Topics in String Theory | Lecture 1
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01:34:22
Computer animation
Transcript: English(auto-generated)
00:05
Stanford University. Let's start with some philosophy. Let's start with some general philosophical principle.
00:21
It's a principle that philosophers call reductionism. Reductionism is the principle or the philosophy that big things are made out of little things and little things are made out of littler things. That's one element of reductionism. How many people would agree with reductionism here?
00:44
Yeah. I mean, you know, molecules are made out of atoms. Atoms are made out of electrons and nuclei. Nuclei are made out of protons and neutrons. Protons and neutrons are made out of quarks and gluons and so forth.
01:04
I call that the building block theory that houses are made out of bricks. Bricks are made out of molecules. And nobody in their right mind mistakes a house for a brick. We all know the bricks from the houses. The bricks are smaller than the houses.
01:21
They're also simpler than the houses. So that's another element of reductionism. As you go deeper and deeper into the layers of reductionism, things get simpler. Or at least we hope they do. That's a pious hope of reductionism.
01:41
I think from what we've learned both from string theory, from the quantum mechanics of gravity and so forth, that modern theories really do spell the end of reductionism. But before you end reductionism, it's interesting to ask how well it does as a philosophy
02:01
and as a theory of elementary particles. If reductionism is right, particularly in that aspect which has to do with simplicity as you go deeper and deeper, you might have expected that by now elementary particle physics would be pretty simple.
02:23
We've gone several, several layers. And is it simple? The answer is no. It is very, very complicated. And to measure how complicated it is, you can simply ask how many different kinds of particles
02:40
are there, and in particular, particles which are unexplained. Well, there's something like about 75 different particles, all of which in the standard model of particle physics. In the standard model of particle physics, maybe only about 20 or maybe even a little bit less
03:02
than that independent particles that don't have tight relationships between each other. So it's maybe 10 to 15 or 20 distinct different particles, depending on how you count. How many parameters? Parameters, again, mean unexplained constants that have
03:20
to go into the theory to make sense out of it. Well, about 20, 20 distinct parameters. But the theory is definitely incomplete. We know that it's incomplete. It doesn't have gravity. It doesn't have dark matter. It doesn't have the particles that are necessary for inflation.
03:44
The theory of cosmic inflation to make sense. And it has a terrible fine tuning problem. We've talked about that fine tuning problem. That in order to overcome this fine tuning problem,
04:01
people introduce things like supersymmetry. My guess is that supersymmetry will really be discovered at the LHC. But if it does, it adds about 100 new parameters. Well, I take that back. It's 100 plus N, where N is an unknown number.
04:24
But that N is not zero because it's necessary for understanding the breaking of supersymmetry, why supersymmetry is not a real. Another 100 parameters, a doubling of the number of all of the particles, plus a whole bunch of stuff that's necessary
04:41
for inflation and other things. By the time you're finished, the standard model of particle physics, together with all of the bells and whistles that have to be added to understand everything, let's say. There's a theory with about 200 parameters, huge number of particles, and totally unexplained connections.
05:05
So it's not simple. It's very, very complicated. And complicated, either you have to say, well, we haven't gotten anywhere near the bottom yet. Or we just have to admit that maybe reductionism isn't working.
05:23
But the fact, the idea that reductionism isn't working, that's not what I meant when I said modern theories sort of spell the end of reductionism. What I meant was a more theoretical fact. A more theoretical fact based on both quantum field theory and string theory.
05:43
So I'll tell you a little bit about what is known. In particular, about the idea that endlessly, well, not necessarily endlessly, but that we can always tell the bricks from the houses. Is it really always true that we can tell which thing is more fundamental than
06:03
which thing? I'm gonna give you a couple of examples of places where in quantum field theory, that idea has broken down, broken down badly. The first example was an example of a very simple kind. I'm not going to explain this. I'm just gonna tell you about it.
06:22
It was studying the quantum field theory of one-dimensional systems, models, models in which there was time and only one dimension of space. Very easy to draw. A dimension of space and a dimension of time, and that's all there is.
06:43
And particles, what was discovered is that there's a simple, there are a number, just in fact almost every theory of this type can be described in terms of particles which are fermions. Remember what fermions are? Fermions are particles that satisfy the Pauli exclusion principle.
07:04
They're the particles which have this odd behavior that they can't go into, that you can't put two of them into the same state. Electrons are fermions, quarks are fermions, photons are not fermions, they're bosons, the opposite of a fermion is a boson,
07:22
and all particles are either fermions or bosons. So in this mathematical theory, you start with some particles which are fermions. The fermion field, the object which describes the fermions, which creates and annihilates the fermions, we call psi.
07:45
The mathematical terminology is not important here. What is important is that the basic starting point is a field theory of fermions. Now, what happens if you put two fermions together? What do you make?
08:03
If you put two of them identical ones together, you make zero. But supposing two not quite identical ones. One sort of right next to the other, but not right on top of it. Then you make a boson, okay? For example, protons are fermions, electrons are fermions, hydrogen atoms are bosons, okay?
08:24
So you take a fermion and a boson, two fermions, and you put them together, almost together. Maybe there's some attractive force between them which holds them together. And these particles, which are now composites, they're clearly composites.
08:42
They can move up and down. They're also particles, but they're composite particles. Those composite particles are bosons, and bosons are also described by fields. You would think that it's not really a fundamental field. You would think that it's a field that is some effective description
09:03
of the two particles stuck together, and you call it phi. Phi creates bosons. It creates pairs of these fermions. That sounds very straightforward, but what was then discovered in these field theories
09:22
is that you could rewrite exactly the same field theory in terms of an underlying starting point which started with the bosons. Let's draw that field theory over here. Now you start with the bosons. The fermions cannot be composites of the bosons because any number of bosons put together
09:45
make another boson, but these fermions can be described in a totally new way. They're described, if we plot, this is not plotting time anymore. This is plotting the field phi as what's called a kink in the field phi,
10:02
a place where the field phi jumps, smoothly jumps. It doesn't jump suddenly. It smoothly jumps over a distance, some distance, jumps from one value to another. It's called a kink. It's called a kink. If you want to picture it, I should have taken off my belt.
10:22
Well, I won't take off my belt, but imagine my belt. Here it is, and here I've laid it out on the blackboard so that it's not twisted. That's got no kink. Now, take the belt and twist it.
10:42
Rotate this end around by two pi, so it's twisted once. It comes back to its original configuration over here, its original configuration over here, but in between, it's twisted. That's a kink. That's a kink in my belt.
11:01
I often do that when I put my belt on and discover two hours later when I'm talking to somebody that my belt is on wrong. That's called a kink. The bizarre thing is that these fermions that we thought we started with, the bricks which built the houses, the fermion bricks which built the boson
11:23
houses, can now be re-represented as kinks in the boson field. Kinks, which are extended, thick, and massive. Much heavier than the bosons.
11:42
Which are the houses? Which are the bricks? Nobody can say it's entirely equivalent. There are parameters in such a theory. Field theories have parameters. It turns out that for some values of some ranges of the parameters, it's much more convenient to think of the fermions as the fundamental
12:04
building blocks, and for another range of the parameters, the bosons are much more efficient at studying the theory, and they are the more useful building blocks. It simply becomes a matter of which is more useful. Is it more useful to think of psi, the fermions, or
12:23
phi, the bosons, as the fundamental objects of the theory? And that depends on the parameters. That depends on a coupling constant. A coupling constant that's usually called G. It doesn't matter what it's called. So, starting with very small G, you discover that it's much more
12:43
useful to think of the fermions as the starting point. Easy to deal with, easy to study. These things are composites that are held together by complicated forces. Now you start changing this coupling constant and increasing it and
13:01
increasing, oh, incidentally, when that G is very small, let's see, that kink is very tight, very small like that. Now you start changing the, and that's why the fermion is a small object.
13:21
The fermion is a small object because it's a small kink. Now you start tuning the coupling constant, making it stronger and stronger. What happens is the kink starts to spread out. It gets less and less point-like. But the boson starts to behave more and more like a simple elementary object.
13:43
So the question of which is fundamental and which is composite doesn't have a unique answer. By varying the constants, you can morph, you can make one thing go into the other. The houses go into the bricks, so to speak.
14:00
That was a case that was known, oh, gee, since I was a very young physicist. The key word is called bosonization. It's making a fermion out of bosons, or four bosons out of fermions. Are there any things like this in elementary particle physics?
14:23
It is believed that there are, and the belief centers around electric and magnetic monopoles. Let me tell you what an electric and magnetic monopole is. An electric monopole could be an electron, could be any charged particle, ordinary charged particle, surrounded by an electric field, usual electric field.
14:48
And let's take these, let's take the particle to be, let's say an electron. The electric charge of an electron is very weak, as a matter of fact. It's a very weak electric charge.
15:02
The amount of charge, and not just because the electron is small, that's actually not the issue. There's a dimensionless quantity. What's a dimensionless quantity called? Anybody know? A fine structure constant? A fine, yeah. The fine structure constant is a measure of how much an electron would
15:21
radiate if you, you know, if you accelerated it suddenly. Or if you plowed it into an anode. If you plowed it into a stop, into a, how much would it radiate? How many photons would it radiate? The answer is that an electron will radiate, on the average,
15:43
about one over a hundred photons. Another way of saying it is the electron will only radiate about one out of a hundred times when it's stopped, radiate a photon. So the electron charge is very weak. And the electron is very simple.
16:01
The electric field around it is rather, is rather weak, because the electric charge is weak. And it doesn't do very much to the neighboring space around it. It doesn't polarize the vacuum. It doesn't create electron-positron pairs to any appreciable amount. Electron is simple.
16:20
It is also believed that in nature, there do exist magnetic monopoles. Most physicists, like myself, believe in the existence of magnetic monopoles. They, they come up in so many theories that by now, they, but they've never been discovered.
16:41
They've never been discovered in the laboratory. A magnetic monopole is like the end of a bar magnet. North, south. If you just imagine the end of the bar magnet with the bar magnet itself being so thin that you couldn't see it, then waving around the bar magnet would look
17:04
like waving around a magnetic monopole where the magnetic field comes out of the magnetic monopole exactly the same way the electric field comes out of the electric monopole. The monopoles that theoretical physics seems to produce have a magnetic charge which is huge, very large.
17:30
The force between two magnetic monopoles would be 10,000 times larger than the force between two electrons at the same distance. That means that the magnetic monopoles make large fields around them and do very,
17:46
very complicated things, make a very complicated mess around them. That complicated mess is extended. It's broad, the same way that the kink was broad, and it's massive. It's very, very heavy because there's so much going on in the vicinity of the monopole.
18:04
I'm not really talking about the end of a bar magnet. I'm talking about the end of the bar magnet without the bar magnet, magnetic monopoles. They haven't been discovered in the laboratory because they're too heavy to make. Will they ever be discovered? Perhaps.
18:21
But most theorists believe in them. But the point is, the more important point is, the mathematics of quantum electrodynamics, which contains monopoles and electrons, is totally unclear about which of them is the elementary particle.
18:40
It depends on the fine structure constantly. It depends on alpha, the fine structure constant. If the fine structure constant, which is basically the square of the electric charge of the electron, if that's much, much less than one, then the electron is the simple one. It's simple, it's almost point-like, it has very little structure, the charge is very weak.
19:05
The monopole has a very, very complicated structure in that limit. The magnetic field is very powerful and does very complicated things to space around it. And that's why it's heavy. What happens if you could, imagine now that you had a dial,
19:24
that you could start dialing, re-dialing the fine structure constant. Start increasing it. What happens is you start to increase it, the field surrounding the electron becomes stronger. Effectively, the electric charge is getting larger.
19:42
The field is getting stronger. It starts to do more complicated things in the vicinity of the electron. What happens to the magnetic monopole? The magnetic monopole starts to shrink. This is not something that I can explain easily. But the fact is it starts to shrink, it gets smaller and smaller.
20:02
It gets lighter and lighter. The electron gets heavier and heavier as alpha gets large. When alpha gets bigger than one, they simply interchange. The magnetic monopole becomes light and small and fundamental. The electron would become heavy, complicated, and full of all kinds of structure.
20:27
And basically, they would just interchange themselves. So again, which is the building block? Is it the electron whose complicated structure here is making up the monopole?
20:43
Or is it the monopole, which is simple, and whose complicated structure is making up the electron? Modern quantum field theories say they're equivalent. You can't tell the difference. Of course, you may want to choose one of them as the starting point. Depending on the fine structure constant,
21:01
it may be more convenient to think of the electrons as fundamental. And less convenient to think about the monopole. And that, of course, is true. And that's why we use electrons as starting points for quantum electrodynamics and not monopoles. Yeah.
21:21
Back to your philosophical point. If there's a belief that reductionism is not the correct view of things, why do you think physicists use calculus, which is the most reductionist of mathematical tools, to constantly determine calculus? Calculus is not necessarily reductionist.
21:42
It just says everything is smooth. Smoothly varying. But it doesn't, in any way, tell you what the fundamental objects are. But with a derivative, you chop it up into teeny-weeny little points to the x's.
22:01
Right. You chop up the things into little distances, and you ask, what's in those little distances? And that tells you what the fundamental things are. In quantum field theory, it's just an endless hierarchy of distance scales.
22:24
And so, you never get to the point where you can decide which one is fundamental. Like a fractal. Like a fractal. Very much like a fractal. For example, describing a curve, you can use it using a derivative. Or one of the few non-reductionist models is general relativity,
22:44
where you describe it as a geodesic under a... Quantum fields fluctuate. And they fluctuate on every scale. So they're never smooth. They're never smooth. And in some sense, some of the great difficulties of understanding quantum field theory,
23:03
the reasons that mathematicians have so much trouble with it, is sort of because, in a certain sense, calculus does break down. In studying the fields, they fluctuate too much. They vary too much. But let's not get into that now.
23:21
All right. Now, what does string theory say? Does string theory have an answer to what are the fundamental building blocks? Well, obviously, string theory has an answer for what the fundamental building blocks is. It must be strings, right? OK. So let me tell you a little bit about... We talked about D-branes, yes?
23:43
All right. So I will just very quickly just remind you what a D-brain is. We don't need to know a lot about the mathematics. Pictures are good enough. D-branes are objects that were discovered through a fairly indirect mathematical route.
24:08
They are part of the theory. You can't get rid of them. They're stuck with it. They're objects which are, first of all, very heavy.
24:20
They could be... They come in different dimensionality. The simplest one is called the D-zero brain. And zero stands for the dimension... What's the dimension of a point? The dimensionality of a point? First of all, what's the dimensionality of a line? One dimension. Dimensionality of a membrane or a two-dimensional surface?
24:42
Two. What's the dimensionality of a point? Zero. So in that sense, particles, point particles, are called zero-dimensional objects. Even if they're not absolute points, they're still regarded as zero-dimensional.
25:06
They are not extended in higher dimensions. So a particle is a D-zero brain. The word brain, incidentally, B-R-A-N-E, brain comes from membrane. A membrane, a surface, is a two-brain or a two-brain, two-dimensional brain.
25:25
What's a string? A one-brain. What's a three-dimensional block of solid stuff? It's a three-brain. And can you picture a four-brain? No, we don't have enough directions to put it into.
25:42
But if we had more directions, we could make four-brains. All right. So a D-zero brain is a kind of particle. The D stands for the mathematician Dirichlet, and it's not important. But the property of these D-brains in string theory is that there are places where strings can end.
26:00
Fundamental strings. Let's call them F-strings. This is an F-string, F standing for fundamental. The building blocks, the things that gravitons are made out of. All the good stuff that we've talked about up until now, the fundamental strings. And D-zero brains are just sites on which a fundamental string can end. In fact, any number of fundamental strings can end on a D-zero brain.
26:24
And that means that D-zero brains can have strings attached to them. And they typically do. If you were to probe a D-zero brain by scattering something off it, you would find out that it has a collection of strings attached to it like that.
26:43
In fact, the harder you probe it, the more string you would find, closer and closer in, and you would eventually come to the conclusion that the D-brain is in some sense made up out of strings. But it's got a lot of strings, and it's heavy. It's much, much heavier than the ordinary strings themselves.
27:03
It's a little core that's very massive, and that core is a place where strings can end. The mathematics that went into this, through its discovery and so forth, is less interesting than the fact that these things are necessarily forced to exist. They're massive, they're complicated, and they are there.
27:23
They're in the theory. Now, that's a D-zero brain. There are also D-one brains. A D-one brain is like a string. I just want to thicken it out, because it's much heavier than an ordinary string.
27:42
Much more mass per unit length. But it also has the property that it's a place where ordinary strings, fundamental strings, can end. And so, again, it's kind of an object which is made up out of these strings.
28:01
A sort of cable. A cable, a thick cable. A thick cable, much thicker than the ordinary strings, and much heavier. Heavier in the sense that per unit length, its mass is much larger. Very much in a sense, well, let's draw two strings next to each other. Here's a D string, and here's an F string.
28:23
A D-one brain can also be called a D string. Here's an F string, a fundamental string. It's thin, it's narrow, it's light. These two objects are related in very much the same way that, this one and this one,
28:47
are related in very much the same way as, can you guess what I'm going to say next? Monopoles and electrons. The fundamental strings are like the electrons, the building blocks, the starting points for string theory.
29:00
These objects are big, heavy, composite structures which are made out of cables of lots of string. They're heavy, and they're obviously composite. String theory has, I said it has no parameters. Now we're going to come back in a minute to the question of whether it has parameters or not.
29:24
For practical purposes for the moment, it does have a parameter. The parameter is a coupling constant, let's call it G. G is a coupling constant, a parameter of the theory, which basically tells you the probability that if a string is wiggling around, it might split in half.
29:45
It's very similar in many ways to the probability that an electron, when accelerated, will emit a photon, string wiggling around, if you grab a piece of it and pull it, it might, it can break. The probability for that is called the coupling constant.
30:02
If the coupling constant is very small, then the F strings are light, they're thin, and they look very fundamental, point-like. Well, not point-like, but line-like. When G is very small, the D string is very heavy, very complicated, and full of F strings.
30:26
Guess what happens as you start increasing G? As you start increasing G, the fundamental string here tends to break off little pieces. Those little pieces don't disappear and fly off, they hang around.
30:42
And they form a kind of, I don't know what to call it, an atmosphere around the fundamental string. And the fundamental string gets more and more complicated. In the same way that the electron got complicated when you started to increase the fine structure constant, the fundamental string starts to develop structures.
31:04
At the same time, well, at the same time, the D string starts to get simpler. The fundamental string gets heavier. Because it gets heavier, it gets harder and harder for the D string to produce fundamental string. And so these structures get thinned out.
31:23
As they get thinned out, the D string gets thinner and thinner. Eventually, at some point, when G is about one, they start to look exactly like each other. And then if you go to even larger coupling constant, the D string gets very simple,
31:40
turns into a thin line-like object, and the fundamental string just gets as complicated as the D string was originally. Which one describes, or which one of these strings, when they form little loops, create particles, create gravitons, create photons, and so forth?
32:02
Well, if G is much less than one, then the fundamental strings, when they close back on themselves, form the particles, the ordinary particles of string theory. But as G gets larger and larger, these things get more and more massive.
32:24
In fact, eventually they turn into black holes. And what's left over is the D strings, which get lighter and lighter, and the graviton is made up out of the D strings. This is called D string fundamental string duality.
32:41
It's not the usual name for it. It's usually called S duality. I do not know what S stands for. I didn't make up the term. I don't know why it's called. Oh, strength duality. Strength. Yeah, strength of the coupling constant. So, again, we find this pattern that you can't say once and for all which thing is more fundamental than which.
33:05
You just find them morphing into each other. Now they morph into each other as the coupling constant varies. But at least you could say, well, at least you can say that if the coupling constant is small, then it's profitable to think of the fundamental strings as fundamental.
33:22
If the coupling constant is very large, switch them. The problem with that is the coupling constant is something that can vary in space. It's a field. G in string theory is not a constant. It's a thing which can vary from place to place. It satisfies field equations just like the gravitational field.
33:49
And so you can easily have a situation in the mathematically idealized string theory where the coupling constant goes from very strong to very weak as you move across the universe.
34:02
And in one place, the D strings are fundamental. In the other place, the F strings are fundamental. And in between, nothing is simple. That's the character of string theory. On a cosmological scale, if it varied or became less massive than F, wouldn't that have an effect on spectra and chemistry?
34:26
Absolutely. That's how we know. That's one of the ways we know that string theory, the mathematically precise version of string theory, is not our world. Is there a dual for the B-tube ring?
34:44
We'll talk about that soon. And there's a fundamental dual for that. Yeah. Yeah. There is. Five rings. Five rings. Just trying to get it straight in my mind.
35:02
The greater likelihood of splitting makes complexity in the F string? Is that why? Yeah. Yeah. Let's go back to quantum electrodynamics for a minute. Now my vertical axis is time. And here's an electron world line.
35:23
It's a point. That means it's a very thin world line. It's not a string. Vertical, remember, vertical for a physicist always means time. Horizontal means space. All right. So here's a point electron moving through time, so to speak.
35:42
The point electron emits and absorbs photons. Now, when the fine structure constant is very small, the emission and absorption of photons is very intermittent. Meaning to say that there aren't very many of these photons being emitted.
36:04
What about the photons themselves? Well, a photon can create and annihilate an electron-positron pair. So that means that the photons can create electron-positron pairs.
36:24
But now each one of these little electrons here can also emit photons. There's a sort of unending hierarchy at smaller and smaller distance scale of structure within the electron.
36:40
As long as the coupling constant is weak, this is a relatively small effect. In fact, it's a small effect. And the electron in the laboratory looks pretty darn point-like. You have to work very hard to scatter things off it and see that the electron has this composite structure there.
37:05
Where does the energy come from? The energy needed for this process is part of the mass of the electron.
37:20
It is part of the mass of the electron. It is the mass of the electron. Where did the energy come from to create the coulomb field around the electron? Well, the point is you don't start without the coulomb field. The coulomb field was always there. Yes. I see things not accurately enough.
37:50
I see two electron pairs being produced. And I don't see the mass of the electron enough to produce an electron pair.
38:01
Will it help if I send it to virtual pairs? Well, obviously you're skinned by the skin of your teeth if you have virtual. No, but mass and energy are the same thing. And so when you say the mass of the electron, you're basically including the energy needed in this concept. All right, but what is that energy? That energy is a kind of potential energy.
38:22
It's a kind of potential energy that's connected with the interactions between the electrons and the photons. The energy of a system in quantum electrodynamics is not just the energy of the electrons plus the energy of the photons. There's also an interaction energy between them.
38:42
And that interaction energy is the source of this. All right, but it's an empirical fact that if you scatter things off an electron at high enough energy, you will see this structure around the electron.
39:06
Well, okay, we can debate whether the energy of the experiment is producing what you see or whether it's seeing what you see. We can debate that.
39:20
But the fact of the matter is that when you scatter things off the electron, what happens is complicated. What happens is, well, it's not so complicated. Most of the times you don't see anything. About 1% of the time you see something. In deep brains, you said that for a couple of constants small, you said the mass of the D1 brain is more than the mass of the F string.
39:51
Would the tension also be more? Yeah, yeah, the tension means the mass per unit length.
40:01
So mass per unit length is called the tension. Right, exactly, energy per unit length. All right, now, as I said, as the fine structure constant starts to get bigger and bigger, this structure starts to proliferate. And the result is that the electron develops this very complicated structure.
40:25
It's no longer something which is very rare or very dilute. The electron gets big, gets heavy, gets all the structure there. Very, very similar thing happens to a string. What is this coupling constant G?
40:42
This coupling constant is the probability that if the string fluctuates, if it undergoes a quantum fluctuation, let's say to a configuration like that, then it's basically the probability that the string splits off and forms a little sort of satellite string around the original string.
41:06
As the coupling constant gets larger and larger, a very similar thing happens. The satellite strings start to proliferate and they form a structure surrounding the string the same way that the electron-positron pairs in the photons surrounded the electron.
41:24
They make it heavier, they give it a structure, and the result is that the F string starts to look more and more like the D string. In the meantime, the D string has more and more trouble emitting or producing F strings.
41:45
Why? Because those F strings are getting heavier and heavier. The result is that the D string gets less and less structure and becomes more like the F string. That's another example of a duality.
42:01
These things are called dualities. This one's called S-duality. The name is not important. It interchanges fundamental strings with D strings. The mathematics of this by now is very tight, even though I'm not trying at all to give you the mathematics.
42:24
Now, there are different versions of string theory. The mathematics of them is not so important, but there are different versions. In one version, all of the D-branes are odd-dimensional.
42:45
So that means that there are D-1-branes, D-3-branes, D-5-branes. How do you stick a D-5-brane into space? We don't have enough dimensions of space. Well, remember that string theory is fundamentally a 10-dimensional theory.
43:03
You've got a lot of extra dimensions. String theory has enough dimensions that you can put in things up to about 8-branes. And then you run out of directions to put the branes in. So one version of string theory, the mathematics tells you that there must be D-1, D-3, D-5, D-7-branes.
43:28
In another version of string theory, which is closely related but different, there are even-dimensional branes. No string theory has both odd-dimensional D-branes and even-dimensional.
43:42
It's just a fact that no version of it has both. This is by no means transparent. I'm telling you facts more than I'm telling you explanations. It would take many hours of mathematics to explain why that's true, but nevertheless, this is a fact.
44:02
So let's go to the version of string theory which has even-dimensional branes instead of odd-dimensional. It doesn't have D-strings. It has D-zero branes. It has point-like particles, which are not quite point-like, but which are very complicated and full of string.
44:25
And it also has fundamental strings that make gravitons and so forth. That's the description when the coupling constant G is much, much less than one. This theory does something very different as G starts to get large.
44:45
It was a great puzzle that nobody knew the answer to. What happens to these objects as G starts to get large? This can't become this. This is a point-like thing. This is a string which could be spread out all over the place.
45:00
There are different kinds of creatures. It's not the case that one will go back and forth into the other. That's not the way it works. Something much more bizarre happens. So I will tell you. Let's see. Before I tell you, I have to...
45:26
I'm going to tell you what happens, and perhaps in the second hour, I can tell you what it means for it to happen. What happens is that a new dimension as G gets large, a new dimension of space materializes.
45:44
Now, that's crazy. That's the silliest thing I ever heard. A new dimension of space materializes. How can a dimension of space materialize? Well, it can't. But what can happen is a very small compact direction can start to expand.
46:01
I'm going to show you how it works to some extent, but let's just begin with that. Let's take ordinary space to start with to be two-dimensional, just for pictures. Really, we're talking about ten-dimensional string theory. Let's take ordinary space.
46:21
How many directions of space does ten-dimensional string theory have? No. Nine. The tenth dimension is time. Right. Okay. So when somebody tells you ten-dimensional string theory, they're talking about a theory with nine dimensions of space. Okay. So let's take a theory with two dimensions of space, just because I can draw it on the blackboard.
46:44
It's not the right theory, but let's just draw it on the blackboard. Here's two dimensions of space. Now, maybe secretly, that two-dimensional space is really three-dimensional. How could it really be three-dimensional?
47:02
It could be three-dimensional because there could be a thickness to it. We could imagine a world, sort of a peanut butter sandwich, with a piece of bread on this side, a piece of bread on this side,
47:26
the bread being infinitely thin, and the peanut butter being real space in between. But with a special rule. The special rule is that when an object goes out here, it reappears at the bottom.
47:42
That's the idea of compactification, of periodicity, that there really isn't an edge to it, but when you go out one end, when you go out on the top piece of bread, you reappear on the bottom piece of bread. Then there's no real edge. Somebody moving vertically would not notice the edge because when he got to the top piece of bread,
48:04
he would just reappear at the bottom piece of bread. That's the idea of one compact dimension. Now, if the compact dimension was small enough, it might not be noticeable to the physicists that live in this world
48:20
that the direction has a little, that there's this extra dimension. That this direction has some, that there's some thickness to the world along a direction that they didn't notice. So they would call this world two-dimensional. What happens as G starts to increase is that the peanut butter sandwich gets thicker and thicker and thicker.
48:48
And eventually, when G gets very large, a whole new dimension of space materializes,
49:01
which the physicists who lived in here would not be able to ignore anymore. They would have discovered that they really live in a world with an extra dimension. That is what happens to this theory, this theory that has D0 brains and strings. Okay, now you say, well, what happens to the D0 brains?
49:22
The D0 brains start getting lighter and lighter, just the same way that the D1 brains did when G gets large. They start getting lighter and lighter and lighter, more and more simple, but what do they turn into? They turn into the gravitons in this extra dimensional theory.
49:44
Just the ordinary gravitons, the ordinary elementary particles that live in this extra dimensional theory. This new theory is now 11 dimensional. We thought it was string theory with only 10 dimensions, and when we started increasing this coupling constant,
50:02
we discovered another dimension of space, and these D0 brains just turned into the gravitons that exist in here. In other words, again, very, very complicated objects turn into very simple light objects.
50:20
Let me tell you what happens to the strings. To understand the strings, go back to the thin sandwich. Go back to the very thin sandwich.
50:41
Now, remember, I told you that this theory has even dimensional brains. Zero is even, so it has D0 brains, but it also has D2 brains, D4 brains, D6 brains, but concentrate in particular on D2 brains. What does a D2 brain mean? It means a membrane. It means a membrane.
51:02
You could have two kinds of membranes stuck into this sandwich. A membrane simply means a surface, a surface of energy. You could stick in a membrane in between the floor and the ceiling, in between the two pieces of bread, sort of embedded in the peanut butter.
51:24
Or if you like, you could think of the top piece of bread as the ceiling, the bottom piece of bread as the floor, and then the two brains stuck in between would be a floating magic carpet that just hovered halfway in between. That's one kind of D2 brain you could have.
51:42
There's another kind that you could have, and the other kind is a kind of ribbon. Let's see if I can draw it.
52:01
It goes from the floor to the ceiling, but it's a ribbon sort of stretched between the floor and the ceiling, vertically, which is extended in the other directions. What happens when the floor and the ceiling get closer and closer?
52:23
What happens to this ribbon? It starts to look more and more like a string. It starts to look more and more like a point-like string. And so when G is very small, not a point-like string, but a line-like string,
52:41
the line-like strings are just these membranes which are oriented vertically in this direction here. And there are also D0 brains, D0 brains being very heavy. Now you start to increase the coupling constant.
53:02
The floor and the ceiling start to separate. The D0 brains just turn into gravitons. They turn into just gravitons moving in the extra dimension. And they're very simple. They're just simple elementary particles in the higher dimensional theory.
53:20
What about the membranes, or what about the strings? The strings now become very, very unstring-like. Very, very unstring-like. They have a lot of membrane in them. They're stretched a long ways. They're very heavy. Why are they so heavy?
53:41
Because there's so much material there vertically here. They turn into something very heavy. The D brains turned into something very light. This is an extremely bizarre story. It is one which is the mathematics was discovered by a bunch of people.
54:04
And the consistency of it, the requirement for it, the need of it was, there was a lot of heavy mathematics which went into it. The need for it to be consistent involved conjectures, mathematical conjectures,
54:23
which the physicists didn't know how to prove. There were conjectures about mathematical structures which mathematicians knew about. The mathematicians had no idea about these conjectures. They'd never heard of these conjectures. But when the physicists told them, look, for these ideas to make any sense, such and such a mathematical theorem has to be true,
54:44
the mathematicians went back and said, oh, yeah, those theorems turned out to be true. So there's really very little doubt that all of this holds together as bizarre as it sounds. But it's just a whole collection of examples of the breakdown of what I call reductionism in the beginning.
55:04
Now, the other ingredient that makes it especially bizarre is that all these things like coupling constants can vary in space. So you can have a variation from place to place where in some places the world looks very, very close to 10-dimensional with very light strings, heavy D0 brains.
55:25
And if you move over a couple of meters or whatever, the theory will change its character, develop a large direction in this direction, strings will turn into very heavy membranes, and D0 brains will turn into gravitons.
55:42
These things are called dualities, these relationships between what happens at one end of a parameter space and the other end of a parameter space. And in many ways, they're very magical and surprising. They're nothing like what was originally expected from this theory.
56:03
What was originally expected was a simple theory, strings make up particles, end of story. What turned out was much, much more complex and much more elusive in a certain sense. Elusive in the sense that it just became totally unclear what the starting objects of the theory are,
56:30
what the starting objects, what the bricks are, and what the houses are. And to this day, we really simply don't know what, if anything, the fundamental objects that the theory is built out of are,
56:45
if there are such objects. Perhaps it's just this way. Perhaps there is no set of objects which are more fundamental than the strings and the brains and so forth, and they just transform into each other. Perhaps there's something underlying the whole thing that's more fundamental than any of them
57:04
and can rearrange itself into these different patterns and form different kinds of structures. So we don't know. We don't know the answer to those questions. All right, let's take a break for 10 minutes.
57:25
Let me just tell you a few more interesting connections I was talking about a few minutes ago with Michael and a couple of other people. There's an enormous web of interconnected ideas and interconnected theories that string theory brings together.
57:43
So let me show you two more interesting ideas. Take a D3 brain. Remember, now, there are those theories that have odd brains and those theories that have even brains. Let's take the case of the odd brain theories, which have D1 brains, fundamental strings, and also D3 brains.
58:09
Now, a D3 brain is like ordinary space. It has three dimensions in which you can move around in. If you are stuck on this brain and you couldn't get off it, perhaps because you were attracted to it,
58:20
you might think you're living in a world of three dimensions. Just as if there was a two-dimensional membrane and you were a little creature that moved around on the membrane, you would think you live in two dimensions. Under certain circumstances, you might really describe your world as being pretty similar to a quantum theory
58:44
or to a theory in two dimensions, two space dimensions. Same thing on three brains. Three brains, in many ways, just behave as if they were just ordinary space. Now, the three brain itself can have all sorts of wiggles on it, all sorts of motions, and it also has, among other things,
59:11
here's a picture of a three brain. I think I should draw it the other way. Let's draw it this way.
59:21
You say, that's not a three brain. It's a two brain. Too bad. I'm not good at drawing three-dimensional figures. Imagine that it's three-dimensional, not two-dimensional. We're going to need the other dimension for additional dimensions, so I don't want to use full three-dimensional.
59:42
You know what I mean. Okay, so that's a D3 brain, and it can do things. It can have wiggles on it and so forth. It can also have strings attached to it, like that. Here's two strings attached to the D3 brain, ordinary strings. Those two strings are the D3 brain.
01:00:00
strings can come along, here they are, one is over here, one is over here, they can come along, they can join and form a single string, okay, so here is the picture, they come along, they join, and they form a single string, and then they go back out and they do something else, they scatter, they scatter, they interact, they do all
01:00:26
the things that particles do, and so on this world of three dimensions, which is not really the full space time, but just a brain, all sorts of things go on, which are in many ways
01:00:42
similar to the things which happen in ordinary quantum field theory in three dimensions. Well, let me give you one interesting thought. Supposing from outside the D3 brain, a fundamental
01:01:04
string comes and ends on the D3 brain, how about the people who live on this D3 brain, who are made up out of the strings wiggling up and down the string, what do they call this object over here? They call it a particle, right? Looks like a particle to them, it's
01:01:22
a little point over here, somebody over here sees a little particle over here. Somehow they've come in from some other direction, he doesn't see the other directions, only sees the directions he lives in, and sees a particle over here. What kind of particle, this is now a fundamental string, what kind of particle? An electrically charged
01:01:46
particle. Well, if we can have fundamental strings, in the theory with odd brains, we also have D-strings. So here's a D-string, and a D-string can also end on a three
01:02:03
brain, that's part of the mathematical story of D-branes. Fundamental strings and D-strings can end on the three brain, that's a D-string. What does that D-string look like to somebody living in here? It also looks like a particle, it's kind of a fatter particle, why is
01:02:25
it fatter? Because the D-string is fatter than the fundamental string, unless the coupling constant is very large of course. If the coupling constant is very large they might get interchanged, but I'm in a world now where the coupling constant is small, the fundamental strings are skinny and thread-like, the D-strings are fat and rope-like, and
01:02:48
a D-string ending on here would look like a bigger, heavier particle. This one looks like an electric charge, can you guess what this one looks like? A magnetic monopole.
01:03:04
So, the duality that connects the fundamental strings with the D-strings is nothing but the duality which connected the electric charges with the magnetic charges of ordinary
01:03:20
field theory. That's a kind of spectacular connection that something we already knew for a long time has a new interpretation in terms of D-strings and fundamental strings, the duality between D-strings and fundamental strings. I'll give you one more example,
01:03:43
one more example which also involves D-strings and F-strings, and I want you to go back to this 11-dimensional theory that we had over here. It's 11 dimensions, the horizontal
01:04:05
axis is 9 dimensions of space, one extra dimension of space plus time. Let's go back to this theory over here. Unfortunately, I can't draw enough dimensions to do this satisfactorily.
01:04:25
In this picture over here, only one dimension of space is compact. The sandwich has only one direction along which it's sandwich-like. I want to imagine taking two dimensions of space and compactifying them. How can I draw that? Well, the maximum number of dimensions
01:04:48
I can draw on the blackboard is three. I can't draw more than three dimensions on the blackboard. If I compactify two of them, that only gives me one more left to think of as all the other dimensions. So I'm just going to have to make do with the world
01:05:06
which has only one large dimension or at least one visible large dimension and two small ones. What does that look like? It looks like this. Here's the two small dimensions and here's the one big dimension which is a stand-in for how many? Seven.
01:05:29
Right. Okay. Now, imagine this is the same theory that had D2 brains.
01:05:43
Just for fun, let's draw this as rather asymmetric. I'm going to draw it asymmetrically so that one of the axes is shorter than the other to make a point.
01:06:01
Now, this theory also has D2 brains. The D2 brains were these things which formed strings when the sandwich was small. Those strings sort of stretched from the ceiling to the floor. Here's the ceiling. Here's the floor. And we can draw those strings.
01:06:26
Let me take another color. This happens to be a string which is stretched out along
01:06:47
the one visible direction that I can draw here. If I could draw more directions, I could make the string wiggle and wave and so forth. But let's just stretch it out along this direction. It's a string. Well, it's not quite a string. It's sort of a ribbon.
01:07:04
But, if these directions are very small, then it looks like a string, right? It looks like a string. And what happens as the sandwich in this direction gets thinner and thinner? It gets more and more string-like, of course. But, in fact, it also gets lighter
01:07:24
and lighter because there's less material in the vertical direction here. But we can also put a string in oriented the other way. How about this string? That's also, from
01:08:01
the point of view of the large dimensions of space, it also looks like a one-dimensional object as long as both axes are small. What is this one called? It's not the same thing. In fact, which one of these two strings would you think is heavier? The bottom
01:08:22
one, because there's more material that way, right? This one's heavy. This one's light. They're both strings. Can you guess what they are? F-strings and D-strings. So this
01:08:41
is another way to think about the relation between F-strings and D-strings. They're membranes which are wrapped around two different directions, two different small directions, one of the directions being larger than the other. Now, what happens if we imagine taking
01:09:05
the space and distorting it so that we start squeezing this direction this way and stretching this one that way? What happens to the two kinds of strings? The F-strings get heavier and heavier, thicker and thicker, more and more material. The D-strings get lighter
01:09:23
and lighter. So we see, again, this is another way to think about D-strings and F-strings. They're all mathematically equivalent, and it's just a small part of an enormous network
01:09:41
of ideas that emerged out of string theory, sometimes connecting one string theory with another string theory, sometimes connecting string theory with quantum field theory, connecting ideas like monopoles and charges with strings and other things, and most of it having very
01:10:06
little to do with what we see in the laboratory. In that picture, can't you view alpha as the ratio of the two dimensions?
01:10:24
Yes. That's exactly what it is. When the ratio, when this direction is small, we would normally call it a small coupling constant, and yeah. That's right.
01:10:41
And these things do not have a finite width because of cyclical nature? Well, they're finite in extent, but they're cyclic. Right. So the bottom here is the same point as the top, so if you walked along the ribbon and you came to here, you would
01:11:01
reappear over here. Likewise, over here, if you went out over here, you'd reappear over here. That gives you a kind of infinity. Well, you can go, it's the same kind of infinity as the Earth, okay?
01:11:21
It's the same kind of infinity as the circle. You can go around it and around it and around it, but never come to the end. But nevertheless, you wouldn't say the distance around here was infinite. No, but in this case, you start out, you go in this direction. You go up like this, like a step. And then you appear at the bottom and you go up another step.
01:11:43
In other words, if you add up all the steps... All that is is going around and around and around and around. And it's just, look, it's taking a circle. This idea of going out the top and reappearing at the bottom is nothing but taking a circle where you just go around and in order to
01:12:05
mathematically exhibit it, you cut it, open it up, draw it on the blackboard as a line, but remember that this point and this point are really the same point so that when you go from here across, you jump across to here. When you go out here, you come here.
01:12:24
Why isn't this a helix rather than just a circle? At each point, this is a circle. Yes, but we're going along in this way and therefore it gets kind of a helix. Well, if you go around as you go forward,
01:12:43
then you get a helix. Yeah. Is there any, this is, of course, a geometrical picture, is there any useful story about how the geometry here connects to the earlier point you made that the D-branes can look like a collection of F-branes where you look very closely and scatter the D-branes
01:13:02
and see a lot of F-branes? From this picture, it's a little bit hard to see. It is useful, it is useful, but you need a little bit more geometric imagination to see how a D-brane can be connected up with an F-brane and I'm reaching a saturation
01:13:24
point of complexity where I, where, well. If you put the two in the same picture and then you oscillate it between the thin
01:13:42
and the narrow, then you get them flip-flopping perpendicular. You're oscillating in space as you move along. Well, let's say if you oscillate the long dimension and the short dimension. Oscillate the time or the space or what? Either. Just the shape. Well, when you say oscillates, oscillates with respect to what?
01:14:03
Just space, number. Space. You're just going to squish one this way and the other one pops up. Yeah, exactly. And if you drew them both in the same diagram, then you've got them changing places. That's right, exactly. You could imagine that as you move along space in this direction, it squishes horizontally
01:14:24
and broadens vertically. So then you would say, over here, the fundamental strings are light. Over here, the fundamental strings are heavy. Now, fundamental is just a name. All right. It's quite clear that which is fundamental and which, there's no, there's no preference
01:14:44
for which one is fundamental. It's just a word. We call the ones which are arranged vertically here fundamental. We call the ones which are arranged horizontal D. And that's right. As you move along here, you can imagine going back and forth. All with time. You could also imagine that with time, these, and that can also happen.
01:15:06
And so you could go back and forth between the two of them. Absolutely. Yeah. Now, let me just sort of finish up these thoughts by saying these precise features
01:15:22
are features of an idealization. The idealization is the idealized supersymmetric string theory. Supersymmetric means that it has bosons and fermions of exactly the same mass. And it's an idealization in the sense that it's not really nature.
01:15:45
In some sense, it's like the idealization of studying perfectly circular orbits. Why do you study circular orbits? Because they're easy to study. It's undoubtedly the first kind of orbit that Newton studied, circular orbits. They had an extra symmetry.
01:16:02
They were highly symmetric and easy to study. The mathematics was easy. They weren't the real planetary orbits. But of course, many of the features of real planetary orbits in simplified form were there for circular orbits.
01:16:22
Again, the kinds of string theories that we really know how to deal with mathematically. String theory is infinitely more complex than the theory of orbits. The kind of theories that we know how to deal with are also especially symmetric. Symmetric meaning to say that they have some mathematical properties which are idealizations,
01:16:45
makes them easy to understand, easier to understand, but is not real nature. What they show us is the kind of things that can happen.
01:17:01
The kind of things, all of these things which happen here are expected to have a reflection of one kind or another in a more realistic theory, but it will be more complicated and it will be less tractable and not so easy to visualize and certainly not so easy to prove anything about.
01:17:23
But it does show us the kind of things that can happen in a string theory and very likely the kinds of things that can happen more generally than just string theory. So, as I said, string theory as we understand it now, the things that we really understand mathematically are over-idealizations.
01:17:45
And so when people argue in the press and in books and silly books for the most part about whether string theory is the right theory of the world or not, the answer is it's not. It's just not. On the other hand, does it have an enormous amount
01:18:03
to teach us about the way that quantum mechanics, gravity, microstructure fits together? Probably yes. That's my opinion in any case. Many of the things really don't depend on the details of string theory, but okay, enough of that sermon.
01:18:25
There are other objects besides D-branes. I think I've probably saturated you with ideas for tonight. There are other objects in the theory.
01:18:41
There are things called fluxes. There are things called orbifolds, things called orientifolds, things, all kinds of structures, which add to the elements that you can put together to create a world. You can take a geometry.
01:19:03
For example, this room with the floor and the ceiling being thought of as the top and bottom of the peanut butter sandwich, maybe even periodically identified. We take that wall, we can take this room, think of it really as one compact direction and two non-compact directions,
01:19:29
and then we can put a D-2-brane into it, a D-brane into it that fills up like a flying carpet halfway between the floor and the ceiling, and that's a new structure that could be there in space.
01:19:42
Then we shrink the size from the floor to the ceiling, but with that flying carpet always stuck in between, it changes the character of physics in that two-dimensional world. We can put one flying carpet in. We can put two flying carpets in.
01:20:01
We can put three flying carpets in, and we can make a whole variety of different worlds by changing the D-brane content that we put into the world. As I said, there are other objects. There are fluxes. We can change the nature of the microscopic world by adding those things or subtracting those things.
01:20:24
What string theory gives us is a bunch of tinker toy parts, a lot of tinker toy parts that we can play with, arrange, rearrange, do complicated things with, and in the process change what the microscopic physics is like, change what particle physics is like,
01:20:45
change what the parameters of nature are like. It gives rise to huge numbers of possibilities, permutations and combinations of how you put these tinker toy pieces together.
01:21:01
How many possibilities? This is a huge number. Ten to the 500 is a number that's often thrown around. Incidentally, it's not very hard to get to ten to the 500. Supposing, yeah, really all you need is 500.
01:21:26
You don't really need 500. It's not such a big number, right? Supposing you have a space which is like a doughnut except it has 500 holes and handles in it.
01:21:40
Now, 500 holes and handles is not a large number for the kind of spaces that string theory uses, Calabi-Yau spaces. The six-dimensional spaces, they're complicated. 500 holes and handles attached to them is not very complicated. Now, we can, around each one of what are called cycles, we can wrap brains.
01:22:06
We can wrap fluxes. If around each one of 500 cycles we can wrap a few brains, three or four brains more or less, or we can put in a few fluxes or whatever a flux is and modify the geometry for each handle
01:22:23
if we could modify the structure in ten different ways, then we would have ten to the 500 possibilities. You know, it's kind of like DNA. You take a DNA chain. If the DNA chain was 500 units long, how many different creatures, how many different possibilities are there for a creature?
01:22:47
Four to the 500. Not 500, but four to the 500. So, with the permutations and combinations of 500 objects being rearranged in maybe four, five, ten ways,
01:23:03
you can make huge numbers of possibilities. And that's what happens. How many Tinkertoy, given a Tinkertoy set, how many different constructions can you make? Well, you have how many of those little wheels? And in each wheel you can put, you know, the numbers get very, very large.
01:23:25
So, the same is true with string theory. And the numbers are large, and any given construction is likely to be rather complicated.
01:23:41
The generic construction that you make is likely to be rather complicated, just like the generic construction you can make with a DNA chain. Well, DNA chains are more than 500 units long. What, 100 million units long? 100 million base pairs long? Still only about 20,000 genes.
01:24:02
How many kinds of creatures can you make? A huge number. Are any of them simple? Well, some of them are simple, but the generic creature that you make is very complicated. It has trunks and ears and all sorts of appendages. It could very well be that that's the reason that particle physics is so complicated,
01:24:25
because a lot of moving parts go into constructing particular string theory construction. I think most string theorists believe this by now, that the world is complicated because there's a lot of moving parts, but not because the rules are complicated.
01:24:42
The rules of DNA are not complicated. You have a long chain, and you either put in a T, a G, an A, a C, whatever the base pairs are, and you put them in an arbitrary sequence of base pairs, and then, what's that? Four of them.
01:25:00
Four of them. What did I say? T, G, C, and A. Right. Yeah, right. They come in pairs, though, you realize. On the other hand, it is, yeah, yeah, but there's two strands, so if you focus on one strand and you move along it, any point along it could be one of four sets, so it's four to the 500 or whatever, four to the 30,000, whatever.
01:25:23
And none of them are particularly simple, but the rules, the basic underlying rules for putting things together are simple. The same is true of string theory in very much the same way, that the basic rules for what you're allowed to do are pretty simple. The number of arrangements that you can make for a particular setup is very large,
01:25:45
and most of them will lead to fairly complicated particle physics. That's the situation we're facing, and the string theory, if string theory is correct, I think we should expect that particle physics will be more complicated,
01:26:07
probably, than we'll ever be able to unravel completely. The question is, is it thought that of the 10 to 500 that there are really only a few that describe this? 10 to the 500, incidentally, is an underestimate.
01:26:22
That was a, yeah, but go ahead. But is it thought that if we had all the information that we would find out only one or a couple of analysis? I know about the duality that you've talked about. Yeah, yeah, there are the dualities, but when you divide out the dualities, the 10 to the 500 is the number that's left over, and it's not 10 to the 500, that's an old number.
01:26:46
But I mean, is it only a few that would, if we knew what it was, it would only be one of those choices? Well, okay, presumably so, presumably so. But there may be many which look very similar.
01:27:03
There may be many, many which look very, very similar. You know, there may be a lot of junk DNA in it. For example, in this picture, the aspect ratio was one, and therefore the F and the Ds were kind of the same thing.
01:27:22
Like, are there some out of those 10 to the 500 where the whole thing becomes a lot simpler? I think you're asking whether there are specially symmetric points. And there are specially symmetric points, yeah. There are specially symmetric points. Our world does not seem to be one of those specially symmetric points.
01:27:43
A specially symmetric point would be one in which the monopole mass and the electron mass were the same. Apparently, we don't live in that world. We live in a lopsided world more like this. Do we know why? No. Long, long ago, I studied communications engineering here at Stanford.
01:28:03
And at that time, what they taught us about coding theory and communication error correction codes was that, and this has always hit with a sense of dire humor, that almost all the codes you can find are really very, very good. But because the only ones you can decode have mathematical structure,
01:28:23
the ones you can actually decode are universally bad. Bad in what sense? Bad in that they don't give you the, they give you just a fraction of the performance that you can get to. Now, it's turned out that in the many years since I studied this, that they have, in fact, found codes that are unbelievably good compared to what we had back in the 70s.
01:28:45
But it reminds me of this, that it's the mathematical structure. If the mathematical structure is understandable, the complexity is too low to explain. Almost anything you can name is too simple to be interesting.
01:29:01
Like, almost every number is small, because any number you name, almost all of them are much bigger. Anything you can describe is probably too, you know, is described in a small number of bits. Yeah, this is probably true.
01:29:20
And I think what it means, if true, if these things are true, is we've got to learn to ask a new class of questions. The question is not exactly what is the set up which, what are the common features? What are the generic features? You know, people are wrestling with those questions.
01:29:44
Yeah, yeah, yeah. Now, will it turn out that way? We don't know. This is, this is, but it doesn't do anybody any good to have ideological warfare in the press over these things.
01:30:01
Okay. Yes, sir. It seems that there wouldn't be a big difference between- Do I, yeah, you'll let her. You'll let her? No. No, he's letting her. Right, I'll let her. It seems that there wouldn't be a big difference between a compact direction that has a very large size and an infinite.
01:30:31
Well- And so, do we know that our three ordinary dimensions really are infinite? Nope, we do not.
01:30:42
We do not. We do not. As a matter of fact, I mean, you know, standard old-fashioned cosmological theories said the three dimensions form a sphere, a growing sphere to be sure, but a three sphere, and so they're all compact. All compact, but growing.
01:31:02
So, no, we don't. We can only say that they're bigger than this or that. The measured flatness of the universe, you know, if you wanted to know how big the Earth was around,
01:31:22
you, going out in the farmer's field, which is, you know, a kilometer by a kilometer, and looking around, all he could do is put a bound on how big the Earth is. From looking at triangles and things over small distances, he could say, well, the Earth is so flat that I suspect it must be at least 60 miles big.
01:31:46
Does a little bit better, measures a little more accurately, triangles at the surface of the Earth, assuming the surface of the Earth was nice and flat and didn't have hills in it, he might be able to say it's 500 miles big or bigger. And that's all he can do until he starts to detect the curvature of the Earth, and when he detects
01:32:05
the curvature of the Earth, then he can say, aha, the Earth looks like it's 24,000 miles in circumference. The same thing, when we look out cosmologically, space looks very flat on very large scales, so all we can say is it's at least as big.
01:32:25
It's at least 40 billion light years on the side, well, it's bigger than that, no, no, it's much bigger than that, 400 light years on the side at least at minimum.
01:32:40
And, but we can't say one way or another whether it's infinite or not. If g can vary over space, how would you be able to detect whether you are? In the real world, it can't. In the real world, which is not as symmetric and as simple as this, it can't. No, no, it may be able to vary, but it'll vary in steps.
01:33:08
We're going to talk about this when we talk about cosmology. What are the kinds of variations that the laws of physics can have from place to place? Consistent with both theory and with what we know experimentally.
01:33:23
And from what we know experimentally is that these changes have to take place in discrete jumps, more or less in jumps. Okay, because if it was continuous, it would seem that you could move along a linear dimension and then end up on one of the curved dimensions and it's become big. No, I think we know with pretty much certainty that it can't continuously, smoothly vary.
01:33:47
What we don't know is whether it can vary in jumps and there are good reasons to think that it varies in jumps. So what happens to a compact dimension in a high gravitational field, like close to a black hole, does it get squished down? Some kinds of black holes, yes.
01:34:02
Other kinds, no. Ordinary Schwarzschild black hole, no. Not in the horizon of a Schwarzschild black hole, no. Horizon of a Schwarzschild black hole is a very ordinary place where nothing special like that happens. I'm losing my voice.
01:34:23
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