A Portal Special Presentation- Geometric Unity: A First Look

hello you found the portal I'm your host Eric Weinstein and I think that today's must be the most unusual episode yet of a podcast that has been marked by almost regular unusual episodes now this is the first podcast that I'm recording at home I don't really have a home recording studio so we're really doing this from chicken wire and masking tape but I am sheltering in place because of the worldwide kovat pandemic and what we've been asked by the state of California and by the federal government is to shelter in place for an upcoming month because today is April 1st now during a pandemic I can assure you that no one is interested in April Fool's jokes so the question is what to do with the April Fool's tradition in a situation in which nobody wants a prank I thought that this was probably the best time to launch an idea that I've been playing with for years and that idea is that it is dangerous to have a world in which we are afraid to talk about what we think is true when I think about what happened during the beginning of the kovat pandemic I find that we were in general intimidated from sharing our fears about the virus we were told that if we wore masks that we were acting in a peculiar fashion if we refused to shake hands that we were behaving in a strange and unpleasant social way we did not want to be alarmist we did not want to be seen as Chicken Little and in fact it was extremely important that we not be seen as xenophobic given that the outbreak was originating in Wuhan China in fact perhaps the most dangerous idea was that this outbreak might have been connected to some research being done in a lab perhaps a bioweapons lab we really don't know where this epidemic began what is the etiology of something that is causing the entire world economy to effectively shut down what I believe is that that silence has been deadly we have many people who have now lost their lives because we did not feel free to exchange ideas to think and to talk and in fact many of the people who warned us first were the freest members of society having been previously canceled by standard mainstream institutions and their associated media so what I thought would be important for in April Fool's Day that no one wants to actually participate in was to deal with an idea that maybe one day a year we should all be free to share crazy ideas that are going around between our ears and in our head we're having conversations with ourselves wondering is anyone else seeing the same thing that I'm seeing but we are too afraid because the social stigma for actually believing in things that maybe things are possible or perhaps there's a conspiracy somewhere perhaps we are ill-prepared for example I believe that our current pandemic is exacerbated because our government and our readiness czars failed to stock adequate supplies and that these supplies were called for in the academic literature for years there was absolutely no excuse not to have personal project protective equipment stocked for doctors and nurses and hospitals to say nothing of all of the people who are in the frontlines of treating patients sick with code now currently I don't believe that you can trust the World Health Organization absolutely not I don't think you can trust the Surgeon General of the United States and I absolutely don't think you can trust the CDC because they are all covering for our inadequacy this was a problem that we always knew was coming and we at one point had stocks which apparently were depleted under a previous administration and not restocked under this administration in fact our fear of dealing with a pervasive institutional incompetence has blinded us to the degradation in our society across all major institutions as I've discussed before on the program I believe that this has a singular etiology that is that because of embedded growth obligations coming from the previous era of unsustainable post-war growth from about nineteen forty five to nineteen seventy one seventy three something like that we built in expectations to our system that cannot currently be met we will not have technology that follows the same break neck pace of innovation as a result we have a system whereby the head of our organizations are forced to cover for their inadequacies because growth is built into the system that cannot be sustained therefore there is not the funding the manpower there is not the wherewithal to continue many of our programs because we do not actually have the ability to continue to simply grow our way out at least so far so what's today's program about well I thought that what I would do is to let go of something that I've been keeping pretty close for I think about 37 years when I was around 19 I started it's hard to talk about when I was around 18 or 19 I was at the University of Pennsylvania and I thought I saw a glimmer of hope I thought I saw that some new equations that were being played with might actually provide a solution to some of the problems that had bedeviled Einstein and others for years in the quest for a unified field theory now it's an embarrassing thing to say that one is a unified field theorist it is effectively equivalent to saying I'm interested in perpetual motion machines or that I have a private cure for cancer that I'm trying on rabbits in my backyard however I actually think that it's important to fess up because that's exactly what this is now in my situation I have an extremely unusual history and I really don't want to get bogged down in all of the things that happened while I was a student trying to develop this theory because it is not a particularly happy story I believe that this theory is an incredibly joyous one now in this situation I want to talk about what it means to have a theory of everything we've never seen one and in fact not only have we never seen a theory of everything we've never even seen I believe a candidate for a theory of everything and because a theory of everything would have to different characteristics they might believe every theory that has gone before we don't think enough about what the difference is between what we would normally call in physics and effective theory and a fundamental one now if you're familiar with the MC Escher drawing called drawing hands it is a lithograph of two hands apparently drawing each other into existence on some kind of a canvas or piece of paper that is sometimes referred to as a strange loop but it in fact is an attempt to answer the question what is the fire that lights itself this is the problem that be devils us when we search for a unified theory that doesn't bedevil us in my opinion in any previous effective theory now why is that well many people confuse a theory of everything is if they imagine that it's a theory in which you can compute every eventualities and it is absolutely not that because the computational power is very different than the question of whether or not the rules are effectively given I've analogized it to a game of chess and knowing all of the rules is equivalent to a theory of everything knowing how to play chess well is an entirely different question but in the case of a theory of everything or a unified field theory if you will many people also take it to be an answer to the question why is there something rather than nothing and I don't think that this is in fact what a theory of everything is meant to be either now why is that well because I believe at some level it is impossible for most of us to imagine a an airtight argument mathematically speaking which coaxes out of an absolute void a something however there's a different question which I think might actually animate us and which is the right question to ask of a potential candidate and that is how does one get everything from almost nothing in the MC Escher drawing or lithograph hands drawing hands or hands what we see is that the paper is presupposed that is if you could imagine a theory of everything it would be like saying if I posit the paper can the paper will the ink into being such that the ink gives rise to the pens and the pens draw the hands which in fact manipulate the pens to use the ink that kind of a problem is one which is of a very different character than everything that is gone before it is also in my opinion an explanation of why the physics community has been stalled for nearly 50 years since around 1973 when the standard model was intellectually in place now consider this we have never had in modern times the drought where no person working in pure fundamental theory has taken a trip to Stockholm just as a rough indicator for contributing to the standard model no one in my opinion since let see Frank will check was born in 1951 no one born after that time has in fact contributed to the standard model in a clear and profound way that is not to say that no work has been done but for the most part the current generation of physicists has for more than 40 years in almost 50 years remained stagnant within the standard paradigm of physics which is positing theories that are then verified by experiment now my belief which is relatively radical is that there is no way to get to our final destination using the tools that have gotten us to where we are now in other words what got you here cannot get you there and in particular one of the biggest problems we have is the political economy of science we have effectively starved our scientific enterprise for resources creating a dire and cutthroat competition which is completely deranged the scientific tradition and so one of the things that's going to happen in this lecture this is that I'm simply going to announce that I have broken and have broken for many years with just about every expectation of standard science that is not to say that the equations or the style of present is going to be foreign quite the contrary I have every intention of writing up some results in standard terminology wherever possible using popular mathematical typesetting programs but it goes far deeper than this my belief is that what we've created is a career structure a journal structure an employment structure an access structure that cannot possibly complete the job and why is that well what if in the last leg in fact we had a situation by which an attempt at the fundamental theory would result almost certainly in career suicide now if you think of that as an explanation you would realize that it has the power to synchronize failure across many seemingly independent experiments and I believe that that's exactly what's been going on through the so called string theory revolutions one two and perhaps three now in that case what happened was a theory became fixed in the minds of really the baby boom generation of physicists because it allowed for infinite elaboration within a mathematical work more particularly a geometric context and those supposed physicists spent their time submitting papers to what's called the high energy section of the so-called preprint archive but in fact most of these papers have nothing to do with high energy physics whatsoever and if you're looking for the the designation it's hep th high energy physics - theory now if you look through those papers they don't seem to have much to do with particles they don't seem to have to do with forces in space-time they seem to have to do with very strange and obscure mathematical issues and in the years since the string theory program got particularly reanimated I guess that would be around 1984 with the anomaly cancellation of Greene and Schwartz what you'll find is is that physics became very active and simultaneously ground to a halt it it failed to remain a physical subject it became something like a medieval quest for the number of angels to dance on the head of a pit now in this circumstance I think it's very important to realize that this is not a paper and we're not submitting to the archive in fact the archive requires people who are not employed at universities to get permission from some member of the community which is called an endorsement which I find absolutely insulting and I refuse to go along furthermore we are expected to cite papers sometimes which are behind paywalls and I think that it's absolutely immoral to ask people to pay outside the system to read the papers to cite other people's work I can go on about the number of things that are currently wrong with the system but instead what I would like to do is to simply joyously reject it I have every intention of simply sharing this with you and jealously guarding my right to Shepherd this through now what is that in two previous episodes we've had interactions with academics which I think are interesting in bear scrutiny in the first case in a in an interview with The Economist's Tyler Cowen I talked to Tyler about the fact that the Boskin Commission was in fact committing economic malpractice now why was that it was because they decided that they needed to transfer a trillion dollars over ten years and that they had found a devious way of doing it which is to adjust the CPI by backing out the amount of adjustment needed to get a trillion dollars they decided that a 1.1 percent overstatement in the CPI would cause a reduction in entitlements that is Medicare and Medicaid payments together with Social Security as well as an increase in taxes because tax brackets are also indexed now to my mind it is absolutely unconscionable to say that you have a right to Train for wealth cryptically by adjusting a fundamental barometer that would be like saying in order to meet our global warming targets we have to recalibrate all the thermometers to show that in fact things had cooled one simply can't do that at science but Tyler's response I found was very interesting his perspective was that this was in fact not a terrible thing because it was quote directionally correct and in general he believed that because the CPI should be considered overstated that this was not the world's most terrible thing to do as an economist I respect Tyler a great deal and I enjoy his company but I have to say that I am absolutely of a different opinion my belief is is that one has no rights and no ability as a scientist to fudge the data to meet social goals in this fashion another interesting interaction was the interaction with Professor ACMA scholar of the University of Chicago now when she listened to episode 19 about Brett Weinstein she found that it was a very compelling episode but strangely even though the point of the episode was to surface breaths long forgotten theory because Brett had not been acknowledged as having predicted that laboratory mice would in particular have radically elongated telomeres where it was thought that all mice had long radically elongated telomeres which has incredible potential implications for a drug testing and all of the work that is done on laboratory rodents as model organisms this is an episode you should definitely listen to if you haven't already but Agnes's perspective was very different than mine her feeling was that because we were in a situation in which the work actually surfaced that the system worked even if it was the case that Brett's name was erased from the history of the development and that his theory was put in a situation in which it was not able to carry the day because in fact there was no record of the fact that a prediction been made now I disagreed with Agnes on that program facili but what I found was is that it was very telling in general our academic population has given up on the previous and quaint idea of decency propriety truth fairness because there simply isn't the resource for everyone now I believe that current science is not necessarily unsalvageable but it will be unsalvageable if we don't get the very people that I rail against far more money and I know that's very confusing but my belief is as the inadequate resources that we have put aside are very similar to the inadequate masks that we have put aside for our doctors we have asked some of the world's most gifted and smartest people to devote their lives to the study of science and technology and we've inadequately prepared them we've put their lives and their families lives under incredible pressures and what I wish to do is to in fact point to the very people who I have been most angry at for years and say the part of the problem is that we need to take a hard look at how we've invested in science and technology and give the very people that I'm most angry at more money I will explain more about this later but I do want to give you an introduction to this episode what I will be doing is to screen a very unusual and somewhat awkward lecture at the University of Oxford now why is it so awkward well first of all I had left standard research perhaps 20 years earlier almost further I'm not a physicist and I have only taken one or two courses in the physics major sequence I think I've taken one semester of mechanics and perhaps I took an advanced general relativity course in college but in general no one goes into a theoretical physics department and attempts to lecture physics physicists on physics and why is that well because physics is incredibly demand and this is almost certainly the world's most interesting and most accomplished intellectual community these are guys that don't miss a trick there are so many things to know and it is such a difficult field that it is effectively almost impossible to contribute from outside chemists don't do it and once in a blue moon mathematicians will attempt to talk about actual real physics so one thing that you're seeing is a very unusual circumstance where somebody is trying to figure out how to give their first lecture in a physics department and it concerns the possibility of a theory which attempts to solve the problem of how does a fire light itself another thing that you'll see is is that it's relatively difficult to read my handwriting I'm not going to make any bones about it I've been very vocal about having learning differences dysgraphia dyslexia all sorts of different issues symbols come extremely difficult to me I don't want to spend this time making excuses what I do want to say is the following I will be attempting to record a short PowerPoint presentation for after the lecture to say at least some of what some of the constructions are more clearly this is not meant to be the actual presentation of the theory what this is is an introduction a down payment and above all a historical account of what happened seven years ago at the University of Oxford when I tried to present these ideas I've talked before about the twin nuclei problem and our need to get off of this planet and if we have a hope of getting off of this planet it really comes from fundamental physics you see a hundred years ago or perhaps 105 when Albert Einstein gave us general relativity he effectively consigned us for life to the solar system why is that well his model his geometric model of space and time effectively creates a speed limit known as C or the speed of light now there are three rocks that are at least interesting for habitation by humans although two of them are marginal the Moon and Mars one of them of course is unbelievable the earth but I doubt that we're going to be able to steward the through our new godlike powers which I've called it - a nucleotide problem of cell and atom we've unlocked the power of both and I don't think we have the wisdom to stay all in one place so the question that I had was if there is any ability to escape to the cosmos that we can see in the night sky where would it come from we are almost positive that Albert Einstein's theory of relativity is in some weird way incomplete the Schwarzschild singularities which give us black holes and the initial singularities of the robertson-walker Freedman universe which are associated with the Big Bang are some clue that there is some subtle flaw united Stein's theory so how to go beyond Einstein I mean what Einstein did to Newton was to recover Newton as a special case of a more general theory that is more flexible and in fact this is the same problem that we have because Albert Einstein's theory is so fundamental we effectively begin every theory of physics seminar with a statement about space-time in other words Albert Einstein is locked in at the ground floor so if we can't get below the ground floor to the foundations it's very difficult to make progress this is one of the things that is making it almost impossible for us to go beyond the initial revolutions of the 20th century do I know that this new theory if it works will allow us to escape I do not there's no one who can I can say that and I don't think I have the skills to develop the physical consequences of the theory even if the theory turns out to be mostly right what I will say is that I think that the theory is the first of its kind that I've seen I believe that in part what you will see is that at a minimum it is like fool's gold it appears to explain why we think we see three or three generations but it also says that perhaps they aren't really three generations of matter perhaps there are only two even though physicists tell us that there are at least three or perhaps more I believe that physics tells us that the universe is chiral that is left-right asymmetric but the theory is itself not chiral instead it chooses to present a different idea which is that perhaps chirality is emergent much the way our hands are individually left-right asymmetric as our pinky is not a reflection of our thumb but the thumb on each hand is a pairing to the other one as is the pinky now what does that mean it means that if perhaps there is matter and there is force that is decoupled from our ordinary world that that matter might restore the parody or the chirality rather would break the chirality and restore parody between these two halves the matter we see in the matter that is missing there are a good number of other things that happen in the theory it replaces space time with what I've termed an observers now an observers is an unusual gadget in that it's thought of as two separate places where physics takes place connected by a map that means effectively that we are in something like a stadium where there is there are stands and there is a pitch and the playing field that we think we see may not in fact be where most of the action is taking place in fact not all of the fields live on the same space so when we see waves and particles dancing around they may have separate origins in each of the two components of the observers what I hope to do after this is to gracefully and gradually develop the theory under my leadership now why do I say that there is a belief in physics and in most fields that the field should behave in a communal fashion and that people should put forward their ideas and other people should joyously build upon them and that the community should be allowed to name the various accomplishments for whoever they say accomplish those things there's not a way there's not a way in hell that I'm letting that happen my experience with this community is is that it simply can't be trusted to behave equitably given the fact that it is so resource starved and constrained people simply do not have the freedom to be generous kind and accurate as to who did what furthermore there is an incredible premium on cherry topping that is who finished something off is considered bizarrely much more important than who found something to begin with imagine you located an island and you named the island after the first person who could plant the flag on the top of the highest peak this is patently offensive and ridiculous there's a story years ago about how Hilbert almost scooped Einstein by giving the Hilbert action from which Einstein's equations could be recovered really not a chance so if Hilbert came up with the Hilbert action and recovered Einstein's equations so what I mean the real theory actually takes place in Einstein and Grossman before Albert Einstein even works out a lot of the flaws in the original theory it's about the ideas it's not about the formulas and it's not about racing to the final form now I know that the community won't agree with that but think about this what I'm doing is taking an incredible risk I'm addressing you here on April Fool's Day and I'm saying that if there is a fool it is certainly me because I have sat on this theory for almost 40 years now I've never known is it true is it false it's impossible to tell when you're only talking to yourself but in this situation what I've done is I've taken a tremendous amount of risk and now I'm trying to share it with you hopefully I know that well Newton did his greatest work when he was sheltering sheltering from a Great Plague in England and I would like to think that perhaps whether or not this is correct simply the act of somebody trying honestly to share hope and some path forward would be uplifting now under the worst circumstances if this doesn't work what do I think is a question I'm asked frequently there are two things that I'll say many years ago around 1987 I put forward some equations that I thought might become my thesis at the Harvard Department of Mathematics and they were disallowed for a variety of reasons those let equations were later discovered in I believe 1994 and I sat in a lecture in which I saw these equations go up on a board the very end at MIT and I looked at those equations and I said huh those are the exact equations I was told could never work why is the leading physicist in the world placing them on the board and saying that these are the equations from which all of something called donaldson theory can be derived what I'm giving you at least at a minimum had the ability years earlier to provide those equations from a different source there's something called Seibert Witten theory which I have no claim on but the actual equations that are called the cyber quittin equations came originally as an outgrowth from investigations of this theory so at a bare minimum the cyber Witten revolution should have happened at Harvard rather than Princeton and it should have been recognized that this theory was capable of at least at a minimum giving birth to that as a side project the other thing that I think is incredibly important is is that we've never seen how a universe that looks like ours could possibly emerge from almost no assumptions whatsoever and I believe that even if this theory were to turn out to be wrong which I don't think is likely I believe that it would give us something to go on we would at least have a first candidate of how a hopeful theory of everything would look and how it would go wrong so under any circumstance I think that I'm going to be fine if the theory doesn't work out I will have at least taken my shot on goal and I think that that's probably more than almost anyone can ask from a life to attempt to make contact with the deepest question that we've ever had which is what is this place and what brought it into being lastly I want to just talk about a personal aspect of this which is what does it mean to come to an end whether or not this theory in fact does what I claim I think it does I don't know but I do know that sooner or later in the era of intercontinental exploration someone found the last landmass and that must have been a very strange moment when there was nothing left to do I think whether or not this theory in fact accomplishes that is one question but we all have to plan for what it is that we think will happen when man at last learns his own source code in fact this was the last edge question that I answered for Jon Brockman which is does something unprecedented happen when man at last learns his own source code I don't know the answer of this but I want to return to the same spirit that I started this when I was 18 or 19 which is that of joyous investigation of brave open hearted undertakings and I also want to bring back a different style of scientific investigation there has been far too much communalism in fact there is a belief that there are no lone researchers and that everything is produced by a community and pardon my french but this is absolute horseshit I have been so long alone with these principles equations and ideas that I don't even know what my adult life will look like once I discourage them and I begin to talk about them with the community at large I've talked to many theoretical physicists who've taken some interest in them but I've never put out enough to absolutely ensure that people are seeing what it is that I'm seeing so whether or not the April Fool's joke is on me I cannot tell you but I can promise you that I'm not trying to play one on you what I hope to show you is a lecture that was the first of three versions of this lecture that were delivered in Oxford over the course of a week and one of the things that has held me back is is that I have a great number of people who I have to thank for effectively being my Underground Railroad when my career got into serious trouble to make sure who made sure that I always had an opportunity to fight another day and some of the most important of those people one of whom occurs on this video is Marcus - so toy and Marcus I just wanted to say thank you for your brave your courage your friendship and your encouragement I know I've been absolutely impossible to you I've made you wait for this and I just want to say how much I love you I also want to thank Isadora singer for effectively saving me from not getting a PhD I think putting pressure on the Harvard Department and for coming to my assistance making sure that I got a postdoc at MIT despite not having any publications at all I'd like to think Raul Bhatt who's no longer with us who I should have invited to my wedding I was very angry at him but I didn't realize that he was saving me in a very difficult situation against the department that probably just wanted to see me gone I'd like to thank Peter Thiel one of my closest friends is like a brother to me for allowing me these seven years since this lecture to lick my wounds to get strong to have a 401k to buy a house and to begin coming back to regular society after a very difficult and strained career I'd like to thank Adil Abdul Ali and Michel Grossberg the two greatest best friends from college a guy could have I'd like to thank my grandfather Harry Rubin who believed in things that couldn't possibly be true and made some of them happen I'd like to thank my parents Karen and les Weinstein for all the good things that they did I'd like to thank my brother Brett Weinstein and his family Heather and the kids for sticking by me and I'd like to thank my in-laws in Bombay and yeah I hope you guys are well and lastly I would very much like to thank my wife and my two kids for putting up with a lot of lost weekend's a lot of lost vacations and believing that just maybe there was something to this and sticking by me all these years so I hope everybody really enjoys this it may not be comprehensible and after this video finishes I'll do a short presentation of some of the constructions that took place not all of the equations and things I think some of them were sort of botched on the board they became disoriented the night before and rearranged things in a way that probably wasn't optimal but I I'll attempt to clarify these things going forward and to begin to present the theory as I see whether or not I can bring myself to once again work on it somewhat close to full time as a 54 year old father of two so sit back relax and coming up next is the first of my three lectures at Oxford University on geometric unity be well [Music] well welcome to this special Simoni lecture and my name is Marcus DeSoto I'm a professor of mathematics here and the Simoni professor for the public understanding of science and Chancellor mone prepared a manifesto when he in dealt this chair to guide the holder of the professorship in their mission and I'd like to read one part of that manifesto to you it said scientific speculation when so labeled and when the concept of speculation and its place in the scientific method has been made clear to the audience can be very exciting it is a very effective communication tool and it is by no means discouraged and it is in the spirit of this part of my mission there's a Simoni professor that I would like to introduce today's Simoni special lecture I first met Eric vine Stein when we were both postdocs at the Hebrew University just over 20 years ago and I had the feeling then that he was working on something big but it wasn't until two years ago that Eric met me in a bar in New York and we began he began to explain the mathematics that he'd been working on in private for the last 20 years as he took me through the equations he had been formulating I began to see emerging before my eyes potential answers to many of the major problems in physics it was an extremely exciting daring proposal and also mathematically so natural that it started to work its magic on me over the last two years I have had the privilege of being taken through the twists and turns of Eric's ideas after our postdocs in Israel when I went the academic route getting my professorship here in Oxford Eric went to more independent roots working in economics government and finance so he comes here today as something of an insider and an outsider a difficult place from which to propose bold ideas but having spent time seeing how powerful these ideas appear to be I felt it was time that Eric shared his ideas more widely as I believe his perspective could give the scientific community a new story to explain some of the big questions on the side books and therefore very happy to provide a platform here in Oxford for Eric to share his ideas on a new theory he calls geometric unity the lecture will be approximately 17 minutes after which we will have a period to ask questions Eric so it's it's a great pleasure to be here in Oxford for those of you who are not aware it is possible that no other university in the world has kept so tightly and kept the faith for so long with Einstein's great vision of a final theory for physics as a theory of pure geometry a sort of elegance and simplicity of the highest order and the names that are associated with Oxford that weigh heavy on me are attea Penrose Siegel Woodhouse Hitchin it's a very long list of people who even when fashion did not hold those ideas in favor always kept the faith that there was much to be learned from the geometric perspective on physics of course unified field theory and some sense acquired a stigma with Einsteins failure to find it in the sense that even someone like Einstein being tempted by the siren song of geometry might lose their footing and go astray and in the years since we've had a replacement theory which is that what is really calling our generations is the is the quest to quantize general relativity and gravity and I'd like to to go back to the sort of earlier perspective that there's no evidence to date in my mind that we are being called to quantize general relativity directly in fact there's been more effort spent on that quest without very tangible results then Einstein spent as one man searching for years for a unified field theory so we have to in some sense begin to undo some of what we think we know in order to truly reconsider and allow me to put some of these Diaz before you today Marcus asked me to begin presenting these ideas here and hopefully this is the first opportunity but if the ideas are not good then lighting on the aisles will lead you to safety and your exits may be behind you but in the event of a good flight hopefully this will begin a conversation rather than n1 I feel in some sense that I'm presenting the works of another man a younger man someone who came of age right in the middle of the Great string theory boom with the anomaly cancellation in 1984 and I look at this work and I see a young person struggling with the idea why can't I see that string theory is going to answer all of these questions over the next 10 years as we were told at the time and making a very dangerous decision which was I think I'm not going to follow that particular path and I'm going to follow another and it's not clear where this path is going to lead us but we're going to explore it today and see as best we can so in some sense I've been able to polish some of that young man's work but I'm also struggling to reconstruct it because as someone spending full time on that theory he knew a lot of things that I no longer know so with that as a beginning I'm just gonna say one disclaimer which is that this is not a usual talk and whatever contract a speaker usually has with the audience right now we're going to break that contract this is a this is a talk about ideas and some of these ideas are bold some of them may offend some people because there's a sense that you don't have a right to be considering those ideas but I go back to the admonition of Jim Watson that said if you're going to try to make progress big progress you are by definition unqualified to be doing whatever it is that you're doing so in that spirit let us begin what is physics to today how do they see it different from the way in which we might imagine the lay person sees physics ed Witten was asked this question in a talk he gave on physics and geometry many years ago and he pointed us to three fundamental insights which were his big three insights in physics and they correspond to the three great equations so the first one is is that somehow physics takes place in an arena and that arena is a manifold X together with some kind of semi roumanian metric structure something that allows us to take length and angle so that we can perform measurements at every point in this space-time or higher dimensional structure leaving us a little bit of headroom the equation most associated with this is the Einstein field equation and of course I've run in to the market so it says that a piece of the Riemann curvature tensor the Ricci tensor - an even smaller piece the scalar curvature multiplied by the metric is equal or plus the cosmological constant is equal to some amount of matter and energy the stress energy tensor so it's intrinsically a curvature equation the second fundamental insight I'm going to begin to start drawing pictures here as well so if this is the space-time manifold the arena the second one concerns symmetry groups which cannot necessarily be deduced from any structure inside of the arena they are additional data that come to us out of the blue without explanation in these symmetries form a non abelian group which is currently su3 color cross su - weak isospin cross u1 weak hypercharge which breaks down to su 3 cross u1 where the broken u1 is the electromagnetic symmetry this equation is also a curvature equation the corresponding equation and it says that this time the curvature of an auxiliary structure known as a gage potential when differentiated in a particular way is equal again to the amount of stuff in the system that is not directly involved in the left-hand side of the equation so it has many similarities to the above equation both involve curvature one involves a projection or a series of projections the other involves a differential operator the Third Point surrounds the matter in the system and here we have a Dirac equation again coupled to a connection but one of the great insights is is that because the reason for the lightness of matter in the natural mass scale of physics has to do with the fact that this sigh really should have two components and the differential operator should map to one component on the other side of the equation but the mass operator should map to another and so if one of the components is missing if the equation is intrinsically lopsided chiral asymmetric then the mass term and the differential term have difficulty interacting which is sort of overcompensating for the mass scale of the universe so you get to a point where you actually have to define a massless equation but then just like over shooting a putt it's easier to knock it back by putting in a Higgs field in order to generate and as if fundamental mass through the Okawa couplings so matter is asymmetric and therefore light and then interestingly he went on to say one more thing he said of course these three central observations must be supplemented with the idea that this all takes place treated in a quantum mechanical fashion our quantum field theory so it's a bit of an aftermarket modification rather than in his opinion at the time one of the core insights I actually think that that's in some sense about right now one of my differences with with the community in some sense is that I question whether the quantum isn't in good enough shape that we don't know whether we have a serious quantum mechanical problem or not we know that we have a quantum mechanical problem the quantum field theory attic problem relative to the current formulations of these theories but we know that in some other cases the quantum becomes incredibly natural sometimes sort of almost magically natural and we don't know whether the true theories that we will need to be generalizing in some sense have beautiful quantum mechanical treatments whereas the affective theories that we're dealing with now may not survive the quantization so what I want to do is I want to met imagine a different sort of incompatibility so let's take our great three theories and just visually treat them as the vertices of a triangle so I'm going to put general relativity in Einstein's formulation and I'm gonna put the probably won't write this again yang-mills Maxwell Anderson Higgs Theory over here and I'm gonna write the Dirac theory what I want to explore is the incompatibility is not at the quantum level but the geometric input all three of these are geometric theories and the question is what are the compatibilities are incompatibilities at the level of geometry before the theory is treated quantum mechanically well in the case of Einstein's general relativity we can rewrite the Einstein theory by saying that there's a projection map due to Einstein of a curvature tensor where I'm going to write that curvature tensor as I would in the yang-mills theory that should be an LC for lemme chavita so the Einstein projection of the curvature tensor of the leve chavita connection of the metric on this side and on this side I'm going to write down this differential operator the adjoint of the exterior derivative coupled to a connection and you begin to see that we're missing an opportunity potentially what if the FAs were the same in both contexts then you're applying to separate operators 1 0 with order and destructive in the sense that it doesn't see the entire curvature tensor the other inclusive but a first-order and so the question is is there any opportunity to do anything that combines these two but the problem is is that the hallmark of the yang-mills theory is the freedom to choose the data the internal quantum numbers that give all the particles their personalities beyond the mass and the spin additional to all of that freedom is some means of taking away some of the redundancy that comes with that freedom which is the action of the gauge group now we can allow the gauge group of symmetries to act on both sides of the equation but the key problem is is that if I act on connections on the right and then take the Einstein projection this is not equal to first taking the projection and then conjugating with the gauge action so the problem is is that the projection is based on the fact that you have a relationship between the intrinsic geometry if this is an add value to form the to form portion of this and the adjoint portion of this are both associated to the structure group of the tangent bundle but the gauge rotation is only acting on one of the two factors yet the projection is making use of both of them so there is a fundamental incompatibility in the claim that Einstein's theory is a gauge theory relies more on analogy than an exact mapping between the two theories what about the incompatibilities between the einstein theory of general relativity and the Dirac theory of matter I was very struck that if we're going to try to quantize gravity and we associate gravity with the spin to field G mu nu we actually have a pretty serious problem which is if you think about spinners electrons quarks as being waves in a medium and you think about photons as being waves in a different medium photons medium does not depend on the existence of a metric one forms are defined whether or not a metric is present yet spinners are not so if we are going to take the spin to G mu nu field to be quantum mechanical if it blinks out and does whatever the quantum does between observations in the case of the photon it's saying that the waves may blink out but the ocean need not blink out in the case of the Dirac theory it is the ocean the medium in which the waves live that becomes uncertain itself so even if you're comfortable with the quantum to me this becomes a bridge too far so the question is how do we liberate the definition how do we get the metric out from its responsibilities it's been assigned far too many responsibilities its responsible for a volume form for differential operators it's responsible for measurement it's responsible for being a dynamical field part of the field content of the system lastly we have the compatibility comparing yang-mills and in the Dirac theory these may be the most mild of the various incompatibilities but it is an incompatibility of naturality where the direct field Einsteins field and the connection fields are all geometrically well motivated we push a lot of the artificiality that we do not understand into the potential for the scalar field that gives everything its mass so we tended to treat it as something of a mysterious fudge factor so the question is if we have a Higgs field why is it here and why is it geometric it has long been the most artificial sector of our models the proposal that I want to put to you today is that one of the reasons that we may be having trouble with unification is is that the duty our duty may be to generalize all three vertices before we can make progress that's daunting because in each case it would appear that we can make an argument that this that and the other vertex are the simplest possible theories that could live at that vertex we know for example the Dirac operator is the most fundamental of all the elliptic operators in Euclidean signature generating all of a Tia singer theory we know that einstein's theory is in some sense a unique spin to massless field capable of communicating gravity which can be arrived at from field theoretic rather than geometric considerations in the yang-mills case it can be argued that the yang-mills theory is the simplest theory that can possibly result where we're taking the simplest lagrangian in the Einstein case looking only at the scalar curvature in the yang-mills case we have no substructure and so we're doing the most simple-minded thing we can do by taking the norm square of the curvature and saying whatever the field strength is let's measure that size so if each one of these as simple as possible doesn't Occam's razor tell us that if we wish to remain in geometric field theory that we've already reached bottom and that what we're being asked to do is to abandon this is merely an effective theory that's possible and I would say that that in some sense represents a lot of conventional wisdom but there are other possibilities there are other possibilities that while each of these may be simplest in its category they are not simplest in their interaction for example we know that Dirac famously took the square root of the klein-gordon equation to achieve the Dirac equation he actually took two square roots one of the differential operator and another of the algebra on which it acts but could not could we not do the same thing by reinterpreting what we saw in Donaldson theory the insurance Simon's theory and finding that there are first-order equations that imply second-order equations that are nonlinear and in the curvature so let's imagine the following we replace the standard model with a true second-order theory we imagine that general relativity is replaced by a true first-order theory and then we find that the true second-order theory admits of a square root and can be linked with the true first-order theory this would be a program for some kind of unification of de rocks type but in the force sector the question is does this really make any sense are there any possibilities to do any such thing so what I'd like to do is I'd like to talk a little bit about what the geometric unity proposal is so we have a division into intrinsic theories and auxiliary theories between physics and mathematics more specifically geometry an intrinsic physical theory would be general relativity an auxiliary physical theory would be the yang-mills theory with the freedom to choose internal quantum numbers at the mathematical level an intrinsic Theory would be to be a little fastidious the older semi Romani in geometry a study of manifolds with length and angle but auxiliary geometry is really what's taken off of late since the revolution partially begun at Oxford when is singer brought insights from Stony Brook to the UK and so we're gonna call this fiber bundle theory or modern gauge theory geometric unity is the search for some way to break down the walls between these four boxes what's natural to one theory is unnatural to another semi romani and geometry is dominated by these projection operators as well as the ability to use the levy chavita connection now some aspects of this are less explored torsion tensors are definable in semi romani in geometry but they are not used to the extent that you might imagine in the case of fiber bundle theory the discovery of physicists that the gauge group was fantastically important came as something of a shock to the mathematicians who had missed that structure and have since exploited it to great effect so what we'd like to do is we'd like to come up with some theory that is intrinsic but allows us to play some of the games that exist in other boxes how can we how can we try to have our cake eat it and use all the full suite of techniques that are available to us so our perspective is is that it is the quantum that maybe the comparatively easy part and that the unification of the geometry which is not occurred maybe what we're being asked to do so let's try to figure out what would a final Theory even look like when I was a bit younger I remember reading this question of Einstein which he said I'm not really interested in some of the details of physics what really concerns me is whether the creator had any choice in how the world was constructed and some people may have read that as a philosophical statement but I took that as an actual call for a research program so I'd like to describe that research program and try to unpack what I think he was saying we talk a lot about unification but we hardly ever actually imagine if we had a unified theory what would it look like let us imagine that we cannot figure out the puzzle of why is there something rather than nothing but if we do have a something that that something has this little structure as possible but still invites us to work mathematically so to me the two great theories that we have mathematically and in physics are calculus and linear algebra if we have calculus and linear algebra I mean imagine that we have some manifold at least one of dimension four but it's not a space-time it doesn't have a metric it's not broken down into two different kinds of coordinates which then have some bleed into each other but still maintains a distinction it's just some sort of flabby proto space-time and in the end it's got to fill up with stuff and give us some kind of an equation so let me write an equation so I have in mind differential operators parameterised by some fields Omega which when composed are not of second-order if these are first-order operators but at zero with order and some sort of further differential operator saying that whatever those two operators are in composition is in some sense harmonic is such a program even possible so if the universe is in fact capable of being the fire that lights itself is it capable of managing its own flame as well and closing up what I'd like to do is to set ourselves an almost impossible task which is to begin with this little data in a sandbox to use the computer science concept so if here's physical reality standard physics is over here we're going to start with the sandbox and all we're going to put in it is x4 and we're going to set ourselves a straight jacketed task of seeing how close we can come to dragging out a model that looks like the natural world that follows this trajectory while it may appear that that is not a particularly smart thing to do I would like to think that we could agree that it is quite possible that if that were to be the case we might say that this is what Einstein meant by a creator which was his anthropomorphic concept for necessity and elegance and design having no choice in the making of the world so with that let us begin to think about what we mean today by geometric unity Jihu comes in four flavors but I'm only getting one shot to do this so I'm going to do the most exciting of them to me there's a completely exhaust flavor and what I'm going to do is I'm going to take the concept of observation and I'm going to break the world into two pieces a place where we do our observation and a place where most of the activity takes place and I'm going to try to do this without loss of generality so in this case we have x4 and it can map into some other space and we're going to call this an observers the idea of an observer is a bit like a stadium you have a playing field and you have stands they aren't distinct entities they're coupled and so fundamentally we're going to replace one space with two excitedness model simply means that U is unrestricted although larger than x4 so any manifold of four dimension higher that is capable of admitting export as an immersion the next model we have is the bundle theoretic in which case use sits over X as a fiber bundle the most exciting which is the one we'll deal with today is the endogenous model where x4 actually grows the space you where the activity takes place so we talked about extra dimensions but these are in some sense not extra dimensions their implicit dimensions within x4 and last to proceed without loss of generality we have the tautological model in that case X 4 equals u and the immersion is the identity and without loss of generality we simply play our games on one space okay now we need rules and the rules are sorry feedback no choice of fundamental metric so we imagine that Einstein was presented with the fork in the road and it's always disturbing not to follow Einsteins path but we're in fact going to turn Einsteins game on its head and see if we can get anywhere with that right so it's also a possibility that because Einstein's theory is so perfect that if there's anything wrong with it it's very hard to untap of it so let's make no choice of fundamental metric and in fact let's go more ambitious and let's say we're going to reverse the logic of Einstein Einstein the metric is fundamental but the levy chavita connection from which we deduce the curvature is emergent right so the fundamental theorem of romani and geometry is is that every connection causes every metric causes a connection to emerge and then the curvature is built on the connection we turn this around we imagine we're looking for a connection and we wish it to build a metric because connections are amenable to quantization in a way that metrics are not the next point is that we always want to have a plan to return to finite dimensions without losing sight of the quantum and lastly we want to liberate matter from its dependence on the metric for its very existence so what we now need to build fermions onto our four dimensional manifold in some way without ever choosing a metric if we're even having to have any hope of playing a game involving matter starting from this perspective of no information other than the most bare information let's get started we take x4 you need metrics we have none we're not allowed to choose one so we do the standard trick as we choose them all so we allow you 14 to equal the space of metrics on X for point wise therefore if we propagate on top of this and you call this the projection operator if we propagate on you 14 we are in some sense following a Fineman like idea of propagating over the space of all metrics but not at a field level that a point wise tensorial level is there a metric on you 14 well we both want one and don't want one if we had a metric from the space of all metrics we could define fermions but we would also lock out any ability to do dynamics we want some choice over what this metric is but we don't want full choice because we want enough to be able to define the matter fields to begin with it turns out that if this is X 4 and this is this particular endogenous choice of U 14 we have a 10 dimensional metric along the fibers so we have a G 10 mu nu further for every point in the fibers we get a metric downstairs on the base space so if we pull back the cotangent bundle we get a metric G 4 mu nu on pi star of the cotangent bundle of X we now define the chimeric bundle right and the chimeric bundle is the sum of the vertical tangent bundle along the fibers with the pullback which we're going to call the horizontal bundle from the base space so the chimeric bundle is going to be the vertical tangent space of ten dimensions to you direct sum the four-dimensional cotangent space which we're going to call horizontal to you and the great thing about the chimeric bundle is is that it has an a priori metric it's kind of metrics on the floor metric on the ten we can always decide that the two of them are naturally perpendicular to each other furthermore it is almost canonically isomorphic to the tangent bundle of the cotangent bundle because we either have four out of 14 or 10 out of 14 dimensions on the nose so the question is what are we missing and the answer is that we're missing exactly the data of a connection so this bundle chimeric see we have c is equal to the tangent bundle of you up to a choice of a connection theta and this is exactly what we wanted we have a situation where we have some field on the manifold X in the form of a connection which is amenable more friendly to quantization which is now determining a metric turning around the levee chavita game and the only problem is is that we've had to buy ourselves into a different space than the one we thought we wanted to work on but now as theta changes the fermions are defined on the chimeric bundle and it's the isomorphism from the chimeric bundle to the tangent bundle of the space U which is varying which means that the fermions no longer depend on the metric they no longer depend on the theta connection they are there if things go quantum mechanical and we've achieved our objective of putting the matter fields and the spin one fields on something of the same footing but and I want to emphasize this one thing most of us we think a lot about final theories and and about unification but until you actually start daring to try to do it you don't realize what the process of it feels like now try to imagine conducting your life or you have no children let's say and no film tropic urges what you want to do is you want to use all of your money for yourself and die penniless right like a perfect finish assuming that that's what you wanted to do it would be pretty nerve-wracking at the end right how many days left do I have how many dollars left I have this is the process of unification in physics you start giving away all of your most valuable possessions and you don't know whether you've given them away too early whether you've husband them too long and so in this process what we've just done is we've started to paint ourselves into a corner we got something we wanted but we've given away freedom we're now dealing with a fourteen dimensional world now let me just sum this up by saying between fundamental and emergent standard model and gr let's do G our fundamental is the metric Mergent is the connection here in GU it is the connection that's fundamental and the metric that's emergent in the next unit of G u so this is sort of the first unit of G you there any quick questions having to do with confusion or may I proceed to the next unit okay the next unit of G U is the unified field content what does it mean for our fields to become unified there are in fact only at this moment two fields that know about X theta which is the connection that we've just talked about and a section Sigma that takes us back so that we can communicate back and forth between U and X we now need field content that only knows about you which now has a metric depending on theta a particular member of the audience is a hedge fund manager who taught me that there is something of a universal trade and a universal trade has four components you have to have a view you have to have a trade expression you have to be able to calculate your cost of carry and you need a catalyst our view is going to be that somebody doesn't understand what trade is possible and we're going to make a trade that looks like one of the worst trades of all time and hopefully if we if we have enough conviction we're gonna have a catalyst to show that we actually got the better part of the deal what is that trade what is it that we think has been blocking progress in gr and romani and geometry as we've said we have the projection operators and we also have the levy chavita connection in the auxiliary theory we have freedom to choose our field content and we have the ability to get rid of much excess through the symmetries of the gauge group we are going to take particle theory we're going to make a bad trade or what appears to be a bad trade which is that we are going to give away the freedom to choose our field content which is already extremely as I think I said in the abstract Baroque with all of the different particle properties and we are going to lose the ability to use the gauge group because we're going to trade it all you have the family cow and you have some magic beans so it's now time to trade the family cow for the magic beans and bring them home and see whether or not we got the better of the deal okay what is it that we get for the leve chavita connection well not much one thing we get is that normally the space of connections is an affine space not a vector space but in affine space almost a vector space a vector space up to a choice of origin but with the leve chavita connection rather than having an infinite plane with an ability to take differences but no real ability to have a group structure you pick out one point which then becomes the origin that means that any connection a has a torsion tensor a which is equal to the connection minus the levy chavita connection so we get a tensor that we don't usually have gauge potentials are not usually well-defined they're only defined up to a choice of gauge so that's one of the things we get for our levy chavita connection but because the gauge group is going to go missing this has terrible properties from with respect to the gauge group it almost looks like a representation but in fact if we let the gauge group act there's going to be an affine shift furthermore as we've said before the ability to use projection operators together with the gauge group is frustrated by virtue of the fact that these two things do not commute with each so now the question is how are we going to prove that we're actually making a good trade okay first thing we need to do is is that we still have the right to choose intrinsic field content we have an intrinsic field theory so if you consider the structure bundle of The Spinners right we built the chimeric bundle so we can define dirac spinors on the chimeric bundle for in Euclidean signature a $14 of dimension to to the dimension of the space / - right so two to the 14 / - 2 to the seventh is 128 so we have a map into a structure group of you 128 at least in Euclidean signature we can get to mix signatures later from that we can form the associated bundle and sections of this bundle are either depending upon how you want to think about it the gauge group H or C a space of Sigma fields nonlinear there's no reason that we can't choose this as field content again we're being led by the nose like a bowl if we want to make use of the symmetries of the theory we have to promote some symmetry to being part of the theory and we have to let it be subjected to dynamical laws we're gonna lose control over it but we're not dead yet right we're fighting for our life to make sure that this trade has some hope so potentially by including symmetries as field content we will have some opportunity to make use of the projection so for those of you who so when I was thinking about this I to be amazed by ships and bottles I must confess that I never figured out what the trick was for ships in bottles but once I saw it I remembered thank you that's really clever so if you've never seen it you have a ship which is like a curvature tensor and imagine that the mast is is the Ricci curvature if you just try to shove it into the bottle you're undoubtedly gonna snap the mast so you imagine you've transformed your gauge fields you've kept track of where the Ricci curvature was you try to push it from one space like add value to forms into another space like add valued one forms where connections live that's not a good idea instead what we do is the following imagine that you're carrying around group theoretic information and what you do is you do a transformation based on the group Theory so you lower the mast you push it through the neck having some string attached to the mast and then you undo the transformation on the other side this is exactly what we're going to hope is going to save us in this bad trade that we've made because we're going to add field content that has the ability to lower the mast and bring the mast back up we're going to hope to have a theory which is going to create a commutative situation but then once we've had this idea we start to get a little bolder let's think about unified content we know that we want a space of connections a for our field theory but we know because we have a levee chavita connection that this is going to be equal on the nose to add valued one forms as a vector space the gauge group represents an ad valued one forms so if we also have the gauge group but we think of that instead as a space of Sigma fields what if we take the semi direct product at a group theoretic level between the two and call this a our group of interest well by analogy we've always had a problem with the Pangkor a group being too intrinsically tied to rigid flat minkovski space what if we wanted to do quantum field theory in some situation which was more amenable to a curved space situation it's possible that we should be basing it around something more akin to the gauge group and in this case we're mimicking the construction where C here would be analogous to the Lorentz group fixing a point in in Minkowski space and AD valued one forms would be analogous to the Momentum's when we take in the semi direct product to create the in homogeneous Lorentz group otherwise known as the Pangkor a group or rather it's double cover to allow spin so we're going to call this the inhomogeneous gauge group or Iggy and this is going to be a really interesting space because it has a couple of properties one is it has a very interesting subgroup now of course H includes into G by just including on to the first factor but in fact there's a more interesting homomorphism brought to you by the levy chavita connection so this magic bean trade is going to start to enter more and more into our consciousness if I take an element H and I map that in the obvious way into the first factor but I map it onto the more ore cart and for I think that's what I wish I remembered more of this stuff into the second factor it turns out that this is actually a group homomorphism and so we have a non-trivial embedding which is in some sense diagonal between the two factors that subgroup we are going to refer to as the tilted gauge group and now our field content at least in the bosonic sector is going to be a group manifold an infinite dimensional function space lead group but a group nonetheless and we can now look at G mod the Tilted gauge group and if we have any interesting representation of H we can form homogeneous vector bundles and work with induced representations and that's what the fermions are going to be so the fermions and our theories are going to be H modules and the idea is that we're going to work with vector bundles curly e of the form in homogeneous gauge group product it over the Tilted gage group now just as in the finite-dimensional case we have a linear and a nonlinear component right because that topological level this is just a cartoon Cartesian product so if we wish to take products of fermions of spin oriole fields we have a place to accept them we can't figure out necessarily how to map them into the nonlinear sector but we don't want to so just the way when we look at supersymmetry we can take products of the spin 1/2 fields and map them into the linear sector we can do the same thing here so what we're talking about is something like a super symmetric extension of the inhomogeneous gauge group analogous to super symmetric extensions of the double cover of the inhomogeneous Lorentz or plonker a go further because this construction is at the level of groups we've left a slot on the left hand side on which to act so for example if we want to take regular representations on the group we can act by the group G on the left hand side because we're allowing the tilted gage group to act on the right hand side so it's perfectly built for representation theory and if you think back to Vig neurs classification and the concept that a particle should correspond to an irreducible representation of the in homogeneous gauge group in homogeneous Lorentz group we may be able to play the same games here up to the issue of infinite dimensionality so right now our field content is looking pretty good it's looking unified in the sense that it has an algebraic structure that is not usually enjoyed by field content and the field content from different sectors can interact and know about each other provided we can drag something of this out of this with meaning now what would it mean to be able to use a gauge group in an intrinsic theory like this we would be talking about something like an action let's say a first-order action and it would take the group G let's say to the real numbers invariant not under the full group but under the tilted gauge subgroup and now the question is do we have any such actions that are particularly nice and could we recognize them the way Einstein did by trying to write down not the action in Hilbert was the first one to write that down but I you know I always feel defensive because I think Einstein and Grossman did so much more to begin the theory and that the Lagrangian that got written down was really just an inevitability so just humor me for this talk and let me call it the Einstein Grossman Lagrangian Hilbert certainly done fantastic things and has a lot of credit elsewhere and he did do it first but here what we we had was that Einstein thought in terms of the differential of the action not the action itself so what we're looking for is equations of motion or some field alpha where alpha belongs to the one forms on the group now in this section of G you unified field content is only one part of it but what we really want is unified field content plus a toolkit so we've restricted ourselves to one gauge group this big unitary group on the spinners using whatever sort of inner product naturally exists on the spinners and not spinners value in an auxiliary structure but intrinsic spinners the toolkit that we have is that the adroit bundle looks like the clifford algebra at the level of vector spaces which is just looking like the exterior algebra on the chimeric bundle that means that it's graded by degrees chimeric bundle has dimension 14 so there's a zero part of one part a two part all the way up to 14 plus we have forms in the manifold and so the question is if I want to look at Omega I valued in the adjoint bundle there's going to be some element Phi I which is pure trace right because it's the same representations appearing where in the usually auxiliary directions as well as the geometric directions so we get an entire suite of invariants together with trivially associated invariants that come from using the Hodge star operator on the form so I'm just going to call them for completeness I'm going to deal with them now this is a tremendous amount of freedom that we've just gained normally we keep losing freedom but this is the first time we actually begin to see that we have a lot of freedom and we're gonna actually retain some of this freedom through the it to the end of the talk but the idea being that I can now start to define operators which correspond to the ship in the bottle problem I can take field content epsilon and PI where epsilon where these are elements of the in homogeneous gauge group in other words epsilon is a is a gauge transformation and pi is an is a gauge potential and I can start to define operators I'm using so in this case if I have a Phi which is one of these invariants in the form piece I can either take a contraction or I can take a wedge product in the Lee algebra piece I can either take a Lee product or because I'm looking at the unitary group there's a second possibility which is I can multiply everything by I and go from skew-hermitian to hermitian and take a Jordan product using anticommutator x' rather than commutator so I actually have a fair amount of freedom and I'm going to use a magic bracket notation which in whatever situation I'm looking for knows what it wants to be is does it want to do contractions is wanting to wedge product leap product Jordan product but the point is I now have a suite of ways of moving forms around so for example I can define a Shia operator that takes I forms valued in the adjoint bundle to much higher degree forms value than the adjoint bundle so for this in this case for example it would take a to form to a D minus 3 plus 2 or a D minus 1 form so curvature is an add value to form and if I had such a she AB operator it would take add value to forms to add value D minus 1 forms which is exactly the right space to be an alpha coming from the derivative of an action this is exactly what Einstein was doing he took the curvature which was large and he bent it back and he sheared off the viol curvature and they took that part and he pushed it back along the space of metrics to give us something which we nowadays call Ricci flow an ability for the curvature to direct us to the next structure well we're doing the same thing here we're taking the curvature and we can now push it back onto the space of connections three plus I so in this case the idea is that we've actually got something for our magic beans we have an ability now to get equations of motion which go along the group in some sense it's as if it was a gradient vector field except we're using forms rather than vectors but now what are the transformation properties well because the curvature so you have XI AB because the curvature of a connection hit by a gauge transformation is equal on the nose to the adjoint action on the Lee algebra of the curvature we know that if we have two possible actions of conjugation under a bracket and the bracket respects the action of the gauge group we know that this is going to be well preserved in other words we're going to get a form that is gauge invariant relative to the tilted gauge group and so as a result we now have the possibility for equations of motion which are well defined even though they involve projection operators because we built the symmetries into the theory and we're working on a group manifold to begin with what about the torsion can we rescue the torsion here again we have good news the torsion is problematic but if I look at a different field which I'm going to call the Augmented torsion and I define it to be the regular torsion which would be pi minus this expression this turns out to be beautifully invariant again so neither this term nor this term is gauge invariant but there they failed to be gauge invariant in exactly the same way so an important principle of life which I took too long to realize is that if you have one disease you're in real trouble but if you have two diseases you always have the possibility of having one disease kill the other disease this is true and renormalization theory it's true in black-scholes theory it's true all over the place so what we have here is we've got more diseases into the theory but an even number of diseases allow us to have no disease at all so now we have two great tensors we've got 1 tensor coming from the curvature and the shiaa operator we have another tensor coming from the torsion and it's augmentation no we're doing okay okay we're not doing physics yet we're just building tools we've built ourselves a little bit of freedom we have some reprieves we've still got some very big debts to pay back for this magic beans trade we're in the wrong dimension we don't have good field content we're stuck on this one spinner we've built ourselves some projection operators we picked up some symmetric nonlinear Sigma field what can we write down in terms of equations of motion let's start with einstein's concept if we do xi AB of the curvature tensor of the gage potential hit with an operator defined by the epsilon Sigma field plus the star operator acting on the Augmented torsion of the pair this contains all of the information when PI is zero in Einstein's tensor in other words there is a spin Oriole analog of the viol curvature Aspen Oriole analog of the traceless Ricci curvature and Aspen Oriole analog of the scalar curvature this operator should shear off the analog of the viol purva Chur just the way Einstein is projection shears off the viol curvature when you're looking at the tangent bundle in this tournament which is now gauge invariant may be considered as containing a piece that looks like lambda times G mu nu or a cosmological constant in this piece here can be made to contain a piece that looks like Einstein's tensor and so this looks very much like the vacuum field equations but we have to add in something else I'm gonna be a little bit vague because I'm still giving myself some freedom as we write this up but we're going to define whatever tensor we need for this term these terms here this is gauge invariant this is gauge invariant and this is gauge invariant with respect to the tilted gauge group these two tensors together should be exact and this tensor on its own should be exact we're going to call the exact tensor the swerve ature so the particular she have operator we call the swerve so that it's swerve curvature plus the adjustment needed for exactness and another gauge invariant term which is not usually gauge invariant so that's pretty cool if that works we've now taken the Einstein equation and we've put it not on the space of metrics but we've put a generalization in an analogue on the space of gauge potentials much more amenable to quantization with much more algebraic structure and symmetry in the form of the in homogeneous gauge group in its homogeneous vector bundle some of which may be super symmetric now the question is we've we've integrated so tightly with the matter field we have to ask ourselves the question can we see unification here let's define matter content in the form of Omega zero tenser than the spinners which is a fancy way of saying spinners together with a copy of the one forms tenser than the spinners and let me come up with two other copies of the same data so I'll make Omega D minus one just by duality so imagine that there's a Hodge star operator and there's a little kid I had the soma cube I don't know if you ever played with one of these things they're fantastic and I later found out that this guy who invented the soma cube which you had to put the others pieces there was one piece that looked like this this object and he was like this amazing guy in the resistance during world war ii so I would like to name this the somatic complex after I guess his name is P at Hine I think so this this complex I'm going to choose to start filling in some operators the exterior derivative coupled to a connection but on the case of spinors we're gonna put a slash through it let's make this the identity we'd now like to come up with a second operator here and this second operator here should have the property that the complex should be exact than the obstruction to it being a true complex to know potency should be exactly the generalization of the Einstein equations thus unifying the spin oriole matter with the intrinsic replacement for the curvature equations well we know that da composed with itself is going to be the curvature and we know that we want that to be hit by a Shia operator and if she has a derivation you can start to see that that's gonna be curvature so you want something like FA followed by she AB over here to cancel then you think okay well how am I going to get at getting this augmented torsion and then you realize that the information in the in homogeneous gauge group you actually have information not for one connection but for two connections so in one case I can do plus star to pick up the a sub PI but I'm also gonna have a derivative operator if I just do a star operation so I need another derivative operator to kill it off here so I'm going to take minus the derivative with respect to the connection H inverse da not H which defines a connection one form as well as having the same derivative cup coming from the levy chavita connection on you so in other words I have two derivative operators here I have to add valued one forms the difference between them is going to be of zero with order and it's going to be precisely the augmented torsion that's the same game I'm going to repeat here so I'm going to do the same thing here I'm going to define a bunch of terms where in the numerator I'm going to pick up the pie as well as the derivative in the denominator because I have no derivative here I'm going to pick up this H inverse da not an H I'm going to do that again on the other side they're gonna be plus and minus signs but it's a magic bracket that knows whether or not should be a plus sign or a minus sign and I apologize for that but I'm not able to keep that straight and then there's gonna be one extra term where all these T's have the epsilon and PI's okay so some crazy series of differential operators on the northern route so if you take the high road or you take the low road when you take the composition of the to the differential operators fall out and you're left with an obstruction term that looks like the Einstein field equations well that's pretty good if true can you go farther well look at how close this field content is to the picture from deformation theory that we learned about in low dimensions the low dimensional world works by saying that symmetries map to field content map to equations usually in the curvature and when you linearize that if you're in low enough dimensions you have Omega 0 Omega 1 sometimes I make a zero again and then something that comes from Omega 2 and if you can get that sequence to terminate by looking at something like a half signature at theorem or a bent back to Ram complex in the case of dimension 3 you haven't a tee a singer theory and remember we need some way to get out of infinite dimensional trouble all right you have to have someone to call when things go wrong overseas you have to be able to get your way home and in some sense we call it a tee and singer and say we're in some infinite dimensional space can't you cut out some finite dimensional problem that we can solve even though we start getting ourselves into serious trouble and so we're going to do the same thing down here we're going to have a mega zero add Omega 1 add direct sum Omega zero add Omega D minus 1 ad and it's almost the same operators and this is now not just a great guess it's actually the information for the deformation theory of the linearized replacement of the einstein field equations so this is computing the director iski tangent space just as if you were doing self-dual theory or chern-simons theory you've got two somatic complexes right one of them is bose one of them is firming the obstruction to both of them is a common generalization of the Einstein field equations what's more is if you if you start to think about this this is some version of Hodge theory with funky operators so you can ask yourself well what are the harmonic forms in a fractional spin context well they're different depending upon whether you take the degree 0 piece together with the degree P so you take the degree one piece let's just take the degree one piece you get some kind of equation so I'm going to decide that I have a Zeta field which is an Omega 1 tensor spinors and a field new jewelry strikes me as a kiddush field new is omega 0 tensor s ok what equation would they solve if we were doing Hodge theory relative to this complex the equation would look something like this there'd be one equation that was very simple and then there'd be one equation that would be like really hard to guess kahshanna I hope I'm not screwing this up but look all these words and I still feel like I'm managing to run out of room now if you have something like that that would be a hell of a Dirac equation right you've got differential operators over here you've got differential operators I guess I didn't write them in but you would have two differential operators over here and you'd have this differential operator coming from this more cartoon form so I apologize and being a little loose here but the idea is you have two of these terms or zeroeth order three of these terms would be first-order and on this side one term would be first-order and that's not there that's right that was a mistake oh no sorry that was a mistake calling it a mistake these are two separate equations right so you have two separate fields nu and Zeta and you have a couple set of differential equations that are playing the role of the Dirac theory coming from the Hodge theory of a complex whose obstruction to being calm ology theory would be the replacement to the Einstein field equations which would be rendered gauge invariant on a group relative to a tilted sub group okay what would so now we've dealt with two of the three sectors is there any generalization of the yang-mills equation well if we were to take the Einstein field equations ation and take the norm square of it oh there's some point I should make here just one second I've been treating this as if everything is first-order well what really happens here is that you've got symmetries you've got symmetric field content you've got ordinary connections and we're neglecting to draw the fact that there have to be equations here too these equations are first-order so why do we get to call this a first-order theory if there are equations here which are of second-order well it's not a pure first-order theory but when I say a first-order theory in this context what I really mean is that the second-order equations are completely redundant on the first-order equations by virtue of the symmetry principle that is any solution of the first-order equations should automatically apply imply a solution of the second order equations so from that perspective I can pretend that this isn't here because it is sufficient to solve the first-order equations so I can now look let's call that entire replacement which we previously called alpha I miss that alpha equal to epsilon because I've actually been using Absalon the portion of it that is just the first-order equations and take the norm square of that that gives me a new Lagrangian and if I solve that new Lagrangian it leads to equations of motion that look like exactly what we said before and it ends up defining an operator that looks something like this da star the adjoint of the Shehab operator so in other words this piece gives you some portion that looks like right from the swerve ature tensor there's going to be some component that's playing the role of Einsteins field equations directly and the Ricci tensor but generalized and then you're gonna have some differential operator here so that the replacement for the yang-mills term instead of da star of fa you've got these two XI a band at XI AB and an adjoint XI AB together in the center generalizing the yang-mills theory then you say well how come we don't just see the yang-mills theory why don't we see general relativity as well but in the full expansion there's also a term that zeroeth order that's effectively acting like the identity which hits this as well so you have one piece that looks like the yang-mills theory and in these second-order equations you also have a piece that looks like the Einstein theory and this is in the vacuum equations so then the question is how do you see the Dirac theory coming out of this and so what we're just trying to put together now before we come out with the manuscript for this is putting these two elliptic complexes together the direct terms go between the two complexes right so the idea is that the stress-energy tensor should be the up and back term and the Dirac equations should come out of the term that goes up and over versus the term that goes over and up and you need some cancellations to make sure that everything is of zero width order properly invariant etc and that's taking little time because frankly I'm not good keeping track of indices minus signs left right - it's a learning-disabled nightmare so we've got one more unit to go I mean there's a fifth unit that has to do with mathematical applications but this is sort of a physics talk for today is there any questions before we go into the last unit and then really handle questions for real all right let me show you the next a little bit we've got problems we're not in four dimensions we're in 14 we don't have great field content because we've just got these unadorned spinners and we're doing gauge transformations effectively on the intrinsic geometric quantities not on some safe auxiliary data that's tensor product with what are our spinners are how is it that we're gonna find anything realistic and then we have to remember everything we've been doing recently has been done on you we've forgotten about X how does all of this look to X so X is sitting down here and all the action is happening up here on you 14 there's a projection operator I've used PI twice it's not here the field contents just projection and I've got a Sigma which is a section what does Zeta pulled back or new pulled back look like on x4 okay let's try to think about how we would come up with this filled content starting from first principles let's imagine that there's nothing to begin with then you have one copy of matter whatever it is that we see in our world the first generation in order for that to become interesting it has to have an equation so it has to get mapped somewhere then we've seen the muon and all the rest of the matter that comes with it we have a second generation then in the mid-1970s pearl finds the tau particle and we start to get panicked that we don't understand what's going on one thing we can do is we could move these equations around a little bit and move the equation for the first generation back and then we could start adding particles let's imagine that we could guess what particles we'd add we'd add a pseudo generation of 16 particles spin three halves never-before-seen not necessarily superpartners but we read a Schwinger matter with familiar internal quantum numbers but potentially so that they're flipped so that matter looks like antimatter to this generation then we add just for the heck of it 144 spin 1/2 fermions which contain a bunch of particles with familiar quantum numbers but also some very exotic looking particles that nobody's ever seen before now we start doing something different we make an accusation one of our generations isn't a regular generation it's an imposter at low energy in a cooled state potentially it looks just the same as these other generations but were we somehow able to turn up the energy imagine that it would unify differently with this new matter that we've posited rather than simply unifying onto itself so two of the generations would unify into themselves but this third generation would fuse with the new particles that we've already added we consolidate geometrically we can add some 0 with order terms and we imagine that there is an elliptic complex that would govern the state of affairs we then choose to add some stuff that we can't see it all that's dark and this matter would be governed by forces that were dark to there might be dark electromagnetism and dark strong and dark weak it might be that things break in that sector completely differently and it doesn't break down to an su 3 cross su 2 cross u 1 because these are different su 3 s su 2 s nu ones and it may be that there would be like a high energy su 5 you know or some p'tee Salam Model imagine then that chirality was not fundamental but it was emergent that you had some complex and as long as there were cross terms these two halves would talk to each other but if the cross terms went away the two terms would become decoupled and just the way we have a left hand and we have a right hand and you asked me right imagine you have a neurological condition and in Oliver Sacks sort of an idiom if somebody's only aware of one side of their body they say oh my god I'm deformed I'm asymmetric right but we actually have a symmetry between the two things that can't see each other then we would still have a chiral world but the chirality wouldn't be fundamental there'd be something else keeping the fermions light and that would be the absence of the cross strands now if you look at what happens in our replacement for the Einstein field equations the term that would counterbalance the scalar curvature if you put these equations on a sphere they wouldn't be satisfied if the T term had a zero expectation value because there would be non-trivial scalar curvature and the curtain to swerve ature terms but there'd be nothing to counterbalance so it's fundamentally the scalar curvature that would coax the valve on the Augmented torsion out of the vacuum to have a nonzero level and if you pumped up that sphere and it smeared out the curvature which you can't get rid of because of topological consider Asians let's say from churned a theory you would have a very diffuse very small turn and that term would be the term that was playing the role of the cosmological constant so in a large universe you'd have a curvature that was spread out and things would be very light and things would get very dark due to the absence of curvature linking the sectors and that turns out to be exactly our complex so in other words just to recap starting with nothing other than a four manifold we built a bundle you the bundle you had no metric but it almost had a metric and had a metric up to a connection there was another bundle on top of that bundle called the chimeric bundle the chimeric bundle had an intrinsic metric we built our spinners on that we restricted ourselves to those spinners we moved most of our attention to the emergent metric on u14 which gave gave us a map between the chimeric bundle and the tangent bundle of u14 we built a tool kit allowing us to choose symmetric field content to define equations of motion on the cotangent space of that field content to form a homogeneous vector bundle with the fermions to come up with unifications of the einstein field equations yang-mills equations and Dirac equations we then broke those things apart under decomposition pulling things back from u14 and we found a three generation model where nothing has been put in by hand and we have a 10 dimensional normal component which looks like the spin 10 theory I can tell you where there are problems in this story I can tell you that when we move from Euclidean metric to minkovski metric we seem to be off by a sign somewhere or I could be mistaken I could tell you that the propagation in 14 dimensions has to be worked out so that we would be fooled into thinking we were in a four dimensional world there are lots of things to ask about this theory but I find it remarkable that tying our hands we find ourselves with new equations unifications and three generations in a way that seems surprisingly rich certainly unexpected and I think I'll stop there thank you very much for your time [Applause] so thanks for watching that video but I thought I would do since that was the first time I'd really presented the theory at all in public and I'd gotten somewhat turned around on my trip to England and trying probably stupidly to do last-minute Corrections got me a bit confused in a few places and I wrote some things on the board I probably shouldn't have I thought I would try a partial explainer for technically oriented people so that they're not mystified by the video and any errors here of my own I'm known to make many so hopefully they won't be too serious but we'll find out so this is a supplementary explainer for the geometric unity talk at Oxford that you just saw first of all I think the most important thing to begin with is to ask what new hard problems arise when you're trying to think about a fundamental theory that aren't found in any earlier theory now every time you have an effective theory which is a partial theory there is always the idea that you can have recourse to a lower-level strata so you don't have to explain in some sense everything coming from very little or nothing I think that the really difficult issue that people don't talk enough about is the problem of the fire that lights itself and I think this was beautifully demonstrated by MC Escher in his famous lithograph drawing hands where he takes the idea of the canvas or the paper as a given but somehow he imagines that the canvas could will into existence the ink needed to draw the hands that move the pen to draw the hands that concept is actually the super tricky part in my opinion about going from effective theories to any attempt at a fundamental theory so with that said what I want to think about is what antecedents does this concept have in physics and I find that there really aren't any candidate theories of everything are unified field theories that I can find that plausibly give us an idea of how a canvas would will an entire universe into being and so that really to me is the conceptual problem that I think b-doubles this and makes the step quite a bit more difficult than some of the previous technical steps if you ask for antecedents however there is one that at least within physics is relatively famous and that is by John Archibald wheeler and it is a picture in some sense of the universe contemplating itself and so this idea that somehow the universe would contemplate itself into existence maybe the letter U is in some sense analogous to the paper and somehow the eye rather than the hand is drawn across to look at a different part of the of the U and whether or not that has meaning is intrinsically always a question people are animated by it but I don't know that people have actually worked on it the quote of Einstein's I think that really speaks to me often the most and maybe even was my thesis problem was he asked whether the creator had any choice in how the universe was constructed and so I think if you believe that the canvas is itself the that which generates all of the content and all of the action you're you're left with a puzzle as to how would you move forward from this it might be easier in a mathematical sense to temporarily put the U on its back to put it more in line with a standard picture that many mathematicians and physicists will be familiar with in sector one of the geometric unity theory space-time is replaced and recovered by the observers contemplating itself and so there are several sectors of G U and I wanted to go through at least four of them in Einstein's space-time we have not only four degrees of freedom but also a spacetime metric representing rulers and protractors if we're going to replace that it's very tricky because it's almost impossible to think about what would be underneath einstein's theory now there's a huge problem in the spin oriole sector which I don't know why more people don't worry about which is that spinners aren't defined for representations of the double cover of gl4 are the general linear groups effective spin analog and as such if we imagine that we will one day quantize gravity we will lose our definition not of the electrons but let's say of the medium in which the electrons operate that is there will be no spin oriole bundle until we have an observation of a metric so one thing we can do is to take a manifold X D as the starting point and see if we can create an entire universe from no other data and not even with a metric so since we don't choose a metric what we instead do is to work over the space of all possible point wise metrics so not quite in the Fineman sense but in the sense that we will work over a bundle that is a quite larger quite a bit larger dimension so for example if X was a four-dimensional therefore D equals four then Y in this case would be d squared which would be 16 + 3 D which would be 12 making 28 divided by 2 which would be 14 so in other words a four-dimensional universe or sorry a four-dimensional proto spacetime not a spacetime but a proto space-time with no metric would give rise to a 14 dimensional observers portion called Y now I believe that in the lecture in Oxford I called that you so I'm sorry for the confusion but of course this shifts around every time I take it out of the garage and that's one of the problems with working on a theory in solitude for many years so we have two separate spaces and we have fields on the two spaces now what I'm going to do is I'm gonna refer to fields on the XD space by hebrew letters so instead of g mu nu for a metric i just wrote gimel mem noon and the idea being that i want to separate latin and greek fields on the y space from the rather rarer field that actually lived directly on X so this is a little bit confusing one way of thinking about it is to think of the observer s-- as the stands plus the pitch in a stadium I think I may have said that in the in the lecture but this is what replaces the questions of where and when in the newspaper story that is a fundamental theory where and when correspond to space and time who and what correspond to bosons and fermions and how and why correspond to equations and the Lagrangian that generates them so if you think about those six quantities you'll realize that that's really what the content of a fundamental theory is assuming that it can be quantized properly most fields and in this case we're going to call the collection of two tuples Omega so the inside of Omega that will be in the first tuple will have epsilon and PI written a sort of a non-traditional variation of how we write this symbol for pi in the second tuple we'll have the letters nu and Zeta and I would like them not to move because they honor particular people who are important so most fields in this case Omega are dancing on Y which was called you in the lecture unfortunately but they are observed via pull back as if they lived on X in other words if you're sitting in the stands you might feel that you're actually literally on the pitch even though that's not true so what we've done is we've taken the U of wheeler we've put it on its back and created a W structure and the W structure is meant to say that there's a bundle on top of a bundle again geometric unity is more flexible than this but I wanted to make the most concrete approach to the possible for at least this introduction and sometimes we don't knit we don't need to state that why would in fact be a bundle you could be an immersion of X into any old manifold but I'd like to go with the most ambitious version of GU first so the two projection maps are PI 2 and PI 1 and what we're going to say up top is is that we're going to have a a symbol Z and an action of a group row on Z standing in for any bundle associated to the principal bundle which is generated as the unitary bundle of the spin of the spinners on the chimeric tangent bundle 2y that's a bit of a mouthful but the key issue was that on the manifold Y there happens to be a bundle which is isomorphic non canonical e to the tangent bundle of Y which can has a definite and canonical metric and in fact there that carries the spinners so this is the way in which we get spinners without ever having to choose a metric but we pick up some technical debt to use the computer science concept by actually having to now work on two different spaces x and y and we're not merely working on x anymore this leads to the Mark of Zorro that is we know that whenever we have a metric by the fundamental theorem of Romani in geometry we always get a connection it happens however that what is missing to turn the canonical chimeric bundle on Y into the tangent bundle of Y is in fact a connection on the space X so there is one way in which we've reversed the fundamental theorem of Romani in geometry where a connection on X leads to a metric on Y so if we do the full transmission mechanism out and gimel on x leads to alpha sub gimel for the leve chavita connection on x alpha sub gimel live leads to g sub alpha which is or sorry the G sub Aleph I'm not used to using Hebrew in math so jisub Alif then is a metric on why and that creates a levy chavita connection of the metric on the space Y as well which then B induces one on the spin oriole bundles in Sector two the in homogeneous gauge group on Y replaces the Pangkor a group and the internal symmetries that are found on X and in fact you use a fermionic extension of the inhomogeneous gauge group to replace the supersymmetric punker a group and that would be with field content 0 forms 10 surd and spinner tensor with spinners direct some one forms tensor two spinners all up on Y as the fermionic field content so that gets rid of the biggest problem because the internal symmetry group is what causes the failure I think of supersymmetric particles to be seen in nature which is we have two different two different origin stories which is a little bit like lilith and in Genesis we can't easily say we have a unified theory if space-time and the SU 3 cross su 2 cross u one group that lives on space-time have different origins and cannot be related in this situation we tie our hands and we have no choice over the the group content so just to fix bundle notation we let H be the structure group of a bundle piece of H over a base space B we use PI for the projection map we've reserved the variation in the PI orthography for the field content and we try to use write principle actions I'm terrible with left and right but we do our best we use H here not G because we want to reserve G for the inhomogeneous extension of H once we move to function spaces so with function spaces we can take the bundle of groups using the adjoint action of H on itself form The Associated bundle and then moved to C infinity sections to get the so-called gage group of automorphisms we have a space of connections typically denoted by a and we're going to promote Omega 1 tensor in the adjoint bundle to notation of script n as the affine group which acts directly on the space of connections now the in homogeneous gauge group is formed as the semi direct product of the gauge group of automorphisms together with the affine group of translations of the space of connections and you can see here is a version of an explicit group multiplication well I hope I got that one right and then we have an action of G that is the inhomogeneous gauge group on the space of connections because we have two different ways to act on connections we can either act by gauge trans transformations or we can act by affine translations so putting them together gives us something for the inhomogeneous gauge group to do we then get a bi connection in other words because we have two different ways of pushing a connection around if we have a choice of a base connection we can push the base connection around in two different ways according to the portion of it that is coming from the gauge transformations curly H or the affine translations coming from curly n we can call this map the BI connection which gives us two separate connections for any point in the in homogeneous gauge group and we can notice that it can be viewed as a a section of a bundle over the base space to come when we find an interesting embedding of the gauge group that is not the standard one in the in homogeneous gauge group so our summary diagram looks something like this take a look at the Tau sub a knot we will find a homomorphism of the gauge group into its inhomogeneous extension that isn't simply inclusion under the first factor we and I'm realizing that I have the wrong pipe reduction just be a simple PI projecting down we have a map from the gate in homogeneous gauge group via the by connection to a cross a connections across connections and that that behaves well according to the difference operator Delta that takes the difference of two connections and gives an honest add value at 1/4 ok the infinitesimal action of the gauge transformation of a gauge transformation or at least an infinitesimal one on a point inside of the group is given by a somewhat almost familiar expression which should remind us of how the first term in the gauge deformation complex for self-dual yang-mills actually get started and so by acting via this interesting embedding of the inhomogeneous gauge group on sorry the embedding of the gauge group inside it's in homogeneous extension but the non-trivial one we get something very close to the original first step of the two step deformation complex now in Sector 3 there are payoffs to the magic beans trade the big issue here is is that we've forgone the privilege of being able to choose and dial in our own field content and we've decided to remain restricted to anything we can generate only from XD in this case X 4 so we generated y 14 from X 4 and then we generated chimeric tangent bundles on top of that we built spinners off of the chimeric tangent bundle and we have not made any other choices so we're dealing what I think it's u 128 u u 2 to the seventh that is our structure group and we it's fixed by the choice of X for not anything else so what do we get well as promised there is a tilted homomorphism which takes the gauge group into its inhomogeneous extension it acts as inclusion on the first factor but it uses the levy chavita connection to create a second sort of more cartan form I hope I remember the terminology right it's been a long time the map is injective because it's injective under the first factor but it actually gives us a non trivial embedding of the gauge group in its in homogeneous extension which makes the whole theory work we then get to see I have operators now a shiev operator is a map from the group crossed the ad valued I forms in this case the particulars about operators were interested in is mapping I forms 2d minus 3 plus I forms so for example it would map a to form 2d minus 3 plus I so if d for example were 14 then and and i were equal to 2 then 14 minus 3 is equal to 11 plus 2 is equal to 13 so that would be an ad valued 14 minus 1 form which is exactly the right place for something to form a current that is the differential of a Lagrangian on this space now the Augmented torsion the torsion is a very strange object it's introduced sort of right at the beginning of learning differential geometry but it really doesn't get used very much one of the reasons it doesn't get used in gauge theory is that it's not gauge invariant it has a gauge invariant piece to it but then a piece that spoils the gauge invariance but we because we have two connections one of the ideas was to introduce two diseases and then to take a difference and as long as the disease is the same in both the difference will not have the disease because both diseases are in polluted but with a minus sign between them so the Augmented torsion is relatively well behaved relative to this particular slanted or tilted embedding of the gauge group in its inhomogeneous extension which this is very nice because now we actually have a use for the torsion we have an understanding of why it may never figured particularly into geometry is that you need two of two connections rather than one to see the advantages of torsion at all so here's an example of one ship-in-a-bottle operator I think this would be sort of analogous if I'm not mistaken to trying to take the Ricci curvature from the entire Riemann curvature but if you think about what Einstein did Einstein had to go further and reduce the Ricci curvature to the scalar curvature and then sort of dial the components of the traceless Ricci and the scalar curvature to get the right proportions so there are many Xie operators and you have to be very careful about which one you want and once you know exactly what it is you're trying to hit you can choose the Shehab operator to be bespoke and get the contraction that you need now I've I've made you guys sit through a lot so I wanted to give you sort of humorously a a feeling of positivity for the exhaustion so the years of anxious searching in the dark with their intense longing their intense alternations of confidence in exhaustion and the final emergence into the light only those who have experienced it can understand it I just always thought this was like the most sensitive and beautiful quote and I wish it were one of his better known quotes but I think it's so singular that it's hard to it's hard to feel what it was that he was talking about because in fact he sort of explains this in the last line so given that you've been on a long journey here is something of what geometric unity equations might look like so in the first place you have the swerved curvature the Shi AB applied to the curvature tensor that in general does not work out to be exact so you can't have it as the differential of a Lagrangian and in fact that we talk about swirls swerves twirls Eddie's there has to be a quadratic Eddy tensor that I occasionally forget when I pull this thing out of mothballs and the two of those together make up what I call the total swerve ature and on the other side of the equation you have the displaced torsion which I've called dysplasia and to get rid of the pesky sort of minus sign and Hodge star operator this would be the replacement for the Einstein equation not on X where we would perceive it but on Y before being pulled back on to the manifold X so a condensation of that would be very simple in simplest terms we would be saying that the swerve ature is equal to visit to the dysplasia and at least in this sector of the four main equations of theoretical physics this would be the replacement for the Einstein equations again on Y before being pulled back to X next is the sketch of the fermionic field content I'm not sure whether that should have been sector for sector three but it's gonna be very brief I showed some pictures during the lecture and I'm not gonna go back through them but I wanted to just give you an idea of where this mysterious third generation I think comes from so if we review the three identities here we see that if we have a space V thought of like as a tangent bundle and then you have spinners built on the tangent bundle when you product tensor product the tangent bundle with its own spinners it breaks up into two pieces one piece is the so-called cart and product which is sort of the some of the highest weights and the other is a second copy of the spinners gotten through the Clifford contraction so that's well known but now what I think fewer people know many people know that the spinners have a sort of an exponential property that is the spinners of a direct song are the tensor product of the spinners of the two summons of the direct Sun so that's a very nice sort of version of an exponential and exponential would take a sum and turn it into a product what happens when you're trying to think about a tangent space in Y is being broken up into a tangent space along an immersed X together with its normal bundle so imagine that x and y are the tangent space to X and a normal bundle so there were read a Schwinger piece that is the spin three-halves piece has a funny kind of an almost exponential property that is they're worried to Schwinger content of a direct sum of vector spaces is equal to the rita Schwinger of the first tensor product did with the ordinary spinners in the second direct sum with the ordinary spinners in the first tensor product it with the Ricci with this re they worry - winger content of the second son man but then there's this extra interesting term which is the spinners on the first sum and tensor product did with the spinners on the second Samantha now recalling that when I started my career we did not know that neutrinos were massive and I figured that they probably had to be massive because I desperately wanted a 16 dimensional space of internal quantum numbers not 15 because my my ideas only work if the space of internal quantum numbers is of dimension 2 to the N and one of my favorite equations at the time was 15 equals 2 to the fourth not literally true but almost true and thankfully in the late 1990s the case for 16 particles in a generation was strengthened when neutrinos were found to have mass but that remaining term in the south-east corner the spinners on X tensor spinners and why looks like the term above it in line 2.15 and that in fact is the third generation of matter in my opinion that is it is not a true generation it is broken off and would unify very differently if we were able to heat the universe to the proper temperature so starting to sum up this is not the full theory I'm just presenting this in part to dip my toe back into the water it's a daunting task to try to address people about something you've been thinking about for a long time and if no idea whether it's even remotely correct this is the Einsteinian replacement and it must be pulled back to X that's the first thing the yang-mills Maxwell peace comes from a direct square of the Einstein replacement that is I don't believe that we're really looking for a unifying equation I think we're looking for a unifying Dirac Square direct famously took the square root of the client Gordon equation and he gave us the Dirac equation and in fact I believe that the Dirac equation and the Einstein equation are to be augmented and fit into the square root part of a direct Square and I believe that the yang-mills content and Higgs version of the klein-gordon equation would go in the square part of the Dirac Square so two of these equations unified differently than two others and the two pairs are unified in the content of a direct square the Dirac piece will be done separately elsewhere when I get around to it and contains the Rita Schwinger field content which is fundamental and new there are only two generations in this model I think people have accepted that there are three but I don't believe that there are three I think that there are two and that the third unifies with other matter at higher energies the quartic Biggs piece comes from the Dirac squaring of a quadratic remember there's a Eddy tensor which is quadratic in the Augmented torsion the metric does multiple duties here is it's the main field in this version of G U with the sort of strongest assumptions as field content on that is originally on X whereas most of the rest of the field content is on but it also acts as the observer pulling back the full content of Y onto X to be interpreted as if it came from X all along generating the internal the the sort of illusion of internal quantum numbers and I should say that the p'tee Salam theory which is usually advertised as think su for cross su 2 across su 2 is really much more naturally spin 6 cross spin for when the trace portion of the space of metrics is put in with the proper sign if you're trying to generate the sector that begins as X 1 comma 3 remember XD where X where D equals 4 is the generic situation but you have all these different sectors I believe that these sectors probably exist if this model is correct but we are trapped in the 1 3 sector so you have to figure out what the implications are for pushing that indefinite signature up into an indefinite signature on the y manifold and there are signatures that make it look like the p'tee salam rather than directly in the spin 10 su 5 line of thinking so we will attempt to present the full theory shortly and shortly keep in mind this took seven years to just bring me to want to come back to this but it must be reassembled from decades of notes and that's part of the problem when you're working alone and you're not really expecting to talk to anybody so I want to thank you for your patience and your time and I just want to read a bunch of names that people who matter to me and if I have done anything wrong this is not no reflection on them marcos de Soto Peter teal is the door singer Raul bot Michael Grossberg Adil Abdul Ali Harry and Sophie Rubin Brett Weinstein and family Heather hanging and Zach and Toby Peter fried Scott Axelrod Nima our Connie Hamed Luiz Alvarez Gamay Edward Frenkel drawer Barnett on slow mo Sternberg David Koch Don Daniel Barr k kharon and less Weinstein Haynes Miller Ralph Camry John Tate Sidney Coleman Graham Siegel Robert Herman and here mr. Milani errors and omissions because I've too many people to thank our are all my own as for the claims that should reflect badly on no one else other than myself and most especially I just want to say that I've asked a tremendous amount from my family to stick with me on this quixotic quest and I want to thank Pia Milani nyla Weinstein and Zev Weinstein I love you all very much and thank you for making this possible I do want to leave you with one thought I really think that we've gotten completely bent out of shape about trying to court formalize and routinize science and it doesn't work you cannot mandate science as social engineering you can't decide that science is always in the zeitgeist and done by committee in fact it is essential to understand that science will not conform to what you want one of the things that I I'm very proud of I think it's quite true is the saying that great science has the scientific method as its radio edit I don't think that great science is actually done the way we say it's done and I think that directs 1963 Scientific American article should be read by absolutely absolutely everyone every time major theories have come out they've almost always been wrong but they're not wrong in an important way and I think that we have to fix the political economy of people racing to correct theories or point out that there is no agreement with the experiment we are killing many of our best ideas by creating a terrible and combative environment which already attempts to apportion credit for work and more importantly risk undertaken by individuals and I just think that I want people to understand that I've always wanted to share this but I I I detest the culture that I saw that cropped up around what has now become known as the cyber Whidden equations when they were put forward there was a period of time where I watched people as if it a feeding trough trying to stay up around the clock to use a new machine tool that had been given to them to claim credit and it profoundly pushed me away from the community we have to become more ethical and we have to honor the people who are trying to speak and act imaginatively now if this doesn't work if it's silly I'll have egg on my face and I'll go on I'll be fine but I'm very worried that maybe that some of the best ideas are between the ears of people without the confidence in the hutzpah and just the sort of almost psychotic drive to push things across the finishing line we've got to be kinder and nicer and more decent and stop stealing people's lives their credit their future and their ability to have families and make a living and that's absolutely essential to me and I look forward to finding out whether this theory has merit to it or is without merit but I guarantee that if I'm going to go down with the ship I'm also not going to be knocked off the ship as I was many years ago completely unfairly and I won't dwell on it but the amount of power you professors have is absolutely almost without parallel because nobody really understands enough to adjudicate disputes that happen in academics I'm going to insist that we fund you better and that you are nicer to the people who depend upon you in this beautiful chain that we call science scientific method and most particularly American science which i think is still the envy of the world so you've been through the portal I know it was a long slog I hope you found it interesting and enjoyable and we'll see you again soon be well everybody stay safe

Channel: Eric Weinstein

Views: 725,368

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Id: Z7rd04KzLcg

Length: 168min 22sec (10102 seconds)

Published: Thu Apr 02 2020