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 15:13, 10 April 2020
, 10 April 2020→Four flavors of GU with a focus on the endogenous version
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<p>[01:07:15] The idea of an observerse is a bit like a stadium. You have a playing field and you have stands. They aren't distinct entities, they're coupled. And so, fundamentally, we're going to replace one space with two. Exogenous model simply means that U is unrestricted, although larger than $$X^4$$, so any manifold of four dimensions or higher that is capable of admitting $$X^4$$ as an immersion. | <p>[01:07:15] The idea of an observerse is a bit like a stadium. You have a playing field and you have stands. They aren't distinct entities, they're coupled. And so, fundamentally, we're going to replace one space with two. Exogenous model simply means that U is unrestricted, although larger than $$X^4$$, so any manifold of four dimensions or higher that is capable of admitting $$X^4$$ as an immersion. | ||
<p>[01:07:41] The next model we have is the bundle-theoretic, in which case, U sits over X, as a fiber bundle. | <p>[01:07:41] The next model we have is the bundle-theoretic, in which case, $$U$$ sits over $$X$$, as a fiber bundle. | ||
<p>[01:07:58] The most exciting, which is the one we'll deal with today, is the endogenous model where $$X^4$$ actually grows the space U, where the activity takes place. So, we talked about extra dimensions, but these are, in some sense, not extra dimensions. They are implicit dimensions within $$X^4$$. | <p>[01:07:58] The most exciting, which is the one we'll deal with today, is the endogenous model where $$X^4$$ actually grows the space U, where the activity takes place. So, we talked about extra dimensions, but these are, in some sense, not extra dimensions. They are implicit dimensions within $$X^4$$. | ||
And last, to proceed without loss of generality, we have the tautological model. In that case, $$X^4$$ equals U. And the immersion is the identity. And without loss of generality, we simply play our games on one space. | And last, to proceed without loss of generality, we have the tautological model. In that case, $$X^4$$ equals $$U$$. And the immersion is the identity. And without loss of generality, we simply play our games on one space. | ||
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. | ||