Lecture 1 | Topics in String Theory

Stanford University let's start with some philosophy let's start with some general philosophical principle 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 yeah I mean no molecules are made 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 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 right we all know the bricks from the houses the bricks are smaller than the houses 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 that's a pious hope of reductionism 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 and as a as a theory of elementary particles if reductionism is right particularly in that aspect 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 we've gone several several layers and is it simple the answer is no it is very very complicated and to measure how complicated is you can simply ask how many different kinds of particles 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 and a standard model of particle physics maybe only about twenty or maybe even a little bit less than that independent particles that don't have tight relationships between each other so it's maybe ten to fifteen or twenty distinct different particles depending on how you count how many parameters parameters again mean unexplained constants that have to go into the theory to make sense out of it well about twenty 20 distinct parameters but the theory is definitely incomplete we know that it's incomplete that doesn't have gravity that doesn't have dark matter it doesn't have the particles that are necessary for inflation or 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 people introduce things like supersymmetry my guess is that supersymmetry will really be discovered at the LHC but if it does it adds about a hundred new parameters well I take that back it's a hundred plus n where n is an unknown number but that in 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 for inflation and other things by the time you 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 are and totally unexplained connections so it's not simple it's it's very very complicated and complicated either you have to say well we haven't gotten anywhere near the bottom yet all we just have to admit that maybe reductionism isn't working 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 so I'll tell you a little bit about what is known in particular about the idea that endlessly will not necessarily endlessly but that that is 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 which thing I'm going to give you some 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 going to tell you about it 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 chenna space and a dimension of time and that's all there is and particles what was discovered is that there's a simple there number just in fact almost every theory in 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 they're the particles which have this odd behavior that they can't go into the state you can't put two of them into the same state electrons are fermions quarks are fermions are photons are not fermions they're bosons the opposite of a fermion is a boson 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 called sigh it's 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 if you put two of them identical ones together you make zero but supposing - 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 of fermions electrons of fermions hydrogen atoms are bosons okay so you take a firm yin and oppose off 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 that clearly composites they can move up and down there are also particles but they're composite particles those composite particles of 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 of the two particles stuck together and you call it Phi Phi creates bosons it creates pairs of these fermions that sounds very in very very straightforward but what was then discovered in these field theories 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 make another boson but these fermions can be described in a totally new way they describe 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 a place where the field Phi jumps smoothly jumps doesn't it doesn't jump R as 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 well I 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 rotate this end around by 2 pi so it's twisted once it comes back to its original configuration over here it's original configuration over here but in between it's twisted that's a kink that's a kink in my belt I often do that I often do that when I put my belt on two hours later when I'm talking to somebody that my belt is on wrong all right that's called a kink the bizarre thing is that these fermions that we start with thought we started with the bricks which built the houses the fermion bricks which build the boson houses can now be re represented as kinks in the boson field kinks which are extended thick and massive much heavier than the bosons 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 is the fundamental 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 which is more useful is it more useful to think of sigh the fermions or v 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 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 increasing Oh incidentally when that G is very small ah let's see that kink is very tight very small like that now you start changing the cup and that's why the fermion is a small object 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 King 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 so the question of which is fundamental and which is composite doesn't have a unique answer by varying the constants you can make you can morph you will make up one thing go into the other the houses go into the bricks so to speak that was a case that was known ROG since I was a very young physicist the key word is called boson ization it's making a fermion out of bosons or for bosons out of fermions are there anything like this in elementary particle physics 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 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 the amount of charge and not just because the electron is small that's actually not the issue this is a dimensionless quantity what's the dimensionless quantity called anybody know a fine structure constant or fine yeah the fine structure constant is a measure of how much an electron would radiate if you you know if you accelerated it suddenly or if you plowed it into a and a node if you plowed it into a stop into a how much I would it radiate how many photons would it radiate the answer is that an electron will radiate on the average 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 stopped radiate a photon so the electron charge is very weak and the electron is very simple the electric field around it is rather is 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 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 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 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 amount of the monopoles that theoretical physics seems to produce have a magnetic charge which is huge very large the force between two magnetic monopoles would be ten thousand times larger than the force between two electrons are the same distance that means that the magnet magnetic monopoles make large fields around them and do very 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 its massive it's very very heavy because there's so much going on in the vicinity of the monopole 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 but most theorists believe in them but the point is the more important point is the mathematics of quantum electrodynamics which contains mana poles and electrons is totally unclear about which of them is the elementary particle it depends on the fine-structure constant 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 1 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 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 that you could start dialing redialing 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 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 monopoles FASTA sure this is not something we that I can explain easily but the fact is it starts to shrink it gets smaller and smaller 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 and basically they were just interchange themselves so again which is the building block is it the electron whose complicated structure here is making up the monopole or is it the monopole which is simple and whose complicated structure is making up the electron modern quantum field theory 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 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 and starting points for quantum electrodynamics and maimana poles yeah pack your philosophical point if if there's a belief that production is not the correct view of thing why physicists use calculus which most production is the mathematical tools oh no calculus is not necessarily reductionist it just says everything is smooth smoothly varying ah but it doesn't in any way tell you what little points yes okay right right you chopped up the things into little poor little distances and you ask what's in those little distances and that tells you what what the fundamental things are okay in quantum field theory is just an endless hierarchy of distance scales and so you never get to the point where you can decide which one is fundamental hmm like a fractal yeah a Fraggle well for example describing a curve you can use it using a derivative or one of the few non reductionist models is general relativity Jessica Warren 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 the reasons that mathematicians have so much trouble with it is sort of because in a certain sense calculus does break down or in studying the fields they fluctuate too much they vary too much but let's not get into that now all right now what a string theory say the string theory have an answer to what is what are the fundamental building blocks well obviously string theory has an answer for it the fundamental building block says it must be strings right okay so let me tell you a little bit about we talked about d-branes yes all right so I will just very quickly just remind you what a D brane is we don't need to know a lot about the mathematics pictures are good enough D brains are objects that were discovered through a fairly indirect mathematical route they are part of the theory you can't get rid of them stuck with it they're objects which are first of all very heavy they could be they come in different dimensionality the simplest one is called the d0 brain and 0 stands for the dimension what's to do what's the dimension of a point the dimensionality of a point where the first of what's the dimensionality of a line one dimension the dimensionality of a membrane or a two-dimensional surface - 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 as zero dimension dimensional they are not extended in higher dimensions so a particle is a d0 brain the word brain incidentally BR a and E brain comes from membrane a membrane a surface is a to brain or a to brain two-dimensional brain 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 but if we have more directions we could make four brains all right so a d0 brain is a kind of particle the d stands for the mathematician there is a and it's not important but the property of these D brains in string theory is that they are places where strings can end fundamental strings let's call them F strings this is an F screen f standing for fundamental the building blocks the things that gravitons are made out of you know all the good stuff that we've talked about up till now the fundamental screens and these zero brains are just sites on which a fundamental string can end in fact any number of fundamental strings can end on a d0 brain and that means that these zero brains can have strings attached to them and they typically do if you were to probe with the zero brain by scattering something off it you would find out that it has a collection of strings attached to it like that in fact the harder you probed it the more string you will find closer and closer in and you would eventually come to the conclusion that the d-brane 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 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 it's 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 they're there in the theory now these that's a d0 brain there are also d1 brains the one brain it's like a string what's I just want to thicken about because it's much heavier than an ordinary string 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 a object which is made up out of these strings or 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 let's draw two strings next to each other here's a D string and here's an F string a DZ ad1 brain can also be called ad string here's an F string a fundamental string it's thin its narrow its light these two objects are related in very much the same way that this one this one I'm 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 point for string theory these objects are big heavy composite structures which are made out of cables of lots of string and heavy and they're obviously composite string theory has I said it has no parameters now we're going to come back to whether we're going to come back in a minute to the question of whether it has parameters or not 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 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 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 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 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 electrons are complicated when you started to increase the fine-structure constant the fundamental string starts to develop structures 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 as they get thinned out the D string gets thinner and thinner eventually at some point when G is about 1 they start to look exactly like each other and then if you go to even law a coupling constant the d-string gets very simple 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 well if G is much less than 1 then the fundamental strings when they close back on themselves form the particles the ordinary particles of a string theory but as G gets larger and larger these things get more and more massive in fact eventually they turn into black holes and what's left over is that these 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 it's not the usual name for it's usually called esto allathee I do not know where that stands for I didn't make up the term I don't know why it's called Oh strange duality strength yeah strength of a coupling constant so again we find this pattern that you can't say once and for all which thing is more fundamental than which 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 couple of the fundamental strings as fun as fundamental 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 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 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 in theory what a cosmological scale I mean if it very committee became less massive than there wouldn't that have effect on spectra and such in chemistry absolutely that's how we know that's one of the ways we know that string theory them the mathematically precise version of string theory is not our world yep dad will talk about much lately and there's school like fun of it all yeah yeah yes it is bye bye um just a train trying to get it straight in my mind the greater likelihood of splitting makes complexity in the upstream yeah 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 it's a point that means it's a very thin world line not 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 that 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 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 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 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 it it's some where does the energy come from or the energy the energy the energy needed for this process is part of the mass of the proton RMS of the electron is part of the mass of the electron it is the massive 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 but I don't I see things much through the sim not accurately enough I see two electron pair being produced and I don't see the mass of electron enough to produce electron pair when how powerful in approving their well yeah obviously you know your skin by by the skin of your teeth you're a virtual energy are the same thing so when you say the mass of the electron you're basically including the energy all right but what is that energy that energy is a kind of potential energy it's a kind of potential energy R that's connected with the interactions between the electrons and the photons the energy of a system in the quantum electrodynamics is not just the energy of the electrons plus the energy of the photons is also an interaction energy between them and that's the event that interaction energy is the source of this but all right but that's it's you know 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 well okay we can we can debate whether the energy of the experiment is producing what you see or whether it's seeing what you see um we can debate that but the fact of the matter is that when you scatter things off the electron what happens is complicated what happens is count well it's not so complicated most of the times you don't see anything about 1% of the time on deep breaths said recovery cost is small you say masta tio the d1 brain is more than massively up strength and with the tension also before juice yeah attention the mask means the tendon of attention means the mass per unit length yeah yeah yeah the mass per unit length is called attention right exactly energy per unit weight all right now um as I said as a cut 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 it's no longer something which is very rare or very dilute the electron begets big gets heavy gets all the structure they're very very similar thing happens to a string what what is this coupling constant gee 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 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 and the photons surrounded the electron 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 why because those F strings are getting heavier and heavier and the result is that the D string gets less and less structure and becomes more like the F screen so that's that's another example of a duality these things are called dualities this one is called s duality the name is not important and 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 now it um 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 so that means that there are d1 brains the three brains the five brains how do you stick a d5 brain into space that we don't have enough dimensions of space well remember that string theory is fundamentally a 10 dimensional Theory you've got a lot of extra dimensions string theory has enough dimensions that you can put in things up to about eight brains and then you run out of directions to put the brains in so one version of string theory the mathematics tells you that there must be the 1 D 3 D 5 D 7 brains in another version of string theory which is closely related but different there are even dimensional brains no string theory has both odd dimensional D brains and even dimensional it's just a fact that no version of it has both not 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 so let's go to the version of string theory which has even dimensional brains instead of odd dimensional it doesn't have these it has these zero brains it has point-like particles which are not quite point-like but which are very complicated and full of string 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 1 this theory does something very different as G starts to get large 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 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 all right I'm going to tell you what happens and perhaps so in the second hour I can tell you why or what what it means for it to happen what happens is that a new dimension of as G gets large a new dimension of space materializes now that's crazy that's the silliest thing I ever heard a new dimension of space materializes how can a dimensional space materialize well it can't but what can happen is a very small compact Direction can start to expand 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 to be able to for pictures really we're talking about 10 dimensional string theory let's take ordinary space how many directions of space does this 10 dimensional string theory have no nine the tenth dimension is time right okay so once when somebody tells you 10 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 a blackboard 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 it could be three dimensional because this because there could be a thickness to it we could imagine a world sort of a peanutbutter sandwich with a piece of bread on this side a piece of bread on this side 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 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 II would just reappear at the bottom piece of bread all right that's that's the idea of an one compact dimension now if the compact dimension was small enough it might not be noticeable to the physicists that live in this world that the direction has a little that is this extra dimension but this direction has some that there's some thickness to the world along a direction that they didn't notice so that we call this world two dimensional what happens as G starts to increase is that the peanut butter sandwich gets thicker and thicker and thicker and eventually when G gets very large a whole new dimension of space materializes 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 the zero 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 in to the gravitons in this extra dimensional theory just the ordinary gravitons the ordinary elementary particles that live in this extra dimensional theory this new theory is now 11 dimensional we thought of a string theory with only 10 dimensions and when we started increasing this coupling constant we discovered another dimensional space and these d0 brains just turned into the gravitons that exists in here in other words again very very complicated objects turn into very simple light objects 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 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 the for brains the six brains but concentrate in particular on d2 brains what is it d2 brain mean it means a membrane it means a membrane you could have two kinds of membranes stuck into this sandwich thus a membrane simply means a surface a surface of energy you could stick in the membrane in between the floor and the ceiling in between the two pieces of bread sort of embedded in the peanut butter all right or if you like you could think of the top piece of bread as the ceiling the bottom piece of bread is the floor and then the two brain stuck in between would be a floating magic carpet that just that just hovered halfway in between that's one kind of d-brane to a d2 brain you could have there's another kind that you can have and the other kind is a kind of ribbon let's see how let's see if I can draw it it goes from the floor to the ceiling but it's a ribbon sort of stretched between the floor in the ceiling vertically which is extended in the other directions what happens when the floor and the ceiling get closer and closer 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 a string and so when G is very small not a point like string but a line like string the line like strings are just these membranes which are oriented vertically in this direction here as and there are also the zero brains the zero brains being very heavy now you start to increase the coupling constant the floor and the ceiling start to separate the zero 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 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 have so heavy because there's so much material they're vertically here they turn into something very heavy the d-branes 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 and the consistency of it the requirement for 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 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 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 the mathematicians went back and said oh yeah those matter those theorems turned out to be true so there's this 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 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 looked very very close to 10 dimensional with very light strings heavy d0 brains and if you move over a couple of metres or whatever the theory will change its character develop a large direction in this direction strings will turn into very heavy membranes and these zero brains will turn into gravitons 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 in many ways they're very magical and surprising then nothing like or was originally expected from this theory originally expect there was a simple theory strings make up particles and the 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 what the starting objects what the things which what the what the bricks are and what the houses are and to this day we really simply don't know what what if anything the fundamental objects that the theory is built out of are if there are such objects perhaps it's just this way perhaps there is no set of objects which are more fundamental than 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 and can rearrange itself can rearrange itself into different 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 for 10 minutes 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 so let me show you two more interesting ideas that take a d3-brane 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 the one brains fundamental strings and also be three brains now that the three brain is like ordinary space it has three dimensions in which you can move around in if you are stuck on this brain you couldn't get off it perhaps because you are attracted to it 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 you might not you know under certain circumstances you might really describe your world as being pretty similar to a to a quantum theory or to a theory in two dimensions to space dimensions same thing in 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 well has among other things here's a picture of a three brain all right I think I shall draw it the other way let's draw it this way you say that's not a three brain it's two brain too bad I can't draw I'm not good at drawing three-dimensional figures imagine that it's 3-dimensional not two-dimensional we're going to need the other dimension for additional dimensions so I don't want to use the full three-dimensional yet 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 brane ordinary strings those two 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 they do something else they scatter they scatter they interact they do all the things that particles do and so on this world of three dimensions which is not really the full space-time but just a brane also two things go on which are in many ways similar to the things which happen in an ordinary quantum field theory in three dimensions well let me give you one interesting thought supposing from outside the d3-brane a fundamental string comes and ends on the d3-brane how about the people who live on this d3-brane 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 a little point over here somebody over here sees a little particle over here somehow they've come in from other some other direction it 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 particle well if we can have fundamental strings and the theory with odd brains we also have these strings so here's a D string and a D string can also end on a three brain that's part of the mathematical story of D brains 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 it fatter because the D string is fatter than the fundamental scale unless the coupling constant is very large of course if a coupling constant is very large they might get interchanged but I'm in a world now with a coupling constant is small the fundamental strings are skinny and thread like these strings are fat and rope like and 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 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 field theory that's a 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 these strings and fundamental strings I'll give you one more example 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 11 dimensions the horizontal axis is 10 is 9 dimensions of space one extra dimension of space plus time let's go back to this theory over here but unfortunately I can't draw enough dimensions to do this satisfactorily in this picture over here only one dimension of space is compact the sandwich has only one direction along which its sandwich like I want to imagine taking two dimensions of space and compacta fiying them how can I draw that well the maximum number of dimensions I can draw on the blackboard is 3 I can't draw more than 3 that I like the 3 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 a world which has only one large dimension or at least one visible lodge dimension and two small ones what does that look like it looks like this here's the two small dimensions and he is the one big dimension which is a stand-in for how many seven right okay now imagine this is the same theory that had d2 brains oh let's just for fun let's draw this as rather asymmetric I want to draw asymmetrically so that one of the axes is shorter than the other to make a point now this theory also has d2 brains the d2 brains were these script were these things which form strings when the sandwich are 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 I will let me take another color this happens to be a string which is stretched out along 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 ah 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 but if these directions are very small then it looks like a string right 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 and lighter because there's less material in the vertical direction here but we can also put a string in and the other oriented the other way how about this string that's also from the point of view of the large dimensions of space it also looks like a one-dimensional object as long as this 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 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 and this is another way to think about 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 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 and lighter so we see again this is another way to think about these strings and F strings they're all mathematically equivalent and it's just a small part of an enormous network of ideas that emerge that of string theory connecting 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 little to do with what we see in the laboratory if that picture can't you you alpha as the ratio or fee once I can we work in that picture can you you alpha as the ratio of the two dimensions yes that's exactly what it is that's exactly that it is when the ratio when this direction is small we would normally call it a small coupling constant and yeah that's right and these things do not have a finite width because cycling for nature well they have a finite and extent but their cyclic right so 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 reappear over here likewise over here if you went out over here you reappear over here that gives you a kind of infinity well you can go ahead it's the same kind of infinity as the earth okay it it's the same kind of infinity as a 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 in fact no but in this case you start out you go this direction you go up like this lot of step and then you then you appear at the bottom and you go up another step in other words people it is if you add up all the steps slowly this is going around and around and around and around 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 mathematically exhibit it you cut it open it up draw it on the blackboard is 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 the year when you go out here you come here why is this a helix rather than just a circle but in each point this is a circle yeah we're going along in this way therefore we gets kind of a helix well if you go around as you go forward yeah yeah yeah is there any distant of course geometrical picture is there any useful story about how the jobs are here connects to the earlier point mated the d-branes can look like a collection about brains or you look very closely scattered even see live from this from this from this picture that's a little bit hard to see um it is useful it is useful but you need a little bit more geometric imagination to see how our D brain can be connected up with an F brain and I'm reaching a saturation point of complexity where I wear well you put the two in the same picture hmm and then you all ate it the between the thin and the narrow then you get those flip-flopping particular oscillating in space as you move along say if you oscillate the long dimension on the short edge also any time or space of what well either just the shape oh but when you say oscillates oscillates with respect and with us just face No thank you just you're just going to squish one this way everyone pops up together right okay if you do them both in the same diagram then you've got yeah that's what ranging places that's right exactly you could imagine that as you move along space in this direction it squishes horizontally and broadens vertically right so then you would say over here the fundamental strings are light over here the fundamental strings are heavy now ever fundamental is just a name all right it's quite clear that which is fundamental in which there's no there's no preference 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 soon as you move along here you can imagine going back and forth all with time you could also imagine that with time these are and that can also happen 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 are features of an idealization the idealization is the idealized supersymmetric string theory super symmetric 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 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 undoubtedly the first kind of orbit that Newton studied circular orbits they have an extra symmetry 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 are in simplified form were there for circular orbits 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 makes them easy to understand easier to understand and are but is not real nature what they show us is the kind of things that can happen 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 but it does show us the kind of things that that can happen in a string theory and very likely the kinds of things that can happen more generally than just just string theory so as I said string theory as we understand it now the piece that the things that we really understand mathematically are over idealizations and so when people argue in the press and then 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 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 um there are other objects besides d-branes I don't I think I probably saturated you with ideas for tonight there are other objects in the theory there are things called fluxes there are things called orbifold things called Oriental folds things all kinds of structures which add to the elements that you can put together to create a world you can take a geometry for example this room with the floor and the ceiling being thought of as the top and bottom of the peanutbutter sandwich maybe even periodically identified we take that wall we can take that this room think of it really as one compact direction and to non-compact directions and then we can put a db2 brain into it adi brain 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 then we shrink the size from the wall of 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 and 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 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 change what what the parameters of nature are like it gives rise to huge numbers of possibilities permutations and combinations of how you put these thinker toy pieces together how many possibilities huge number 10 to the 500 is a number that's often thrown around incidentally it's not very hard to get the pen to the 500 supposing yeah really all you need is 500 you don't really need 500 it's not such a big number right supposing you have a space which has which is like a doughnut except that has 500 holes and handles in it now 500 holes in handles is not a large number for the kind of spaces that that string theory uses calabi-yau spaces the six dimensional spaces that complicated 500 holes and handles attach them is not very complicated now we can around each one of what are called cycles we can wrap brains we can wrap fluxes if around each one of 500 cycles we can wrap a few brains 3 or 4 brains more or less or we can put in a few fluxes or whatever flux is and modify the geometry for each handle if we could modify the structure in ten different ways then we would have 10 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 4 to the 500 not 500 but 4 to the 500 right so with the permutations and combinations of 500 objects being reached being rearranged and maybe 4 or 5 10 ways you can make huge numbers of possibilities and that's what happened that's how many Tinkertoy are given a tinkertoy set how many different constructions can you make well you have how many how many of those little wheels and in each wheel you can put the you know the numbers get very very large so the same is true with string theory and the numbers are large and any given construction is likely to be rather complicated the generic construction that you make is likely to be rather complicated just like the generic construction you can make with a DNA chain while DNA chains are more than 500 units long they're 100 million units long 100 million base pairs long still only about 20,000 our genes how many quick kinds of creatures can you make a huge number or any of them simple well some of them are simple but the generic creature that you make is very complicated as trunks and ears and all sorts of sorts of appendages it could very well be that that's the reason that particle physics are so complicated because a lot of moving parts go into constructing particular string theory construction that's 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 complicated the rules of DNA are not complicated you have a long chain and you either put on a T or G and a and C whatever whatever the base pairs are and you put them in an arbitrary sequence of base pairs and then just what's that for what did I say t GC na yeah right they come in pairs though you realize on the other hand it is yeah yeah but there's two were this to stringer there's two strands so if you focus on one strand and you move along at any point along it could be one of four sets so it's four to the five hundred or whatever fourth of a 30,000 wherever and none of them are particularly simple but the rules the basic underlying rules for putting things together a circle the same is true of string theory very much 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 and most of them will lead the 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 that the particle physics will be more complicated probably than we'll ever able be able to unravel completely which is it thought that of the fort of ten to 500 that that they're really only a few then describes the strength of a 500 incidentally is an underestimate that was a epigram if we had all the information that we would find that only one or a couple of banal I know about the duality that you've talked yeah yeah there are the dualities but there were new sort of when you see when you divide out the dualities the 10 to the 500 is for the number that's left over it's not 10 to the 500 that's a whole number but I mean is it only a few that work with if we knew what it was it would only be one of those choices well ok presumably so presumably so but there may be many which look very similar and maybe many many which look very very similar you know there may be a lot of junk DNA in it the aspect ratio or one and therefore the identities were kind of rare same thing right like are there some of those came to the power 500 where the whole thing becomes a lot so there are think you're asking whether there are especially symmetric points and there are specially symmetric points yeah there are especially symmetric points our world does not seem to be one of those specially symmetric points especially 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 Engineering near Stanford and the at that time what they taught us about coding theory and communication error correction codes was that innocence always said with a sense of dire human that almost all the codes you can find are really very very good but because the only ones you can decode have mathematical structure the ones you can actually decode or universally bad mechanisms embedded they don't give you the thinking just fraction of the performance that you could get to now it's turned out that in many years since I studied this that they have background codes are unbelievably good compared to what we have back in the seventh but it reminds me of this yeah that it's the mathematical structure when that if mathematical structures is understandable the complexity is too low to explain yeah almost anything you can name is too simple to be interesting like almost every number is small because any number you name almost all of them are much bigger and anything you can describe is probably to the theorists described in a small number of bits yeah this is probably true 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 what the and you know with people are wrestling with those questions yeah yeah yeah now will it turn out that way we don't know this is uh but it doesn't do anybody any good to have ideological warfare and the press over these things okay yes it seems that there were a big difference between you and you no matter no no it seems that there wouldn't be a big difference between a compact direction that has a very large size and an infinite well and and so do we know there are three ordinary dimensions really are infinite no you're not you do not as a matter of fact I mean you know standard old-fashioned cosmological theories said the three dimensions form a sphere the growing sphere to be sure but a three sphere and so they'll all compact or compact but growing so no we don't we can only say that they're bigger than this or that the the measured flatness of the universe you know if you want to know how big the earth was around you going out in the farmer's field which is you know a kilometer by a kilometer and looking around all you could do is put a bound on how big the earth is from looking at triangles and things and no over small distances you can say well the earth is so flat that I suspect there must be at least 60 miles big 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 we can do until he starts to detect the curvature of the earth and when he detects the curvature of the earth and he's haha the earth looks like it's twenty four thousand miles in circumference 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 it's at least um forty billion light years on the side well it's bigger than that no no it's much bigger than that four hundred light years on the side at least at minimum and but we can't we can't say one way or another whether it's infinite real world it can't in the real world which is not as symmetric and as simple as this it can't no no no okay it may be able to vary but it will vary in steps you know we're going to talk about this when we talk about cosmology what are the kinds of what other kinds of variations that the laws of physics can have from place to place consistent with both theory and with what we know experimentally and from what we know experimentally is that these changes take have to take place in discrete jumps more or less jobs no I think we know with pretty much certainty that it can't continuously smoothly very well we don't know is whether it can vary in jumps and there are good reasons to think that it varies and jobs some kinds of black holes yes other kinds no ordinary Schwarzschild black hole no not nothing 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 for more please visit us at stanford.edu

Channel: Stanford

Views: 148,941

Rating: 4.8978548 out of 5

Keywords: physics, science, math, thought, theory, string theory, quantum mechanics, atoms, universe, particle physics, reductionism, theoretical, philosophy, parameter, dark matter, gravity, cosmic

Id: NZ-ElsvYKyo

Length: 94min 27sec (5667 seconds)

Published: Thu Jun 02 2011

Reddit Comments

[u/necroforest]

I watched Susskind's GR series - these things are excellent. Unfortunately for me (a non-physicist), I think i'd have to watch the QM series and the 3-part particle physics series before being able to start this one :(

[u/DROP_TABLE]

Thanks, there goes my weekend.

[u/[deleted]]

Thanks, wish I found this earlier....