Cumrun Vafa: String Theory | Lex Fridman Podcast #204

the following is a conversation with kamran vaffa a theoretical physicist at harvard specializing in string theory he is the winner of the 2017 breakthrough prize in fundamental physics which is the most lucrative academic prize in the world quick mention of our sponsors headspace jordan harmon just show squarespace and all form check them out in the description to support this podcast as a side note let me say that string theory is a theory of quantum gravity that unifies quantum mechanics and general relativity it says that quarks electrons and all other particles are made up of much tinier strings of vibrating energy they vibrate in 10 or more dimensions depending on the flavor of the theory different vibrating patterns result in different particles from its origins for a long time string theory was seen as too good not to be true but has recently fallen out of favor in the physics community partly because over the past 40 years it has not been able to make any novel predictions that could then be validated through experiment nevertheless to this day it remains one of our best candidates for a theory of everything or a theory that unifies the laws of physics let me mention that a similar story happened with neural networks in the field of artificial intelligence where it fell out of favor after decades of promise and research but found success again in the past decade as part of the deep learning revolution so i think it pays to keep an open mind since we don't know which of the ideas in physics may be brought back decades later and be found to solve the biggest mysteries in theoretical physics string theory still has that promise this is the lex friedman podcast and here is my conversation with kamran vaffa what is the difference between mathematics and physics well that's a difficult question because in many ways math and physics are unified in many ways so to distinguish them is not an easy task i would say that perhaps the goals are of math and physics are different uh math does not care to describe reality physics does that's the major difference but a lot of the thoughts processes and so on which goes to understanding the nature and reality are the same things that mathematicians do so in many ways they are similar mathematicians care about deductive reasoning and physicists or physics in general we care less about that we care more about interconnection of ideas about how ideas support each other or if there's a puzzle con discord between ideas that's more interesting for us and part of the reason is that we have learned in physics that the ideas are not sequential and if we think that there's one idea which is more important and we start with there and go to the next idea and next one and deduce things from that like mathematicians do we have learned that the like the third or fourth thing we deduce from that principle turns out later on to be the actual principle and from a different perspective starting from there leads to new ideas which the original one didn't lead to and that's the beginning of a new revolution in science so this kind of thing we have seen again and again in the history of science we have learned to not like deductive reasoning because that gives us a bad starting point to think that we actually have the original thought process should be viewed as the primary thought and all these are deductions like the way mathematicians sometimes does so in physics we are learning to be skeptical of that way of thinking we have to be a bit open to the possibility that what we thought is a deduction of a hypothesis actually the reason that's true is the opposite and so we reverse the order and so this this switching back and forth between ideas makes us more fluid about a deductive fashion of course it sometimes gives a wrong impression like physicists don't care about rigor they just you know they just say random things you know they are willing to to say things that are not backed by you know the logical reasoning that's not true at all so despite despite this fluidity in saying which one is a primary thought we are very careful about trying to understand what we have really understood in terms of relationship between ideas so that's that's the that's an important ingredient and in fact solid math being behind physics is i think uh one of the attractive features of a of a physical law so we look for beautiful math underpinning can we dig into that process of starting from one place and then the uh ending up at like the fourth step and realizing all along that the place you started at was wrong so is that happen when there's a discrepancy between what the math says and what the physical world shows is that how you then can go back and do the revolutionary idea for different starting place altogether perhaps i'll give an example to see see how it goes and in fact the historical example is newton's work on classical mechanics so so newton formulated the laws of mechanics uh you know the force f equals to m a and his other laws and they look very simple elegant and so forth later when we studied more examples of of mechanics and other similar things physicists came up with the idea that the notion of potential is interesting potential was an abstract idea which kind of came you could take its gradient and relate it to the force so you don't really need it apiary but it solved helps some thoughts and then later euler and lagrange reformulated newtonian mechanics in a totally different way in the following fashion they said if you take if you want to know where particle at this point and at this time how does it get to this point at the later time is the following you take all possible paths connecting this particle from going from the initial point to the final point and you compute the action on what is an action action is the integral over time of the kinetic term of the particle minus its potential so you take this integral and each path will give you some quantity and the path it actually takes the physical path is the one which minimizes this integral or this action now this sounded like a backwards step from newton's newton's form that seems very simple f equals to m a and you can write f is minus the gradient of the potential so why would anybody start formatting such a simple thing in terms of this complicated looking principle you have to study the space of all paths and all things and find the minimum and then you get the same equation so what's the point so euler and lagrange's formulation of newton which is a which was kind of recasting in this language is just a consequence of newton's law f equals m it gives you the same fact that this path is a minimum action now what we learned later last century was that when we deal with quantum mechanics newton's law is only an average correct and the particle going from one to the other doesn't take exactly one path it takes all the paths yes with the with the amplitude which is proportional to the exponential of the action times an imaginary number i and so this fact turned out to be the reformulation of quantum mechanics we should start there as the basis of the new law which is quantum mechanics and newton is only an approximation on the average correct when we say amplitude you mean probability but yes the amplitude means if you com sum up all these paths with exponential i times the action if you sum this up you get the number complex number you square the norm of this complex number gives you a probability to go from one to the other is there ways in which mathematics can lead us astray when we use it as a tool to understand the physical world yes i would say that mathematics can lead us astray as much as all physical ideas can lead us so sure if you get stuck in some something then you can easily fool yourself that just like the thought process we have to free ourselves of that sometimes math does that rule like say oh this is such a beautiful math i definitely want to use it somewhere and so you just get carried away and you just get maybe carried too far away so that is certainly true but i wouldn't say it's more dangerous than all physical ideas to me new math ideas uh is as much potential to lead us astray as all physical ideas which could be long-held principles of physics so i'm just saying that we should keep an open uh mind about the role the math plays not to be antagonistic towards it and not to over overwhelming it we should just be open to possibilities what about looking at a particular characteristics of both physical ideas and mathematical ideas which is beauty you think beauty leads us astray meaning um and and you offline showed me a a really nice puzzle that illustrates this this idea a little bit now maybe you can speak to that or another example where uh beauty makes it tempting for us to assume that the the law and the theory we found is actually one that perfectly describes reality i think that beauty does not lead us astray because i feel that beauty is a requirement for principles of physics so beauty is a fundamental in the universe i think beauty is fundamental at least that's the way many of us view it it's not emergent it's not immersion i think i think hardy is the mathematician who said that there's no permanent place for ugly mathematics and so i think the same is true in physics that if we find a principle which looks ugly we're not going to be that's not the end stage so therefore beauty is going to lead us somewhere now it doesn't mean beauty is enough it doesn't mean if you just have beauty if i just look at something is beautiful then i'm fine no that's not the case beauty is certainly a criteria that every good physical theory should pass that's at least the view we have why do we have this view that's a good question it is a partly uh you could say based on experi experience of science over centuries partly is a philosophical view of what what what reality is or should be and uh in principle you know it could have been ugly and we might have had to deal with it but we have gotten maybe uh confident through examples after examples in the history of science to look for beauty and our sense of beauty seems to incorporate a lot of things that are essential for us to solve some difficult problems like symmetry we find symmetry beautiful and the breaking of symmetry beautiful somehow symmetry is a is a fundamental part of how we conceive of beauty at all layers of reality which is interesting like uh in in both the visual space like when we look at art we look at each other as human beings the way we look at creatures in the biological space the way we look at chemistry and then into the physics world as as the work you do it's kind of interesting it makes you wonder like which one is the chicken or the egg is symmetry the the chicken and our conception of beauty the egg or the other way around or somehow the fact that every the symmetry is is part of reality is it somehow creates the brain that then is able to perceive it or maybe that's this is just because we maybe it's so obvious it's almost trivial that symmetry of course will be part of every kind of universe that's possible uh and then our any kind of organism that's able to observe that universe is going to appreciate uh symmetry well these are good questions we don't have a deeper understanding of why we get attracted to symmetry why do laws of nature seem to have symmetries underlying them and the reasoning or the examples of whether if it wasn't symmetric we would have understood it or not we could have said that yeah if there were you know things which didn't look that great we could understand them for example we know that symmetries get broken and we have appreciated nature in the broken symmetry phase as well the word we live in has many things which do not look symmetric but even those have underlying symmetry when you look at it more deeply so we have gotten maybe spoiled perhaps by by the appearance of symmetry all over the place and we look for it and i think this is this is perhaps related to the sense of aesthetics that scientists have and we don't usually talk about it among scientists in fact it's kind of a philosophical view of why do we look for simplicity or beauty or so forth and uh i think in a sense scientists are ma a lot like philosophers sometimes i think especially modern science seems to shine away sean's philosophers and philosophical views and i think at their peril i think i think in my view science owes a lot to philosophy and in my view many scientists in fact probably all good scientists are perhaps amateur philosophers they may not state that they are philosophers or they they may not like to be labeled philosophers but in many ways what they do is like what is philosophical takes of things looking for simplicity or symmetry is an example of that in my opinion or seeing patterns you see for example another example of the symmetry is like how you come up with new ideas in science you see for example an idea a is connected with an idea b okay so you you study this connection very deeply and then you find the cousin of an idea a let me call it a prime and then you immediately look for b prime if a is like b and if there's an a prime then you look for b prime why well it completes the picture why well it's philosophically appealing to have more balance in terms of that and then you look for b prime and behold you find this other phenomena which is a physical phenomenon which you call b prime so this kind of thinking motivates asking questions and looking for things and it has guided scientists i think through many centuries and i think it continues to do so today and i think if you look at the long arc of history i suspect that the things that will be remembered is the philosophical flavor of the ideas of physics and chemistry and computer science and mathematics like i think the actual details will be shown to be incomplete or maybe wrong but the philosophical intuitions will carry through much longer there's a sense in which if it's true that we haven't figured out most of how things work currently that uh it'll all be shown as wrong and silly it'd almost be a historical artifact but the the human spirit whatever like the the longing to understand the the way we perceive the world the way we conceive of it of our place in the world those those ideas will carry on i completely agree in fact i believe that uh almost well i believe that none of the principles or laws of physics we know today are exactly correct all of them are approximations to something they are better than the previous versions that we had but none of them are exactly correct and none of them are going to stand forever so i agree that that's the process we are heading we are improving and yes indeed the thought process and that philosophical take is common so when we look at you know older uh scientists or maybe even all the way back to greek philosophers and the things that the way they thought and so on almost everything they said about you know nature was incorrect but the way they thought about it and many things that they were thinking is still valid today for example they thought about symmetry breaking they were trying to explain the following they were this is a beautiful example i think they had figured out that the earth is round and they said okay earth is around they have you know they have seen the length of the shadow of this meter stick and they have seen that if you go from the equator upwards north they find that depending on how far away you are the length of the shadow changes and from that they have either they had even measured the radius of the earth to good accuracy that's brilliant by the way the fact that they did that very brilliant very brilliant so these greek philosophers were very smart and so they had taken it to the next step they asked okay so the earth is round why doesn't it move they thought it doesn't move they they were looking around nothing seemed to move so so they said okay we have to have a good explanation it wasn't enough for them to you know be there so they really want to deeply understand that fact and they come up with a symmetry argument and the symmetry argument was oh if the earth is a spherical it must be at the center of the universe for sure so they said the earth is at the center of the universe it makes sense and they said you know if the earth is going to move which direction does it pick any direction it picks it breaks that spherical symmetry because you have to pick a direction and that's not good because it's not symmetrical anymore so therefore the earth decides to sit put because it would break the symmetry so so they had the incorrect science they thought earth doesn't move and they but they had this beautiful idea that symmetry might explain it but they were even smarter than that aristotle didn't agree with this argument he said why do you think symmetry prevents it from moving because the preferred position not so he gave an example he said suppose you are a person and you put we put you at the center of a circle and we spread food around you on a circle around you loaves of bread let's say and we say okay stay at the center of the circle forever are you going to do that just because of the symmetric point no you're going to get hungry you're going to move towards one of those levels of bread despite the fact that it breaks the symmetry so from this way he tried to argue being at this symmetric point may not be the preferred thing to do and this idea of spontaneous mystery breaking is something we just used today to describe many physical phenomena so spontaneous symmetry breaking is the feature that we now use but this idea was there thousands of years ago but applied incorrectly to the physical world but now we are using it so these ideas are coming back in different forms so i agree very much that the thought process is more important and these ideas are more interesting than the actual applications that people may find today did they use the language of symmetry and the symmetry breaking and spontaneous symmetry that's really interesting yes because like i could see a conception of the universe that kind of tends towards perfect symmetry and is stuck there like they not stuck there but achieves that optimal and stays there the idea that you would spontaneously break out of symmetry like have these perturbations like jump out of symmetry and back that's not that's a really difficult idea to uh to load into your head like where where does that come from and then and then the idea that you may not be at the center of the universe right that is a really tough idea right so symmetry sometimes is an explanation of being at the symmetric point is sometimes a simple explanation of many things like if you have a bowl a circular ball then the bottom of it is the lowest point so if you put a you know pebble or something it will slide down and go there at the bottom and stays there at the symmetric point because the preferred point the lowest energy point but if that same symmetric circular ball that you had had a bump on the on the bottom the bottom might not be at the center it might be on a circle on the table yeah in which case the pebble would not end up at the center would be the lower energy point symmetrical but it breaks the symmetry once it picks a point on that circle so so we can't have symmetry reasoning for where things end up or symmetry breakings like this example would suggest we talked about beauty i find geometry to be beautiful uh you have uh a few examples that are geometric in nature in your book how can geometry in ancient times or today be used to understand reality and maybe how do you think about geometry as a distinct tool in mathematics and physics yes geometry is my favorite part of math as well and greeks were enamored by geometry they tried to describe physical reality using geometry and principles of geometry and symmetry platonic solids the five solids they had discovered had these beautiful solids they thought it must be good for some reality there must be explaining something they attached you know one to air one to fire and so forth they try to give physical reality to symmetric objects these symmetric objects are symmetries of rotation and discrete symmetry groups we call today of rotation group in three dimensions now we know now we kind of laugh at the way they were trying to connect that symmetry to you know the laws of the the realities of of physics but actually it turns out in modern days we use symmetries in not too far away exactly in these kind of thoughts processes in the following way in the co in the context of string theory which is this the field i study we have these extra dimensions and these extra dimensions are compact tiny spaces typically but they have different shapes and sizes we have learned that if you if these extra shapes and sizes have symmetries which are related to the same rotation symmetries that the greek we're talking about if they enjoy those discrete symmetries and if you if you take that symmetry and quotient the space by that in other words identify points under these symmetries you get properties of that space at the singular points which force emanates from them what forces forces like the ones we have seen in nature today like electric forces like strong forces like weak forces so these same principles that was were driving them to connect geometry and symmetries to nature is driving today's physics now much more you know modern ideas but nevertheless the symmetries connecting geometry to physics in fact often we sometimes we have we ask the following questions suppose i want to get this particular you know physical reality i want to have this particles with these forces and so on what do i do it turns out that you can geometrically design the space to give you that you say oh i put the sphere here i would do this i will shrink them so if you have two spheres touching each other and shrinking through to zero size that gives you strong forces if you have one of them it gives you the weak forces if you have this you get that and if you want to unify forces do the other thing so these geometrical translation of physics is one of my favorite things that we have discovered in modern physics in the context of strength theory the sad thing is when you go into multiple dimensions and we'll talk about it is we start to lose our capacity to uh visually intuit the world we're discussing and then we go into the realm of mathematics and we'll lose that unfortunately our brains are such that we're limited but before we go into that mysterious beautiful world let's take a small step back and you also in your book have this kind of through the space of puzzles through the space of ideas have a brief history of physics of physical ideas now we we talked about newtonian mechanics uh leading all through different lagrangian hamiltonian mechanics can you describe some of the key ideas in the history of physics maybe lingering on each from electromagnetism to relativity to quantum mechanics and to today as we'll talk about with quantum gravity and strength theory sure so um i mentioned the classical mechanics and the euler lagrangian formulation one of the next important milestones for physics were the discoveries of laws of their christian magnetism so maxwell put put the discoveries all together in the context of what we call the maxwell's equations and he noticed that when he put these discoveries that you know faradays and others had made about electric and magnetic phenomena the in terms of mathematical equations it didn't quite work there was a mathematical inconsistency now uh you know one could have had two attitudes won't say okay who cares about math i'm doing nature you know electric force magnetic force math i don't care about but it bothered him it was inconsistent the equations you were writing the two equations he had written down did not agree with each other and this bothered him but he figured out you know if you add this jiggle this equation by adding one little term there it works at least it's consistent what is the motivation for that term he said i don't know have we seen it in experiments no why did you add it well because of mathematical consistency so he said okay math forced him to do this term he added this term which we now today call the maxwell term and once he added that term his equations were nice you know differential equations mathematically consistent beautiful but he also found the new physical phenomena he found that because of that term he could now get electric and magnetic waves moving through space at a speed that he could calculate so he calculated the speed of the wave and low and behold he found it's the same as the speed of light which puzzled him because he didn't think light had anything to do with electricity and magnetism but then he was courageous enough to say well maybe light is nothing but these electric and magnetic fields moving around and he didn't he wasn't alive to see the verification of that prediction and indeed was true so this mathematical inconsistency which which we could say you know this mathematical beauty drove him to this physical very important connection between light and electric magnetic phenomena which was later confirmed so then physics progresses and it comes to einstein einstein looks at maxwell's equation this is beautiful these are a nice equation except we get one speed light who measures this light speed and he asks the question are you are you moving are you not moving if you move the speed of light changes but maxwell's equation has no hint of different speeds of light it doesn't say oh only if you're not moving you get the speed it's just you always get this speed so einstein was very puzzled and he he was daring enough to say well you know maybe everybody gets the same speed for light yeah and that motivated his theory of special relativity and this is an interesting example because the idea was motivated from physics from maxwell's equations from the fact that people tried to try to measure the properties of ether which was supposed to be the medium in which the light travels through and the idea was that only in that in that medium the speed the speed of if you're at rest with respect to the ether this speed the speed of light then if you're moving the speed changes and people did not discover it michaelson and morley's experiments showed there is no ether so uh then einstein was courageous enough to say you know light is the same speed for everybody regardless of whether you're moving or not and the interesting thing is about special theory of relativity is that the under the math underpinning it is very simple it's linear algebra nothing terribly deep you can teach it at a high school level if not earlier okay is does that mean einstein's especially relativity is boring not at all so this is an example where simple math you know linear algebra leads to deep physics einstein's theory of special relativity motivated by this inconsistency at maxwell equation would suggest for the speed of light depending on who observes it what's the most daring idea there that that the the speed of light could be the same everywhere that's the basic that's the guts of it that's the core of einstein's theory that statement underlies the whole thing speed of light is the same for everybody is hard to swallow and it doesn't sound right it sounds completely wrong on the face of it and it was it took einstein to make to make this the daring statement it would be it would be laughing in some sense how could possibly how could anybody make this possibly ridiculous claim and it turned out to be true how does that make you feel because it it still sounds ridiculous it sounds ridiculous until you learn that our intuition is at fault about the way we conceive of space on time the way we think about space on time is wrong because we think about the nature of time as absolute and part of it is because we live in a situation where we don't go with very high speeds that our speeds are small compared to the speed of light and therefore the phenomena we we observe does not distinguish the relativity of time the time also depends on who measures that there's no absolute time when you say it's noon today now it depends on who's measuring it and it not everybody would agree with that statement and to see that you will have to have fast observer moving you know speeds close to speed of light so so this shows that our intuition is at fault and a lot of the discoveries in physics precisely is getting rid of the wrong old intuition and it is funny because we get rid of it but it always lingers in us in some form like even when i'm describing it i feel like a little bit like isn't it you know funny as you're just feeling the same way it is yes it is but we kind of replace it by an intuition and actually there's a very beautiful example of this how physicist do this try to replace their intuition and i think this is one of my favorite examples about how physicists develop intuition it goes to the work of galileo so you know again uh let's go back to greek philosophers or maybe aristotle in this case now again let's let's make a criticism he thought that objects the heavier objects fall faster than the lighter objects makes sense it kind of makes sense and you know people say about feather and swan but that's because of the air resistant but you might think like if you have a heavy stone and a light pebble the heavy one will fall first if you don't you know do any experiments that's the first gut reaction i would say everybody would say that's the natural thing galileo did not believe this and he kind of did the experiment famously it said he went on the top of piso tower and he dropped you know these heavy and light stones and they fell at the same time when they he dropped it at the same time from the same height okay good so he said i'm done you know i've showed that the heavy and lighter objects fought the same time i did the experiment scientists at that time did not accept it why was that because at that time science was not just experimental the experiment was not enough they didn't think that they have to sort their hands in doing experiments to get to the reality they said why is it the case why so galileo had to come up with an explanation of why heavier and lighter objects fought the same ray this is the way he convinced them using symmetry he said suppose you have three bricks the same shape the same size same as everything and we hold these three bricks at the same height and drop them which one will fall to the ground first everybody said of course we know that symmetry tells you know they're all the same shape same size same height of course they fall at the same time yeah we know that next next it's trivial he says okay what if we move these bricks around with the same height does it change the time they hit the ground they said if it's the same height again by the symmetry principle because the height translation horizontal translation the symmetry no it doesn't matter they all fall the same rate good doesn't matter how close i bring them together no it doesn't okay suppose i make the two bricks touch and then let them go do they fall out the same raid yes they do but they said well the two bricks that touch are twice more mass than this other brick and you just agreed that they fought the same rate they say yeah yeah we just agreed that's right that's strange yes so he deconfused them by the symmetry design so this way of repackaging some intuition a different intuition when the intuitions clash then you then you decide on the you replace the intuition that's brilliant i i in some of these dif more difficult physical ideas physics ideas in the 20th century in the 21st century it starts becoming more and more difficult than replace the intuition you know what does the world look like for an object traveling close to the speed of light you start to think about like the edges of supermassive black holes and you start to think like what what's that look like or uh i've been re into gravitational waves recently it's like when the fabric of space-time is being morphed by gravity like what's that actually feel like if i'm writing a gravitational wave what's that feel like i mean i think some of those are more sort of hippie not useful uh intuitions to have but if you're an actual physicist or whatever the particular discipline is i wonder if it's possible to meditate to sort of uh escape through thinking prolonged thinking and meditation on a war on a world like live in a visualized world that's not like our own in order to understand a phenomenon deeply so like replace the intuition like through rigorous meditation on the idea in order to conceive of it i mean if we talk about multiple dimensions i wonder if there's a way to escape with the three-dimensional world in our mind in order to then start to reason about it it's uh the more i talk to topologists the more they seem to not operate at all at all in the visual space they really trust the mathematics like which is really annoying to me because topology and differential geometry feels like it has a lot of potential for beautiful pictures yes i think they do actually i would not be able to uh do my my research if i don't have an intuitive feel about geometry and i i will get to it as you mentioned late uh before that how for example in strength there you deal with these extra dimensions and i'll be very happy to describe how we do it because with that intuition we will not get anywhere and i i don't think you can just rely on formalism i don't i don't think any physicist just relies on formalism that's not physics that's not understanding so we have to intuit it and that's crucial and this there are steps of doing it and we learned it might not be trivial but we learned how to do it similar to this galileo picture i just told you you have to build these gradually but about to connect the bricks literally yeah so yeah so then uh so going back to your question about this the path of the history of the science so i was saying about the existing magnesium and the special relativity where simple idea led to special relativity but then he went further thinking about acceleration in the context of relativity and he came up with general relativity where he talked about you know the fabric of space time being curved and so forth and matter affecting the the curvature of the space on time so so this gradually became a connection between geometry and physics namely he replaced newton's you know gravitational force with a very geometrical beautiful picture it's much more elegant than newton's but much more complicated mathematically so so when we say it's simpler we mean in some form it's simpler but not in pragmatic terms of equation solving the equations are much harder to solve in einstein's theory and in fact so much so much harder that einstein himself couldn't solve many of his many of the cases he thought for example you couldn't solve the equation for a spherical symmetric matter uh like like if you had this symmetric sun he didn't think you can actually write this solve his equation for that and a year after he he said that it was solved by by short child so it was it was that hard that he didn't think it's going to be that easy so yeah the formalism is hard but the contrast between the special relativity and general relativity is very interesting because one of them has almost trivial math and the other one has super complicated math both are physically amazingly important and so so we have learned that you know the physics may or may not require complicated math we should not shy from using complicated math like einstein did nobody einstein wouldn't say i'm not going to touch this math because it's too much you know tensors or you know curvature and i don't like four-dimensional space-time because i can't see four-dimension he wasn't doing that he was willing to abstract from that because physics drove him in that direction but his motivation was physics physics pushed him just like newton pushed to develop calculus because physics pushed him that he didn't have the tools so he had to develop the tools to answer his physics questions so his motivation was physics again so to me those are examples which showed that math and physics have this symbiotic reality relationship which which kind of reinforce each other here i'm using i'm giving you examples of both of them namely newton's work led to development of mathematics calculus and in the case of einstein he didn't develop the premium geometry just use them so so it goes both ways and in the context of modern physics we see that again and again it goes both ways let me ask a ridiculous question you know you talk about your favorite soccer player at a bar i'll ask the same question about einstein's ideas which is uh which one do you think is the biggest leap of genius is it the uh e equals mc squared is the brownian motion is it special relativity is the general relativity which which of of the famous set of papers he's written in 1905 and in general his work was the biggest leap of genius in my opinion special relativity the idea that speed of light is the same for everybody is the beginning of everything he did at the beginning is this the beginning it's just once you embrace that weirdness the all the weirdness i would say that's that's it even though he says the most beautiful moment for him yes he says that is when he realized that if you fall in an elevator you don't know if you're falling or whether you're in the whether you're in the falling elevator or whether you're next to the earth gravitational field that that to him was his aha moment which inertial mass and gravitational mass being identical geometrically and so forth as part of the theory not because of uh you know some some funny coincidence uh that's for him but i feel from outside at least it feels like the speed of light being the same is the is the really aha moment the general relativity to you is not like the conception of space time in a sense the conception of space time already was part of the speciality when you talk about length contraction so general relativity takes that to the next step but beginning of it was already space link contracts time dilays so once you talk about those then yeah you can dilate more or less different places than it's curvature so you don't have a choice so it's kind of started just with that same simple thought speed of light is the same for all where does uh quantum mechanics come into view exactly so this is the next step so einstein's you know uh develops general activity and is beginning to develop the foundation of quantum mechanics at the same time the photoelectric effects on others and um so so quantum mechanics overtakes in fact einstein in many ways because he doesn't like the probabilistic interpretation of quantum mechanics and the formulas that's emerging but physicists march on and try to for example combine einstein's theory of relativity with quantum mechanics so dirac takes special relativity tries to see how is it compatible with quantum mechanics can we pause and briefly say what is quantum mechanics oh yes sure so quantum mechanics so i i discussed briefly when i talked about the connection between newtonian mechanics and the euler lagrangian formulation of of the newtonian mechanics and interpretation of this audio dot grunge formalism in terms of the paths that the particle take so when we say a particle goes from here to here we usually think it classically it follows a specific trajectory but actually in quantum mechanics it falls follows every trajectory with different probabilities and so there's this fuzziness now most probable it's the path that you actually see and the deviation from that is very very unlikely and probabilistically very minuscule so in everyday experiments we don't see anything deviated from what we expect but quantum mechanics tells us that the things are more fuzzy things are are not as precise as the line you draw things are a bit like cloud so if you go to microscopic uh scales like atomic scales and lower these phenomena become more pronounced you can see it much better the electron is is not at the point but the clouds spread out around the nucleus and so this fuzziness this probabilistic aspect of reality is what quantum mechanics describes can i briefly pause on that on that idea do you think this is quantum mechanics is just a really damn good approximation a tool for predicting reality or does it actually describe reality do you think reality is fuzzy at that level well i think that reality is fuzzy at that level but i don't think quantum mechanics is necessarily the end of the story right so um so quantum mechanics is certainly an improvement over classical physics that much we know by experiments and so forth whether i'm happy with quantum mechanics whether i view quantum mechanics for example the the thought the measurement uh description of quantum mechanics am i happy with it am i thinking that's the end stage or not i don't i don't think we're at the end of that story and many physicists may or may not view this way some do some don't but i think that it's the best we have right now that's for sure it's the best approximation for reality we know today and so far we don't know what it is the next thing that improves it or replaces it and so on so but as i mentioned before i don't believe any of the laws of physics we know today are friends that's exactly correct it doesn't bother me yes i'm not like dogmatic say i have figured out this is the law of nature i know everything no no that's that's the the beauty about science is that we are not dogmatic and we are we are willing to in fact we are encouraged to be skeptical of what we ourselves do so you were talking about dirac yes i was talking about direct right so direct was trying to now combine this schrodinger's equations which which was described in the context of you know trying to talk about how these probabilistic waves of electrons move for the atom which was good for for speeds which were not too close to the speed of light to what happens when you get to the near the speed of light so then you need relativity so then dirac tried to combine einstein's relativity with quantum mechanics so he tried to combine them and he wrote this beautiful equation the dirac equation which roughly speaking take the square root of of the einstein's equation in order to connect it to schrodinger's time evolution operator which is first order in time derivative to get rid of the the naive thing that einstein's equation would have given which is second order so you have to take a square root now square root usually has a plus or minus sign when you take it and when he did this he originally didn't notice this didn't pay attention to this plus or minus sign but later physics pointed out to direct says look there's also this minus sign and if you use this minus sign you get negative energy in fact it was very very annoying that you know somebody else tells you this obvious mistake you make paulie famous physicist told direct this is nonsense you're going to get negative energy with your equation with negative energy without any bottom you can go all the way down to negative infinite energy so it doesn't make any sense direct thought about it and then he remembered paulie's exclusion principle before just before him paulie had said you know there's this principle called the exclusion principle that you know two or two electrons cannot be on the same orbit and so direct said okay you know what all these negative energy states are filled orbits occupied so according to you uh mr paulie there's no place to go so therefore they only have to go positive sounded like a big cheat and then paulie said oh you know what we can change orbits from one orbit to another what if i take one of these negative energy orbits and put it up there then it seems to be a new particle which has opposite properties to the electron has positive energy but it has positive charge what is that like the iraq was a bit worried he said maybe that's proton because proton has plus charge he wasn't sure but then he said oh maybe it's proton but then they said no no no it has the same mass as the electron cannot be proton because proton is heavier the iraq was stuck he says well then maybe another part we haven't seen by that time dirac himself was getting a little bit worried about his own equation and his own crazy interpretation yes until a few years later anderson in photographic cosmic uh in the photographic place that he had gotten from this cosmic rays he discovered a particle which goes in the opposite direction that the electron goes when there's a magnetic field and with the same mass exactly like what the iraq had predicted and this was what we call now positron and in fact beginning with the work of dirac we know that every particle has an anti-particle and so this idea that there's an anti-particle came from the simple math you know there's a plus and a minus from the directs quote-unquote mistake so again trying to combine ideas sometimes the math is smarter than the person who uses it to apply it and you try to resist it and then you you kind of confront it by criticism which is the way it should be so physicist comes and said no no that's wrong and you correct it and so on so that is the development of the idea there's particle there's antiparticle and so on so this is the beginning of development of quantum mechanics and the connection with relativity but the thing was more challenging because we had to also describe how electric and magnetic fields work with quantum mechanics this was much more complicated because it's not just one point electric and magnetic fields were everywhere so you had to talk about fluctuating and a fuzziness of electrical field and magnetic fields everywhere and the math for that was was was very difficult to deal with and this led to a subject called quantum field theory fields like electric and magnetic field to be quantum had to be described also in a wavy way feinman in particular was one of the pioneers along with schwinger's and others to try to come up with the formalism to deal with fields like electric and magnetic fields interacting with electrons in a consistent quantum fashion and they just developed this beautiful theory quantum electrodynamics from that and later on that same formalism quantum field theory led to the discovery of other forces and other particles all consistent with the idea of quantum mechanics so that was how physics progressed and so basically we learned that all particles and all the forces are are in some sense related to particle exchanges and so for example electromagnetic forces are are mediated by a particle we call photon and uh and so forth and the same for other forces that they discovered strong forces and the weak forces so so we got the sense of what quantum field theory is is that a big leap of uh of an idea that uh particles are fluctuations in the field like the idea that everything is a field is the old einstein light is a wave both a particle and a wave kind of idea is that is that a huge leap in our understanding of conceiving the universe's fields i would say so i would say that on viewing the particles this duality that bore mentioned between particles and waves that waves can behave sometimes like particles sometimes like waves is one of the biggest leaps of imagination that quantum mechanics made physics do so i agree that that is quite remarkable is duality fundamental to to the universe or is it just because we don't understand it fully like we'll eventually collapse into a clean explanation that doesn't require duality like th that that a phenomenon could be two things at once and both to be true so that seems weird so in fact i i i was going to get to that when we get to string theory but maybe i can comment on that now duality turns out to be running the show today is the whole thing that we are doing in strength duality is the name of the game so it's the most beautiful subject i want to talk about let's let's talk about it in the context let's talk about the other strengths so we uh do want to take a next step into because we mentioned general relativity we mentioned quantum mechanics is there something to be said about quantum gravity yes that's exactly the right point to talk about so namely we have talked about quantum fields and i talked about electric forces photon being the particle carrying those forces so for gravity quantizing gravitational field which is this curvature of space time according to einstein you get another particle called graviton so what about gravitons should be there no problem so then you start computing it what do i mean by computing it well you compute scattering of one graviton off another graviton maybe with graviton with an electron and so on see what you get feynman had already mastered the this quantum electrodynamics you said no problem let me do it even though these are such weak forces the gravity is very weak so therefore to see them these quantum effects of gravitational waves is was impossible it's even impossible today so feynman just did it for fun he usually you know had this mindset that i want to do something which i will see an experiment but this one let's just see what it does and he was surprised because the same techniques he was using for doing the same calculations quantum electrodynamics when applied to gravity failed the formula seemed to make sense but he had to do some integrals and he found that when he does those integrals he got infinity and it didn't make any sense now there are similar infinities in the other pieces that but he had managed to make sense out of those before this was no way he could make sense out of it he just didn't know what to do he didn't feel as an urgent issue because nobody could do the experiment so he was kind of said okay there's this thing but okay we don't know how to exactly do it but but that's the way it is so in some sense a natural conclusion from what feynman did could have been like gravity cannot be consistent with quantum theory but that cannot be the case because gravity is in our universe quantum mechanics is our universe they both together somehow it should work so it's not acceptable to say you know they don't work together so so that was a puzzle how does it possibly work it was left open and then we get to the string theory so this is the puzzle of quantum gravity the particle description of quantum gravity fails so the infinity shows up what do we do what do we do with infinity let's get to the fun part let's talk about string theory yes uh let's uh discuss some technical basics of uh string theory what is string theory what is the string how many dimensions are we talking about what are the different states how do we represent the elementary particles and the laws of physics using this new framework so string theory is the idea that the fundamental entities are not particles but extended higher dimensional objects like one-dimensional strings like loops these loops could be open like with two ends like an interval or a circle without any ends so and they're vibrating and moving around in space so how big they are well you can of course stretch it and make it big or you can just let it be whatever it wants it can be as small as a point because the circle can shrink to a point and be very light or you can you know stretch it and becomes very massive or it could oscillate and become massive that way so depends on which kind of state you have in fact this string can have infinitely many modes depending on which kind of oscillation it's doing like a guitar has different harmonics string has different harmonics but for the string each harmonic is a particle so each particle will give you ah this is a more massive harmonic this is a less mass so the lightest harmonic so to speak is no harmonics which means like a string strung to a point and then it becomes like a massless particles or light particles like photon and graviton and so forth so when when you look at tiny strings which are strong to a point the lightest ones they look like the particles that we we think they're like particles in other words from far away they look like a point but of course if you zoom in there's this tiny little you know little circle that's there that's strong to almost a point should we be imagining this is to the visual intuition should we be imagining literally strings that are potentially connected as a loop or not when you and when somebody outside of physics is imagining a basic element of string theory which is a string should we literally be thinking about a string yes you should literally think about string but string with zero thickness with zero thickness so notice it's a it's a it's a loop of energy so to speak if you can think of it that way and so there's a tension like the regular string if you pull it there's you know you have to you have to stretch it but it's not like a thickness like you're made of something it's just energy it's not made of atoms or something like that but and it is very very tiny much smaller than uh elementary particles of physics much smaller so we think if you let the string to be by itself the lowest state they'll be like a fuzziness or a size of that tiny little circle which is like a point about could be anything between we don't know the exact size but in different models have different sizes but something of the order of 10 to the minus let's say 30 centimeters so 10 to the minus 30 centimeters just to compare with the size of the atom which is 10 to the minus 8 centimeters is 22 orders of magnitude smaller so so unimaginably small very small so we basically think from far away string is like a point particle and that's why a lot of the things that we learned about point particle physics carries over directly to strings so therefore there's not not much of a mystery why particle physics was successful because string is like a particle when it's not stretched but it turns out having this size being able to oscillate get bigger turned out to be resolving these puzzles that feynman was having in calculating his diagrams and it gets rid of those infinities so when you're trying to do those infinities the regions that give infinities to feynman as soon as you get to those regions then this string starts to oscillate and these oscillation structure of the strings resolves those infinities to finite answer at the end so the size of the string the fact is one dimensional gives a finite answer at the end resolves this paradox now perhaps it's also useful to recount of how string theory came to be yes because it wasn't like somebody said well let me solve the problem of einstein's solve the problem that feynman had with unifying einstein stated with quantum mechanics by replacing the point by a string no that's not the way the thought process the thought process was much more random physicist veneziano in this case was trying to describe the interactions they were seeing in colliders in in accelerators and they were seeing that some process in some process when two particles came together and joined together and went they were separately in one way and the opposite way they behaved the same way in some way there was a symmetry a duality which she didn't understand the particles didn't seem to have that symmetry he said i don't know what it is what's the reason that these colliders and experiments we're doing seems to have the symmetry but let me write a mathematical formula which exhibits that symmetry he used gamma functions beta functions and all that you know complete math no physics other than trying to get symmetry out of his equation he just wrote down a formula as the answer for a process not not a method to compute it just say wouldn't it be nice if this was the answer yes this is looked at this one that's intriguing it has the symmetry all right but what is this where is this coming from which which kind of physics gives you this so i don't know yeah a few years later people saw that oh the equation that you're right is the process you're writing in the intermediate channels that particles come together seems to have all the harmonics harmonic sounds like a string let me see if what you're describing has anything with the strings and people try to see if what he's doing has anything with the strings oh yeah indeed if i study scattering of two strings i get exactly the formula you wrote down that was the reinterpretation of what he had written in the formula as a string but still had nothing to do with gravity it had nothing to do with resolving the problems of gravity with quantum mechanics it was just trying to explain a process that people were seeing in hydronic physics collisions so it took a few a few more years to get to that point they did notice that physics notice that whenever you try to find the spectrum of strings you always get a massive particle which has exactly the properties that the graviton is supposed to have and no particle in hydronic physics that had that property you are getting a massless graviton as part of this scattering without looking for it it was forced on you people were not trying to solve quantum gravity quantum gravity was pushed on them i don't want this graviton get rid of it they couldn't get rid of it they gave up trying to get rid of it physicists said shark and shorts said you know what strength is theory of quantum gravity they change their perspective altogether we are not describing the hydronic physics we are describing this theory of quantum gravity and that's when string theory probably got like exciting that this could be the unifying theory exactly it got exciting but at the same time not so fast namely it should have been fast but it wasn't because particle physics through quantum filter was so successful at that time this is mid 70s standard model of physics electromagnetism and unification of electromagnetic forces with all the other forces were beginning to take place without the gravity part everything was working beautifully for particle physics and so that was the shining golden age of quantum field theory and all the experiments standard model this and that unification and spontaneous symmetry breaking was taking place all of them was nice this was kind of like a sideshow and nobody was paying so much attention this exotic string is needed for quantum gravity ah maybe there's other ways maybe we should do something else so yeah it wasn't paid much attention to and this took a little bit more effort to try to actually connect it to to the reality there are a few more steps first of all there was a puzzle that you were getting extra dimensions string was not working well with three spatial dimensions on one time it needed extra dimension now there are different versions of strings but the version that ended up being related to having particles like electron what we call fermions needed 10 dimensions what we call super string now why super white the word super it turns out this uh this version of the string which had fermions had an extra symmetry which we call supersymmetry this is a symmetry between a particle and another particle with exactly the same properties same mass same charge etc the only difference is that one of them has a little different spin than the other one and one and one of them is the boson one of them is a fermion because of that shift of spin otherwise they're identical so there was this symmetry string theory had the symmetry in fact supersymmetry was discovered through string theory theoretically so theoretically the first place that this was observed when when you were describing these fermionic strings so that was the beginning of the study of supersymmetry was the via string theory and then it had remarkable properties that you know this symmetry meant and so forth that people began studying supersymmetry after that and that was continuation that was kind of a tangent direction at the beginning for string theory but people in particle physics started also thinking oh supersymmetry is great let's see if we can have supersymmetry in particle physics and so forth forget about strings and they developed on a different track as well supersymmetry in different models became a subject on its own right understanding supersymmetry and what does this mean because it unified bosons and fermi and unifies some ideas together so photon is a boson electron is a fermion could things like that be somehow related it was a kind of a natural kind of a question to try to kind of unify because in physics we love unification now gradually string theory was beginning to show signs of unification it had graviton but people found that you also have things like photons in them different excitations of string behave like photons another one behaves like electron so a single string was unifying all these particles into one object that's remarkable it's in ten dimensions though it is not our universe because we live in three plus one dimension how could that be possibly true so this was a conundrum it was elegant it was beautiful but it was very specific about which dimension you're getting which structure you're getting it wasn't saying oh you just put d equals to four you'll get your space time dimension that you want no it didn't like that it said i want ten dimensions and that's the way it is so it was very specific now so people try to reconcile this by the idea that you know maybe these extra dimensions are tiny so if you take three macroscopic spatial dimensions on one time and six extra tiny spatial dimensions like tiny spheres or tiny circles then it avoids contradiction with manifest fact that we haven't seen extra dimensions in experiments today so that was a way to avoid conflict now this was a way to avoid conflict but it was not observed in experiments a string observed in experiments no because it's so small so it's beginning to sound a little bit funny similar feeling to the way perhaps drag had felt about this positron plus or minus you know it was beginning to sound a little bit like oh yeah not only i have to have ten dimension but i also have to this i have to also listen and so you so conservative physicists would say um you know i haven't seen these experiments i don't know if they are really there are you pulling my leg i do you want me to imagine things that are not there so this was an attitude of some physicist towards string theory despite the fact that the puzzle of gravity and quantum mechanics merging together work but still was this skepticism you're putting all these things that you want me to imagine there are these extra dimensions that i cannot see uh-huh and you want me to believe that stream that you have not even seen experiments are real uh-huh okay what else do you want me to believe so it was kind of beginning to sound a little funny now i was i would pass forward forward a little bit further um a few decades later when string3 became the mainstream of efforts to unify the forces and particles together we learned that these extra dimensions actually solved problems they weren't in nuisance the way they originally appeared first of all the properties of these extra dimensions reflected the number of particles we got in four dimensions if you took these six dimensions to have like six five holes or four holes that tend to change the number of particles that you see in four dimensional space time you get one electron and one muon if you had this but if you did the other j shape you get something else so geometrically you could get different kinds of physics so it was kind of in a mirroring of geometry by physics down in the macroscopic space so these extra dimensions were becoming useful fine but we didn't need the extra dimensions to just write an electron in three dimensions we did we wrote it so so what was there any other puzzle yes there were hawking hawking had been studying black holes in mid 70s following the work of wickenstein who had predicted that black holes have entropy so wickenstein had tried to attach the entropy to the black hole if you throw something into that black hole the entropy seems to go down because you have something entropy in outside the black hole and you throw it entropy was you it black was unique so the entropy did not have any blackout no entropy so you seem the entropy seem to go down and so that's against the laws of thermodynamics so beckenstein was trying to say no no therefore black must have an entropy so he was trying to understand that he found that if you assign entropy to the to be proportional to the area of the black hole it seems to work and then hawking found not only that's correct he found the correct proportionality factor of factor of one quarter of the area and planck units is the correct amount of entropy and he gave an argument using quantum semi-classical arguments which barely which means basically using a little bit of a quantum mechanics because he didn't have the full quantum mechanics of string there he could do some aspects of approximate quantum arguments so heuristic quantum arguments led to this entropy form formula but then he didn't answer the following question he was getting a big entropy for the black hole the black hole with the size of the horizon of a black hole is huge has a huge amount of entropy what are the microstates of this entropy when you say for example the gaseous entropy you count where the atoms are you count this this bucket or that but there's an information about there and so on you count them for the black hole the way hawking was thinking there was no degree of freedom you throw them in and there was just one solution so where are these entropy what are what are these microscopic states they were hidden somewhere so later in string theory uh the work that we did with my colleague strong manager in particular showed that these ingredients in string theory of black hole arise from the extra dimensions so the degrees of freedom are are hidden in terms of things like strings wrapping these extra circles in these hidden dimensions and then we started counting how many ways like the strings can wrap around this circle and the extra dimension or that circle and counted the microscopic degrees of freedom and lo and behold we got the microscopic degrees of freedom that hawking was predicting four dimensions so the extra dimensions became useful for resolving a puzzle in four dimensions the puzzle was where are the degrees of freedom of the black hole hidden the answer hidden in the extra dimensions the tiny extra dimensions so then by this time it was beginning to we see aspects that extra dimensions are useful for many things it's not a nuisance it wasn't to be kind of you know be ashamed of it was actually in the welcome features new feature nevertheless how do you intuit the 10-dimensional world so yes it's a feature for describing certain phenomena like the the entropy in black holes but what you said that to you a theory becomes real or becomes powerful when you can connect it to some deep intuition so how do we intuit yes ten dimensions yes um so i will i will explain uh how some of the analogies work first of all we do a lot of analogies and by analogies we build intuition so i will i will start with this example i will try to explain that if we are in 10 dimensional space if we have a seven dimensional plane and eight dimensional plane we ask typically in what space do they intersect each other in what dimension that might sound like how do you possibly give an answer to this so we start with lower dimensions we start with two dimensions we say if you have one dimension and a point do they intersect typically on a plane the answer is no so a line one dimensional a point zero dimension on a two dimensional plane they don't typically meet but if you have a one-dimensional line and another line which is one plus one on a plane they typically intersect at a point typically means if you're not parallel typically they intersect at a point so one plus one is two and in two dimension they intersect at the zero dimensional point so you see two dimension one and one two two minus two is zero so you get point out of intersection okay let's go to three dimension you have a plane two dimensional plane and a point do they intersect no two and zero how about a plane and a line a plane is two dimensional and a line is one two plus one is three in three dimension a plane and a line meet at points which is zero dimensionals three minus three is zero okay so plane and the line intersect at the point in three dimensions how about the plane on a plane in three d well plane is two and this is two two plus two is four in three d four minus three is one they intersect on a one dimensional line okay we're beginning to see the pattern okay now come to the question we're in ten dimensions now we have the intuition we have a seven dimensional plane and eight dimensional plane in ten dimension they intersect on a plane what's the dimension well seven plus eight is 15 minus 10 is 5. we draw the same picture as two planes and we write seven dimension eight dimension but we have gotten the intuition from the lower dimensional one what to expect it doesn't scare us anymore so we draw this picture we cannot see all the seven dimensions by looking at this two-dimensional visualization of it but it has all the features we want it has so i we draw this picture which is seven seven and they they meet at the five-dimensional plane it says five so we have we have build this intuition now this is an example of how we come up with intuition let me give you more examples of it because i think this will show you that people have to come up with intuitions to visualize that otherwise we will be a little bit uh lost so what you just described is kind of uh in these high dimensional spaces focus on the meeting place of uh two planes in high dimensional spaces exactly how the planes meet for example what's the dimension of their intersection and so on so how do we come up with the intuition we borrow examples from door dimensions build up intuition and draw the same pictures as if we are talking about 10 dimensions but we are drawing the same as the two dimensional plane because we cannot do any better but our our our words change but not our pictures so your senses we can have a deep understanding of reality by looking at its at slices a lower dimensional slice exactly exactly and this this is that comes brings me to the next example i want to mention which is sphere let's think about how do we think about the sphere well the sphere is a sphere you know the round nice thing but sphere has a circular symmetry now i can describe the sphere in the following way i can describe it by an interval which is think about this going from the north of the sphere to the south and at each point i have a circle attached to it so you can think about the sphere as a line with a circle attached with each point the circle shrinks to a circle string to a point at endpoints of the interval so i can say oh one way to think about the sphere is an interval where at each point on that interval there's another circle i'm not drawing but if you like you can just draw it say okay i won't draw it so from now on is this mnemonic i draw an interval when i want to talk about the sphere and you remember that the end points of the interval mean a strong circle that's all and they say yeah i see that's a sphere good now we want to talk about the product of two spheres that's four dimensional how can i visualize it easy you just take an interval and it's another interval that's just going to be a square yeah a square is a four dimensional space yeah why is that well at each point on the square there's two circles one for each of those directions you drew and when you get to the boundaries of each direction one of the circles shrink on each edge of that square and when you get to the corners of the square all both circles shrink this is a sphere times a sphere i have divine interval i just described for you a four-dimensional space do you want the six-dimensional space no problem take the take a corner of a room in fact if you want to have a sphere times a stick take sphere times the sphere times the sphere take a cube a cube is a rendition of this six dimensional space this two sphere times another sphere times on the sphere where three of the circles i'm not drawing for you for each one of those directions there's another circle but each time you get to the boundary of the cube one circle shrinks when the boundaries meet two circuit strings when three boundaries meet all the three circles shrink so i just give you a picture now mathematicians come up with amazing things like you know what i want to take a point in space and blow it up you know these concepts like topology and geometry complicated how do you do in this picture it's very easy blow it up in this picture means the following you think about this cube you go to the corner and you chop off a corner chopping off the corner replaces the point yeah you raise the point by triangle yes that's called blowing up a point and then this triangle is what they call p2 projective two space but these pictures are very physical and you feel it there's nothing amazing i'm not talking about six dimension four plus six is ten the dimension of string theory so we can visualize that no problem okay so that's building the intuition to a complicated world of string theory nevertheless these objects are really small and just like you said experimental validation is very difficult because the objects are way smaller than anything that we currently have the tools and accelerators and so on to uh to reveal through experiment so there's a kind of skepticism that's not just about the nature of the theory because of the 10 dimensions as you've explained but in that we can't experimentally validate it and it doesn't necessarily to date maybe can correct me predicts something fundamentally new so it's it's beautiful as an explaining theory which means that it's very possible that it is a fundamental theory that describes reality and unifies the laws but there's still a kind of skepticism and uh me from a sort of an outside observer perspective have been observing a little bit of a growing cynicism about string theory in the recent few years can you describe the cynicism about sort of by cynicism i mean a cynicism about the hope for this theory of pushing theoretical physics forward yes can you do describe why this is cynicism and how do we reverse that trend yes first of all the criticism uh for string theory uh is healthy in some in a sense that in science we we have to have different viewpoints and that's good so i don't i welcome criticism uh and the the the reason for criticism and i think that is a valid reason is that there has been zero experimental evidence for string theory that is no experiment has been done to show that there's you know there's this little loop of energy moving around and so that's a valid valid uh objection and valid worry and if i were to say you know what string theory can never be verified or experimentally checked that's the way it is they would have every right to say what you're talking about is not science because in science we will have to have experimental consequences and checks the difference between string theory and something which is not scientific is that string 3 has predictions the problem is that the predictions we have today of string theory is hard to access by experiments available with the energies we can achieve with the colliders today it doesn't mean there's a problem with string theory it just means technologically we're not that far ahead now we can have two attitudes you say well if that's the case why are you studying this subject because you can't do experiment today now this is becoming a little bit more like mathematics in that sense you say well i want to learn i want to know how the nature works even though i cannot prove it today that this is it because of experiments that should not prevent my mind not to think about it that's right so that's the attitude many string tears follow that that that should be like this now so that's that's the answer to the criticism but there's actually a better answer to the criticism i would say we don't have experimental evidence for string theory but we have theoretical evidence for string theory and what do i mean by theoretical evidence for string theory string theory has connected different parts of physics together it didn't have to it has brought connections between part of physics although suppose you're just interested in particle physics suppose you're not even interested in gravity at all it turns out there are partic properties of certain particle physics models that string theory has been able to solve using gravity using ideas from string theory ideas known as holography which is relating something which has to do with particles to something having to do with gravity why did it have to be this rich this subject is very rich it's not something we were smart enough to develop it came at us as i explained to you the development of string theory came from accidental discovery it wasn't because we were smart enough to come up with idea oh yeah string of course has gravity no it was accident discovery so some people say it's not fair to say we have no evidence for string theory graviton gravity is that evidence for string theory it's predicted by string theory we didn't put it by hand we got it so there's a qualitative check okay gravity is a prediction of string theory it's a postdiction because we know gravity existed but still logically it is a prediction because really we didn't know it had that graviton that we later learned that oh that's the same as gravity so literally that's the way it was discovered it wasn't put in by hand so so there are there are many things like that that there are there are different facets of physics like questions in condensed matter physics questions of particle physics questions about this and that has have come together to find beautiful answers by using ideas from string theory at the same time as a lot of new math has emerged that's an aspect which i wouldn't emphasize as evidence to physicists necessarily because they will say okay great you got some math but what's to do with reality but as i explained many of the physical principles we know of have beautiful math underpinning them so it certainly leads further confidence that we may not be going astray even though that's not the food proof as we know so so there are these aspects that give further evidence for string theory connections between each other connection with the real world but then there are other things that come about and i can try to give examples of that so so these are further evidences and these are certain predictions of string theory they are not as as as detailed as we want but there are still predictions why is the dimension of space on time three plus one see i don't know just just deal with it three plus one but in physics we want to know why well take a random dimension from one to infinity what's your random dimension a random dimension from one to infinity would not be four eight would most likely be a humongous number if not infinity i mean there's no if you choose any any reasonable distribution which goes from one to infinity three or four would not be your pick the fact that we are in three or four dimension is already strange the fact that string says sorry i cannot go beyond 10 or maybe 11 or something the fact that they're just upper bound the range is not from 1 to infinities from 1 to 10 or 11 or what not it already brings a natural prior oh yeah three or four is you know it's just on the average if you if you pick some of the compactifications then it could easily be that so in other words it makes it much more possible that it could be theory of our universe so the fact that the dimension already is so small it should be surprising we don't ask that question we should be surprised because we could have conceived of universes with our predimension why is it that we have such a small dimension that's number one so oh so so good theory of the universe should give you an intuition of the why it's four or three plus one and it's not obvious that it should be that that should be explained we take that as a as an assumption but that's a thing that should be explained yeah so we haven't explained that in string here actually i did write a model within string theory to try to describe why we end up with three uh plus one space time dimensions which are big compared to the rest of them and even though this has not been uh the technical difficulties to prove it is is still not there but i will explain the idea because the idea connects to some other piece of elegant math which is the following consider a a universe made of a box three-dimensional box or in fact if we start in string theory nine-dimensional box because we have nine spatial dimensions at one time so imagine a nine-dimensional box so we should imagine the box of the typical size of the string which is small so the universe would naturally small start with a very tiny nine dimensional box what do strings do well strings go you know go around the box and move around and vibrate and all that but also they can wrap around one side of the box to the other because i'm imagining a box with periodic boundary conditions so what we call the torus so the string can go from one side to the other this is what we call a winding string the string can wind around the box suppose you have you now evolve the universe because there's energy the universe starts to expand but it doesn't it doesn't expand too far why is it well because there are these strings which are wrapped around from one side of the wall to the other when the universe the walls of the universe are growing it is stretching the string and the strings are becoming very very massive so it becomes difficult to expand it kind of puts a halt on it in order to not with a halt a string which is going this way and a thing which is going that way should should uh intersect each other and disconnect each other and unwind so a string which is winds this way and the string which finds the opposite way should find each other to to to reconnect and this way disappear so if they find each other and they did these they disappear but how can strings find each other well the string moves and another string moves a string is one dimensional one plus one is two and one plus one is two and two plus two is four in four dimensional space time they will find each other in a higher dimensional space time they typically miss each other oh interesting so if the dimensions were too big they would miss each other they wouldn't be able to expand so in order to expand they have to find each other and three of them can't find each other and those can expand and the other one will be stuck so that explains why within string theory these particular dimensions are really big and full of exciting stuff that could be an explanation that's the model we we we suggested with my colleague brandenburger but it turns out to be related to a deep piece of math you see for mathematicians manifolds of dimension bigger than four are simple four dimension is the hardest dimension for math it turns out and it turns out the reason it's difficult is the following it turns out that in higher dimension you use you use what's called surgery in mathematical terminology where you use these two dimensional tubes to maneuver them off of each other so you have two plus two becoming four and higher than four dimension you can pass them through each other without them intersecting in fourth dimension two plus two doesn't allow you to pass them through each other so the same take things that work in higher dimension don't work in four dimension because two plus two is four the same reasoning i was just telling you about strings finding each other and four ends up to be the reason why four is much more complicated to classify for mathematicians as well so so there might be these these things so i cannot say that this is the reason that string theory is is giving you three plus one but it could be a model for it and so so there are these kind of ideas that could underlie why we have three extra dimensions which are large and the rest of our small but absolutely we have to have a good reason we cannot leave it like that can i ask a tricky human question so you are one of the seminal figures in string theory you got the breakthrough prize you worked with edward whitten there is no nobel prize that has been given on string theory you know credit assignment is tricky in science i've it makes you quite sad especially big like ligo big experimental projects when so many incredible people have been involved and yet the nobel prize is annoying in that it's only given to three people who do you think gets the nobel prize for string theory uh at first if it turns out that it um if not in full then in part is is a good model of the way the physics of the universe works who are the key figures maybe let's put nobel prize aside or the key figures i like the second version of the question because i think to try to give a prize to one person in string there doesn't do justice to the diversity of the subject that to me is so there was quite a lot of incredible people there in the history of quite a lot of people i mean starting with vanessa who wasn't talking about strings yes i mean he wrote down the the beginning of a string so we cannot ignore that for sure and so so you start with that and you go on with various other figures and so on so there are different epochs in string theory yes and different people have been pushing it and so for example the early epoch we just told you people like uh like veneziano and nambu and the saskan and others were pushing it green and shorts were pushing it and so forth so this was or shark and so on so these were the initial periods of pioneers i would say of string theory and then there were there were the mid 80s that uh edward whitten was the major proponent of string theory and he really changed the landscape of string theory in terms of what people do and how how we view it and i think his efforts brought a lot of attention to the community about a high energy community to focus on this effort as the correct theory of unification of forces so he brought a lot of research as well as of course the first rate work he himself did to this area so that's in 80s and onwards and also in mid 90s where he was one of the proponents of the duality revolution in string theory and with that came a lot of these other ideas that you know led to breakthroughs involving for example the example i told you about black holes and holography and the work that was later done by maldasena about the properties of duality between particle physics and quantum gravity and the connections the deeper connections of holography and it continues and there are many people within this range which i haven't even mentioned they have done fantastic important things how it gets recognized i think is secondary in my opinion than the appreciation that the effort is collective that in fact that to me is the more important part of science that gets forgotten for some reason humanity likes heroes and science is no exception we like heroes but i i personally try to avoid that trap i i feel and in my work most of my work is with colleagues i have much more collaborations than soul author papers and i enjoy it and i think that that's to me one of the most satisfying aspects of science is to interact and learn and debate ideas with colleagues because that influx of ideas enriches it and that's why i i find it interesting to me science if i was in an island and if i was developing strength here by myself and had nothing to do with anybody it would be much less satisfying in my opinion even if i could take credit i did it yeah it won't be as satisfying sitting alone with the yeah with a big metal drinking champagne no i think i think to me the collective work is more exciting and you mentioned my getting the breakthrough when i was getting it i made sure to mention that it is because of the joint work that i've done with colleagues at that time it was around 180 or so collaborators and i acknowledge them in the in the web page for them i write all of their names and the collaborations that led to this so to me science is fun when it's collaboration and yes there are more important and less important figures as in any field and that's true that's true in strength here as well but i think that i would like to view this as a collective effort so setting the heroes aside the nobel prize is a celebration of um what's the right way to put it that this idea turned out to be right so like you look at uh einstein didn't believe in black holes right and then black holes got their nobel prize right do you think string theory will get its nobel prize nobel prizes if you were to bet money if this was like if this was an investment meeting and we had to bet all our money do you think he gets the nobel prizes i think it's possible that none of the living physicists will get the nobel prize on string theory but somebody will because because unfortunately the technology available today is not very encouraging in terms of seeing directly evidence for string theory do you think this ultimately boils down to the nobel prize will be given when there is some direct or indirect evidence there would be but uh but i think that part of this breakthrough prize was precisely the appreciation that when we have sufficient evidence theoretical as it is and not experiment because of this technology lag you appreciate what what you think is the correct path so there are many people who have been have been recognized precisely because they may not be around when it actually gets experimented even though they discovered it so so there are there are many things like that that's going on in in science so i think that i would i would want to attach less significance to the recognitions of people and i i have i have a i have a second review on this which is there are people who you know who look at these works that people have done and put them together and you know make the next big breakthrough and they get identified with you know perhaps rightly with many of these you know new new visions but they are on the shoulders of these little scientists yes which don't get any recognition you know yeah you did this little work oh yeah you did this little work oh yeah yeah five of you oh yeah this showed this pattern and then somebody else it's not fair yeah to me to me those little guys which which kind of like like seem to do a little calculation here a little thing there which is not doesn't doesn't rise to the occasion of this grandiose kind of thing doesn't make it to the new york times headlines and so on deserve a lot of recognition and i think they don't get enough i would say that there should be this nobel prize for you know they have these doctors without borders a huge group they should do similar thing these string theories without borders kind of everybody is doing a lot of work and i think that i i would like to see that efforts recognized i think in the long arc of history we're all little guys and girls standing on the shoulders of each other i mean it's all going to look tiny in retrospective we celebrate the new york times uh it you know as a newspaper or the idea of a newspaper in a few centuries from now will be long forgotten yes especially in the countries of string theory we should have a very long term view yes exactly just as a tiny tangent we mentioned edward wooden and he in a bunch of walks of life for me as an outsider comes up as a person who is uh widely considered as like one of the most brilliant people in the history of physics just as a powerhouse uh of a human like the uh the exceptional places that a human mind can rise to yes uh you've gotten a chance to work with him what's he like yes more than that he was my advisor a phd advisor so i got to know him very well and i benefited from his insights in fact what you said about him is accurate he is he's not only brilliant but you know he is he's also multifaceted in terms of the impact he has had in not only physics but also mathematics you know he's got in the fields medal because of his work in mathematics and rightly so you know he has used his knowledge of physics in a way which impacted deep ideas in modern mathematics and that's an example of of the power of of these ideas in modern high energy physics and string theory that the applicability of it to to modern mathematics so he's uh he's quite uh exceptional individual we don't we don't come across such people a lot in history so i think yes indeed he's one of the rare figures in this history of of the subject he has had great impact on a lot of aspects of not just string theory a lot of different areas in physics and also yes in mathematics as well so i think what you said about him is accurate i had the pleasure of interacting with him as a student and and later on as colleagues writing papers together and so on what impact do you have on your life like what have you learned from him if you were to look at the trajectory of your mind of the way you approached science and physics and mathematics how did he uh perturb that trajectory yes he did actually so i can explain because when i was a student i i i the biggest impact by him uh clearly as a grad student at princeton so i think that was the time where i was a little bit confused about the relation between math and physics i got a double major in mathematics and physics at mit and because i really enjoyed both and i write the elegance and the rigor of mathematics and i like the power of ideas and physics and its applicability to reality and what it teaches about the real world around us but i saw this tension between rigorous thinking in mathematics and lack thereof in physics and this troubled me to no end i was troubled by that so i was at crossroads when i decided to go to graduate school in physics because i did not like some of the lack of rigors i was seeing in physics on the other hand to me mathematics even though it was rigorous something it it sometimes were i didn't see the point of it in other words when i see when i see you know the math theorem by itself could be beautiful but i really wanted more than that i want to say okay what did it teach us about something else something more than just math so i wasn't i wasn't that enamored with just math but physics was a little bit bothersome nevertheless i decided to go to physics and i decided to go to princeton and i started working with edward whitten as my thesis advisor and um at that time i was trying to put physics in rigorous mathematical terms i took quantum fifth theory i tried to make rigorous out of it and so on and no matter how hard i was trying i was not being able to do that and i was falling behind from my classes i was not learning much physics and i was not making it rigorous and to me it was this dichotomy between math and physics what am i doing i like math but this is not exactly risk there comes ed written as my advisor and i see him in action thinking about math and physics he was amazing in math he knew all about the math it was no problem with him but he thought about physics in a way which did not find this tension between the two it was much more harmonious for him he would draw the feynman diagrams but he wouldn't view it as a formalism he was viewed oh yeah the particle goes over there and this is what's going on and so wait you're thinking really is this particle this virtual this is really electron going there right yeah it's not it's not the formula perturbation no no you just feel like the electron you're moving with this guy and do that and so on and you're thinking invariantly about physics or the way he thought about relativity like you know i was thinking about you know this momentum says he was thinking invariantly about physics just like the way you think about invariant concepts in relativity which don't depend on the frame of reference he was thinking about the physics in in variant ways that the way that doesn't gives you a bigger perspective so this gradually helped me appreciate that interconnections between ideas and physics replaces mathematical rigor that the different facets reinforce each other you say oh i cannot rigorously define what i mean by this but this thing connects with this other physics i have seen and this other thing and they together form an elegant story and that replaced for me what i believed as a solidness which i found in math as a rigor and was solid i found that replaced the rigor and solidness in physics so i found okay that's the way you can hang on to it is not wishy-washy it's not like somebody is just not being able to prove it just making up a story it was more than that and it was no tension with mathematics in fact mathematics was helping it like friends and so much more harmonious and gives insights to physics so that's i think one of the main things i learned from interactions with written and i think that now perhaps i have taken that to a far extreme maybe he wouldn't go this far as i have namely i use physics to define new mathematics in a way which would be far less rigorous than a physicist might necessarily believe because i take the physical intuition perhaps literally in many ways that could teach us the man so now i've gained so much confidence in physical intuition that i make bold statements that sometimes you know takes math math friends off guard so an example of it is mirror symmetry so so we were studying these compactivation of string string geometries this is after my phd now i've by the time i've come to harvard we're studying these aspects of string compact education on these complicated manifolds six dimensional spaces called calabial manifolds very complicated and i noticed with a couple other colleagues that there was a symmetry in physics suggested between different calabias it suggested that you couldn't actually compute the euler characteristic of a calabria or the characteristic is counting the number of points minus the number of edges plus the number of faces minus so you can count the alternating sequence of properties of the space which is the topological property of a space so holy cat axis of the calabia was a property of the space and so we noticed that from the physics formalism if string moves in a calabia you cannot distinguish we cannot compute the euler characteristic you can only compute the absolute value of it now this bothered us because how could it do not compute the actual sign unless the both sides were the same so i conjectured maybe for every calabia with the other character is positive there's one with negative i told this to my colleague yao who was whose namesake is calabia um that i'm making this conjecture is it possible that for every calabia there's one with the opposite euler characteristic sounds not reasonable i said why he said well we know more claudia's with negative other characters than positive i said but physics says we cannot distinguish them at least i don't see how so we conjectured that for every calabia with one side there's the other one despite the mathematical evidence despite the mathematical evidence despite the expert telling us is not the right idea if a few years later this symmetric mirror symmetry between the sign with the opposite sign was later confirmed by mathematicians so this is actually the opposite view that is physics is so sure about it that you're going against the mathematical wisdom telling them they better look for it so taking the uh the the physical intuition literally and then having that drive the the mathematics exactly and by now we are so confident about many such examples that has affected modern mathematics in ways like this that we are much more confident about our understanding of what string theories these are another aspects other aspects of why we feel string terrorists cry it's doing these kind of things i've been hearing you talk quite a bit about uh string theory landscape and the swamp what the heck are those two concepts okay very good question so let's go back to what i was describing about feinman yes feinman was trying to do these diagrams for graviton and electrons and all that he found that he's getting infinities he cannot resolve okay the natural conclusion is that field theories and gravity and quantum theory don't go together and you cannot have it so in other words field theories and gravity are inconsistent with quantum mechanics period string theory came up with examples but didn't address the question more broadly that is it true that every field theory can be coupled to gravity in a quantum mechanical way it turns out that final is essentially right almost all particle physics theories no matter what you add to it when you put gravity in it doesn't work only rare exceptions work so string theory are those rare exceptions so therefore the general principle that feynman found was correct quantum field theory and gravity and quantum mechanics don't go together except for jules exceptional cases there are exceptional cases okay the the total vastness of quantum field theories that are there we called the set of quantum field theories possible things which ones can be consistently coupled to gravity we call that subspace the landscape the rest of them we call the swampland it doesn't mean they are bad quantum field theories they are perfectly fine but when you couple them to gravity they don't make sense unfortunately and it turns out that the the ratio of them then the number of theories which are consistent with gravity the to the ones which without the ratio of the area of the landscape to the swamp land in other words is measured zero and so the swamp land is infinitely large the swampland's infinitely large so let me give you one example take a theory in four dimension with matter with maximum amount of supersymmetry can you get it turns out a theory in four dimension with maximum amount of supersymmetry is characterized just with one thing a group what we call the gauge group once you pick a group you have to find your theory okay so does every group make sense yeah as far as quantum field theory every group makes sense there are infinitely many groups there are infinitely many quantum field theories but it turns out there are only finite number of them which are consistent with gravity out of that same list so you can take any group but only fine number of them the ones whose what we call the rank of the group the ones whose rank is less than 23. anyone bigger than rank 23 belongs to the sworn plan they're infinitely many of them they're beautiful field theories but not when you include gravity so so then this becomes a hopeful thing so in other words in our universe we have gravity therefore we are part of that jewel subset now is this joule subset small or large yeah it turns out that subset is humongous but we believe still finite the setup possibility is infinite but the set of consistent ones i mean the set of quantum features are infinite but the consistent ones are finite but humongous the fact that they're humongous is the problem we are facing in string theory because we do not know which one of these possibilities the universe we live in if we knew we could make more specific predictions about our universe we don't know and that is one of the challenges with string theory which point on the landscape which corner of this landscape do we live in we don't know so what do we do well there are there are principles that are beginning to emerge so i will give you one example of it you look at the patterns of what you're getting in terms of these good ones the ones which are in the landscape compared to the ones which are not you find certain patterns i'll give you one pattern you find in the all the ones that you get from string theory gravitational force is always there but it's always always the weakest force however you could easily imagine field theories for which gravity is not the weakest force for example take our universe if you take mass of the electron if you increase the mass of electron by huge factor the gravitational attraction of the electrons will be bigger than the electric repulsion between two electrons and the gravity will be stronger that's all it happens that's not the case in our universe because electron is very tiny in mass compared to that just like our universe gravity is the weakest force we find in all these other ones which are part of the good ones the gravity is the weakest force this is called the weak gravity conjecture we conjectured that all the points in the landscape have this property our universe being just an example of it so there are these qualitative features that we are beginning to see but how do we argue for this just by looking patterns just by looking string theory has this no that's not enough we need more more reason more better reasoning and it turns out there is the reasoning for this turns out to be studying black holes ideas of black holes turn out to put certain restrictions of what a good quantum filter should be it turns out using black hole the fact that the black holes evaporate the fact that the black holes evaporate gives you a way to to check the relation between the mass and the charge of elementary particle because what you can do you can take a charged particle and throw it into a charged black hole and wait it to evaporate and by the looking at the properties of evaporation you find that if it cannot evaporate particles whose mass is less than their charge then it will never evaporate you'll be stuck and so the possibility of a black hole evaporation forces you to have particles whose mass is sufficiently small so that the gravity is weaker so you connect this fact to the other fact so we begin to find different facts that reinforce each other so different parts of the physics reinforce each other and once they all kind of come together you believe that you're getting the principle correct so weak gravity conjecture is one of the principles we believe in has a necessity of these conditions so these are the predictions string they are making is that enough well it's qualitative it's a semi-quantity it's just that mass of the electron should be less than some number but that number is if i call that number one the mass of the electron turns out to be 10 to the minus 20 actually so it's much less than one it's not one but on the other hand there's a similar reasoning for a big black hole in our universe and if that evaporation should take place gives you another restriction tells you the mass of the electron is bigger than 10 to the is now in this case bigger than something it shows bigger than 10 to the minus 30 in the planck unit so you find uh-huh the mass of the electron should be less than one but bigger than ten to the minus thirty in our universe the mass of the electron stands to minus twenty okay now this kind of you could call postdiction but i would say it follows from principles that we now understand from string theory first principle so we are making beginning to make these kinds of predictions which are very much connected to aspects of particle physics that we didn't think are related to gravity we thought just take any electron mass you want what's the problem it has a problem with gravity and so that conjecture has also a happy consequence that it explains that our universe like why the heck is gravity so weak as a force uh and that's not only an accident but almost a necessity if these forces are to coexist effectively exactly so that's that's that's the reinforcement of of of what we know in our universe but we are finding that as a general principle so we want to know what aspects of our universe universe is forced on us like the weak gravity conjecture and other aspects do we how much of them do we understand can we have particles lighter than neutrinos or maybe that's not possible you see the neutrino mass it turns out to be related to dark energy in a mysterious way naively there's no relation between dark energy and a mass of a particle we have found arguments from within the swampland kind of ideas why it has to be related and so so they're beginning to be these connections between graph consistency of quantum gravity and aspects of our universe gradually being sharpened but we're still far from a precise quantitative prediction like we have to have such and such but that's the hope that we are going in that direction coming up with the theory of everything that unifies uh general relativity and quantum field theories um this is one of the big dreams of human civilization us descendants of apes wondering about how this world works so a lot of people dream what are your thoughts about sort of other out there ideas on theories of everything or unifying theories so there's a quantum loop gravity there's also more sort of like a friend of mine eric weinstein beginning to propose something called geometric unity so these kinds of attempts whether it's through mathematical physics or through other avenues or with stephen wolfram a more computational view of the universe again in his case it's these hyper graphs that are very tiny objects as well similarly string theory and trying to grapple with this world what do you think is there any of these uh theories that are compelling to you that are interesting that may turn out to be true or at least may turn out to contain ideas that are useful yes i think the latter i would say that the containing ideas that are true is my opinion was what these some of these ideas might be for example quantum gravity is to me not a complete theory of gravity in any sense but they have some nuggets of truth in them and typically what i expect happen and i have seen examples of this within string theory aspects which we didn't think are part of string theory come to be part of it for example i'll give you one example string was believed to be 10 dimensional and then there was this 11 dimensional super gravity and nobody know what the egg is that why are we getting 11 dimensional super gravity where a string is saying it should be 10 dimensional 11 was the maximum dimension you can have a super gravity but string was saying sorry we're 10 dimensional so for for a while we thought that theory is wrong because how could this be because string tear is definitely theory of everything we later learned that one of the circles of string theory itself was tiny that we had not appreciated that fact and we discovered by doing thought experiments and string theory that there's got to be an extra circle and that circle is connected to an 11-dimensional perspective and that's what later on god's called m theory so so so there are these kind of things that you know we do not know what exactly string theory is we're still learning so we do not have a final formulation of string theory it very well could be that different facets of different ideas come together like loop quantum gravity or whatnot but i wouldn't put them on par namely loop quantum gravity is a scatter of ideas about what happens to space when they get very tiny for example you replace things by discrete data and try to quantize it and so on and you know it sounds like a natural idea to quantize space you know if you were naive trying to do quantum space you might think about trying to take points and put them together in some discrete fashion in some way that is reminiscent of quantum gravity string theory is more subtle than that for example i would just give you an example and this is the kind of thing that we didn't put in by hand we got it out and so it's more subtle than so what happens if you squeeze the space to be smaller and smaller well you think that after a certain distance the notion of distance should break down you know when it goes smaller than planck scale should break down what happens in string theory we do not know the full answer to that but we know the following namely if you take a space and bring it smaller and smaller if the box gets smaller than the planck scale by a factor of 10 it is equivalent by the duality transformation to a space which is 10 times bigger so there's a symmetry called a t duality which takes l to one over l well l is measured in plank units or more precise string units this inversion is a very subtle effect and i would not have been or any physicist would not have been able to design a theory which has this property that when you make the space smaller it is as if you are making it bigger that means there is no there is no experiment you can do to distinguish the size of the space this is remarkable for example einstein would have said of course i can measure the size of the space what do i do well i take a flashlight i send the light around measure how long it takes for the light to go around the space and bring back and find the radius or circumference of the the universe what's the problem i said well suppose you do that and you shrink it and say well they get smaller and smaller so what i said well it turns out in string theory there are two different kinds of photons one photon measures one over l the other one measures l and so this duality reformulates oh fast and when the space gets smaller it says oh no you better use the bigger perspective because the smaller one is harder to deal with so you do this one so so these examples of loop quantum gravity have none of these features these features that i'm telling you about we have learned from string theory but they nevertheless have some of these ideas like topological as gravity aspects are emphasizing the context of loop quantum gravity in some form and so these ideas might be there in some kernel in some corners of string there in fact i wrote a paper about topological string theory and some connections with potentially loop quantum gravity which could be part of that so there are little facets of connections i wouldn't say they're complete but i would say most probably what will happen to some of these ideas the good ones at least they will be absorbed within to strength theory if they are occurring let me ask a crazy out there question can physics help us understand life so uh we spoke so confidently about the laws of physics being able to explain reality but and we even said words like theory of everything implying that the word everything is actually describing everything is it possible that the four laws we've been talking about are actually missing they are accurate in describing what they're describing but they're missing the description of a lot of other things like emergence of life uh and emergence of perhaps consciousness so is there do you ever think about this kind of stuff where we would need to understand extra physics to try to explain the emergence of these complex pockets of interesting weird stuff that we call life and consciousness in this big homogeneous universe that's mostly boring and nothing is happening so first of all we don't claim that string theory is the theory of everything in the sense that we know enough what this theory is we don't know enough about string theory itself we are learning it so i wouldn't say okay give me whatever i will tell you what is how it works no however i would say by definition by definition to me physics is checking all reality any form of reality i call it physics that's my definition i mean i may not know a lot of it like maybe the origin of life and so on maybe a piece of that but i would call that as part of physics to me reality is what we're after i don't claim i know everything about reality i don't claim string theory necessarily has the tools right now to describe all the reality either but we are learning what it is so i would say that i would not put a border to say no you know from this point onwards it's not my territory somebody else's but whether we need new ideas on string clear to describe other reality reality features for sure i believe as i mentioned i don't believe any things any of the laws we know today is final so therefore yes we will need new ideas this is a very tricky thing for us to understand and uh be precise about but just because you understand the physics doesn't necessarily mean that you understand the emergence of chemistry biology life intelligence consciousness so those are built it's like you might understand the way bricks work yes but to understand what it means to have a happy family right you you don't construct you don't get from the bricks so directly you you right in theory you could uh if you ran the universe over again but just understanding the rules of the universe doesn't necessarily give you a sense of the weird beautiful things that emerge right no so let me let me describe what you just said so there are two questions one is whether or not the techniques are used and let's say quantum field theory and so on will describe how the society works yes okay that's far distance far for different scales of questions that we're asking here the question is is there a change of is there a new law which takes over that cannot be connected to the other laws that we know or of more fundamental laws that we know do you need new laws to describe it i don't think that's necessarily the case in many of these phenomena like chemistry or so on you mentioned so we do expect you know in principle chemistry can be described by quantum mechanics we don't think there's going to be a magical thing but chemistry is complicated yeah indeed there are rules of chemistry that you know chemists have put down which has not been explained yet using quantum mechanics do i believe that they will be something described by quantum mechanics yes i do i don't think they are going to be sitting there in this just forever but maybe it's too complicated and maybe you know we will wait for very powerful quantum computers or what not to solve those problems i don't know but i don't think in that context we have no principles to be added to fix those so by i'm perfectly fine in the intermediate situation to have rules of thumb or you know principles that chemists have found which are working which are not founded on the basis of quantum mechanical laws which does their job similarly as biologists do not found everything in terms of chemistry but they think you know there's no reason why chemistry cannot they don't think necessarily they're doing something amazingly not possible with chemistry coming back to your question does consciousness for example bring this new ingredient if indeed it needs a new ingredient i would call that new ingredient part of physical law we have to understand it to me that so i wouldn't put a line to say okay from this point onwards you cannot it's disconnected it's totally disconnected from strength or whatever we have to do something else it's not a line what i'm referring to is can physics of a few centuries from now that doesn't understand consciousness be much bigger than the physics of today where the the textbook grows it definitely will i would say i will grow i would not i don't know if it grows because of consciousness being part of it or we have different view of consciousness i do not know where the consciousness will fit i'm not it's going to be hard for me to to to to guess i mean i can make random guesses now which probably most most likely is wrong but let me just do just for the sake of discussion you know i could say you know you know brain could be their quantum computer classical computer their arguments against this being a quantum thing so it's probably classical and if it's classical it could be like what we are doing in machine learning slightly more fancy and so on okay people can go to this argument to no end and to know whether consciousness like this or not or life does it have any meaning or is there is there a phase transition where you can say does electron have a life or not the at what level does the particle become live maybe there is no definite definition of life in that same way that you know we cannot say electron if you you know a good i like this example quite a bit um you know we distinguish between liquid and a gas phase like water is liquid or or vapor is gas we say they're different you can distinguish them actually that's not true it's not true because we know from physics that you can change temperatures and pressure to go from liquid to the gas without making any phase transition so there is no point that you can say this was a liquid and this was a gas you can continuously change the parameters to go from one to the other so at the end it's very different looking like you know i know that water is different from vapor but you know there's no precise point this happens i feel many of these things that we think like consciousness clearly that person is not conscious on the other one is so there's a difference like water and vapor but there's no point you could say that this is conscious there's no sharp transition so it could very well be that what we call uh heuristically in daily life consciousness is similar or life is similar to that i don't know if it's like that or not i'm just hypothesizing that's possible like there's no there's no discrete phases there's no phase transition like that yeah yeah but this you might there might be you know concepts of temperature and pressure that we need to understand uh to describe what the heck consciousness in life is that that we're totally missing yeah i think that's not a useless question even those questions is back to our original discussion of philosophy i would say consciousness and free will for example are topics that are very much so in the realm of philosophy currently yes but i don't think they will always be i agree with you i agree with you and i think i am i'm fine with some topics being part of a different realm than physics today because we don't have the right tools just like biology was i mean before we had dna and all that genetics and all that gradually began to take hold i mean when mandela when people were beginning with face experiments with biology and chemistry and so on they gradually they came together so it wasn't like together so yeah i'll be perfectly understanding of a situation where we don't have the tools so do these experiments that you think has defines the consciousness in different form and gradually we will build it and connect it and yes we might discover new principles of nature that we didn't know i don't know but i would say that if they are they will be deeply connected with yes we we have never we have seen in physics we don't have things in isolation you cannot you cannot compartmentalize you know this is gravity this is electricity this is that we have learned they all talk to each other there's no way to to make them you know in one corner and don't talk so same thing with anything anything which is real so consciousness is real so therefore we have to connect it to everything else so to me once you connect it you cannot say it's not reality and once this reality is physics i call it physics it may not be the physics i know today for sure it's not but but i wouldn't i would i would be surprised if there's disconnected realities that you know you cannot you cannot imagine them as a part of the same soup so i guess uh god doesn't have a biology or chemistry textbook and mostly or maybe uh he or she reads it for fun biology and chemistry but when you're trying to get some work done it'll be going to the physics textbook okay uh what advice let's put on your wise visionary hat what advice do you have for young people today you've um are you've dedicated your book actually to your kids to your family what advice would you give to them what advice would you give to young people today thinking about their career thinking about life of how to live a successful life how to live a good life yes uh yes i have three sons and in fact to them i have uh i have tried not to give too much advice so even though i've tried to kind of not give advice maybe indirectly it has been some impact my oldest one is doing biophysics for example and the the second one is doing machine learning and the third one is doing theoretical computer science so there are there are these facets of interest which are not too far from my area but i have not tried to to impact them in in that way but and they have followed their own interests and i think that's the advice i would give to any young person follow your own interest and let it that take you wherever it takes you um and this i did in my own case that uh i was planning to study economics and electrical engineering when i started at mit and you know i discovered that i'm more passionate about math and physics and at that time i didn't think math and physics would make a good career and so i was kind of hesitant to go in that direction but i did because i kind of felt that that's what i'm driven to do so i didn't i don't regret it i'm i'm lucky in the sense that you know society supports people like me who are doing you know these abstract stuff which which may or may not be experimentally verified even let's not apply to the data technology in our lifetimes i'm lucky i'm doing that and i feel that uh if people follow their interest they will find a niche that they're good at and this coincidence of hopefully their interests and and abilities are kind of align at least to some extent to be able to drive them to something which is successful and not to be driven by things like you know this doesn't make a good career or this doesn't do that and my parents expect that or what about this and i think ultimately you have to live with yourself and you only have one life and it's short very short i can tell you i'm getting yes i'm getting there so i know it's short so you really want not to not to not to do things that you don't want to do so i think follow your interest my strongest advice to young people yeah it's scary when your interest doesn't directly map to a career of the past or of today so you're almost anticipating future careers that could be created is scary um but yeah there's something to that especially when the interest and the ability align you'll pay you'll pave a path that will find a way to make money especially in this society in the in in the capitalistic united states society it feels like um ability and passion paves the way yes at the very least you can sell funny t-shirts yes you've mentioned uh life is short do you think about um your mortality are you afraid of death uh i don't think about my mortality i think that i don't think about my debt and i don't think about death in general too much first of all it's something that i can't too much about and i think it's something that doesn't it doesn't drive my everyday action it is natural to expect that it's somewhat like the time reversal situation so we believe that we have this approximate symmetry in nature time reversal going forward we die going backwards we get born yeah so what was it to get born it wasn't such a good or bad feeling i have no feeling of it so you know who knows what the death will feel like uh the moment of death or whatnot so i don't know it is not known but uh in what form do we exist before or after again it's something that it's uh it's partly philosophical maybe i like how you draw comfort from symmetry it does seem that there is something asymmetric here breaking of symmetry because there's there's something to the uh creative force of the human spirit that goes only one way right that it seems the finiteness of life is the thing that drives the creativity and so it does seem that that um at least the contemplation of of the finiteness of life of mortality is a thing that helps you get your stuff together yes i think that's true but actually i have a different perspective on that a little bit yes namely uh suppose i told you you have you're immortal yes i think your life will be totally boring after that because you will not there's i think part of the reason we have enjoyment in life is the finiteness of it yes and so i think mortality might be a blessing and immortality may not so i think that we value things because we have that finite life we we appreciate things we want to do this we want to do that we have motivation if i told you no you have infinite life oh i don't i don't need to do this today i have another it's a billion or trillion or infinite life so why do i do now there is no motivation a lot of the things that we do are driven by that finiteness this refinedness of these resources so i think it's a blessing in disguise i don't regret it that we have more finite life and i think i think that the the process of uh being part of this thing that you know the the reality to me part of what attracts me to science is to connect to that immortality kind of namely the laws the reality is beyond us to me i'm i'm i'm resigned to the fact that not only me everybody is going to die so this is a little bit of a consolation none of us are going to be around so therefore okay and none of none of the people before me are around so therefore yeah okay this is something everybody goes through so so taking that minuscule version of okay how tiny we are and how short time it is and so on to connect to the deeper truth beyond us the reality beyond us is what sense of quote-unquote immortality i would get namely i at least i can hang on to this little piece of truth even though i know i know it's not complete i know it's going to be imp imperfect i know it's going to change and it's going to be improved but having a little bit deeper insight than than just the naive thing around us little earth year and little galaxy and so on makes me feel a little bit more uh more pleasure to to live this life so i think that's the way i view my my role as a scientist yeah this the scarcity of this life helps us appreciate the beauty of the the immortal the universal truths of that physics present us and maybe maybe one day physics will will have something to say about that that beauty in itself explaining why the heck it's so beautiful to appreciate the laws of physics and yet um why it's so tragic that we uh we would die so quickly yes we do so quickly so that can be a bit longer that's for sure it would be very nice maybe physics will help out well karma and it was uh an incredible conversation thank you so much once again for painting a beautiful picture of the history of physics and it kind of presents a hopeful um view of the future physics so i really really appreciate that it's a huge honor that you talked to me waste all your valuable titles me i really appreciate it thanks alex it was a pleasure and i loved talking with you and this is wonderful set of discussions i really enjoyed my time with this discussion thank you thanks for listening to this conversation with comrade vapha and thank you to headspace jordan harmorger show squarespace and all form check them out in the description to support this podcast and now let me leave you with some words from the great richard feynman physics isn't the most important thing love is thank you for listening and hope to see you next time you

Channel: Lex Fridman

Views: 177,206

Rating: 4.9203415 out of 5

Keywords: agi, ai, ai podcast, artificial intelligence, artificial intelligence podcast, cumrun vafa, electrons, general relativity, lex ai, lex fridman, lex jre, lex mit, lex podcast, mit ai, multidimensional, physics, quantum gravity, quantum physics, quarks, string theory

Id: j4_VyRDOmN4

Length: 133min 21sec (8001 seconds)

Published: Sun Jul 25 2021

Reddit Comments

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[u/carry4food]

Some of the stuff went over my head but thats okay. Im tired of hearing String Theory and Physics explained in such a way that targets children and cable news viewers.

Lex need to be not afraid to really dig deep into some topics as thats what can set him apart from Bro Rogan. Id like to see some more physics/math people on !