron becomes massive because of this propagating through space. It keeps bumping into this condensate, which isn't like the ether, that fills the universe.
And it keeps bumping into. It keeps bumping into it, every 10 to the minus 17 centimeters or so. That's why the length scale, 10 to the minus 17 centimeters is important. It's actually a property of nature. But that's what it does. So it picks up in inertia, because it bumps into it every 10 to the minus 17 centimeters or so.
Now, every single thing in the universe is quantum fluctuating at tiny distances. It's the same argument over and over again. We'll all start getting bored. So this condensate is fluctuating. It has huge fluctuations. It doesn't want to be uniform on the scale of 10 to the minus 17 centimeters. This is the whole problem.
Quantum fluctuations are big. They get bigger and bigger at shorter and shorter distances. Nonetheless, we have a universe that seems to have correlations across much, much, much larger distances than that. So really, what this condensate wants to do is fluctuate like hell. And the electron wants to fluctuate like hell.
So the electron would want to be enormously heavier than what we actually see it to be. It would want to be 16 orders of magnitude heavier than we see it to be, because this typical distance wants to be 10 to the minus 33 centimeters, not 10 to the minus 17 centimeters. Now, that's evidently also not what the world looks like.
If that is what the world looked like, you and I would all be black holes. We'd be so massive-- the constituents that make up the atom-- everything would get so much more massive than they are now that the strength of gravity would be just as big as everything else. And there would be no stable matter of any form. We'd all be collapsed into horrible black holes-- a highly unpleasant universe.
By the way, just a brief comment-- the reason why, in our world, we actually have such a large diversity of different scales-- there's humans. There's planets. The fact that there is such a big diversity of them turns out to be a direct consequence of the weakness of gravity. So really, the weakness of gravity is not only necessary for any kind of macroscopic world to arise but, actually, also generates the very rich structure of different length scales that we see.
But our current answer then, in the theory that we actually have and have tested to, why is gravity weak, is-- well, it looks like it wants to do that. So once again, we have to do exactly the same thing. We fine-tune. We say that there is this parameter that would say how often it bangs into the Higgs field. And we just adjust things against each other, now, not to 1 part in 10 to the 120, but to 1 part in 10 to the 30-- it's still pretty bad-- in order to accommodate this very basic fact.
So the questions, why is the universe big? Why is gravity weak? All special cases of the general question, why-- in a universe with violent short-distance quantum fluctuations-- do we have, nonetheless, macroscopic order?-- is the question that we're going to address. So back to this picture.
Our understanding, now, of that scale invokes a 1 part in 10 to the 30 tuning. That invokes a 1 part in 10 to the 120 tuning. If we didn't do these tunings-- if we imagined putting a bunch of theorists in a space ship, closing the windows, giving them the laws that we have of the standard model of gravity, ask them to predict what the universe would look like without letting them look outside-- of course, it isn't a very consistent experiment. Because if they're in the spaceship to begin with, the universe-- anyway-- but if you do that, they would not, in a million years, predict the world that we see.
What they would say is-- ah-- there are these huge fluctuations. My guess is that the world looks like that. All the scales are stacked right on top of each other. And it's a horrendously unpleasant universe. So what controls these violent quantum fluctuations? Why is there a macroscopic universe?
Well, let's talk about the second problem. The first problem is more confusing. So we'll defer it to the end. Let's talk about the second problem, the problem of the fluctuations in-- well, we can phrase it, actually, in general terms. Let's phrase it in general terms first.
So we have these quantum fluctuations. As the box gets smaller, they get bigger and bigger and bigger. This problem-- I want to emphasize-- does not come from some detailed part of a sixth decimal place of some esoteric calculation. We run into this problem for precisely the reason I've told you, which is almost identical to the correct technical reason for it.
We run into it as a direct consequence of putting together relativity and quantum mechanics. Special relativity and quantum mechanics, vacuum quantum fluctuations, just directly lead to this problem. So it's just an absolutely direct consequence of the marriage of quantum mechanics with this notion of space-time that Einstein gave us.
Now, let's say we are trying to understand why it is that we don't have these big huge fluctuations at distances shorter than 10 to the minus 17 centimeters. Well, there is a very qualitative prediction. Something new should happen, as I shrink the box down to around 10 to the minus 17 centimeters.
Let's say nothing new happens at 10 to the minus 17 centimeters. Let's say something new does happen, but at 10 to the minus 28 centimeters. It doesn't help. Because then these fluctuations are huge, huge, huge down to 10 to the minus 28 centimeters. So it still doesn't help explain why we have this nice scale where the electron bangs into the condensate every 10 to the minus 17 centimeters or so.
So this argument just tells us that something new has to happen at 10 to the minus 17 centimeters. At some level-- this is the $5 billion argument, because this is one of the very strong arguments we have that we expect some dramatic new physics to show up at the Large Hadron Collider, which we'll talk about tomorrow. That's exactly the scale we're about to probe. But something has got to give, like, right around the corner.
Now, what could it be? There's a number of historical precedents for it. But let me give you one of them. There are other times in the history of physics where exactly this sort of question was confronted, this style of answer was given and was exactly correct. In fact, it was correct in even more profound ways and more surprising ways than people realized.
For instance, at the turn of the century, classical physicists had a really serious puzzle, because they looked at the point-like electron and they saw that there's some energy stored in the electric field around the electron. They calculated that energy. That energy got bigger and bigger as they went to smaller and smaller distances close to the electron. And they found that energy could become infinite.
So this was a serious puzzle for classical physicists. And they thought. And they thought. And they said, OK, in order to avoid this problem, something new has got to happen at some distant scale that they worked out. It turned out to be around 10 to the minus 13 centimeters. And around 10 to the minus 13 centimeters, if something new happened, well, then the energy stored in the electric field around the electron wasn't too much bigger than the mc squared of the electron.
So it might be OK. But if you made it much, much smaller than that, it would be crazy. Because once again, you'd have this huge positive contribution to the mass of the electron-- the energy of the electron-- which you would have to cancel against some other contribution in order to understand why the electron had the mass it had. So this was a serious puzzle.
And the way they try to solve it is to give the electron a small size. They tried to make it around 10 to the minus 13 centimeters big. They tried. And they tried. And these theories failed in every imaginable way. They didn't work. But that's because they were missing quantum mechanics and relativity.
We now know the correct answer to this problem. The correct answer is actually, at even larger distances than 10 to the minus 13 centimeters, something new did happen. The new thing was quantum mechanics-- electrons and positrons, vacuum fluctuations, that whole story. These vacuum fluctuations-- one thing they do is-- you see, as you get to distances shorter than 10 to the minus 11 centimeters, where these vacuum fluctuations for electrons and positrons become important, you can't actually tell anymore which one of these electrons is the central one.
There's just this whole big cloud-- many, many electrons and one fewer positron. And so it just doesn't look point-like anymore. And this classical crisis completely disappeared. So I'm giving you an example of this. Precisely the same sort of argument came up. And the solution was pretty dramatic. The solution was an extension of space-time plus quantum mechanics that doubled the world.
I'm giving that analogy, because the best candidate solution we have to our problem today has exactly the same character. Ah-- yeah. Let me-- now, if this slide seems to be completely out of place, it isn't.
So all of these arguments about the something new needing to show up at 10 to the minus 17 centimeters were purely internal theoretical arguments-- quantum mechanics, relativity, this, that, violent quantum fluctuations. And we arrive at a conclusion. Something new has got to happen around 10 to the minus 17 centimeters.
It turns out that, from a completely different part of physics, from the opposite distance scale, from the largest possible distances-- not the smallest possible distances-- but from cosmology-- from astrophysics and cosmology, there is other evidence that something new should be happening at 10 to the minus 17 centimeters. It's a part of the wonderful unity of this subject.
And that evidence has to do with something probably many of you have heard of, which is that, in addition to the dark energy, which is mostly what dominates the energy of the universe today, there's also been evidence for a long time that there is dark matter, that most of the mass in the universe is not made out of us. So we're a very tiny component of all the mass and energy in the universe, or even a very tiny component of the mass.
And most of the mass that's out there is in the form of dark matter. One of the early pieces of evidence for this was that people looked at galaxies. The stars around the galaxy go at some velocity around the galaxy. And you can indirectly measure how fast they're orbiting around the center of the galaxy. Now, if what's keeping them bound to the galaxy is just standard Newtonian gravity, then you would expect that, if the stars are getting further and further out, while they're further and further away, the gravitational force is getting pretty small.
They've basically seen all the mass that they're going to see. So their velocity had better slow down, if they're going to remain bound in this orbit-- just that very basic argument. So if you would expect that, if you measure the velocity of the stars as a function of distance, it would eventually go down, as you went out to larger and larger distances. Well, that's not what was measured. What's measured is that, more or less, the velocity of the stars go to a constant, as you go further and further out.
So what do we do? Do we chuck everything? This is evidence that Newton was wrong, gravity is wrong, everything is wrong. Or do we try to do something else? As I've mentioned a number of times, you never know ahead of time whether the right thing to do is to think that everything's going to hell and we have to change everything or you just keep pushing with the theory that you have.
But the best idea is to push the theory that you have as far as you can and see if it breaks. In fact, if this dark matter seems mysterious to you, I want to remind you that the way many of the distant planets in the solar system were discovered were exactly like this. The distant planets in the solar system were first inferred by the fact that there seemed to be funny things in the motion of planets far away that you could, even back then in the 1800s, have said, oh, Newton's wrong.
Or you could say, no. There's another planet out there somewhere. It's tugging on it-- dark planet. And dark planet was the right answer, over and over again. That's how Neptune was discovered-- Uranus, Pluto. So anyway, the conventional explanation is that what's explaining this is that there's actually a huge amount of other matter here. We're a tiny component of it.
There's actually a huge cloud of dark matter surrounding surrounding the galaxy. And that matter is explaining the fact that this velocity flattens out. Now, you can ask, how much of this dark matter do you need? And well, you can come up with the energy density you need for the dark matter. But you can ask, where could it have come from?
And if we imagine we go back earlier in time, in the Big Bang, everything was a hot soup. And if we imagine that, eventually-- this dark matter has got to have extremely weak interactions with us. Otherwise, we would have seen it already. And it would have shined light. But if we go back early enough, we can assume that the interactions eventually become strong enough that everyone's in a big hot soup with each other early in the Big Bang.
So you have a lot of these particles, the dark matter particles. The universe expands. It cools. And eventually-- so we know how much dark matter and all the other matter there was very early in the history of the universe. And then we can just churn standard physics to figure out how much of the dark matter is left today and see what it would take for the right amount to be left.
Well, this is a calculation you give to cosmology graduate students. And they come back. And they tell you that we need to have the dark matter have interactions. The dark matter with ordinary matter needs to have interactions like this. And in fact, we can predict what the needed range of this interaction is. The range should be around 10 to the minus 17 centimeters.
That number, 10 to the minus 17 centimeters, is popping out of a completely different part of physics. And it's giving us evidence that there has to be new physics, minimally, in the dark matter. And where should it be coming in? The interaction length, the strength, the range, should be around 10 to the minus 17 centimeters. So this is quite remarkable.
We have these deep theoretical reasons to suspect something new happening at 10 to the minus 17 centimeters. And we have this direct experimental clue that there is something new happening at 10 to the minus 17 centimeters. This isn't the unique particle that could be the dark matter. This argument is correct. But the dark matter could still be something else.
But in a sense, it's the most canonical possible picture for dark matter that we could have. And it's quite remarkable that it's telling us the same scale. This is often called the WIMP miracle, because this kind of dark matter is often called the Weakly Interacting Massive Particle. And the WIMP miracle is that the needed range is exactly what we think it should be from other arguments.
All right, so I've given you this deep theoretical reason. So let's go back to the deep theoretical question. There is this problem with the fluctuations of space-time. Something new has got to happen at 10 to the minus 17 centimeters. Whatever that new thing is, it can't be something dinky. It can't be, oh, there is this one extra particle.
It has to do something radical. It has to remove these violent vacuum fluctuations. Those violent vacuum fluctuations are hardwired into space-time plus quantum mechanics. So it stands to reason that, if you're going to solve this problem, if you're going to give a good solution to this problem, you have to modify one of those two things. You have to change one of those two things in some way.
It's ironic that a lot of today's lecture is going to be about modifying or extending your notion of space-time, when yesterday's lecture was all about the fact that space-time is doomed anyway. What I'm really saying is, we have to modify space-time first. And then it's doomed later.
But all of this stuff is happening at 10 to the minus 17 centimeters. This is still gargantuan distances compared to 10 to the minus 33 centimeters, which is what we were talking about a lot yesterday. OK, so that's the picture we're after.
We're looking for some kind of extension of space-time that actually explains why the pencil was standing on its tip. It's a little hand holding it up. It's stabilizing it. It's removing these huge vacuum quantum fluctuations. So we're looking for that little hand.
And there have been many ideas. I think it's fair to say that there have been two classes of ideas in the 30-some odd years people have been thinking about this problem. There have been two basic classes of ideas for what might solve it. And both of them, in one guise or another, involve some extension of our notion of space-time.
One of those set of ideas involves invoking extra dimensions-- again, in one guise or another. Something you learned yesterday is that dimensions are not necessarily so different from ordinary physics, right? So extra dimensions aren't necessarily so different from ordinary physics. The inside of that tin can was completely equivalent to something going on on the boundary of the tin can.
But anyway, it invokes, in one way or another, extra dimensions. Extra dimensions are an interesting idea. I've enjoyed thinking about them. But they're not the deepest idea. They're not the deepest idea for what can solve this problem.
For some reason, especially in popular books and in various presentations to the general public, people get more excited about the idea of extra dimensions of space. But it's really not a very deep idea-- really at all-- really at all. This is a much, much deeper idea. It's a much deeper and much more important idea, so I want to tell you about it.
And it's called supersymmetry. Supersymmetry is also a kind of extra dimension, but a much more interesting one. Supersymmetry says, in addition to our usual four dimensions, there are extra dimensions. But the extra dimensions are not measured. The distances in these extra dimensions are not measured with the same numbers we use to measure the distance in the ordinary dimensions.
We use ordinary numbers to measure distances in ordinary dimensions-- 5 meters, 7 seconds. Those numbers have the property that a times b is equal to b times a. They're ordinary numbers. It turns out that, in supersymmetry, we have these extra dimensions. But the distance in these extra dimensions is not measured in ordinary numbers.
You can say, in some sense, they're measured by quantum numbers-- quantum mechanical numbers-- which satisfy the following funny multiplication rule that a times b is equal to negative b times a. Now, if a times b is equal to negative b times a, in particular, a times a is negative a times a. So a-squared is 0. OK? That fact is going to be very important in a moment.
But anyway, if we go back to our picture here, we have an electron zipping along. When the electron moves in the quantum dimension rather than the ordinary dimension, then we see it, in our four-dimensional world, as another particle. We see it as another kind of particle whose properties are almost identical to that of the electron. In fact, it has the same charge.
But I'll tell you what small property's a little different in a second. But think about it, for the moment, as just some partner to the electron-- almost identical properties. Now, if this was an ordinary dimension, then there's many ways that the electrons could pop in that direction. You could make it go slowly in that direction. You could make it go fast in that direction.
There's all sorts of things that you could do, but not for this quantum dimension. In this quantum dimension, you can't take more than two steps, because a-squared is 0. So you try to go two steps, and you're already dead. You can only take one step in this quantum direction. So either, the particles move in our direction or they move in our direction with one step in the quantum dimension. And that's it.
So that means that, for every particle we have in nature, there has to be a partner to it, which is the analog of that when it's taking one step in the quantum dimension. These partners are called superpartners. So if I have the electron, then this particle is called the superpartner of the electron.
So notice how eerily similar this is to the anti-matter story. We have an extension of our notion of space-time, this timing incorporating these quantum dimensions. It once again doubles the world. In addition to ordinary particles, we have ordinary particles and their superpartners. So let me introduce the superpartners.
So here's the electron. Remember, the electron, as we've said a couple of times, is like a bit of a spinning top. It spins around at some rate. The selectron would have exactly the same properties, but just simply wouldn't spin. So that's the thing that distinguishes-- same charge, everything else. So it's "selectron," because it's a superpartner of the electron.
It's also "silly." But once again, these things were invented in the '70s. So the names were invented in the '70s, so you can't blame my generation for it then. OK, the superpartner of the quark is the squark. The superpartner of the photon is the photino. I don't know why it's not the sphotino, other than, I guess, it's hard to say.
But anyway, all these guys exist. And remember, I told you, these quantum dimensions do not violate the rules of relativity and quantum mechanics. If you like, they're a very, very special kind of theory that combines relativity and quantum mechanics. It's so special that, in fact, it can be interpreted as having these extra quantum dimensions. So it's just a good old-fashioned theory, but with a very interesting symmetry.
So to describe the menu of what's going on, I still have to give you these little stick figures and something that tells you that this theory is-- I've explained the super part, but not the symmetry part. There are supposed to be a complete equivalence between what's going on in the quantum dimensions and the ordinary dimensions.
If this supersymmetry was perfectly realized in our nature, there would be, just, complete equivalence between what's going on in the quantum dimensions and the ordinary dimensions. And you would notice that from the fact that these interaction strengths of the electron and the photon-- there would be that stick figure. There's also another stick figure of an electron, a selectron and the photino. And those interaction strengths are just identical.
So that's how you would see that there's perfect symmetry between the ordinary dimensions and the quantum dimensions. Now, of course, we haven't seen these guys. We haven't seen any of these selectrons. We haven't seen any of these photinos. We haven't seen all these particles of these identical properties to us, other than their spins being a little bit different.
But as I mentioned before, already we've seen, a number of times, the similarity between the weak interactions and electromagnetism, between the strong interactions and the electromagnetism. They're there. They're there. They're there at short distances. They're just being obscured, because of various accidents at long distances. These accidents at long distances we sometimes call symmetry breaking. But all it means is that, if you go to short enough distances, you'll see what's really going on.
So in this case, that means that supersymmetry has got to show up, if we go to short enough distances. Now where, from our general arguments, must it show up? It must show up near 10 to the mine 17 centimeters. Otherwise, it's not going to help with anything.
But how does this actually help the problem? How does it remove the violent quantum fluctuations? Well, this is how it does it. Let's take our big box. And we shrink it in size until it gets down to the neighborhood of 10 to the minus 17 centimeters. In that neighborhood, you all of a sudden see that it's possible to go into these quantum dimensions as well.
So you're trying to fluctuate a lot in this direction. But then you see these quantum dimensions around too. Now, the laws at this scale, now, tell you that there should be a perfect symmetry between what's going on in the quantum dimensions and what's going on in the other dimensions. But you can't have wild fluctuations in the quantum dimensions. You can't even take more than two steps in it, never mind wiggle back and forth like mad.
So the fact that these are these funny quantum dimensions tell you you can't have big fluctuations in that direction. How can that possibly be consistent with what looked like big fluctuations in our direction? The only possible consistent story is that those big fluctuations are actually absent and they were removed by the presence of this supersymmetry.
That actually, really technically, happens. So the fluctuations-- they're there. They get bigger and bigger, as you hit 10 to the minus 17 centimeters. But they don't get bigger after that. As you go to shorter and shorter distances-- none of these gigantic quantum fluctuations survive at distances much shorter than 10 to the minus 17 centimeters.
We thought, on general grounds, we needed an extension of space-time to solve this problem. Here is an extension of space-time. Here's how it solves the problem.
Now, just so you have an idea-- if we collide two of our ordinary particles together with enough energy, we can give enough energy so that we can pop some particles off into the quantum dimensions. So there are some quarks inside this proton. We'll talk about it tomorrow. This will hopefully happen at the LHC. But we can collide two protons with enough energy so that two of the quarks in there can pop off into the quantum dimensions. And it looks like we've produced two pairs of squarks.
Now, these particles aren't infinitely long-lived. In fact, they have a typical lifetime of around 10 to the minus 27 seconds. That's how long it takes light to travel the distance 10 to the minus 17 centimeters. And OK, so this squark is going to decay to a quark and, let's say, a photino. That's one of the allowed stick figures.
This could do something more complicated-- go through a more complicated chain and end up with something that has this photino again. So we'll talk about these things a lot more tomorrow. For now, all I want to do is mention that, no matter what you do, when you make these things, you always end up with this photino sitting down here at the bottom. That photino, in turn-- according to those stick figure rules that I drew-- can't decay into anything else. So the photino is just stable.
That's interesting. So it's a massive particle with a range around 10 to the minus 17 centimeters. It's neutral. It's stable. It will be made early in the Big Bang. It would survive out today. That's a perfect candidate for the dark matter of the universe. So this super partner of the photon is a very nice candidate for what the dark matter might be.
You see, from this theoretical point-of-view, it's not the particularly fundamental deep thing. It just happens that it's there. And we've seen that sort of thing happen in physics a lot, where there is some deeper structure and it does various things as ancillary small consequences. And the ancillary small consequence of this picture is that there is dark matter.
But if it's true, it would be quite a remarkable picture, because dark matter would actually be light. But it's light when the light moves in the quantum dimensions. So the motion of light in the quantum dimensions would be the photinos that make up the dark matter of the universe.
Now, there is one more remarkable hint that this idea of supersymmetry showing up around 10 to the minus 17 centimeters is correct. Remember, I told you, one of the great accomplishments of this standard model of particle physics was that it allowed us, for the first time, to even entertain the possibility that the strong force, the weak force, and the electromagnetic force were somehow-- well, they were being described in the same mathematical language for the first time.
They looked basically the same. And there are some detailed differences between them. For example, the interaction strengths were a little bit different. Electromagnetism was 1/137. The strong interactions-- it's dimension strength was 1/10. And there are a few other detailed differences between them. But it allowed us to entertain, really seriously, for the first time, that they were part of a more unified whole.
One of the necessary things that should be true, if they're actually part of a more unified whole, is that those interaction strength should actually be equal to each other. And the other thing that we learn is that the interaction strengths aren't a constant. They gradually change, as you go to shorter and shorter distances. Now, we can take what we know in the standard model and figure out what those interaction strengths would look like, as we went to shorter and shorter distances.
I'm plotting it. I'm plotting this 1 over distances. So shorter distances is going to the right. And I'm plotting 1 over the strength of the interaction, because it turns out that lets me draw straight lines. But if I do this, I find that the strong force-- so 1 over the strength of a strong force is around 10. 1 over the strength of e and m is around 100. So I'm plotting something that looks like this.
I find that the strong force gets weaker as we go to shorter distances. So 1 of its strength gets bigger. The weak force does this line. And "e and m" does that line. It's either I'm in quotes because it's not really quite "e and m," but it's some mixture of e and m and the weak force. But anyway, it doesn't matter right now.
But anyway, there is a picture that you can draw. And you find three lines roughly converging to each other and coming tantalizingly close to actually meeting. But they don't actually meet. So this is what would happen if we extrapolated what we knew in the standard theory-- nothing else-- to shorter distances.
But now, we know that we should expect something new. At 10 to the minus 17 centimeters, we should expect that we have supersymmetry. So we can ask what happens if you include the supersymmetric particles in that calculation. And this is what happens.
Those three lines converge to a point perfectly, to within percent accuracy. This, by far, did not have to happen. Two lines will meet in a point. But it's not at all guaranteed that three lines meet in a point. So again, this is something that we didn't put in by hand.
We didn't put in dark matter by hand. We get dark matter out. We don't demand that something wonderful happens with the relative strength of the interaction as we go to short distances. But we find that something wonderful does happen. If we include supersymmetry, at distances around 10 to the minus 30 centimeters, all these interactions become quantitatively equal.
So that really allows us to entertain the possibility that these forces are all unified. They're coming from a bigger force with exactly the same interaction strength. And that's being hidden at long distances, where long is long compared to 10 to the minus 30 centimeters.
You know you're making progress in physics where a simple calculation quickly gets you something that looks right. Einstein thought for 30 years about how to get a unified theory. He never saw anything like this. This is the strongest hint we've ever had that the idea of a unification of the modern forces is actually correct and is on the right track.
And notice that the place where this is unifying is not so far from where gravity becomes important. So gravity is right around the corner. It really seems like there might be some theory out there that would unify these forces and unify it also with gravity. Of course, if this was an even longer lecture series, we'd talk about how string theory might do that. But that's not what we're going to do now.
So now, I'm going to switch gears. After all these marvelous possible successes-- so once again, everything there in those last two things that I said, which were very strong positive hints that we're on the right track, et cetera-- none of that is confirmed by experiment yet. We haven't detected dark matter directly. We have not seen these superpartners. We hope to see them at the LHC, as we'll talk about tomorrow.
These are all circumstantial hints that we're on the right track. But we don't know that it's true. However, there are at least very positive hints that we're up to something good with trying to solve that problem. But let's go back and talk about the even bigger problem. What happens with that vacuum energy density?
And here, it turns out that the analogous arguments that tell us we should expect something new to happen at 10 to the minus 17 centimeters, for the second problem, for this problem would have led us to expect something new to happen involving gravity now-- something new to happen around 1 millimeter. Nope.
There doesn't seem to be anything obviously strange going on with the laws of physics around 1 millimeter. So the same argumentation that I remind you worked 100 years ago with the problem with the infinite [INAUDIBLE] energy of the electron, which leads us to think about supersymmetry and all these other wonderful ideas with these circumstantial evidence that we're on the right track now-- the same line of argumentation just runs into a brick wall with the problem. It just flat out does not work.
And no one has a good mechanistic explanation today-- no one has a good explanation for why the vacuum energy is small, why the cosmological constant is small. No one has found the hand that might hold it up. So what I'm going to tell you now, in the last 10 minutes, is another kind of argument that people have talked about, which might explain why it's small.
There's many ways to start this discussion. But this is one of them. So I mentioned, last time, that one of the features of string theory that was discovered in the 1990s was that there was actually a single underlying theory-- one theory. That was just a really remarkable theoretical fact, which had another remarkable consequence that had lots and lots of solutions.
We could take that theory and find many, many different solutions, where it's a 10 or 11-dimensional theory. But there are many, many different ways of rolling up the internal dimensions to come up with a theory that was four-dimensional at long distances.
By the way, there was something that smelled pretty good about that basic philosophy. Because that standard model that I showed you looked a little bit complicated, right? It has a bunch of moving parts. There's gluons. There's W's, photons, 19 parameters. It's beautiful and successful. But it had many, many moving parts.
If you want to imagine how that might arise from something even simpler, well, this gives you a way how. The underlying theory can be completely unique. But depending on which solution, which particular way you rolled up the extra dimensions, you would come up with different possibilities for what the world looked like at long distances. So it's a good way of getting some more complex things out of a very simple underlying structure.
And what was discovered in the '90s-- that it was so simple-- the theory was completely unique-- many, many different solutions-- lots of different classical limits-- and roughly speaking, it had zillions of solutions. Now before 1995, zillions was millions. After 1995 and especially in the early 2000s, it became clear that zillions is zillions. Zillions is 10 to the 1,000-- 10 to the 1,000-- actually, in some sense, infinite.
But let's just say 10 to the 1,000, because it doesn't make any difference anyway. The number of atoms in the universe is 10 to the 88. So 10 to the 1,000 is nothing to be sniffed at. It's a very, very, very, very big number.
So the set of all these solutions of string theory were called the string landscape. And the second word is uttered, controversy begins. But I want to tell you, roughly, how it could work. So first, I want to give you a rough idea. How do you get all these zillions of solutions? Where does it come from?
It's actually a very basic property of exponentials. Let me give you a little toy analogy, which is, essentially, exactly how it works in string theory too. Imagine you have a smallish number, not 10 to the 1,000, but just around 1,000. Little wells-- little double wells-- they're not identical. They're all a little different from each other.
And what you can do is put a ball in either the top or the bottom component of each well. So imagine there's some potential energy, say, associated with the ball in one well and the ball in the other one. So because you have roughly 1,000 of these, you have, roughly, 2 to the power of 1,000 different configurations that you could have.
For each one, you can choose whether it's in the top or the bottom. So there's two choices for the first, two choices for the second, two choices for the third. By the time you go out to 1,000, there's 2 to the 1,000 different ways that you could arrange them.
They're not all identical. So if you added up all the energies for every one of the particles, you wouldn't get the same set of numbers. You'd all get a slightly different set of numbers. So we'd get some distribution. You'd get, roughly, 2 to the 1,000 numbers.
The biggest they can get is if they're in the top ones. The smallest they could get is if they're all on the bottom ones. You have to fit 2 to the 1,000 numbers between those two extremes, which aren't very extreme. So you're going to get an incredibly dense-- incredibly dense-- set of possible different energies that you might arrive at. The typical splitting between these energies would be, roughly, 1/2 to the 1,000.
And so that means that, just statistically, for no deep reason-- just statistically-- there is going to be something here whose typical energy is 1/2 to the 1,000, compared to what you would think it is naturally-- just a complete statistical accident.
I didn't have to put in a number that was big as 10 to the 1,000. I just had to put in the number of about 1,000, which is a much more reasonable number, and let the power of exponentials take over. So it's very easy to get an exponentially large number of different possibilities out of relatively simple building blocks.
In string theory, each one of these double wells correspond to some slightly different way that you could have rolled up the extra dimensions, so you get to a four-dimensional world-- and detail different ways. Do you turn on a magnetic field in this direction? Do you do something like that? So they're all just slightly different, discrete, detailed things that you can do. But you'd see, it adds up quickly. And so that's how you can get these 10 to the 1,000-- huge numbers of numbers of solutions.
Now, there is a very important consequence of this, which has to do with the fact that-- now, let's imagine that it's the real situation. So this cartoon is representing one of those configurations that we might get in the actual theory. And let's say that we're talking about one of those 2 to the 1,000 choices. And let's say it happens have a positive vacuum energy-- positive lambda-- big positive Lambda.
There's no reason for it to be small, right?-- big positive Lambda. What would the universe look like? Well, it would expanding. It would be accelerating-- accelerating like mad. Now, in a classical world, that would be all you would ever get. It would sit there accelerating like mad. And that would be that.
But remember, in quantum mechanics, anything that can happen does. And there is some chance to have one of these tumbling events that we talked about. So there's some chance, let's say, for the configuration that was over there to tunnel across that barrier and end up over there. That would be something, now, that has lower energy than the one that we started with.
Now, what would that look like? I have this universe around it, exploding around it. When you tunnel, you can't, everywhere in space at exactly the same time, make this transition. This transition is occurring because of quantum fluctuations. So somewhere, in this region, the fluctuation happened. And luckily, you're able to go over the barrier.
But now, once you're over the barrier on the other side, there's now kinetic energy. So there's a little bubble that's made. It isn't like it's happening everywhere in space. You make a little bubble. But now, that bubble wants to grow. That bubble wants to grow, because there's less energy on the inside than on the [INAUDIBLE].
So the bubble wants to grow. It grows. And it grows at the speed of light. So it grows amazingly fast. So if you started in this high state, you'd go to the low state-- poof. It's expanding out really, really fast. If we ignored, for the moment, that the underlying universe is accelerating, then what would happen is that, here, the bubble would be made. There, the bubble would be made. There, the bubble would be made.
All these bubbles would smash into each other. It would completely destroy the original space. And everything would end up in the new vacuum-- in this new lower vacuum. And then it would happen again. It might happen again. And you would just start from one place. And then, in a few steps, you'd end up in the lowest of all possible energy configurations.
But the situation changes dramatically, because the universe is accelerating. What happens is you make this bubble and it's expanding out at the speed of light. But remember that the acceleration is happening even faster than that. So by the time you make this other bubble in this place and it's expanding at the speed of light, the space between them is growing so quickly that these bubbles just never ram into each other.
And so this inflation keeps going on forever. It just never ends. Space just keeps getting made-- more and more and more of it. You make this bubble. You make that bubble. Inside one of these bubbles, there will be some vacuum energy. So we make another bubble inside that. Inside that one, there will be one. You make another bubble inside that.
And the whole picture goes on forever. It's a dramatic difference by turning on gravity and getting this phenomenon of inflation to take place. So this picture, for obvious reasons, is called eternal inflation. So you make a bubble. A little later, you made a bubble inside that one-- a bubble there, a bubble there, a bubble there. But they never ram into each other.
It's not quite true. They ram into each other occasionally, which is very interesting, but not in a way that changes the story right now. Inflation goes on forever. By the way, every now and then, you jump to an energy density that's negative. Negative energy density doesn't inflate.
It turns out, in this picture, when you hit a negative energy density, the universe instantly hits a big crunch. So there are also some very nasty places in this picture where, if you end up in there, you just crunch instantly. But now, you see, you get an extremely interesting global picture of the universe. No matter where you start-- no matter where you start-- you're going to go down. You'll go up.
You'll go down. You'll go up-- down, up, down. It goes on forever. Every one of these 2 to the 1,000 possibilities is realized somewhere in this space-time. In fact, not only is it realized once, every one of them is realized an infinite number of times.
So that just fascinating. There's 2 to the 1,000 different possible worlds. Or let's call it 10 to the 1,000 possible worlds. And they're all realized somewhere in this gigantic space-- in one of these bubbles somewhere.
So I can draw the picture, also, like this, drawing the bubbles. Well, it's hard to draw accurate pictures. But imagine that you have a universe. And it bubbles off another one as a bubble inside. It bubbles off another one-- another one-- another one. And it's this infinite fractal. It's an infinite fractal.
And I stress-- these are really worlds, even though it's one unique underlying theory. It's a unique underlying theory. It has many solutions. And these solutions will all look at long distances, like one of those menus that we talked about. They'll have their own stick figures. They'll have their own electrons and photons and quarks and gluons and other things like that.
But they'll be different. They'll be different in detail. It's quite remarkable. People used to think that a holy grail of physics would be a unified theory of everything that would unify the strong force, weak force, electromagnetism, and gravity together in one super thing. Often, the wishes we have before we understand things better turn out to be not even as grand as they could have been.
What this theory is doing is unifying our world with 10 to the 1,000 other worlds that would naively look radically different. We're all the same thing. All these worlds are solutions of the same underlying theory. So it's an even deeper notion of unification than I think any of us could have imagined. So there's just one fabric. And it leads to all these different possibilities at very large distances.
OK, but this still doesn't seem to be any help to explain why we found this very, very minuscule energy of the vacuum, except for the following final observation. Let's go to the middle of one of these regions. Let's say-- I don't know-- we go there. And there, the energy is big. The energy of the vacuum is really big.
In that universe, things are exploding every 10 to the minus 43 seconds. It's doubling in size every minus 43 seconds. OK, that universe is just empty. Everything is getting ripped to shreds constantly. Now, let's say a very much smaller fraction of those universes-- roughly 1 over 1 million of those universes, will have a vacuum energy that's 1 million times smaller than Planckian.
OK, in those universes, it's doubling in size every 10 to the minus 40 seconds. That's also empty. 10 to the minus 40 seconds is plenty fast. So you can try to make things smaller. You're looking at a smaller and smaller and smaller fraction of all these possible worlds, where it's just not empty-- simply not empty. It has any chance of having anything in it.
And you find that, if it was going to look anything like our world, even roughly, the value of the vacuum energy cannot be more than, really, a few times what we've observed it to be now. In other words, if we go backward, if we take our universe and ask, how much bigger could we have made the vacuum energy and just not have our universe be empty?-- something very dramatic, like, empty-- full empty.
You can make the vacuum energy, maybe, 10 times bigger, 5 times bigger than its value that we observe. If you make it much bigger than that, our universe is empty. So that's very striking that, actually, the value that we observe is very close to a dangerous value, beyond which it would just be empty. From this global picture, it's like most of the universe is empty. It's empty, empty, empty in incredibly tiny fraction of it.
But a tiny fraction of infinity is a lot. A very tiny fraction of it-- there are places where it's not empty. Now, is it so surprising that we might find ourselves in such a place? We live on a rock called the Earth. We don't live in interstellar space. The volume the Earth takes up, out of the volume of the whole universe, is around 1 part in 10 to the 60. That's not a deep pressing problem of theoretical physics.
There's a good reason we don't live in interstellar space. It's because, how could we? We have to live where there is some structure. So in this picture, most of the universe is lethal and empty, except a tiny few places, like there, where accidentally-- because there are so many possible worlds-- accidentally, the size of the vacuum energy is small enough that we can consistently live there.
This kind of reasoning is often called the Anthropic principle. And it's a really terrible name for it, because it makes you think that it's putting human beings at the center of everything. I hope you see, from the way I've described it, that it's exactly the opposite. This is a much more depressing view of the universe than even the ones that we've had so far.
We are 10 to the 1,000 times less relevant than we thought we were before-- at least. It's a very hostile deadly universe out there. And we're lucky to be in a little corner of it where, accidentally, we can exist-- if this picture is correct. By the way, it's even more bleak than that. If this is the way things are, then that means there are zillions and zillions of different possible states.
That means that, since we have such a tiny, tiny positive value, anything close to us is very likely to have a big negative value. And that means the next thing that's going to happen to us is that we're going to tunnel into a big crunch. So that's the very likely future of our own universe is that everything is going to end up in a big crunch and a very catastrophic end.
So that's unfortunately the best explanation we have, so far, for the smallness of the value of the vacuum energy. I say "unfortunately," because it's demoting our importance in the grand scheme of things a huge amount. And it's simultaneously making it harder for us to come up-- starting from very first principles-- with a unique prediction for what the world should look like.
That's one of the things that physicists hope to do, is to come up with first principles with a unique prediction-- why the mass of the electron is so-and-so? Why is the strength of the weak interaction so-and-so? These 19 numbers-- we hoped there would be some unique underlying theory and would predict those numbers uniquely.
In this picture of the world, there is a unique underlying theory. But there are so many different possible low-energy worlds that those numbers just don't come out uniquely. It's not the fault of the theory. The theory is unique. But the solutions that are complicated enough to look like us-- they have four dimensions and so on-- there's just many, many of them. And that actually has a positive benefit.
There are so many of them that it becomes possible, somewhere in this multiverse, for structure to exist and for us to be here. So that's the question. Are we a tiny part of a vast multiverse? And I think it's clear that if-- and it's a very, very big if-- if it's true, then it's the modern Copernican revolution. In fact, it puts Copernicus to shame. So we're not the center of the solar system or the galaxy-- blah-blah.
But we're one part in 10 to the 1,000 of some vast multiverse that just does not give a damn about our existence in the least. So if that's true-- but people spend a lot of time having polemic philosophical discussions about this. But in fact, what's wonderful about this is it's a problem that's a real physics problem, because there's a major conceptual issue associated with it.
We can make this analogy. But another analogy people like to use is to say the Earth goes around the Sun at a nice distance from the Sun. A little closer in, we'd boil and die. A little farther out, we'd freeze and die.
So that's not because there was some benevolent creator that put us just at the right distance. It's because there's lots and lots of solar systems, probably, lots and lots of planets. Mostly it's too hot. Mostly it's too cold. Sometimes, like Goldilocks, it's just right.
And it's not surprising. Again, we're not surprised with that, because we can build telescopes and see that there are other solar systems, see that these other environments are actually out there. If you can have a gigantic diversity of environments, then it becomes possible to have this sort of explanation for why things seem so perfectly adjusted right around you.
But it's important to be able to see those other environments. And there is a conceptual physics problem here-- no philosophy. There's a conceptual physics problem. Can we see these other universes in any way? Can we build the analog of a telescope to see them? That's the only way we could be convinced that they're there, if there's even some in-principle experiment we could do to see them.
And it seems like we can't, very naively, because we're stuck in this accelerating universe. I told you yesterday, we're stuck in this accelerating universe. What we see out there is everything we're ever going to see. And all of this wonderful multi-verse is out here, somewhere where light from those regions will never, ever, ever make it to us.
So now, this is a really interesting physics problem. Because on the one hand, if you just follow the equations, it tells you those reasons exists. It tells you to trust this global picture, where there's this big multiverse-- everything that we talked about. On the other hand, we appear not to be able to observe any of them directly.
So does that make sense? Is it consistent? Is it just mathematically consistent? Does it make physics sense? This is an open problem. I think it's one of the hardest and most interesting open problems in this part of theoretical physics-- is to see if it's possible to make progress on this purely internal theoretical puzzle.
Someone might come tomorrow and write a paper with a perfect interpretation of the whole thing that's obviously correct. And we'd all be thrilled. I think we'll know the solution when someone hands it to us. But I want to stress, it's not just a philosophical issue of whether we like it or don't like it.
There are some very hard and deep physics problems that are exposed by this picture which, once again-- once again-- tell us that the biggest conceptual puzzles involve the use of the words "quantum mechanics" and "cosmology" in the same sentence. And once again, this issue of emergent time needs to be understood a lot better.
So there are these two problems of understanding why the universe is big, why gravity is weak. I told you that we have a very, very nice candidate set of ideas for why gravity is weak-- finding the hand that holds it up. That idea involves an extension of our notion of space-time to supersymmetry.
There is circumstantial evidence that it's on the right track. And that's something that will be checked experimentally in this decade. So we'll really know something about that, experimentally, soon. So on that front, there's very big help from experiments on the way.
There's also the problem of why the universe is big. For that problem, at the moment, we have no analogous explanation. We have no pencil that holds up the hand. And this picture of the multiverse that I told you is, at the moment, the best attempt we have at a scientific explanation for why this is true.
There is always the other explanation that someone loves us. But if you don't want the explanation that someone loves us and has adjusted the parameters just to allow for our existence, then-- that's a sort of explanation that also fits. I want to stress that it's not some capricious explanation. And maybe you could come up with other ones.
One of the reasons people take it seriously is that it seems to be an inevitable consequence of many of the best ideas we have for resolving the other puzzles. You just follow your nose. And you combine this idea that there could be lots and lots of solutions. That just seems to be easy. It seems to happen in this theory.
You combine that with the fact that, when there's positive energy, the universe inflates, and just those two ingredients alone immediately give you this multiverse picture. And there's nothing you can do about. Whether or not there is ultimately some anthropic principle associated with why we're here, that picture-- that there is this gigantic multiverse with most of the regions being lethal-- just seems to be a consequence of the best theories we have in physics right now.
So perhaps, it's true. Perhaps, it's roughly true. Perhaps, part of it's true. And it's not being interpreted correctly. In the early days of quantum mechanics, it took people 30 years to sort it out, starting from good starts in roughly the right direction. So we don't know. But it's the best we can do right now.
Even there, there's some help coming from experiments. Because experiments, this decade, as we'll discuss tomorrow, are also going to measure something about the acceleration rate of our universe. And while we can't conceive of an experiment that will directly confirm this picture, it could easily be that certain experimental results will just rule it out instantly.
So there are things that can instantly falsify it. And we'll talk about some of them tomorrow too. So after these two lectures of speculation, tomorrow's going to be completely devoted to our experimental friends who, very wisely, pay no attention to us and go back down to their grungy labs and screw around with knobs and dials and actually bang things into each other, see what comes out, which is what's going to dominate a lot of the rest of the activity in this field in the next 10 years.
So that's what tomorrow will be about. Thanks a lot.
I failed. I failed.
YUVAL GROSSMAN: They really love you.
NIMA ARKANI-HAMED: I failed again. I had promised Yuval that, today, I was not going to go one minute over one hour. So I'm very sorry.
YUVAL GROSSMAN: Space-time is doomed, [INAUDIBLE] of his timeframe. If you want to leave, leave. If you want, we'll take a few questions. So if you have some questions, then ask some. We can have another 5 minutes of discussion. Yes?
AUDIENCE: Can you say something about energy creates the [INAUDIBLE]?
NIMA ARKANI-HAMED: Right-- so really the statement is that-- well, the real answer is, no. I can't. But that's because the question isn't a very well-posed question. What I can tell you is this. What I can tell you is that, according to general relativity, energy-mass curves space.
It actually curves space-time, which is very important, not just space. Often, people draw these sort of rubber sheet. There's some rubber sheet analogy for what the curving space-time looks like. That's a nice analogy for just curving space. But it's really curving space-time. And in cosmology, the time parts are very important.
If you're curving something, it means that the two lines can't keep going and keeping exactly the same distance from each other forever. Something is flat. You have two parallel lines. They'll keep a constant distance between them together. But it might be curved. And they would meet each other. Or they'll get further and further apart from each other.
And the fact that they get further and further apart from each other is a reflection of the underlying curvature. So if you take two lines on the surface of a sphere and you send them up, then, down at the equator, they're far apart. But they'll converge at the North Pole. And they'll hit each other. So the fact that they get closer to each other and hit each other is because the surface of that sphere, or the surface of the earth, is curved.
Now, what happens is that, in general relativity, energy and mass curve space-time. And so exactly the same thing happens, not in the analogy the motion in space on the surface of the sphere, but the motion in time, as the universe gets bigger and bigger. In fact, the universe getting bigger and bigger is really the way we interpret the fact that these two lines are now getting further and further apart from each other.
They're getting further and further apart from each other as a reflection of, again, the curvature of the space-time. So that's just what the theory says. The theory says that there's curvature of space-time. And it forces the actual space to be getting bigger.
So when I say there's space being invented all the time, I mean, through no known mechanism. It just keeps getting bigger. A very important lesson we've learned for hundreds of years is that we shouldn't get too caught up in what people sometimes call the word problem in physics. When you have a theory, it's actually the theory that tells you the questions that make sense to ask. It's not you ahead of time.
It's the theory or nature that tells you what the questions that are sensible to ask are. And so it just says that space grows. You can ask, why, how, but it's not a--
AUDIENCE: [INAUDIBLE] expanding geometry.
NIMA ARKANI-HAMED: Right.
AUDIENCE: What' we're seeing is the expanding universe--
NIMA ARKANI-HAMED: that's right
AUDIENCE: --it's a static geometry. [INAUDIBLE].
NIMA ARKANI-HAMED: Well, I'm saying--
NIMA ARKANI-HAMED: So the word "static" involves time. But if you like, there is a space-time. There is a--
NIMA ARKANI-HAMED: --space-time. That's right. There is a space-time geometry. There is a space-time geometry. And things are just moving. And that's moving. So I'm doing it too. Things are lines, in that there are other trajectories in that space-time geometry. And the trajectories have the property that, in a direction that-- for other reasons we'll call time, because it's a direction in which you can causally separate events-- in the direction you happen to call time, you find that the lines in that geometry diverge from each other. so that's-- right.
YUVAL GROSSMAN: Do you have one final question? You--
AUDIENCE: Yeah, I was wondering-- I have a question from last time. [INAUDIBLE] I was wondering how you presumed an anti-de Sitter space [INAUDIBLE] capacity, because it's similar to [INAUDIBLE]. I was also wondering how that fits with, I guess, de Sitter space-time and [INAUDIBLE]--
NIMA ARKANI-HAMED: Right-- right-- right.
NIMA ARKANI-HAMED: So--
YUVAL GROSSMAN: Can you repeat the question?
NIMA ARKANI-HAMED: Yeah, so the question was that, yesterday, I said that this picture we have for what gravity in anti-de Sitter space looks like. That it's just completely described by a normal theory that lives on the boundary. I explained yesterday how that picture allows us to resolve the information paradox and resolve it by saying that there is no information paradox. The information comes back out. Conservative quantum mechanics wins.
And the question is, was it very important for it to be empty de Sitter space in that argument? And what happens instead to de Sitter space? Which is what the uniformly accelerating universe is technically called. So I think the correct statement is that, if you want to talk about making just this normal small black hole-- a black hole in this room, a black hole the size of my head.
If you want to make a black hole in the size of my head and you knew you aimed laser beams. You make the black hole. You wait for it to evaporate. You see things that go out. The question of whether information is or isn't lost in that process is very, very unlikely to depend on whether, on the 10 billion year light year length scale, the universe happens to be negatively curved or positively curved-- if on the 10 billion years time scale it happens to be anti-de Sitter space or de Sitter space.
Maybe that's wrong. Maybe what's going on in this room depends, in some crazily subtle way, on what's going on 10 billion light years from here. But if that's the case, it will have many more interesting consequences than the black hole information problem. We'll have to come to grips with it with many, many other things. It's staggeringly unlikely to be true.
But if we just assume that it can't have any effect on what's going on in here, then for the purposes of this thought experiment-- for the purpose of the thought experiment of making a black hole and watching it evaporate-- it's perfectly good enough to imagine-- imagine-- a slightly different universe that is not ours, but where we lived in anti-de Sitter space instead-- curved on the 10 billion year time scale.
So in that universe, it's simply essentially proven that there's no information lost. Now, that doesn't mean that we're done, because there's many, many other questions that we want to have the answer to, other than just that one. And in fact, the fact that our universe is not the static tin can but that, on the 10 billion year time scale, right now, is actually accelerating, totally removes-- completely removes-- the tools that we have developed to give some precise definition of what's going on-- a precise understanding of what is going on.
And that's what I talked about yesterday. But there's lots and lots of things we're going to have to understand before we can come up with that.
NIMA ARKANI-HAMED: Well, again, if the black hole is much smaller than 10 billion light years, then it's very unlikely that it matters. Maybe, if you're talking about a black hole that's almost as big as the de Sitter space, then it will matter a lot, of course. But that's, again, at least in our universe, that's a black hole that's so big that we have, once again, other trouble if it's lying around.
YUVAL GROSSMAN: OK, so we have one more lecture tomorrow. And thank you very much.
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Renowned theoretical physicist Nima Arkani-Hamed delivered the fourth in his series of five Messenger lectures on "The Future of Fundamental Physics" Oct. 7.
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.