[This post is written by Timothy Nguyen, a mathematician and an author of the recently released paper “A Response to Geometric Unity”.]
On April 2, 2020, Eric Weinstein published a video of his Oxford lecture 2013 in which he presented his theory of everything “Geometric Unity” (GU). Since then, Weinstein has appeared in interviews with Sabine Hossenfelder, Brian Keating, Lee Smolin, Max Tegmark, and Stephen Wolfram to discuss his theory.
Theo, my anonymous physicist co-author, and I became aware of Weinstein and Geometric Unity through his podcast, The Portal. We have independently communicated with Weinstein about discord and both concluded that Weinstein was unable to provide an adequate explanation for GU or why it was a compelling theory.
These difficulties in communicating with Weinstein motivated our response paper. Suffice it to say that it was not an easy task as it involved watching his YouTube talk repeatedly and carefully timestamping its content in order to cite the material. These will be displayed in our response paper as clickable links for those who wish to verify that our transcription of Weinstein’s presentation is correct.
Here is the general overview of how GU makes a claim on a theory of everything. Basically, GU claims that there is a set of equations in 14 dimensions intended to include the Einstein equations, the Dirac equation, and the Yang-Mills equations. Since the Einstein equations describe gravity, the Dirac equation takes into account fermions, and the Yang-Mills equations take into account oak theories that describe the strong and electroweak forces, all fundamental forces and particle types are therefore considered superficially. As we understand it, GU tries in this very limited and weak sense to position itself as a theory of everything.
The most noticeable flaw in Weinstein’s presentation is that it does not contain quantum theory. Establishing a consistent quantum theory of gravity alone has defied the efforts of nearly a century of intense research and is part of what makes formulating a theory of everything an enormous challenge. If GU overlooks this obstacle, it means that it does not claim to be a theory of everything.
Our results are that, despite its status as the Theory of Everything, GU has serious technical gaps in both mathematical and physical terms. In summary:
- GU introduces a Shiab operator that overlooks a required complexation step. Omitting this step creates a mathematical error, but precludes the inclusion of a physically sound quantum theory.
- The choice of the calibration group for GU naively leads to a quantum measurement anomaly, which makes the quantum theory inconsistent. Any simple attempt to eliminate this anomaly would make it impossible for the Shiab operator to define it, which reinforces the previous objection.
- GU’s setup claims it will have supersymmetry. The adoption of supersymmetry is very restrictive in 14 dimensions. This implies that the proposed measuring group by GU may not be correct and that the theory given is incomplete.
- Essential technical details of GU are omitted, so that many of the central claims cannot be checked.
Coincidentally, the night before our response paper was published, Weinstein announced on Lex Fridman’s podcast that he was planning to publish a paper on GU on April 1st. We look forward to Weinstein’s response to the problems we have identified.