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

==== The Current Picture of Physics ====

''[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.

==== Motivations for Geometric Unity ====

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

==== The Observerse and Four Versions of GU ====

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

====== Constructing Endogenous GU: Choosing All Metrics ======

''[https://youtu.be/Z7rd04KzLcg?t=4224 01:10:24]''<br>

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.

====== Chimeric Bundle ======

''[https://youtu.be/Z7rd04KzLcg?t=4337 01:12:17]''<br>

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 the vertical tangent space of 10 dimensions to \(U\), direct sum the cotangent space, which we're going to call horizontal, to \(U\). And the great thing about the chimeric bundle is that it has an a priori metric. It's got a metric on the 4, a metric on the 10, and we can always decide that the two of them are naturally perpendicular to each other.

====== Observerse Conclusion ======

''[https://youtu.be/Z7rd04KzLcg?t=4467 01:14:27]''<br>

But, and I want to emphasize this: one thing most of us—we think a lot about final theories 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. And, try to imagine conducting your life where you have no children, let's say, and no philanthropic urges, and 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 do 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 husbanded 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 14-dimensional world.

Well, let me just sum this up by saying: between fundamental and emergent, standard model and GR... Let's do GR. Fundamental is the metric, emergent is the connection. Here in GU, it is the connection that's fundamental and the metric that's emergent.

[01:31:38] 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 $$\mathcal{G}$$ let's say to the $$\mathbb{R}$$. Invariant, not under the full group, but under the tilted gauge subgroup, $$\mathcal{H_{\tau}}$$.  

[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.

[01:33:43] So we've, we've restricted ourselves to one gauge group, this big unitary group on the spinors using whatever sort of inner product naturally exists on the spinors. And not spinors valued in an auxiliary structure, but intrinsic spinors.