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 14:50, 10 April 2020
, 10 April 2020→Connecting the Three Observations of Witten
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<p>[00:50:23] That should be an "LC" for Levi-Civita. So, the Einstein projection of the curvature tensor of the Levi-Civita connection of the metric on this side, and on this side, I'm going to write down this differential operator: the adjoint of the exterior derivative coupled to a connection. | <p>[00:50:23] That should be an "LC" for Levi-Civita. So, the Einstein projection of the curvature tensor of the Levi-Civita connection of the metric on this side, and on this side, I'm going to write down this differential operator: the adjoint of the exterior derivative coupled to a connection. | ||
<p>[00:50:47] And you begin to see that we're missing an opportunity, potentially. What if the $F_A$s were the same in both contexts? Then you're applying two separate operators: 1) zeroth-order and destructive, in the sense that it doesn't see the entire curvature tensor; the other) inclusive, but of first-order. And so the question is, is there any opportunity to do anything that combines these two? | <p>[00:50:47] And you begin to see that we're missing an opportunity, potentially. What if the $$F_A$$s were the same in both contexts? Then you're applying two separate operators: 1) zeroth-order and destructive, in the sense that it doesn't see the entire curvature tensor; the other) inclusive, but of first-order. And so the question is, is there any opportunity to do anything that combines these two? | ||
<p>[00:51:15] But the problem is, is that the hallmark of the Yang-Mills theory is the freedom to choose the data, the internal quantum numbers that give all the particles their personalities beyond the mass and the spin. | <p>[00:51:15] But the problem is, is that the hallmark of the Yang-Mills theory is the freedom to choose the data, the internal quantum numbers that give all the particles their personalities beyond the mass and the spin. | ||
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<p>[00:53:20] I was very struck that if we're going to try to quantize gravity and we associate gravity with the spin 2 field $$G_{\mu \nu}$$, we actually have a pretty serious problem, which is, if you think about spinors, electrons, quarks as being waves in a medium. And you think about photons as being waves in a different medium. Photon’s medium does not depend on the existence of a metric. One forms are defined whether or not a metric is present, it's spinors or not. | <p>[00:53:20] I was very struck that if we're going to try to quantize gravity and we associate gravity with the spin 2 field $$G_{\mu \nu}$$, we actually have a pretty serious problem, which is, if you think about spinors, electrons, quarks as being waves in a medium. And you think about photons as being waves in a different medium. Photon’s medium does not depend on the existence of a metric. One forms are defined whether or not a metric is present, it's spinors or not. | ||
<p>[00:54:02] So if we're going to take the spin two $$G_{mu nu}$$ field to be quantum mechanical, if it blinks out and does whatever the quantum does between observations. In the case of the photon, it's saying that the waves may blink out, but the ocean need not blink out. In the case of the Dirac theory, it is the ocean, the medium in which the waves live that becomes uncertain itself. So even if you're comfortable with the quantum, to me, this becomes a bridge too far. So the question is: How do we liberate the definition? | <p>[00:54:02] So if we're going to take the spin two $$G_{\mu \nu}$$ field to be quantum mechanical, if it blinks out and does whatever the quantum does between observations. In the case of the photon, it's saying that the waves may blink out, but the ocean need not blink out. In the case of the Dirac theory, it is the ocean, the medium in which the waves live that becomes uncertain itself. So even if you're comfortable with the quantum, to me, this becomes a bridge too far. So the question is: How do we liberate the definition? | ||
<p>[00:54:47] How do we get the metric out from its responsibilities? It's been assigned far too many responsibilities. It's responsible for a volume form. For differential operators. It's responsible for measurement. It's responsible for being a dynamical field, part of the field content of the system. Lastly, we have the compatibilities and incompatibility between Yang-Mills and in the Dirac theory, these may be the most mild of the various incompatibilities, but it is an incompatibility of naturality where the Dirac field, Einstein's field, and the connection fields are all geometrically well motivated, we push a lot of the artificiality that we do not understand into the potential for the scalar field that gives everything its mass. | <p>[00:54:47] How do we get the metric out from its responsibilities? It's been assigned far too many responsibilities. It's responsible for a volume form. For differential operators. It's responsible for measurement. It's responsible for being a dynamical field, part of the field content of the system. Lastly, we have the compatibilities and incompatibility between Yang-Mills and in the Dirac theory, these may be the most mild of the various incompatibilities, but it is an incompatibility of naturality where the Dirac field, Einstein's field, and the connection fields are all geometrically well motivated, we push a lot of the artificiality that we do not understand into the potential for the scalar field that gives everything its mass. | ||