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 23:37, 18 July 2020
, 18 July 2020→Physics in the 21st Century
| Line 243: | Line 243: | ||
<p>[00:43:12] And, of course, I'm running into the margin. Okay. | <p>[00:43:12] And, of course, I'm running into the margin. Okay. | ||
<p>[00:43:18] So, it says that a piece of the [[Riemann curvature tensor]] or the Ricci tensor minus an even smaller piece, the scalar curvature multiplied by the metric is equal plus the cosmological constant is equal to some amount of matter and energy, the stress energy tensor. So it's intrinsically a curvature equation. | <p>[00:43:18] So, it says that a piece of the [[Riemann curvature tensor]], or the Ricci tensor minus an even smaller piece, the scalar curvature multiplied by the metric is equal, plus the cosmological constant, is equal to some amount of matter and energy, the stress energy tensor. So it's intrinsically a curvature equation. | ||
<p>[00:43:47] The second fundamental insight... I'm going to begin to start drawing pictures here as well. | <p>[00:43:47] The second fundamental insight... I'm going to begin to start drawing pictures here as well. | ||
<p>[00:43:55] So, if this is the space-time manifold, "the arena"; the second one concerns symmetry groups which cannot necessarily be deduced from any structure inside of "the arena". They are additional data that come to us out of the blue without explanation and these symmetries | <p>[00:43:55] So, if this is the space-time manifold, "the arena"; the second one concerns symmetry groups which cannot necessarily be deduced from any structure inside of "the arena". They are additional data that come to us out of the blue without explanation and these symmetries from a non-Abelian group, which is currently SU(3) "color" x SU(2) "weak" x U(1) "weak hypercharge", which breaks down to SU(3)xU(1), where the broken U(1) is the electromagnetic symmetry. | ||
<p>[00:44:54] This equation is also a curvature equation | <p>[00:44:54] This equation is also a curvature equation. The corresponding equation, the curvature of an auxiliary structure known as a gauge potential when differentiated in a particular way is equal, again, to the amount of stuff in the system that is not directly involved in the left-hand side of the equation. So, it has many similarities to the above equation. Both involve curvature. One involves a projection or a series of projections. The other involves a differential operator. | ||
<p>[00:45:44] The third point surrounds the matter in the system. | <p>[00:45:44] The third point surrounds the matter in the system. | ||
| Line 257: | Line 257: | ||
<p>[00:46:12] One of the great insights is that the reason for the lightness of matter in the natural mass scale of physics has to do with the fact that this $$\psi$$ really should have two components and the differential operators should map to one component on the other side of the equation, but the mass operators should map to another. | <p>[00:46:12] One of the great insights is that the reason for the lightness of matter in the natural mass scale of physics has to do with the fact that this $$\psi$$ really should have two components and the differential operators should map to one component on the other side of the equation, but the mass operators should map to another. | ||
<p>[00:46:33] And so if one of the components is missing, if the equation is intrinsically lopsided, chiral, asymmetric | <p>[00:46:33] And so if one of the components is missing, if the equation is intrinsically lopsided, chiral, asymmetric; then the mass term and the differential term have difficulty interacting, which is sort of overcompensating for the mass scale of the universe, so you get to a point where you actually have to define a massless equation. But then, just like overshooting a putt, it's easier to knock it back by putting in a [[Higgs field]] in order to generate an "as-if" fundamental mass through the [[Yukawa couplings]]. | ||
<p>[00:47:15] Let me, for consistency, say "matter is asymmetric", okay. "and therefore light". | <p>[00:47:15] Let me, for consistency, say "matter is asymmetric", okay. "and, therefore [also], light". | ||
<p>[00:47:35] And then interestingly, he went on to say one more thing. He said, of course, these three central observations must be supplemented with the idea that this all [be] treated in quantum mechanical fashion or quantum field theoretic [fashion]. So it's a bit of an after-market modification rather than, in his opinion at the time, one of the core insights. | <p>[00:47:35] And then interestingly, he went on to say one more thing. He said, of course, these three central observations must be supplemented with the idea that this all [be] treated in quantum mechanical fashion or quantum field theoretic [fashion]. So it's a bit of an after-market modification rather than, in his opinion at the time, one of the core insights. | ||
<p>[00:48:07] I actually think that that's in some sense about right. No. One of my differences with the [modern-day physics] community in some sense is I question whether the quantum isn't in good enough shape. We don't know whether we have a serious quantum mechanical problem or not. We know that we have a quantum mechanical problem, a quantum field theoretic problem, [but only] relative to the current formulations of these theories. | <p>[00:48:07] I actually think that that's in some sense about right. No. One of my differences with the [modern-day physics] community -- in some sense -- is I question whether the quantum isn't in good enough shape. We don't know whether we have a serious quantum mechanical problem or not. We know that we have a quantum mechanical problem, a quantum field theoretic problem, [but only] relative to the current formulations of these theories. | ||
<p>[00:48:31] But we know that in some other cases, the quantum becomes incredibly natural, sometimes sort of almost magically natural, and we don't know whether the true theories that we will need to be generalizing, in some sense, have beautiful quantum mechanical treatments. Whereas the effective theories that we're dealing with now may not survive the quantization. | <p>[00:48:31] But we know that in some other cases, the quantum becomes incredibly natural, sometimes sort of almost magically natural, and we don't know whether the true theories that we will need to be generalizing, in some sense, have beautiful quantum mechanical treatments. Whereas the effective theories that we're dealing with now may not survive the quantization. | ||