Quanta magazine has an intriguing article by Siobhan Roberts out about Michael Atiyah, and what he’s up to these days. It mentions some new ideas about twistor theory I hadn’t heard about, that emerged from a conversation with Penrose, which Penrose wrote up as Palatial twistor theory and the twistor googly problem. Penrose explains the name:

The majestic ambiance of the unusual location (Buckingham Palace) of a brief discussion with Atiyah, no doubt provided inspiration for the initial thought that non-commutative twistor algebra should be the key to those subsequent developments described in this paper.

The Quanta article explains:

One day in the spring of 2013, for instance, as he sat in the Queen’s Gallery at Buckingham Palace awaiting the annual Order of Merit luncheon with Elizabeth II, Sir Michael made a match for his lifelong friend and colleague, Sir Roger Penrose, the great mathematical physicist.

Penrose had been trying to develop his “twistor” theory, a path toward quantum gravity that’s been in the works for nearly 50 years. “I had a way of doing it which meant going out to infinity,” Penrose said, “and trying to solve a problem out there, and then coming back again.” He thought there must be a simpler way. And right then and there Atiyah put his finger on it, suggesting Penrose make use of a type of “noncommutative algebra.”

“I thought, ‘Oh, my God,’” Penrose said. “Because I knew there was this noncommutative algebra which had been sitting there all this time in twistor theory. But I hadn’t thought of using it in this particular way. Some people might have just said, ‘That won’t work.’ But Michael could immediately see that there was a way in which you could make it work, and exactly the right thing to do.” Given the venue where Atiyah made the suggestion, Penrose dubbed his improved idea “palatial twistor theory.”

The article links to this recent talk about the role of beauty in mathematics, and describes some very speculative ideas he’s been working on, which I guess correspond to for instance this paper.

About this kind of work he has this to say:

If you try to direct science, you only get people going in the direction you told them to go. All of science comes from people noticing interesting side paths. You’ve got to have a very flexible approach to exploration and allow different people to try different things. Which is difficult, because unless you jump on the bandwagon, you don’t get a job.

Worrying about your future, you have to stay in line. That’s the worst thing about modern science. Fortunately, when you get to my age, you don’t need to bother about that. I can say what I like.

When asked if he’s risking his reputation this way, he has this sensible response:

My reputation is established as a mathematician. If I make a mess of it now, people will say, “All right, he was a good mathematician, but at the end of his life he lost his marbles.”

A friend of mine, John Polkinghorne, left physics just as I was going in; he went into the church and became a theologian. We had a discussion on my 80th birthday and he said to me, “You’ve got nothing to lose; you just go ahead and think what you think.” And that’s what I’ve been doing. I’ve got all the medals I need. What could I lose? So that’s why I’m prepared to take a gamble that a young researcher wouldn’t be prepared to take.

**Update**: For an alternate source of information about “palatial twistor theory”, see slides here, video here.

Whenever possible, could you link to non paywalled

versions of articles. Some of your readers may not have

an academic affiliation that allows them access.

wam,

I generally do try to do that. In this case, I don’t know of any other source for Penrose’s “palatial twistor” paper, if anyone else does, please let us know.

Is this it? Or a similar paper “Towards an Objective Physics of Bell Non-Locality: Palatial Twistor Theory”

Downloads the PDF from http://www.ijqf.org

Dom,

Thanks. That’s similar, not the same, refers for details to the other one.

There is no non-paywall version that I could find. Heck, my library, I found, only subscribes to the Proceedings of the RS via a two-year moving paywall, which means I will only be able to read this article in 2017!

David Roberts (and others),

I’ve added a couple links, to a set of slides and a video of Penrose lecturing on this. The drawings in the slides may in any case be more helpful than the graphic-free paper.

Thanks for links. ‘In person’ is invariably better than ‘on paper’. In RP’s

case it makes a big difference – how else to understand his prelapsarian

graphics. How he fits it all onto a transparency using magic markers

is somewhat miraculous. For other, possibly more primitive examples

look into the back issues of Twistor Newsletter.

Can you actually make some critical comments about “twister theory” as you do “string theory”, please? Just quoting Penrose on twistors is like blogging quotes from Witten on string theory.

I realise that the amount of existing hype for each is vastly different, so that it is justified to treat twistors as news, rather than hype, but what about the connections of the 2 spinors in twistors with the usual standard model spinors?

anon,

“twistor theory” isn’t a subject that has led to any specific well-defined physical theory, but I think it’s very interesting in the way that it shows that one can study 4d geometry in a way that builds in spinors and conformal invariance from the beginning. It has always seemed to me that you need some new ideas before building qfts based on this kind of geometry. Arkani-Hamed several years back was claiming a new approach to qft based on these variables, but what has come out of that (theories based on amplitudes, defined in terms of volumes of geometrical objects) leads to interesting things, but nothing that seems to me to answer questions about the SM and its relation to gravity.

The reason for bringing this up in the blog post was the claim by Atiyah and Penrose that there’s a new idea here. I’ve spent a little time looking at it, still don’t understand well enough to see if it goes somewhere. The sort of quantization Penrose is trying to do always has confused me, because it seems to be purely quantum mechanical, whereas I’d like to see what this does for QFT. Thinking more deeply about this (and whether the “palatial twistors” help) seems worthwhile, I haven’t had the time recently to do so.

Peter,

Speaking of Arkani-Hamed and his Amplituhedron work, if I remember correctly that was tied rather explicitly to N=4 supersymmetric Yang-Mills theory. I gather that it also borrowed heavily from Penrose’s twistor theory, but I wonder whether these new “palatial” ideas either implicitly or explicitly depend upon supersymmetric theories?

Also, given the rather disheartening news for SS theories now that the LHC has significantly constrained the parameter space, is Arkani-Hamed working on something else? All I can find from him lately seems to be “motivational” talks and papers on the way forward for particle theory and under consideration next generation colliders.

Very interesting article on M.Atiyah. He says he is going back reading Einstein and Dirac and finding stuff people missed. It would be great to see what he has found.

Manyoso,

For something very recent from him, see

https://www.youtube.com/watch?v=1HRdqNcgOOo

Some motivational stuff about colliders, etc, but also a long section on the latest on amplitudes. There’s the usual story about motivating work on amplitudes by hopes for finding a common origin of spacetime and QM, but I don’t see any particular progress towards that.

Three may be one, but I don’t know of any relation of the “palatial” stuff to SUSY.

If people want to skip to the ‘new’ material in Penrose’s talk, for instance if they are familiar with twistors, then jump to 45 minutes in (yes, I had to watch all that to find the actual point). He then says that palatial twistor theory is not any sort of quantum gravity, but then proposes another deformation of the algebra to make more commutators nonzero—he explicitly calls it a ‘crazy new proposal’—to maybe be able to do something. The comments Penrose makes in the question time are some of the best bits.