Tuesday, March 02, 2021

[Guest Post] Problems with Eric Weinstein's “Geometric Unity”

[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 released a video of his 2013 Oxford lecture in which he presents his theory of everything “Geometric Unity” (GU). Since then, Weinstein has appeared in interviews alongside Sabine Hossenfelder, Brian Keating, Lee Smolin, Max Tegmark, and Stephen Wolfram to discuss his theory. 

In these interviews, Weinstein laments that the scientific community is dismissive of GU because he has not released a technical paper, but insists that scientists should be able to understand the substantive content of GU from the lecture alone (see here and here). In fact, Weinstein regards the conventional requirement of writing a paper to be flawed, since he questions the legitimacy of peer review, credit assignment, and institutional recognition (see here, here, here, and here).

Theo, my anonymous physicist coauthor, and I became aware of Weinstein and Geometric Unity through his podcast The Portal. We independently communicated with Weinstein on Discord and we both came to the conclusion that Weinstein was unable to provide an adequate explanation of GU or why it was a compelling theory. 

I also became increasingly skeptical of Weinstein’s claims when I pressed him about his alleged discovery of the Seiberg-Witten equations before Seiberg and Witten (see here, here, here, and here), a set of equations which was the central focus of my PhD thesis and several resultant papers. When I asked Weinstein for certain mathematical details about how he had arrived at the Seiberg-Witten equations, his vague responses led me to doubt his claims. Though Weinstein proposed to host a more in-depth discussion about GU and the requisite math and physics, no such discussion ever materialized.

These difficulties in communicating with Weinstein is what motivated our response paper. Suffice it to say that it was no easy task, as it required repeatedly watching his YouTube lecture and carefully timestamping its content in order to cite the material. These appear as clickable links in our response paper for those who wish to verify that our transcription of Weinstein's presentation is accurate.

Here's the high-level overview of how GU makes a claim towards a Theory of Everything. Essentially, GU asserts that there is a set of equations in 14 dimensions that are to contain the Einstein equations, Dirac equation, and Yang-Mills equations. Because the Einstein equations describe gravity, the Dirac equation accounts for fermions, and the Yang-Mills equations account for gauge-theories describing the strong and electroweak forces, all fundamental forces and particle types are therefore superficially accounted for. It is our understanding that it is in this very limited and weak sense that GU attempts to position itself as a Theory of Everything.

The most glaring deficiency in Weinstein’s presentation is that it does not incorporate any quantum theory. Establishing a consistent quantum theory of gravity alone has defied the efforts of nearly a century’s worth of vigorous research and is part of what makes formulating a Theory of Everything an enormous challenge. For GU to overlook this obstacle means that it has no possible claim on being a Theory of Everything.

Our findings are that even aside from its status as Theory of Everything, GU contains serious technical gaps both mathematical and physical. In summary:
  • GU introduces a “shiab” operator that overlooks a required complexification step. Omitting this step creates a mathematical error but including it precludes having a physically sensible quantum theory. 
  • The choice of gauge group for GU naively leads to a quantum gauge anomaly, thereby rendering the quantum theory inconsistent. Any straightforward attempt to eliminate this anomaly would make the shiab operator impossible to define, compounding the previous objection. 
  • The setup of GU asserts that it will have supersymmetry. In 14 dimensions, adopting supersymmetry is highly restrictive. It implies that the proposed gauge group of GU cannot be correct and that the theory as stated is incomplete. 
  •  Essential technical details of GU are omitted, leaving many of the central claims unverifiable.

Coincidentally, the night before we posted our response paper, Weinstein announced on Lex Fridman’s podcast that he plans on releasing a paper on GU on April 1st. We look forward to seeing Weinstein's response to the problems we have identified.