Editing Theory of Geometric Unity
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<div style="float:right;padding:20px;">__TOC__</div> | |||
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<blockquote style="width:500px">"The source code of the universe is overwhelmingly likely to determine a purely geometric operating system written in a uniform programming language." - Eric Weinstein </blockquote> | |||
* A first video presentation of the theory is available on [https://www.youtube.com/watch?v=Z7rd04KzLcg Youtube] | * A first video presentation of the theory is available on [https://www.youtube.com/watch?v=Z7rd04KzLcg Youtube] | ||
* A transcript of the talk is available [[A_Portal_Special_Presentation-_Geometric_Unity:_A_First_Look|here]]. | * A transcript of the talk is available [[A_Portal_Special_Presentation-_Geometric_Unity:_A_First_Look|here]]. | ||
* | * Notes by the community on the talk are available in a [https://docs.google.com/document/d/1gPU_bJR5wBs7MCsNGCW5Y06Jh3SzarX5OnJHyLxQfDQ/edit Google Doc] | ||
* [https://www.youtube.com/watch?v=wf0_nMaQ6tA#t=2h16m27s Discussion on the Joe Rogan show] | * [https://www.youtube.com/watch?v=wf0_nMaQ6tA#t=2h16m27s Discussion on the Joe Rogan show] | ||
== Key Ideas == | == Key Ideas == | ||
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{| class="wikitable" | {| class="wikitable" | ||
| '''1.''' The Arena (<math> | | '''1.''' The Arena (<math> Xg_{\mu\nu}</math>) | ||
| <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} =Β \left( \ | | <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} =Β \left( \frac{1}{c^4} 8\pi GT_{\mu\nu}\right)</math> | ||
|- | |- | ||
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<math> SU(3) \times SU(2) \times U(1)</math> | <math> SU(3) \times SU(2) \times U(1)</math> | ||
| <math>d_A^*F_A=J(\psi)</math> | | <math>d_A^*F_A=J(\psi)</math> | ||
|- | |- | ||
| '''3.''' Matter | | '''3.''' Matter | ||
Antisymmetric, therefore light | Antisymmetric, therefore light | ||
| <math> | | <math>\partial_A \psi = m \psi</math> | ||
|} | |} | ||
'''Key guiding question:''' what are the compatibilities and incompatibilities | '''Key guiding question:''' what are the compatibilities and incompatibilities on the geometric level before the theory is created quantum mechanical. Β | ||
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* From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection of the metric $$P_E(F_{\Delta^LC})$$ | |||
* From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection $$d^\star_A F_A$$ | |||
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=== Problem Nr. 1: Einstein's Theory of General Relativity is not a proper Gauge Theory === | === Problem Nr. 1: Einstein's Theory of General Relativity is not a proper Gauge Theory === | ||
'''Idea:''' What if the $$F$$'s are the same in both contexts? | |||
' | But we're applying two different operators. | ||
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'''Thus the question becomes:''' Is there any opportunity to combine these two operators? | '''Thus the question becomes:''' Is there any opportunity to combine these two operators? | ||
A problem 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. We can allow the gauge group of symmetries to act on both sides of the equation, but the key problem is that: | A problem 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. We can allow the gauge group of symmetries to act on both sides of the equation, but the key problem is that: $$P_E(F_{\Delta^{LC} h}) \neqΒ h^{-1} P_E(F_{\Delta^{LC} }) h $$. If we act on connections on the right and then take the Einstein projection, this is not equal to first taking the projection and then conjugating with the gauge action. The gauge rotation is only acting on one of the two factors. Yet the projection is making use of both of them. So there is a fundamental incompatibility in the claim that Einstein's theory is a gauge theory relies more on analogy than an exact mapping between the two theories. Β | ||
=== Problem Nr. 2: Spinors are sensitive to the metric === | === Problem Nr. 2: Spinors are sensitive to the metric === | ||
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<blockquote> | <blockquote> | ||
"So if we're going to take the spin-2 | "So if we're going to take the spin-2 $$G_{\mu\nu}$$ field to be quantum mechanical, if it blinks out and does whatever the quantum does between observations. In the case of the photon, it is 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?" | ||
How do we get the metric out from its responsibilities? It's been assigned far too many responsibilities. It is 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." | How do we get the metric out from its responsibilities? It's been assigned far too many responsibilities. It is 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." | ||
</blockquote> | </blockquote> | ||
=== Problem Nr. 3:Β The Higgs field introduces a lot of arbitrariness === | === Problem Nr. 3:Β The Higgs field introduces a lot of arbitrariness === | ||
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[[File:Geometric unity puzzle pieces.png|500px|right]] | [[File:Geometric unity puzzle pieces.png|500px|right]] | ||
[[File:GU | [[File:GU proposal.png|right|500px|right]] | ||
We may have to generalize all three vertices before we can make progress. That's daunting because in each case, it would appear that we can make an argument that the three vertices are already the simplest possible theories that could live at these vertices. | "We may have to generalize all three vertices before we can make progress. That's daunting because in each case, it would appear that we can make an argument that the three vertices are already the simplest possible theories that could live at these vertices. | ||
* We know, for example, the Dirac operator is the most fundamental of all the elliptic operators and Euclidean signature generating all of the Atiyah-Singer theory. | * We know, for example, the Dirac operator is the most fundamental of all the elliptic operators and Euclidean signature generating all of the Atiyah-Singer theory. | ||
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So, let's imagine the following: we replaced the standard model with a true second-order theory. We imagine the general relativity is replaced by a true first-order theory. And then we find that the true second-order theory admits of a square root and can be linked with the true first order theory. | So, let's imagine the following: we replaced the standard model with a true second-order theory. We imagine the general relativity is replaced by a true first-order theory. And then we find that the true second-order theory admits of a square root and can be linked with the true first order theory. | ||
This would be a program for some kind of unification of Dirac's type, but in the force sector. The question is, "does this really make any sense? Are there any possibilities to do any such thing?" | |||
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== Layman Explanations == | |||
a theory is like a newspaper story | |||
* where/when -> space/time | |||
Β | * who/what -> fermions/bosons | ||
* how/why -> rules/what generates the rules (equations and lagrangians) | |||
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== Frequently Asked Questions == | == Frequently Asked Questions == | ||
Β | Please help answer these questions! | ||
What will this theory predict? | What will this theory predict? | ||
When will Eric release the next part? | When will Eric release the next part? | ||
Why hasn't Eric gone through the normal scientific route? Arxiv.org? Academic journals? | Why hasn't Eric gone through the normal scientific route? Arxiv.org? Academic journals? | ||
== Related existing theories == | |||
Causal Fermion Systems: | |||
[https://www.uni-regensburg.de/mathematik/mathematik-1/] | |||
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