Theory of Geometric Unity: Difference between revisions

The '''Theory of Geometric Unity''' is an attempt by Eric Weinstein to derive a unified field theory by recovering the different, seemingly incompatible geometries of fundamental physics from a general structure with minimal assumptions.

<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>

* 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?"

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. And 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.