Unification, Spinors, Twistors, String Theory

Last month I recorded a podcast with Curt Jaimungal for his Theories of Everything site, and it’s now available with audio here, on Youtube here. There are quite a few other programs on the site well worth watching.

Much of the discussion in this program is about the general ideas I’m trying to pursue about spinors, twistors and unification. For more about the details of these, see arXiv preprints here and here, as well as blog entries here.

About the state of string theory, that’s a topic I find more and more disturbing, with little new though to say about it. It’s been dead now for a long time and most of the scientific community and the public at large are now aware of this. The ongoing publicity campaign from some of the most respected figures in theoretical physics to deny reality and claim that all is well with string theory is what is disturbing. Just in the last week or so, you can watch Cumrun Vafa and Brian Greene promoting string theory on Brian Keating’s channel, with Vafa explaining how string theory computes the mass of the electron. At the World Science Festival site there’s Juan Maldacena, with an upcoming program featuring Greene, Strominger, Vafa and Witten.

On Twitter, there’s now stringking42069, who is producing a torrent of well-informed cutting invective about what is going on in the string theory research community, supposedly from a true believer. It’s unclear whether this is a parody account trying to discredit string theory, or an extreme example of how far gone some string theorists now are.

To all those celebrating Thanksgiving tomorrow, may your travel problems be minimal and your get-togethers with friends and family a pleasure.

Update: If you don’t want to listen to the whole thing and don’t want to hear about spinors and twistors, Curt Jaimungal has put up a shorter clip where we discuss among other things the lack of any significant public technical debate between string theory skeptics and optimists. He offers his site as a venue. Is there anyone who continues to work on string theory and is optimistic about its prospects willing to participate?

Update: For two more clips from the podcast, there’s one about spinors, and one about “spacetime is not doomed”.

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22 Responses to Unification, Spinors, Twistors, String Theory

  1. Anonymous says:

    Multiverses are getting mixed press, too. I subscribe to the IAI newsfeed, and this recent article came up:


  2. Peter Woit says:

    I think the whole multiverse nonsense was a disaster for string theory and string theorists know this. Vafa’s “swampland” program is explicitly an acknowledgement that saying “the multiverse did it” is indefensible and destroys your scientific credibility: you need another answer to the problem of inherently not being able to predict anything.

    What non-swampland others seems to be doing now is trying to avoid ever mentioning the “multiverse did it” answer unless backed into a corner and forced to come up with something.

  3. neo says:

    with Vafa explaining how string theory computes the mass of the electron

    string theory computes the mass of the electron –could you elaborate is this a new result ?

  4. Peter Woit says:

    Maybe someone with more time to waste can explain Vafa’s argument. My impression is that Keating didn’t take it seriously. From a quick scan of the transcript, Vafa at one point says that even if there were some experimental result that disagreed with string theory, to him it would just mean that one needed to understand string theory differently.

  5. David Appell says:

    What is Vafa’s Formula for the mass of the electron, and where is it published?

  6. Peter Woit says:

    David Appell,
    There is no Vafa Formula, this is just complete nonsense, very disturbing to hear it come from someone like Vafa (without any challenge from Keating).

    It’s typical “swampland” argumentation, based on a general conjecture about quantum gravity theories (“weak gravity conjecture”) which has little to do with string theory, and just gives not a number but some absurdly weak bound, many many orders of magnitude from the mass. Vafa then goes on to explain (around 34:00) that even if a “prediction” like this was falsified, he wouldn’t see that as a reason to doubt string theory, it would just mean that one needed to understand “string theory” differently. This has become religion, not science and I don’t understand how this has happened and why anyone continues to take it seriously.

  7. Low Math, Meekly Interacting says:

    Glad this finally got posted. I was rather hoping to come out with a greater understanding of twistors, but not so much. Even Penrose, a masterful expositor, seems to have a hard time conveying what twistors are all about to a lay crowd, so I can’t say my hopes were reasonable.

  8. David Appell says:

    Thanks Peter. Happy Thanksgiving.

  9. Peter Woit says:

    Penrose has given various versions of more physical elementary explanations of twistors, but the problem is that this is all about a new way to think about space-time in highly relativistic and conformally invariant regimes, far from ordinary intuition.

    If you’re happy with complex variables I do think there is a very simple way to understand twistors and spinors: a point in spacetime is a complex two-plane in C^4. Elements of this C^4 are twistors. Spinors at a point are tautological: elements of the complex two-plane.

    The problem with this though is that it gives you complexified space-time, and you have to understand which points are “real”. The “real structures” that determine this for Minkowski spacetime and Euclidean spacetime are not obvious (and quite different in the two cases).

  10. Peter Woit says:

    James Smith,
    Yes, there’s a fundamental problem with twistor theory that Penrose likes to call the “googly problem”: twistor theory is naturally chiral, with points right-handed spinors. The traditional problem is how to understand left-handed spacetime degrees of freedom in twistor language. This problem is normally considered in Minkowski signature spacetime. I’m arguing that if you Wick rotate and look at Euclidean signature spacetime the problem becomes a virtue: you can describe physical spacetime just using right-handed degrees of freedom, with the left-handed ones now internal degrees of freedom.

  11. Marvin says:

    Hi Peter,

    In Vafa interview, the prediction by string theory of the mass of the electron happen at around 14:40, not 34:00.

    This said, as you had explained above, this prediction is extremely vague.

    I can’t understand why they look satisfied whit these weak results.

  12. Peter Woit says:

    Thanks, that’s right. What’s at around 34:00 is where Vafa responds to the question of what he would do if experiment falsified a “prediction” of string theory, like the electron mass one:

    “I will go back and search my on my understanding of string theory. And perhaps we we, we made a mistakes along with our understanding, because I think part of an issue is that we don’t have a complete formulation based on what string theory is. So we are kind of on a difficult platform to be that sure is string theory, right? Because string theory fails to do that. You have to know exactly what string theory is, and we don’t know that yet. So I would go back and check my understanding of the subject.”

    This pretty much answers the question Keating used as title for the interview: “Is String Theory Actually Science?”

  13. Adam Treat says:

    Peter Woit,

    Your point is well taken, but if I can play the devil’s advocate for a minute consider if Vafa’s reply was:

    “I will go back and search my on my understanding of physics. And perhaps we we, we made a mistakes along with our understanding, because I think part of an issue is that we don’t have a complete formulation based on what physics is. So we are kind of on a difficult platform to be that sure is physics, right? Because physics fails to do that. You have to know exactly what physics is, and we don’t know that yet. So I would go back and check my understanding of the subject.”

    I honestly think this is what is going through Vafa’s head when he says things like this.

  14. Peter Woit says:

    Adam Treat,
    I’m sure it’s right that in his mind Vafa is identifying “string theory” = “fundamental physics”, but that’s exactly the problem. At this point as far as he’s concerned there is no way string theory can be wrong, the only open question is what sort of string theory is the right one. This really isn’t science anymore and this attitude is killing off the subject of fundamental physics.

  15. Schratter says:

    While we still don’t quite know what Twistors are or how they relate to physics, we did learn that Garrett Lisi slept on Woit’s couch, once again demonstrating that modern physics is mostly just sociology.

  16. Peter Woit says:

    Being on the list of people whose couch Garrett slept on is not exactly membership in a small, exclusive club…
    If you want to know what twistors are and what they have to do with physics, there are lot of places to learn about this (see for instance slides from my talks in recent years, on my website). You’re not going to understand this sort of thing by listening to two people talking on a podcast like this.

  17. zovi says:

    Have anyone here have a take at Oppenheim’s paper “A postquantum theory of classical gravity?” in PhysRevLett X ?

  18. Simone Speziale says:


    To complement Peter’s answer to LMMI’s question, I think it is always nice to give a geometric intuition of twistors by recalling the interpretation of their incidence relation in the case of conformally flat spacetime: each zero-helicity twistor describes a light ray in Minkowski, each non-zero-helicity twistor describes a twisting null congruence in Minkowski spacetime, or alternatively what is called an alpha-plane in complexified Minkowski spacetime. The set of such flat alpha-planes is useful because it is integrable and spans the manifold CP^3. This is the manifold whose complex structure is associated to the conformal metric structure of Minkowski’s spacetime, and this result gives a 4d (limited) extension of the beautiful equivalence between conformal metric structures and complex structures that we have in 2d.

    For those interested in a bit more details, recall that to each spinor we can associate a light-like direction at the origin of Minkowski space: This is done taking the ratio of the spinor’s components, and interpreting it as a stereographic coordinate on the celestial sphere. With this construction we see that the complex structure of CP^1 can be associated to the celestial sphere. Twistors are bi-spinors, and the way light rays are reconstructed from the incidence relation is roughly speaking with one spinor giving the direction of the light ray, and the second spinor giving the shift away from the origin. The space of light rays is a 5d manifold (2d for the direction of a light ray in the origin, and 3d of independent translations), therefore there is no complex structure that can be associated to it. However, the pair of spinors has to satisfy the special “zero-helicity” property in order to describe a light ray. In general, it describes a 6d space of complexified light rays called alpha-planes mentioned above. The incidence relation is invariant under complex rescaling of the spinors, hence this 6d space is a CP^3 inside C^4.

    The difficulty in going beyond (conformally) flat spacetime is that to define a twistor space associated with a curved manifold, you would need the alpha-planes to be integrable, so that they span a complex manifold. This is the manifold whose complex structure would be associated to the conformal spacetime metric. But integrability of the alpha-planes requires the self-dual part of the Weyl tensor to vanish (A preferred chirality enters the theory from the start, because the incidence relation treats the two spinors in an asymmetric way).
    Hence this basic construction only works for curved Euclidean or complex spacetimes, and one has to figure out some alternative way of proceeding in order to treat real Lorentzian spacetimes.

    Concerning the latest developments by Penrose, he is working to overcome this limitation using inputs from non-commutative geometry, in a version of twistors that he refers to as Palatial Twistor Theory.

  19. Peter Woit says:

    I don’t want to host a discussion of the proposal in the Oppenheim paper here, since I know nothing about it and it’s very far from my own interests. There is one aspect of this though that I would like to understand better. Somehow it got very wide media coverage, see for instance this in the Guardian
    This is despite the experts of very different kinds contacted by the journalist agreeing to take odds of 5000:1 that this doesn’t work.

    I’m thinking that quite possibly I could get better odds than that on my ideas about chiral Euclidean gravity from Rovelli and Pennington, so how do I get a story in the Guardian?

  20. Martin S. says:

    @zovi: It was described at Quanta a few months ago.

  21. Peter Woit says:

    Simone Speziale,
    Thanks a lot for providing that physical/geometric description of twistors and more background!

    This may be the deformation of too much time spent in math departments, but I’m very much seduced by the simple mathematical structure in the complexified case (a point in complex spacetime is exactly the chiral spinor space). The Minkowski real form where we visualize physics adds a much more complicated structure. The Euclidean real form is much simpler, even though its relation to the physical Minkowski story is tricky to understand.

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