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

So, with that as 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, 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.

So, with that as 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, 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.

''[https://youtu.be/Z7rd04KzLcg?t=2507 00:41:47]''<br>

''[https://youtu.be/Z7rd04KzLcg?t=2507 00:41:47]''<br>

What is physics to physicists 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.

What is physics to physicists 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.

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 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? 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 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?"

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 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? 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 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?"

[[File:GU Presentation Intrinsic-Auxiliary Diagram.png|thumb|right]]

[[File:GU Presentation Intrinsic-Auxiliary Diagram.png|thumb|right]]

So, if here is 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 \(X^4\). And we're going to set ourselves a strait-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, if here is 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 \(X^4\). And we're going to set ourselves a strait-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.

[[File:GU Presentation Flavors Diagram.png|thumb|right]]

[[File:GU Presentation Flavors Diagram.png|thumb|right]]