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 03:48, 11 April 2020
, 11 April 2020→Four flavors of GU with a focus on the endogenous version
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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. | 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>[01:09:16] And in fact, let's go more ambitious. And let's say we're going to reverse the logic of | <p>[01:09:16] And in fact, let's go more ambitious. And let's say we're going to reverse the logic of Einstein. The metric is fundamental, but the Levi-Civita connection from which we deduced the curvature is emergent, right? So the fundamental theorem of Riemannian geometry is that every connection causes every metric causes a connection to emerge. | ||
<p>[01:09:36] And then the curvature is built on the connection. We turn this around | <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>[01:09:56] And lastly, we want to liberate matter from its dependence on the metric for its very existence. So we now need to build [[fermions]] onto our four-dimensional manifold in some way without ever choosing a metric, if we're even going to have any hope of playing a game involving matter, starting from this perspective of no information other than the most bare information. | <p>[01:09:56] And lastly, we want to liberate matter from its dependence on the metric for its very existence. So we now need to build [[fermions]] onto our four-dimensional manifold in some way without ever choosing a metric, if we're even going to have any hope of playing a game involving matter, starting from this perspective of no information other than the most bare information. | ||