A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
Revision as of 00:51, 12 April 2020
, 12 April 2020→Part IV
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<p>[02:09:44] 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 term. Now, if you look at what happens in our replacement for the Einstein field equation. The term that would counterbalance the scalar curvature. | <p>[02:09:44] 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 term. Now, if you look at what happens in our replacement for the Einstein field equation. The term that would counterbalance the scalar curvature. | ||
<p>[02:10:02] 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 in the swervature terms, but there'd be nothing to counterbalance it. So it's fundamentally the scalar curvature that would coax the on the augmented torsion out of the vacuum. | <p>[02:10:02] 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 in the swervature terms, but there'd be nothing to counterbalance it. So, it's fundamentally the scalar curvature that would coax the veb[?] on the augmented torsion out of the vacuum. | ||
<p>[02:10:22] Yeah. To have a non zero level. And if you pumped up that sphere and it's smeared out, the curvature, which you can't get rid of because of topological considerations, let's say from Chern–Weil theory. You would have a very diffuse, very small term. And that term would be the term that was playing the role of the cosmological constant. | <p>[02:10:22] Yeah. To have a non-zero level. And if you pumped up that sphere and it's smeared out, the curvature, which you can't get rid of because of topological considerations, let's say from Chern–Weil theory. You would have a very diffuse, very small term. And that term would be the term that was playing the role of the cosmological constant. | ||
<p>[02:10:44] So when 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. | <p>[02:10:44] So when 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. | ||
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<p>[02:11:07] So in other words, just to recap, starting with nothing other than a four-manifold, we built a bundle $$U$$. The bundle $$U$$ 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. | <p>[02:11:07] So in other words, just to recap, starting with nothing other than a four-manifold, we built a bundle $$U$$. The bundle $$U$$ 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. | ||
<p>[02:11:29] We built our spinors on that. We restricted ourselves to those spinors. We moved most of our attention to the emergent metric on $$U^{14}$$ which gave us a map between the chimeric bundle and the tangent bundle of | <p>[02:11:29] We built our spinors on that. We restricted ourselves to those spinors. We moved most of our attention to the emergent metric on $$U^{14}$$ which gave us a map between the chimeric bundle and the tangent bundle of $$U^{14}$$. We built a toolkit allowing us to choose symmetric field content, to define equations of motion on the cotangent space of that field content | ||
<p>[02:11:57] to form a homogeneous vector bundle with the | <p>[02:11:57] 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 $$U^{14}$$ 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. | ||
<p>[02:12:34] I can tell you where there are problems in this story. I can tell you that when we moved 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 on a four-dimensional world. | <p>[02:12:34] I can tell you where there are problems in this story. I can tell you that when we moved 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 on a four-dimensional world. | ||