User:Aardvark/GU: Difference between revisions

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.

* 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]].

* 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]

== Motivations ==

<!-- <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>

* 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.)

* From Einstein's general relativity, we take the Einstein projection of the curvature tensor of the Levi-Civita connection $$\nabla$$ of the metric $$P_E(F_{\nabla})$$

* From Yang-Mills-Maxwell-Anderson-Higgs theory of gauge fields, we take the adjoint exterior derivative coupled to a connection $$d^\star_A F_A$$

'''Idea:''' What if the $$F$$'s are the same in both contexts?

Further, supposing these $$F$$'s are the same, then why apply two different 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: $$P_E(F_{\nabla h}) \neq  h^{-1} P_E(F_{\nabla}) h $$. 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.

"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?"