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

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<p>[02:14:15] First of all, I think the most important thing to begin with is to ask what new hard problems arise when you're trying to think about a fundamental theory that aren't found in any earlier theory. Now every time you have an effective theory, which is a partial theory, there is always the idea that you can have recourse to a lower level strata.
<p>[02:14:15] First of all, I think the most important thing to begin with is to ask what new hard problems arise when you're trying to think about a fundamental theory that aren't found in any earlier theory. Now every time you have an effective theory, which is a partial theory, there is always the idea that you can have recourse to a lower level strata.
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<p>[02:15:32] And I find that there really aren't any candidate, um, theories of everything or unified field theories that I can find that plausibly give us an idea of how a canvas would will an entire universe into being. And so that really to me is the conceptual problem that I think bedevils this and makes, uh, the step quite a bit more difficult than some of the previous technical steps.
<p>[02:15:32] And I find that there really aren't any candidate, um, theories of everything or unified field theories that I can find that plausibly give us an idea of how a canvas would will an entire universe into being. And so that really to me is the conceptual problem that I think bedevils this and makes, uh, the step quite a bit more difficult than some of the previous technical steps.


<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 hands.
<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>[02:16:25] And, uh, 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 a, he.
<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.
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<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>[02:16:48] Just 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>[02:17:56] 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>[02:17:03] 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>[02:19:10] 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>[02:17:28] In sector one of the geometric, uh, 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 a, 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>[02:20:02] 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>[02:17:56] 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.
<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.
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<p>[02:18:18] 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.
<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.
 
<p>[02:18:39] Is to take a manifold $$X^d$$ as the starting point and see if we can create an entire universe from no other data and not even with the 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.
 
<p>[02:19:06] A quite larger, quite a bit larger dimension. 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 space-time, but a produce based on, with no metric would give rise to a 14 dimensional.
 
<p>[02:19:36] Um, 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 . 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 a hebrewwordsidon’tknow. 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 lived 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 Boseons and Fermi ions and how and why correspond to. Um, 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.
 
<p>[02:21:10] Uh, 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.


<p>[02:21:36] So most fields, in this case, Omega, um, are dancing on . Y, which was called U in the lecture, unfortunately, but they are observed via pullback as if they lived on X. In other words, if you're sitting in the stands, you might feel that you're actually literally on the pitch, even though that's not true. So what we've done is we've taken the U of Wheeler, we've put it on its back and created a W structure
<p>[02:21:36] So most fields, in this case, Omega, um, are dancing on . Y, which was called U in the lecture, unfortunately, but they are observed via pullback as if they lived on X. In other words, if you're sitting in the stands, you might feel that you're actually literally on the pitch, even though that's not true. So what we've done is we've taken the U of Wheeler, we've put it on its back and created a W structure
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