A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions
A Portal Special Presentation- Geometric Unity: A First Look (edit)
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<p>[01:13:00] Furthermore, it is almost canonically isomorphic to the tangent bundle or the cotangent bundle, because we either have 4 out of 14, or 10 out of 14 dimensions, on the nose. So the question is, what are we missing? And the answer is that we're missing exactly the data of a connection. So this bundle, chimeric $$C$$. We have $$C$$ equal to the tangent bundle of $$U$$ up to a choice of a connection $$\theta$$. | <p>[01:13:00] Furthermore, it is almost canonically isomorphic to the tangent bundle or the cotangent bundle, because we either have 4 out of 14, or 10 out of 14 dimensions, on the nose. So the question is, what are we missing? And the answer is that we're missing exactly the data of a connection. So this bundle, chimeric $$C$$. We have $$C$$ equal to the tangent bundle of $$U$$ up to a choice of a connection $$\theta$$. | ||
<p>[01:13:32] And this is exactly what we wanted. We have a situation where we have some field on the manifold X in the form of a connection which is amenable, more friendly to quantization, which is now determining a metric turning around the Levi-Civita game. And the only problem is, is that we've had to buy ourselves into a different space than the one we thought we wanted to work on. | <p>[01:13:32] And this is exactly what we wanted. We have a situation where we have some field on the manifold $$X$$ in the form of a connection which is amenable, more friendly to quantization, which is now determining a metric turning around the Levi-Civita game. And the only problem is, is that we've had to buy ourselves into a different space than the one we thought we wanted to work on. | ||
<p>[01:13:55] But now as theta changes, the fermions are defined on the chimeric bundle, and it's the isomorphism from the chimeric bundle to the tangent bundle of the space U, which is variant, which means that the fermions no longer depend on the metric. They no longer depend on the theta connection. They are there if things go quantum mechanical, and we've achieved our objective of putting the matter fields and the spin one fields on something of the same footing. | <p>[01:13:55] But now as $$\theta$$ changes, the fermions are defined on the chimeric bundle, and it's the isomorphism from the chimeric bundle to the tangent bundle of the space $$U$$, which is variant, which means that the fermions no longer depend on the metric. They no longer depend on the $$\theta$$ connection. They are there if things go quantum mechanical, and we've achieved our objective of putting the matter fields and the spin-one fields on something of the same footing. | ||
<p>[01:14:27] But, and I want to emphasize this: One thing, most of us, we think a lot about final theories and and about unification, but until you actually start daring to try to do it, you don't realize what the process of it feels like. And I try to imagine conducting your life where you have no children | <p>[01:14:27] But, and I want to emphasize this: One thing, most of us, we think a lot about final theories and and about unification, but until you actually start daring to try to do it, you don't realize what the process of it feels like. And, I try to imagine conducting your life where you have no children and let's say no philanthropic urges. | ||
<p>[01:14:54] And what you want to do is you want to use all of your money for yourself. And die penniless, right? Like a perfect finish. Assuming that that's what you wanted to do, it would be pretty nerve wracking at the end, right? How many days left do I have? How many dollars left do I have? This is the process of unification. | <p>[01:14:54] And what you want to do is you want to use all of your money for yourself. And die penniless, right? Like a perfect finish. Assuming that that's what you wanted to do, it would be pretty nerve-wracking at the end, right? How many days left do I have? How many dollars left do I have? This is the process of unification. | ||
<p>[01:15:12] In physics, you start giving away all of your most valuable possessions, and you don't know whether you've given them away too early, whether you husband them too long. And so in this process, what we've just done is we've started to paint ourselves into a corner. And we got something we wanted, but we've given away freedom. | <p>[01:15:12] In physics, you start giving away all of your most valuable possessions, and you don't know whether you've given them away too early, whether you husband them too long. And so in this process, what we've just done is we've started to paint ourselves into a corner. And we got something we wanted, but we've given away freedom. | ||
<p>[01:15:30] We're now dealing with a 14 dimensional world. | <p>[01:15:30] We're now dealing with a 14-dimensional world. | ||
<p>[01:15:39] Well, let me just sum this up by saying: between fundamental and emergent, standard model and GR. Let's do GR. Fundamental is the metric | <p>[01:15:39] Well, let me just sum this up by saying: between fundamental and emergent, standard model and GR (general relativity). Let's do GR (general relativity). Fundamental is the metric; emergent is the connection. Here in GU (Geometric Unity), it is the connection that's fundamental and the metric that's emergent. | ||
<p>[01:16:23] And the next unit of GU. So this is sort of the first unit of G U. Are there any quick questions having to do with confusion or may I proceed to the next unit? | <p>[01:16:23] And the next unit of GU. So this is sort of the first unit of G U. Are there any quick questions having to do with confusion or may I proceed to the next unit? | ||
===== Part II: Unified Field Content ===== | |||
<p>[01:16:36] Okay. The next unit of GU is the unified field content. What does it mean for our fields to become unified? There are, in fact, only at this moment, two fields that know about X. Theta, which is the connection that we've just talked about, and a section sigma that takes us back so that we can communicate back and forth between U and X. We now need field content that only knows about U, which now has a metric depending on theta. | <p>[01:16:36] Okay. The next unit of GU is the unified field content. What does it mean for our fields to become unified? There are, in fact, only at this moment, two fields that know about X. Theta, which is the connection that we've just talked about, and a section sigma that takes us back so that we can communicate back and forth between U and X. We now need field content that only knows about U, which now has a metric depending on theta. | ||