A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

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A Portal Special Presentation- Geometric Unity: A First Look

 

 

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* https://www.youtube.com/watch?v=wf0_nMaQ6tA#t=2h16m27s

[https://theportal.wiki/images/b/b9/Geometric-Unity-A-First-Look_-_YouTube.vtt Raw transcript file]

===== Geometric Unity: A First Look =====

<p><span style="color:#de2898;">'''Eric Weinstein: '''</span>[00:00:00] 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 COVID pandemic.

<p>[00:00:25] 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.

<p>[00:00:47] 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 COVID pandemic, I find that we were, in general, intimidated from sharing our fears about the virus.

<p>[00:01:12] We were told that if we wore masks, that we were acting in a peculiar fashion. If we refuse 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.

<p>[00:01:36] In fact, perhaps the most dangerous idea was that this outbreak might've 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 me entire world economy to effectively shut down?

<p>[00:01:55] 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.

<p>[00:02:17] So what I thought would be important for an 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?"

<p>[00:02:40] 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 protective equipment stocked for doctors and nurses and hospitals to say nothing of all of the people who are in the front lines of treating patients sick with COVID. 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.

<p>[00:03:33] This was a problem that we always knew it 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.

<p>[00:03:56] 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 1945 to 1971-73, something like that, we built in expectations to our system that cannot currently be met.

<p>[00:04:16] We will not have technology that follows the same breakneck pace of innovation. As a result, we have a system whereby the heads 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.

<p>[00:04:37] 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, um, 19, I started. It's hard to talk about it.  

<p>[00:05:12] 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.

<p>[00:05:37] 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. Um, 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.

<p>[00:06:12] 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.

<p>[00:06:34] And because a theory of everything would have to have different characteristics than I 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 an effective theory and a fundamental one. Now, if you're familiar with the [[M. C. Escher]] drawing called "[[Drawing Hands]]", it is a lithograph of two hands apparently drawing each other into existence.

<p>[00:07:02] 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 bedevils us when we search for a unified theory that doesn't be devil us, in my opinion, in any previous effective theory.

<p>[00:07:25] Now, why is that? Well, many people confuse a Theory of Everything as if they imagine that it's a theory in which you can compute every eventuality. 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.

<p>[00:07:46] 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?

<p>[00:08:05] 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, 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 [theory].

<p>[00:08:35] And that is, how does one get everything from almost nothing? In the M.C. Escher drawing or lithograph "Hands Drawing Hands" or "Drawing 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?

<p>[00:09:07] That kind of a problem is one which is of a very different character than everything that has 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.  

<p>[00:09:26] Now consider this. We have never had, in modern times a 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's see, [[Frank Wilczek]], who was born in 1951, no one born after that time has, in fact, contributed to the [[Standard Model]] in a clear and profound way.

<p>[00:09:54] 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 and 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.

<p>[00:10:21] 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 has completely deranged the scientific tradition.

<p>[00:10:43] And so one of the things that's going to happen in this lecture 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 presentation is going to be foreign.

<p>[00:10:58] Quite the contrary. I have every intention of writing up some results, in standard terminology, wherever possible, using a popular mathematical type-setting programs. But it goes far deeper than that. My belief is that what we've created is a career structure, a journal structure, and employment structure, and access structure that cannot possibly complete the job.

<p>[00:11:23] 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.

<p>[00:11:49] 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 or more particularly, a geometric context.

<p>[00:12:14] And those supposedly physicists spent their time submitting papers to what's called the high energy section of the so-called preprint [[arXiv]]. But in fact, most of these papers have nothing to do with high energy physics (HEP) whatsoever. And if you're looking for the designation, it's hep-th, high energy physics dash theory.

<p>[00:12:36] 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 and spacetime. 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 [[Green]] and [[Schwarz]], what you'll find is that physics became very active and simultaneously ground to a halt. 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 pin. Now, in this circumstance, I think it's very important to realize that this is not a paper, and we are not submitting to the arXiv.

<p>[00:13:21] In fact, the arXiv 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 with. Furthermore, we are expected to cite papers sometimes which are behind paywalls.

<p>[00:13:41] 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 could 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.

<p>[00:14:06] Now, what does that mean? In two previous episodes, we've had interactions with academicians, which I think are interesting and bear scrutiny. In the first case in a, in an interview with the economist, [[Tyler Cowen]], I talked to Tyler about the fact that the [[Boskin Commission]] was in fact committing economic malpractice.

<p>[00:14:26] Now. Why was that? It was because they had decided that they needed to transfer a trillion dollars over 10 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% 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 transfer 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 have cooled.

<p>[00:15:18] One simply can't do that in science. But Tyler's response, I found it was very interesting. His perspective was that this was, in fact, not a terrible thing because it was "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.

<p>[00:15:41] 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 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 [[Agnes Callard]] of the University of Chicago.

<p>[00:16:05] Now, when she listened to [[episode 19]] about [[Bret Weinstein]], she found that it was a very compelling episode, but strangely, even though the point of the episode was to surface Bret's long forgotten theory, because Bret had not been acknowledged as having predicted that laboratory mice would in particular have radically elongated [[telomere]]s where it was thought that all mice had long, radically elongated telomeres which has incredible potential implications for drug testing and all of the work that is done on laboratory, rodents as model organisms.

<p>[00:16:43] 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 Bret's name was erased from the history of the development.

<p>[00:17:02] 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 had been made. Now, I disagreed with Agnes on that program vociferously. 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 [enough] resources for everyone.

<p>[00:17:56] 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 family's lives under incredible pressures. And what I wished to do is to, in fact, point to the very people who I have been most angry at for years, and say that 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.

<p>[00:18:26] 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.  

<p>[00:18:49] 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.

<p>[00:19:29] 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 gonna make any bones about it. I've been very vocal about having learning differences, [[dysgraphia]], [[dyslexia]], all sorts of different issues.

<p>[00:20:29] 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.

<p>[00:21:50] The [[Schwarzschild singularities]], which give us black holes, and the initial singularities of the [[Friedmann Robertson Walker]] universe, which are associated with the Big Bang, are some clue that there is some subtle flaw in Einstein'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.

<p>[00:22:37] 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. And there's no one who can uh 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.

<p>[00:23:24] 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 [is] 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 parity or the chirality.

<p>[00:24:32] That means effectively that we are in something like a stadium. There are stands and there is a pitch/playing field that we think we see; [the pitch/playing field] 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 observerse.

<p>[00:25:29] There's not a way, there's not a way in hell, that I'm letting that happen. My experience with this community 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.

<p>[00:26:06] 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 equation, so what?

<p>[00:26:26] I mean the real theory actually takes place in Einstein and Grossmann, 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.

<p>[00:26:45] 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.

<p>[00:27:11] Hopefully I know that. Well, Newton did his greatest work when he was 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 earnestly to share hope and some path forward would be uplifting. Now, under the worst circumstances, if this doesn't work?  

<p>[00:28:06] 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.

<p>[00:29:01] The other thing that I think is incredibly important is that we've never seen how a univers 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.

<p>[00:29:20] 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.

<p>[00:29:50] 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.  

<p>[00:30:00] I don't know, but I do know that sooner or later in the era of intercontinental land exploration, someone found the last landmass, and that must've been a very strange moment when there was nothing left to do.

<p>[00:30:20] 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 John Brockman, which is: "Does something unprecedented happened when man, at last, learns his own source code?".

<p>[00:30:43] I don't know the answer to 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.

<p>[00:31:31] I've talked to many theoretical physicists who have 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.

<p>[00:31:49] 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 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.

<p>[00:32:15] And some of the most important of those people, one of whom occurs on this video is [[Marcus du Sautoy]]. And Marcus, I just wanted to say thank you for your bravery, 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.

<p>[00:32:34] I also want to thank [[Isadore Singer]] for effectively saving me from not getting a PhD. By, 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.  

<p>[00:32:56] I'd like to think Raoul Bott, 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 401(k), to buy a house. And, to begin coming back to regular society after a very difficult and strained career.  

<p>[00:33:46] 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 Bret Weinstein and his family, Heather and the kids, for sticking by me. And I'd like to thank my inlaws in Bombay, India, and 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 weekends, a lot of lost vacations.

<p>[00:34:42] But 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.

<p>[00:35:09] Be well.

=== Oxford Lecture ===

==== Introduction by Marcus du Sautoy ====

<p>[00:35:23] <span style="color:#fa8a3b;">'''Marcus du Sautoy: '''</span> Well, welcome to this special [[Simonyi lecture]] and my name is Marcus du Sautoy. I'm a professor of mathematics here [at Oxford University] and the Simonyi Professor for the Public Understanding of Science. And [[Charles Simonyi]] prepared a manifesto when he endowed this chair to guide the holder of the professorship in their mission.

<p>[00:35:40] And, I'd like to read one part of that manifesto to you. It said:

<blockquote> Scientific speculation, when so labelled, 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. [https://www.simonyi.ox.ac.uk/about-marcus/the-oxford-simonyi-professor-for-the-public-understanding-of-science/] </blockquote>

And it is in the spirit of this part of my mission as the Simonyi professor that I would like to introduce today's Simonyi Special Lecture.  

I first met Eric Weinstein when we were both post-docs 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 at a bar in New York.

<p>[00:36:24] And we began, he began to explain the mathematics teaching 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 it's 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 a more independent route working in economics, government, and finance.

<p>[00:37:05] 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 that 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 to some of the big questions on the scientific books.

<p>[00:37:30] I'm 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 70 minutes after which we will have a period to ask questions. Eric.

==== Beginning of the lecture ====

===== Introductory Remarks =====

<span style="color:#de2898;">'''Eric Weinstein: '''</span>[00:37:51] So 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 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.

<p>[00:38:16] And the names that are associated with Oxford that weigh heavy on me are [[Michael Atiyah|[Michael] Atiyah]], [[Sir Roger Penrose|[Roger] Penrose]], [Graeme] [[Segal]], [[Nick Woodhouse|[Nick] Woodhouse]], [[Nigel Hitchin|[Nigel] 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.

<p>[00:38:38] Of course, unified field theory in some sense, acquired a stigma with Einstein's 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 quest to quantize general relativity and gravity.

<p>[00:39:06] And, I'd like to go back to the sort of earlier perspective that there is 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 than Einstein spent as one man searching for years for unified field theory.

<p>[00:39:33] 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 ideas before you today.

<p>[00:40:10] 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 ten 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.

<p>[00:41:05] So with that, this is a beginning, I'm just going to 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 talk about ideas and some of these ideas are bold.

<p>[00:41:25] 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."

<p>[00:41:41] So in that spirit, let us begin.

===== Physics in the 21st Century =====

<p>[00:42:13] 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-Riemannian]] [[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 head room. The equation most associated with this is the [[Einstein field equation]].

<p>[00:43:18] So, it says that a piece of the [[Riemann curvature tensor]] or the Ricci tensor minus an even smaller piece, the scalar curvature multiplied by the metric is equal plus the cosmological constant is equal to some amount of matter and energy, the stress energy tensor. So it's intrinsically a curvature equation.

<p>[00:43:55] 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 and these symmetries for a non-Abelian group, which is currently SU(3) "color" x SU(2) "weak" x U(1) "weak hypercharge", which breaks down to SU(3)xU(1), where the broken U(1) is the electromagnetic symmetry.

<p>[00:45:44] The third point surrounds the matter in the system.

<p>[00:46:12] One of the great insights is that the reason for the lightness of matter in the natural mass scale of physics has to do with the fact that this $$\psi$$ really should have two components and the differential operators should map to one component on the other side of the equation, but the mass operators should map to another.

<p>[00:46:33] 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 overshooting a putt, it's easier to knock it back by putting in a [[Higgs field]] in order to generate an "as-if" fundamental mass through the [[Yukawa couplings]].

<p>[00:47:35] 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 [be] treated in quantum mechanical fashion or quantum field theoretic [fashion]. So it's a bit of an after-market modification, rather than his opinion at the time, [or] one of the core insights.

<p>[00:48:07] I actually think that that's in some sense about right. No. One of my differences with the [modern-day physics] community in some sense is I question whether the quantum isn't in good enough shape. We don't know whether we have a serious quantum mechanical problem or not. We know that we have a quantum mechanical problem, a quantum field theoretic problem, [but only] relative to the current formulations of these theories.

<p>[00:48:31] 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 effective theories that we're dealing with now may not survive the quantization.

===== Connecting the Three Observations of Witten =====

<p>[00:49:14] So I'm going to put general relativity and Einstein's formulation. And, I'm going to put, the probably won't write this again. Yang-Mills, Maxwell, [Philip Warren] Anderson, Higgs theory, over here, and I'm going to write the Dirac theory.

<p>[00:49:39] What I want to explore is the incompatibilities, not at the quantum level. But the geometric input. All three of these are geometric theories. And the question is, what are the compatibilities or 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.

<p>[00:50:23] That should be an "LC" for Levi-Civita. So, the Einstein projection ($$P_{E}$$) of the curvature tensor of the Levi-Civita connection ($$F_{\nabla^{LC}}$$) 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.

<p>[00:51:15] 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.

<p>[00:51:34] In addition 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 that.

<p>[00:52:03] 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 ad-valued two-form, the two-form portion of this and the adjoint portion of this are both associated to the structure group of the tangent bundle.

<p>[00:52:52] 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?

<p>[00:53:20] I was very struck that if we're going to try to quantize gravity and we associate gravity with the spin-2 field $$G_{\mu \nu}$$, we actually have a pretty serious problem, which is, if you think about spinors, electrons, quarks as being waves in a medium. And you think about photons as being waves in a different medium. [The] photon’s medium does not depend on the existence of a metric. One-forms are defined whether or not a metric is present, it's spinors or not.

<p>[00:54:02] So if we're going to take the spin-2 $$G_{\mu \nu}$$ field to be quantum mechanical, if it blinks out and does whatever the quantum does between observations. In the case of the photon, it is 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?"

<p>[00:55:33] Yes. So we tend 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?"

<p>[00:55:59] The proposal that I want to put to you today is that one of the reasons that we may be having trouble with unification this is that the duty, our duty, may be to generalize all three vertices before we can make progress.

<p>[00:56:23] 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 and Euclidean signature generating all of the Atiyah-Singer theory.

<p>[00:56:47] 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 consideration. 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-squared of the curvature and saying whatever the field strength is, let's measure that size. So if each one of these is simplest 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 as 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.

<p>[00:57:54] For example, we know that Dirac famously took the square root of the [[Klein-Gordon equation]] to achieve the Dirac equation. You actually took two square roots, one of the differential operator, and another of the algebra on which it acts. But could we not do the same thing by re-interpreting what we saw in Donaldson theory and Chern-Simons theory and finding that there are first-order equations that imply second-order equations that are nonlinear in the curvature?

<p>[00:58:50] This would be a program for some kind of unification of Dirac's type, but in the force sector. The question is, "does this really make any sense? Are there any possibilities to do any such thing?"

===== Introduction to Geometric Unity (GU) =====

<p>[00:59:34] So we have a division into intrinsic theories and auxiliary theory. Between physics and mathematics. More specifically, geometry. And 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.  

And so we're going to 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-Riemannian geometry is dominated by these projection operators as well as the ability to use the Levi-Civita connection.

<p>[01:01:34] 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 fit? How can we try to have our cake eat it. And use all the full suite of techniques that are available to us?

===== A research program for a Unified Theory =====

<p>[01:02:35] So I'd like to describe that research program and try to unpack what I think he was saying.

<p>[01:02:47] We talked a lot about unification, but we hardly ever actually imagine if we had a unified theory, what would it look like?

<p>[01:02:57] 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's something that has as little structure as possible, but it 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.

<p>[01:03:17] 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 spacetime. 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.

<p>[01:03:36] It's just some sort of flabby proto-spacetime, and in the end it has got to fill up with stuff and give us some kind of an equation. So let me write an equation.

<p>[01:04:13] So I have in mind differential operators parameterized by some fields, $$\omega$$, which when composed are not of second-order, if these are first-order operators, but as zeroth-order in some sort of further differential operator saying that whatever those two operators are in composition is, in some sense, harmonic.

<p>[01:05:11] So, if here this physical reality.

<p>[01:05:56] 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.

===== Four flavors of GU with a focus on the endogenous version =====

<p>[01:06:19] So with that, let us begin to think about what we mean today by Geometric Unity. GU 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.  

<p>[01:06:42] There's a completely exogenous flavor.  

<p>[01:07:15] The idea of an observerse 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. Exogenous model simply means that $$U$$ is unrestricted, although larger than $$X^4$$, so any manifold of four dimensions or higher that is capable of admitting $$X^4$$ as an immersion.

<p>[01:07:58] The most exciting, which is the one we'll deal with today, is the endogenous model where $$X^4$$ actually grows the space $$U$$, where the activity takes place. So, we talked about extra dimensions, but these are, in some sense, not extra dimensions. They are implicit dimensions within $$X^4$$.  

Okay? Now we need rules. The rules  a choice of fundamental metric. So we imagine that Einstein was presented with a fork in the road, and it's always disturbing not to follow Einstein's path, but we're in fact going to turn Einstein's game on its head and see if we can get anywhere with that. Right. 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 unthink it because everything is built on top of it. So let's make no choice of fundamental metric.

<p>[01:09:36] 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.

<p>[01:10:23] Let's get started. We take $$X^4$$, we need metrics. We have none. We're not allowed to choose one. So we do the standard trick. We choose them all.

<p>[01:10:36] So we allow $$U^{14}$$ to equal the space of metrics on $$X^4$$ pointwise. Therefore, if we propagate on top of this, let me call this the projection operator. If we propagate on $$U^{14}$$ we are, in some sense, following a Feynman-like idea of propagating over the space of all metrics, but not at a field level, at a pointwise tensorial level.

<p>[01:11:22] It turns out 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 $$g^{10}_{\mu\nu}$$.

<p>[01:12:17] We now define the chimeric bundle, right? And the chimeric bundle is this direct 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 $$T^{10}_V(U) \oplus T^{4}_H(U)$$. And the great thing about the chimeric bundle is that it has an a priori metric. It's got a metric on the four, a metric on the 10, and we can always decide that the two of them are naturally perpendicular to each other.

<p>[01:13:00] Furthermore, it is almost canonically isomorphic to the tangent bundle or the cotangent bundle, because we either have 4 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 $$C$$. We have $$C$$ equal to the tangent bundle of $$U$$ up to a choice of a connection $$\theta$$.

<p>[01:13:32] 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 Levi-Civita game. And the only problem is that we've had to buy ourselves into a different space than the one we thought we wanted to work on.

<p>[01:13:55] 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 variant, 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.

<p>[01:15:39] Well, let me just sum this up by saying: between fundamental and emergent, standard model and GR (general relativity). Let's do GR (general relativity). Fundamental is the metric; emergent is the connection. Here in GU (Geometric Unity), it is the connection that's fundamental and the metric that's emergent.

===== Part II: Unified Field Content =====

<p>[01:16:36] Okay. The next unit of GU 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 $$U$$, which now has a metric depending on $$\theta$$.

<p>[01:17:48] 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 going to have a catalyst to show that we actually got the better part of the deal.

<p>[01:18:16] In GR and Riemannian geometry, as we've said, we have the projection operators and we also have the Levi-Civita connection.

<p>[01:18:31] 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.

<p>[01:18:50] We're 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.

<p>[01:19:09] And we're going to lose the ability to use the gauge group because we're going to trade it all.

<p>[01:19:40] 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.

<p>[01:20:35] You pick out one point, which then becomes the origin. That means that any connection $$A$$ has a torsion tensor, $$T_A$$, which is equal to the connection, $$A$$ minus the Levi-Civita connection ($$\nabla^{LC}$$). So we get a tensor that we don't usually have. Gauge potentials are not usually well-defined. They're are only defined up to a choice of gauge.

<p>[01:21:00] So that's one of the things we get for our Levi-Civita 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.

<p>[01:21:21] 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 other. So now the question is, how are we going to prove that we're actually making a good trade?

<p>[01:22:00] A 14-dimensional manifold has Dirac spinors of dimension-two to the dimension of the space divided by two. Right?

<p>[01:22:36] At least in Euclidean signature. We can get to mixed signatures later. From that, we can form the associated bundle, $$\Gamma^{\infty}((P_{U(8)}) \times_{ad}\U($))$$.

<p>[01:23:25] There's no reason that we can't choose this as field content. Again, we're being led by the nose like a bull. 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 going to lose control over it.

====== Ship in a Bottle (Shiab) Operator ======

<p>[01:24:06] So when I was thinking about this, I used to be amazed by ships in bottles. I must confess that I never figured out what the trick was for ships in bottles, but once I saw it, I remembered thinking, 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 the Ricci curvature.