# eric weinstein geometric unity portal

Given how bloated and self-referential modern physics have become without offering many testable predictions (string theory anyone?) 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. [02:28:10] Yeah. [01:49:32] And, then you realize that the information in the inhomogeneous gauge group, you actually have information not for one connection, but for two connections. In Einstein spacetime, we have not only four degrees of freedom, but also a spacetime metric representing rulers and protractors. A Portal Special Presentation- Geometric Unity: A First Look. Now, to my mind, it is absolutely unconscionable to say that you have a right to transfer wealth cryptically by adjusting a fundamental barometer. [01:33:22] Now in this section of GU unified field content is only one part of it, but what we really want is unified field content plus a toolkit. Who I should have invited to my wedding. [00:50:23] That should be an "LC" for Levi-Civita. In other words, we're going to get a form that is gauged invariant relative to the tilted gauge group. You are right that it is small in the specific Einstein-Cartan case …. We use $$H$$ here, not, $$G$$ because we want to reserve $$G$$ for the inhomogeneous extension of $$H$$, once we moved to function spaces. [01:10:36] So we allow $$U^{14}$$ to equal the space of metrics on $$X^4$$ pointwise. [01:05:11] So, if here this physical reality. [00:48:54] So what I want to do is I want to imagine a different sort of incompatibilities. [02:27:46] We then get a bi connection. Eric Weinstein is a mathematician working on a theory called, “Geometric Unity”. The portion of that is just the first-order equations and take the norm square of that. 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.

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. [00:25:48] Furthermore, there is an incredible premium on cherry-topping.

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. We can't easily say we have a unified theory. Ok, that helps me get the right feeling about spinors but what the hell are they?

Now, currently, I don't believe that you can trust the World Health Organization. but then there's this extra interesting term, which is the spinors on the first summand tensor producted with the spinors on the second summand. He did not. But if they cross terms went away, the two terms would become decoupled. That maybe things are possible or perhaps there's a conspiracy somewhere. That was a mistake, calling it a mistake. And this tensor on its own should be exact. [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.

[02:29:23] The infinitesimal action of the gauge transformation of a gauge transformation, or at least an infinite testable 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 gets started. [00:55:33] Yes. Now the inhomogeneous 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. For example. [01:38:38] This is exactly what Einstein was doing. [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. [01:06:19] So with that, let us begin to think about what we mean today by Geometric Unity. We're fighting for our life to make sure that this trade has some hope. Do I know that this new theory, if it works, will allow us to escape? That, in general, does not work out to be exact, so you can't have it as the differential of a Lagrangian. Join us as we seek portals that will carry us through the impossible- and beyond. Into The Impossible livestream, with Stephen Wolfram & Eric Weinstein: The Nature of Mathematical Reality; 40: Introducing The Portal Essay Club – What if everyone is simply insane? [01:36:27] And I can start to define operators. [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. And that's what the fermions are going to be. [02:09:44] Then, we would still have a chiral world, but the chirality wouldn't be fundamental. But I, I'd like to go with the most ambitious version of GU first. Well, look it how close to this field content is to the picture from Deformation theory that we learned about in low dimensions.

In that Clifford algebra you can identify a certain multiplicative subgroup called spin group (or spin^c).

[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.

So the question is, if we have a Higgs field: "why is it here and why is it geometric?". Again, geometric unity is more flexible than this, but I wanted to make the most concrete approach to this possible for at least this introduction. So if we pull back the cotangent bundle, we get a metric $$g^4_{\mu\nu}$$ on $$\Pi^*$$ of the cotangent bundle of $$X$$. This is gauge invariant. So we get a tensor that we don't usually have. (In fact, particles are actually defined as objects that transform under irreducible unitary representations of a larger group, the Poincare group). We're stuck on this one spinor. [02:14:15] 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. Lastly, we have the compatibilities and incompatibility between 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 Dirac field, Einstein's 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. [00:25:29] There's not a way, there's not a way in hell, that I'm letting that happen. I've talked before about the twin nuclei problem and our need to get off of this planet. Well, as promised, there is a tilted homomomorphism which takes the gauge group into its inhomogeneous extension. How does all of this look to $$X$$?

[00:58:50] This would be a program for some kind of unification of Dirac's type, but in the force sector. 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?". He tried to fake it and fool me. 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. [00:59:12] So what I'd like to do is I'd like to talk a little bit about what the Geometric Unity (GU) proposal is. The map is injective because it's injective under the first factor, but it actually gives us a nontrivial embedding of the gauge group in its inhomogeneous extension, which makes the whole theory work. [00:55:52] It has long been the most artificial sector of our models. 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. 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. This is just a (time thirsty) hobby.”. [00:24:32] That means effectively that we are in something like a stadium. And we've inadequately prepared them. 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.

A podcast hosted by Eric Weinstein, The Portal is a journey of discovery. 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 have a space of connections, typically denoted by A, and we're going to promote a $$\Omega_1$$, a tensor in the adjoint bundle to a notation of. If somebody is only aware of one side of their body and they say, "Oh my God, I'm deformed, I'm asymmetric!" This is the process of unification. We're now dealing with a 14-dimensional world. So for those of you who... [01:24:06] So when I was thinking about this, I used to be amazed by ships in bottles. It's been assigned far too many responsibilities. We imagine the general relativity is replaced by a true first-order theory. That gives me a new Lagrangian, and if I solve that new Lagrangian, it leads to equations of motion. 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.

Well, if we were to take the Einstein field equation generalization and take the norm square of it.

[01:34:28] Which is just looking like the exterior algebra, $$\wedge^{*}(C)$$ on the chimeric bundle; that means that it is graded by degrees. In a bit more detail, for any (reasonable) vector space such as R^n endowed with a norm you can construct a so called Clifford algebra. Geometric Unity is the search for some way to break down the walls between these four boxes. 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 imagine that $$X$$ and $$Y$$ are the tangent space to $$X$$ and a normal bundle. The equation would look something like this. It may be null, but it probably isn’t, and no one discusses it in standard textbooks because, except in the vicinity of Planck energy, it’s so minuscule that it’s not experimentally verifiable.

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