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

<P> [[File:Slide1.jpg]]

<p>[02:16:00] If you ask for antecedents, however, there is one that, at least within physics, is relatively famous, and that is by John Archibald Wheeler. And it is a picture in some sense of the universe contemplating itself. And so this idea that somehow the universe would contemplate itself into existence, um, maybe the letter U is in some sense analogous to the paper and somehow the eye, uh, rather than the hand is drawn across to look at a different part of the, of the U. And whether or not that has meaning is intrinsically always a question. People are animated by it, but I don't know that people have actually worked on it. The quote of Einstein's, I think that really speaks to me often the most, and maybe even was my thesis problem was he asked whether the creator had any choice in how the universe was constructed. And so I think if you believe that the canvas is itself, um, the...

<p>[02:17:03] That which generates, um, all of the content and all of the action, you're, you're left with a puzzle as to how would you move forward from this? It might be easier in a mathematical sense, uh, to temporarily put the U on its back, to put it more in line with a standard picture that many mathematicians and physicists will be familiar with.

<p>[02:17:28] In sector one of the Geometric Unity theory spacetime is replaced and recovered by the observerse contemplating itself. And so there are several sectors of GU and I wanted to go through at least four of them. In Einstein spacetime, we have not only four degrees of freedom, but also a spacetime metric representing rulers and protractors.

<p>[02:17:56] If we're going to replace that. It's very tricky because it's almost impossible to think about what would be underneath Einstein’s theory. Now, there's a huge problem in the spinorial sector, which I don't why more people don't worry about. Which is that spinors aren't defined for representations of the double cover of GL four R the general linear group’s effective spin analog. And as such, if we imagine that we will one day quantize gravity, we will lose our definition, not of the electrons, but let's say of the medium in which the electrons operate. That is, there will be no spinorial bundle until we have an observation of a metric. So one thing we can do is to take a manifold $$X^d$$ as the starting point and see if we can create an entire universe from no other data. Not even with a metric. So since we don't choose a metric, what we instead do is to work over the space of all possible point-wise metrics. So not quite in the Feynman sense, but in the sense that, um, we will work over a bundle that is of a quite larger, quite a bit larger dimension.

<p>[02:19:10] So for example, if X, uh, was a four dimensional, therefore d equals four, then Y in this case would be d squared, which would be 16 plus three d, which would be 12 making 28 divided by two, which would be 14. So in other words, a four dimensional universe, or sorry, a four dimensional proto-spacetime, not a spacetime, but a proto-spacetime with no metric would give rise to a 14 dimensional observerse portion called Y. Now, I believe that in the lecture in, um, Oxford, I called that U, so I'm sorry for the confusion, but of course, this shifts around every time I take it out of the garage. And that's one of the problems with working on a theory in solitude for many years. So we have two separate spaces and we have fields on the two spaces.

<p>[02:20:02] Now what I'm going to do as I'm going to refer to fields on the $$X^d$$ space by Hebrew letters. So instead of $$G_{\mu \nu}$$ for a metric, I just wrote gimmel mem nun. And the idea being that I want to separate Latin and Greek fields on the Y space from the, uh, rather rarer field that actually live directly on X.

<p>[02:20:27] So this is a little bit confusing. One way of thinking about it is to think of the observerse as the stands plus the pitch in a stadium. I think I may have said that in the, in the lecture, but this is what replaces the questions of where and when in the newspapers story that is a fundamental theory. Where and when correspond to space and time.

<p>[02:20:49] Who and what correspond to bosons and fermions. And how and why correspond to equations and the Lagrangian that generates them. So if you think about those six quantities, you'll realize that that's really what the content of a fundamental theory is, assuming that it can be quantized properly. Most fields and in this case, we're going to call the collection of two tuples omega. So the inside of omega that will be in the first tuple will have epsilon and pi written sort of an nontraditional variation of how we write this symbol for Pi. In the second Tuple, we'll have the letters, uh, nu and zeta. And I would like them not to move because they honor particular people who are important.