Eric Weinstein on Geometric Unity

Eric Weinstein is a Harvard math Ph. D. who has been working as an economist here in New York for many years, and someone I’ve often enjoyed talking to over the years. Going back to his days as a graduate student, he has been working on some of his own far out of the mainstream ideas about geometry and physics (which I’ve never seen the details of). Eric has finally gotten to the point where he is willing to talk about these ideas publicly, and he is giving a lecture today in Oxford, something that was arranged by Marcus du Sautoy. The Guardian has a long article about him and his work here.

There’s a bit of an analogy with the Garrett Lisi physics outsider story here, although I think Eric will get less media attention since he doesn’t have the surfing angle going for him. Both he and Garrett are pursuing what seems to me one of the deepest questions around: what is the relationship between the SU(3)xSU(2)xU(1) geometry of the Standard Model, and the 4d pseudo-Riemannian geometry of space-time and general relativity? Garrett was trying to understand this in terms of E(8) symmetry, and I’m looking forward to seeing what Eric’s ideas about this are. I’m not sure when he’ll have a paper out on the arXiv, or whether some sort of version of his lecture will be available.

Update: The Guardian now has a very enthusiastic article about this by Marcus du Sautoy, while New Scientist has a skeptical take here.

Update: See Jennifer Ouellette for a critical take on the Guardian coverage.

Update: It seems that claims that physicists were not invited to Weinstein’s talk are not true: an announcement and posters were sent to the physics department, but did not get widely disseminated. For a small amount of info about the talk, see the comment here from “Leaker”.

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76 Responses to Eric Weinstein on Geometric Unity

  1. Nameless says:

    OK, “Einstein-Cartan or something like that”. Point is, if you’re doing unification, you will end up predicting (or, more likely, assuming) the effect of spin on the geometry. It may be null, but it probably isn’t, and no one discusses it in standard textbooks because, except in the vicinity of Planck energy, it’s so minuscule that it’s not experimentally verifiable.

  2. Peter Woit says:

    Thanks Leaker,

    That sounds consistent with the little that I’ve heard directly from Eric about this.

  3. Oldster says:

    I tend to agree with Roger Penrose that spin has been one of the great mysteries in quantum mechanics. As best as I can recall, he said it was one of two primary mysteries in a talk at NYU back in the late 1990’s. At the moment, I don’t remember what the second one was, but I’d agree that spin’s effect on geometry is a necessary problem to be solved by a complete unification. But until a specific model is proposed, even the magnitude of the effect remains unclear. You are right that it is small in the specific Einstein-Cartan case …

  4. nasren says:

    Oldster — I think this is right. Atiyah has said the same thing. And understand spin and I think we’ll understand entanglement a lot better.

  5. Nameless says:

    The effect of spin is likely small quite generally, from dimensional arguments. An iron magnet with spins of its atoms perfectly aligned has average spin density on the order of 10^-5 J*s/m^3. If spin is coupled to geometry through the same G as the stress/energy tensor, we can construct a quantity *G/c^3 with dimensions of inverse length, somehow related to the curvature of spacetime induced by spin, which works out (if I’m not mistaken) to about (10^40 m)^-1.

  6. cormac says:

    Hi Peter, I’m a teeny bit surprised at your reaction – isn’t this exactly the sort of hype you are usually so critical of? No paper have been published, not even an abstract, so why all the fuss? Perhaps you have seen something something we don’t…
    As regards the du Sautoy article, I think it’s an editorial. Think of all those published papers that never got a mention, never mind an editorial.
    Btw, I was suprised by du Sautoy’s sentence
    “One proposal for the source of this push involves reintroducing the cosmological constant into Einstein’s Field Equations. But this cosmological constant has always seemed very arbitrary and a retrospective fix.”
    As a constant of integration, there is no particular reason for the cc to be zero, which is why it never really went away

  7. Tony Smith says:

    Peter can you give a description of

    the 14-dimensional bundle of all metrics over a 4-dimensional manifold

    with details such as its bundle structure (base manifold and fibre),
    symmetry groups, etc ?


  8. Peter Woit says:

    Hi Cormac,

    There’s an infinite amount of hype about science out there, I try to only spend time denouncing that part of it which seems most problematic, hype about ideas that are hugely influential despite their failures (string theory, SUSY, multiverses). When Marcus du Sautoy gets the Oxford String Theory Group renamed as the Oxford Geometric Unity Group, despite Weinstein’s ideas not working out, then I’ll add them to the list to denounce. Right now, I just don’t see the problem of Weinstein getting too much attention for his ideas as a major one for physics.

    Another reason for not writing more about this is that I don’t know much about what is going on, which seems to be a good time to wait a bit before commenting more. Lots of people have been denouncing du Sautoy for not inviting physicists to the talk, when it turns out he did. Eric definitely needs to get a paper or slides or something out with details of his ideas, maybe that’s imminent, maybe not, we’ll see.

    I’ll write more about this soon though…

  9. Peter Woit says:


    The metric tensor is a symmetric bilinear form, so 10 components in 4 d. So, you could make a bundle over your 4d spacetime, with 10d fibers given by the symmetric bilinear forms on the tangent space.

    Beyond that, Eric is the one who needs to get details of this out, not me, since I’m still in the dark…

  10. Oldster says:

    Nameless, yes, you can do that as long as you’re not dealing with some more exotic structure analogous to the original Weyl or Kaluza-Klein unified fields. In structures like those, the factor of G may not always lie between the physical and the geometric, that’s all.

  11. Alex says:

    “The metric tensor is a symmetric bilinear form, so 10 components in 4 d. So, you could make a bundle over your 4d spacetime, with 10d fibers given by the symmetric bilinear forms on the tangent space.”

    Considering that there are 12 Gauge bosons, 14 sounds a wee bit low then… Well, we’ll see, or not.

    “One proposal for the source of this push involves reintroducing the cosmological constant into Einstein’s Field Equations. But this cosmological constant has always seemed very arbitrary and a retrospective fix.”

    Yes, that’s indeed strange. If I am not mistaken, in an effective field theory approach of SM + Einstein-Hilbert, the cosmological constant appears automatically as a counterterm. The problem has been for decades that naively, one has to tune it small, not that it is there in the first place.
    The way the paragraph is phrased sounds to me like du Sautoy does not really know the stuff.

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  14. Jamie Vicary says:

    Those who missed it the first time need only wait 2 more days — for it seems Weinstein is giving a re-run this Friday at 2pm in the Mathematical Institute in Oxford. Maybe the particle physicists will come this time!

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  16. PhiGuy110 says:

    Given how bloated and self-referential modern physics have become without offering many testable predictions (string theory anyone?) it’s not surprising to me that real insight could come from outside the ivory tower echo-chamber. I think Weinstein probably deserves a fair hearing and open minds. However, without a paper or predictions, it’s hard to say much of anything, good or bad. I look forward to following the story as it works it way through the physics community. I reckon that we’ll know sooner rather than later whether there is anything to this.

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  20. kevin dowd says:

    I would like to say that the faster than light neutrino gjys always get a bad wrap. AFAIK they stood up there and said we have this data, we can’t get rid of it, it looks funky, and we ask you help in showing where we went wrong.

    No wild claims .. I thought they were embarassed they had these results and could not suppress them because, well, you just don’t go around suppressing data you don’t like without a reason. And then later of course it was a cable problem. But they didn’t know that.

  21. Peter Woit says:

    kevin dowd,

    “And then later of course it was a cable problem. But they didn’t know that.”

    That’s why they get the bad rap. They should not have gone public until they had checked their cables. It’s not about “suppressing data”, it’s about how hard you work looking for what could be the source of the problem when there is something weird in your data. Some members of the collaboration refused to put their names to the paper, knowing they hadn’t checked things carefully enough to justify going public.

    Anyway, that story doesn’t really have much to do with this one.

  22. King Ray says:

    I think Eric’s tweet from May 29 is instructive:

    “You’ll get an article whenever I’ve time to finish one & only because I really want to give you one. This is just a (time thirsty) hobby.”

    It seems like he is more interesting in getting attention than in contributing to science.

  23. Peter Woit says:

    King Ray,

    I know Eric pretty well, and he’s not doing this to get attention, get on TV, get a book deal, etc. As far as I know, the Guardian blog posts were not his idea. He seriously believes in what he is doing, has been working on it completely quietly for many years, and is deeply conflicted about discussing his ideas in public. Yes, he really needs to get a paper written so others can see what he has, but it’s not because he’s trying to get attention that he hasn’t done that yet.

  24. King Ray says:


    I stand corrected. It sounds like things haven’t sufficiently converged yet for him to feel comfortable writing a paper–perhaps there are too many loose ends still. I’ve found that writing things down helps clear things up sometimes. The theory sounds like a large extrapolation on the SM though.

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