Eric Weinstein: How Not to Formulate a Theory of Everything
Introduction
One of the ultimate aims of theoretical physics is to arrive at a simple and consistent set of physical laws describing the universe. While this may seem to be a fanciful wish, the history of physics is one of the successive revolutions of simplification. For instance, Newton’s laws summarize classical mechanics into three simple principles, Maxwell’s equations unify electricity and magnetism, and Schrodinger’s equation encapsulates the wave-nature of quantum physics, to name but a few examples. The past century saw two further great strides in simplification through the advent of Einstein’s General Theory of Relativity, combining the principles of relativity with gravitation, and Quantum Field Theory, combining the principles of relativity with quantum mechanics. What has remained fairly elusive however is how to combine General Relativity and Quantum Field Theory together in a satisfactory and consistent way. A successful marriage of these two theories would provide a core missing piece of what physicists generally refer to as a “Theory of Everything”. While there may be disagreements as to what a workable unification of gravity and the principles of quantum mechanics may end up being (for instance whether it involves “quantizing gravity”), few if any doubt that some reconciliation between the two theories must be achieved.
Needless to say, the elusiveness of obtaining a Theory of Everything for the past century makes clear the enormous challenge such an endeavor poses. It is therefore instinctive that any proposal for a Theory of Everything, certainly one conceived by a lone individual, ought to be viewed from a position of healthy skepticism.
Enter Eric Weinstein. Weinstein received his PhD in mathematical gauge theory from Harvard in 1992, where his dissertation studied the self-dual Yang-Mills equations. These equations have had a profound impact on mathematics and physics, and Weinstein’s thesis extended their construction from dimension four to dimension eight. After several postdoctoral positions, Weinstein left academia in 1998 with his dissertation appearing to be the only trail he left behind. Working in various roles as an economist, he re-emerged onto the mathematical physics scene in 2013 with a lecture given at Oxford on his theory of physics “Geometric Unity” (GU). Weinstein was provided this opportunity through the invitation of mathematician Marcus du Sautoy, who wrote a glowing accolade of Weinstein published in The Guardian. A look at Weinstein’s CV shows that he had the ideas for Geometric Unity dating back to at least 1995 through a seminar he gave at MIT/Harvard on “A Program for Geometric Unification”. The Oxford lecture, however, was an isolated incident that made no impact in any social or scientific circles as no paper or follow-up materials were produced.
Fast forward to 2019 and Weinstein has launched his podcast The Portal, bringing on high-profile guests such as Peter Thiel (his employer), Andrew Yang, and Gary Kasparov. The topics covered by the podcast are diverse, including Weinstein’s interest in physics. On April 2, 2020, Weinstein released a special Portal episode on Youtube, in which he discusses his thoughts about Geometric Unity, posts the recorded Oxford lecture of 2013, and provides some supplementary information in a PowerPoint presentation. This highly idiosyncratic presentation of a theory of physics was also spearheaded by many appearances on UCSD astrophysicist Brian Keating’s podcast (see here, here, here, here, here). To the uninitiated, this endorsement appeared to give legitimacy to Weinstein’s ideas, since Keating and the invited podcast guests which Weinstein jousted (Sabine Hossenfelder, Lee Smolin, Max Tegmark, Stephen Wolfram) are all professional scientists. Much of the discussion among these guests centered around Weinstein’s criticism of the scientific community, which most significantly begets his unwillingness to submit his ideas in the form of a scientific paper. In fact, he repeatedly suggested that his work could be understood solely from watching his Oxford lecture and that writing a paper was not necessary (see here and here).
Already the trajectory and medium of Geometric Unity should raise alarm bells as to the seriousness of the work. The proper method of announcing a scientific result is to write a technical paper that can be read and evaluated by the relevant experts. This is true for all success stories in math and science: never has anyone earned credit for an idea without writing it down or being directly involved as such. Even the rare success stories centered around a lone, relatively isolated individual involve a proper manuscript being procured and evaluated (Grigori Perelman, who solved the Poincare conjecture, and Yitang Zhang, who solved a weak form of the Goldbach conjecture, come to mind). As scientists receive misguided proposals for scientific theories on a regular basis, Weinstein’s proposal would ordinarily be dismissed alongside the pile of other “crackpot” theories were it not for his fame and clout as a podcaster, his frequent appearances on high profile podcasts (Joe Rogan’s and Lex Fridman’s), and his invitations to discuss his work with respected physicists on Brian Keating’s podcast.
However, after much resistance, Weinstein finally committed his ideas behind Geometric Unity in paper form, which he released in April 2021 on Keating’s and Rogan’s podcasts. What has been the reception of GU now that the paper has been released? The short answer is that the work is so lacking in competence that it has received practically zero attention from the scientific community. This article will discuss the deficiencies of GU via two avenues: through the content of the work itself and through the scientific rebuttal of the work which I co-authored based on the 2020 GU video (prior to the 2021 GU paper release).
GU: The Paper
A quick look over the GU document already reveals its glaring deficiencies as a piece of scientific work. To summarize, what Weinstein has done is to release a manuscript with the essential details omitted, rendering his theory with little substance. In order to better understand the situation, let us make a cartoon analogy of establishing a Theory of Everything by creating a forced checkmate in the game of chess. The latter is achieved by exhibiting a collection of potential moves such that no matter what the opponent does, some subcollection of moves will guarantee a checkmate. We verify such a forced checkmate by a detailed examination of its correctness and soundness: Are all the steps employed legitimately? Has every possible foil to the proposed set of moves been considered? Is there indeed a checkmate? Only when all such doubts have been settled can we say that we have ascertained the forced checkmate.
Now science is not as simple as the above analogy suggests since science is a never-ending process of accumulation and refinement of knowledge (unlike a chess match, which ultimately comes to an end). But the chess metaphor is apt insofar as during a chess game there are clear indicators of progress: for instance, the capturing of pieces, the threatening of the king, and the securing of more advantageous positions. With this in mind, the chess equivalent of the GU program put forth by Weinstein’s manuscript would be the claim “Here’s a recipe for a forced mate in ten, except moves four through ten are omitted and there’s a queen somewhere on the board but we don’t know or remember where it is”. Undoubtedly, such a claim is senseless to evaluate. And so it is with GU as well, because the paper fails to put forth much that is precise or verifiable.
The very first disclaimer of Weinstein’s paper, which sets the tone for the entire work, is immediately brought to the reader’s attention at the bottom of page one:
Here is a sample of further disclaimers appearing throughout the document:
Finally, the entire starting section of the Summary of GU reads
These apologetic remarks could be acceptable in a set of private notes, but suffice it to say, it is hard to extend such charity to an author when he has been publicly advertising his work as a Theory of Everything for years.
Ordinarily, the proper route to take when faced with uncertainty, such as expressed in the above, is to form a precise question or conjecture. For example, the most famous open problem in mathematics, the Riemann Hypothesis, puts forth a well-formulated conjecture based on strong yet inconclusive evidence. No such conjectures can be easily identified in Weinstein’s paper. A second way forward is to prove a statement of the form “If Y is true, then X follows” and then go about trying to establish Y in lieu of directly trying to solve X or else pose Y as a conjecture. Thus, in another version of Weinstein’s paper, there could have been statements along the lines of “If there is an operator that does Y or if there is an isomorphism Z, then X follows.” But instead what we have from GU is a haphazard array of fragments, anecdotes, and assertions with no clear relationship between their logical dependencies or what might be sufficient conditions for a meaningful result. Yes, there are definitions and some well-founded constructions here and there, but that’s akin to just providing the starting chess position. We are left in the dark about what advancements, if any, will be made.
But at a high level, we can say the following: There is no serious discussion or proposal about how to arrive at a quantum theory of gravity. In fact, it’s not even clear how any standard physics arises from GU. There is no well-defined Lagrangian (i.e. one exempt from the multitude of disclaimers) and no hint as to how physics on the underlying 14-dimensional space of the theory recovers the physics of the observable 4-dimensional universe. Rather than a Theory of Everything being presented, what we are given instead, to put it mildly, is inadequate speculation.
GU: The Response Paper
A little over a month prior to the release of GU, my coauthor Theo Polya and I released our Response to Geometric Unity paper based on the 2013 Oxford lecture (the only available material on GU at the time); our motivations for writing this response have been discussed here. In our paper, we described four objections to the GU work that we were able to discern from the video. The first of these (and the most severe) was the observation that the so-called “Shiab operator”, a fundamental object of GU, was impossible to define as stated since it would violate a certain non-isomorphism between two spaces. Needless to say, Weinstein’s inability to construct the Shiab operator in his paper, as gleaned from the above disclaimers and others in his paper, was inevitable.
For those interested in the details, it is unfortunate that the error Weinstein commits is a relatively simple one (albeit as a needle buried in the haystack of the GU lecture). Namely, he asserts the existence of an isomorphism of bundles of representations, which, however, only holds if one complexifies the bundles. The two bundles in question are the following: one is the bundle whose fiber is the Lie algebra of 128x128 skew-Hermitian matrices, and the other is a bundle whose fiber is the real Clifford algebra in 14-dimensions (isomorphic to the algebra of 128x128 real-valued matrices). These bundles only become isomorphic (as representations of the 128-dimensional unitary group) after complexification. To make the details more accessible, I have given an explicit illustration of this phenomenon in two dimensions here. Altogether, by neglecting complexification, Weinstein cannot construct the Shiab operator. Furthermore, even if Weinstein introduced complexification, it introduces other fatal problems which we discuss in our paper.
In looking over how this issue might have been addressed in the GU paper following our response paper, it is unclear whether Weinstein actually wishes to complexify or not (likely not since he fails to explicitly do so in the appropriate manner). In fact, though Weinstein considers spaces with mixed signature metrics alongside the associated mixed signature unitary groups, the latter are still real Lie groups and hence their Lie algebras are real. Hence, it appears Weinstein does not consider any complexified bundles in his work (real Lie algebras will not give rise to complexified adjoint representations). As it stands, the only straightforward reading of the material is that Weinstein has made a basic mathematical error. Without any indication of how this error is to be addressed, the current status of GU is that it has landed dead on arrival.
To date, my paper with Theo Polya constitutes the only scientific response GU has received, and given how events have transpired, it likely will remain the only such response.
Conclusion
There may be the germs of some interesting mathematical perspectives arising from Geometric Unity, just like any arrangement of chess positions can contain interesting sub-configurations here or there. But even such a modest claim places the burden of proof on Weinstein, alone or with collaborators, to work out the arrangement of the missing pieces. Else as it stands, Geometric Unity is an incomplete and flawed proposal which no one else is obligated to digest, much less complete. And as to Weinstein’s far grander claim of possessing the keys to a genuine Theory of Everything, the limited scope of Geometric Unity makes it inconceivable how such a claim could possibly hold true. Like most rough drafts, Geometric Unity in its current form should have been developed further before being released, regardless of whether its author is an academician or an entertainer.
Disclaimer: All opinions are those of the author and not of his employer or collaborators.
