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

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 ===== Third Generation is an Imposter =====
-[02:07:10] We'd had a pseudo-generation of 16 particles. Spin 3/2, never before seen. Not necessarily super-partners, Rarita-Schwinger matter with familiar internal quantum numbers, but potentially so that they're flipped so that matter looks like anti-matter to this generation. Then we add just for the heck of it, 144 spin-1/2 fermions, which contain a bunch of particles with familiar quantum numbers, but also some very exotic looking particles that nobody's ever seen before.
+[[File:GU Oxford Lecture Two-Step Complex Slide.png|thumb|right]]
-[02:07:46] Now, we start doing something different. We make an accusation. One of our generations isn't a regular generation. It's an impostor. At low energy, in a cooled state, potentially, it looks just the same as these other generations, but where are we somehow able to turn up the energy, imagine that it would unify differently with this new matter that we've posited rather than simply unifying onto itself. So two of the generations would unify unto themselves, but this third generation would fuse with the new particles that we've already added. We consolidate geometrically. We can add some zero-th order terms, and we imagine that there is an Elliptic complex that would govern the state of affairs.
+''[https://youtu.be/Z7rd04KzLcg?t=7614 02:06:54]''<br>
+One thing we could do is we could move these equations around a little bit and move the equation for the first generation back, and then we can start adding particles. Let's imagine that we could guess what particles we'd add.
-[02:08:36] We then choose to add some stuff that we can't see at all; that's dark. And this matter would be governed by forces that were dark too. There might be dark electromagnetism and dark-strong and dark-weak. It might be that things break in that sector completely differently and it doesn't break down to SU(3)xSU(2)xU(1) because these are different SU(3), SU(2), and U(1)s, and it may be that there would be like a high-energy SU(5).
+[[File:GU Oxford Lecture Pseudo Generation Slide.png|thumb|right]]
+[[File:GU Oxford Lecture 144 Fermions Slide.png|thumb|right]]
-[02:09:05] Or some [[Pati-Salam Model]]. Imagine then that chirality was not fundamental. But it was emergent that you had some complex and as long as they were cross terms, these two halves would talk to each other. But if they cross terms went away, the two terms would become decoupled. And just the way we have a left hand and we have a right hand, and you asked me, right?
+''[https://youtu.be/Z7rd04KzLcg?t=7630 02:07:10]''<br>
+We'd add a pseudo-generation of 16 particles, spin-3/2, never before seen. Not necessarily superpartners, but Rarita-Schwinger matter with familiar internal quantum numbers, but potentially, so that they're flipped, so that matter looks like anti-matter to this generation. Then we add, just for the heck of it, 144 spin-1/2 fermions, which contain a bunch of particles with familiar quantum numbers, but also some very exotic looking particles that nobody's ever seen before.
-[02:09:27] Imagine you have a neurological condition and in an Oliver Sacks sort of idiom. If somebody is only aware of one side of their body and they say, "Oh my God, I'm deformed, I'm asymmetric!" But we actually have a symmetry between the two things that can't see each other.
+[[File:GU Oxford Lecture Grand Unification Geometry Slide.png|thumb|right]]
+[[File:GU Oxford Lecture Gauge Invariant 0th Terms Slide.png|thumb|right]]
+[[File:GU Oxford Lecture Elliptic Sequence Slide.png|thumb|right]]
-[02:09:44] Then, we would still have a chiral world, but the chirality wouldn't be fundamental. There'd be something else keeping the fermions light, and that would be the absence of the cross term. Now, if you look at what happens in our replacement for the Einstein field equations, the term that would counterbalance the scalar curvature, if you put these equations on a sphere, they wouldn't be satisfied if the T term had a zero expectation value because there would be non-trivial scalar curvature in the swervature terms, but there'd be nothing to counterbalance it. So, it's fundamentally the scalar curvature that would coax the VEV [vacuum expectation value] on the augmented torsion out of the vacuum.
+''[https://youtu.be/Z7rd04KzLcg?t=7666 02:07:46]''<br>
+Now we start doing something different. We make an accusation. One of our generations isn't a regular generation: it's an impostor. At low energy, in a cooled state, potentially, it looks just the same as these other generations, but were we somehow able to turn up the energy, imagine that it would unify differently with this new matter that we've posited rather than simply unifying onto itself. So two of the generations would unify onto themselves, but this third generation would fuse with the new particles that we've already added. We consolidate geometrically. We can add some zeroth-order terms, and we imagine that there is an elliptic complex that would govern the state of affairs.
-[02:10:22] Yeah. To have a non-zero level. And if you pumped up that sphere and it's smeared out, the curvature, which you can't get rid of because of topological considerations, let's say from Chern–Weil theory. You would have a very diffuse, very small term. And that term would be the term that was playing the role of the cosmological constant.
+[[File:GU Oxford Lecture Dark Matter Slide.png|thumb|right]]
-[02:10:44] So when a large universe, you'd have a curvature that was spread out. And things would be very light and things would get very dark due to the absence of curvature linking the sectors.
+''[https://youtu.be/Z7rd04KzLcg?t=7716 02:08:36]''<br>
+We then choose to add some stuff that we can't see at all, that's dark. And this matter would be governed by forces that were dark too. There might be dark electromagnetism, and dark strong, and dark weak. It might be that things break in that sector completely differently, and it doesn't break down to an \(\text{SU}(3) \times \text{SU}(2) \times \text{U}(1)\) because these are different \(\text{SU}(3)\)s, \(\text{SU}(2)\)s, and \(\text{U}(1)\)s, and it may be that there would be like a high energy \(\text{SU}(5)\), or some Pati-Salam model. Imagine then that chirality was not fundamental, but it was emergent—that you had some complex, and as long as there were cross terms these two halves would talk to each other. But if the cross terms went away, the two terms would become decoupled.
-[02:11:01] And that turns out to be exactly our complex.
+''[https://youtu.be/Z7rd04KzLcg?t=7762 02:09:22]''<br>
+And just the way we have a left hand and we have a right hand, and you ask me, right, imagine you have a neurological condition in an Oliver Sacks sort of an idiom, if somebody is only aware of one side of their body and they say, "Oh my God, I'm deformed, I'm asymmetric!" But we actually have a symmetry between the two things that can't see each other. Then we would still have a chiral world, but the chirality wouldn't be fundamental. There'd be something else keeping the fermions light, and that would be the absence of the cross terms. Now if you look at what happens in our replacement for the Einstein field equations, the term that would counterbalance the scalar curvature, if you put these equations on a sphere, they wouldn't be satisfied if the \(T\) term had a zero expectation value: because there would be non-trivial scalar curvature in the swervature terms, but there'd be nothing to counterbalance it. So it's fundamentally the scalar curvature that would coax the VEV (vacuum expectation value) on the augmented torsion out of the vacuum to have a non-zero level. And if you pumped up that sphere and it smeared out the curvature, which you can't get rid of because of topological considerations—let's say from Chern-Weil theory—you would have a very diffuse, very small term. And that term would be the term that was playing the role of the cosmological constant.
+''[https://youtu.be/Z7rd04KzLcg?t=7844 02:10:44]''<br>
+So in a large universe, you'd have a curvature that was spread out, and things would be very light, and things would get very dark due to the absence of curvature linking the sectors. And that turns out to be exactly our complex.
 ==== Lecture Conclusion ====