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Theory of Geometric Unity: Difference between revisions
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The '''Theory of Geometric Unity''' is an attempt by Eric Weinstein to produce a unified field theory by recovering the different, seemingly incompatible geometries of fundamental physics from a general structure with minimal assumptions. For the latest updates on the theory, visit '''https://geometricunity.org/'''. | |||
* 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] | ||
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* Preliminary notes by the community on the talk are available in a [https://docs.google.com/document/d/1gPU_bJR5wBs7MCsNGCW5Y06Jh3SzarX5OnJHyLxQfDQ/edit Google Doc] | * Preliminary 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] | ||
* [https://www.youtube.com/watch?v=N_aN8NnoeO0 PBS SpaceTime] | |||
<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> | <div style="float:right;padding:20px;">__TOC__</div> | ||
<blockquote style="width:80%;max-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> | |||
== Project Ideas == | == Project Ideas == | ||
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* Unpack Eric's first talk by providing additional explanations for the concepts and problems introduced. One possible format would be to annotate it in a [https://genius.com/web-annotator Genius.com] format. | * Unpack Eric's first talk by providing additional explanations for the concepts and problems introduced. One possible format would be to annotate it in a [https://genius.com/web-annotator Genius.com] format. | ||
* Organize voice/video chats to watch the talk together and stop every few minutes to discuss it. (Multiple calls would be needed to go through the whole talk.) | * Organize voice/video chats to watch the talk together and stop every few minutes to discuss it. (Multiple calls would be needed to go through the whole talk.) | ||
*3 | |||
== Key Ideas == | == Key Ideas == | ||
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{| class="wikitable" | {| class="wikitable" | ||
| '''1.''' The Arena (<math> | | '''1.''' The Arena (<math> X, g_{\mu\nu}</math>) | ||
| <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \left( \dfrac{8 \pi G}{c^4} T_{\mu\nu}\right)</math> | | <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \left( \dfrac{8 \pi G}{c^4} T_{\mu\nu}\right)</math> | ||
| the Einstein field equations, which describe gravity in the theory of general relativity | | the Einstein field equations, which describe gravity in the theory of general relativity | ||
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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 === | ||
* From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection of the metric | * From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection <math>\nabla</math> of the metric <math>P_E(F_{\nabla})</math> | ||
* From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection | * From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection <math>d^\star_A F_A</math> | ||
'''Idea:''' What if the | '''Idea:''' What if the <math>F</math>'s are the same in both contexts? | ||
Further, supposing these | Further, supposing these <math>F</math>'s are the same, then why apply two different operators? | ||
'''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: <math>P_E(F_{\nabla h}) \neq h^{-1} P_E(F_{\nabla}) h </math>. 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. | ||
=== 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 <math>G_{\mu\nu}</math> 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> | ||
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[[File:GU vision.png|right|400px|right]] | [[File:GU vision.png|right|400px|right]] | ||
Let's talk about what the Geometric Unity (GU) proposal is. First of all, we observe that we have a division into intrinsic theories and auxiliary theory and between physics and mathematics. | Let's talk about what the Geometric Unity (GU) proposal is. First of all, we observe that we have a division into intrinsic theories and auxiliary theory and between physics and mathematics. An intrinsic physical theory would be general relativity. An auxiliary physical theory would be the Yang-Mills theory, with the freedom to choose internal quantum numbers. | ||
At the mathematical level, an intrinsic theory would be, the older semi-Riemannian geometry. The study of manifolds with length and angle. Auxiliary geometry is what we're going to call fiber bundle theory or modern gauge theory. | At the mathematical level, an intrinsic theory would be, the older semi-Riemannian geometry. The study of manifolds with length and angle. Auxiliary geometry is what we're going to call fiber bundle theory or modern gauge theory. | ||
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When will Eric release the next part? | When will Eric release the next part? | ||
On the Lex Fridman Podcast, Eric states that he may release a paper on April Fool's day, 2021 | |||
on the topic of Geometric Unity. | |||
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? | ||
Answer: He is planning on releasing his theory through the traditional route of publishing | |||
an academic paper in the near future. He is unlikely to publish in any academic journal that | |||
[ | has a paywall - he has voiced concerns over price gouging that many academic journals engage | ||
in. | |||
[[Category:Geometric Unity]] | |||
[[Category:Mathematics]] | |||
[[Category:Physics]] | |||