Re: What is the Twistor Theory about?

Hello Yevgeniy,

I'm not an expert on twistor theory or twistor string theory, so I'm afraid my response will be based on the same sort of literature-search and browsing of abstracts that you can do yourself.

Twistor theory was invented by Roger Penrose in the 1960s, and was briefly thought to be a new avenue towards a Grand Unified Theory. Penrose worked on it for decades, but it didn't really answer the quantum-gravity questions Penrose hoped it would. Just a few years ago, though, Ed Witten began applying the "twistor" concept to some aspects of string theory, and this avenue seems to be productive and useful.

However, in the end it is not a new theory of physics. The things you normally think of as "new theories"---Randall-Sundrum, SO(10) grand unification, large extra dimensions---are ideas for actual new physical phenomena. The problem is, it's comparatively easy to write down new theories, and comparatively hard (sometimes impossible) to solve the equations they generate. You always want to ask some basic questions about your theory: "Does it give a 4-dimensional world? Does it allow for "inflation" at the big bang? Does it make spacetime stable, or does the universe explode or implode with no provokation? Does it explain gravity?" Hopefully your theory can answer these questions by spitting out some sort of equations---but sometimes the equations are simply too complicated to solve. Twistor string theory, if I understand correctly, is just a new way of solving the equations generated by existing theories.

In that sense, it plays a role similar to the role of the Feynman diagram. When quantum field theory---by Paul Dirac, to a large extent---it generated extremely messy and complicated equations even for very simple phenomena. It was absurdly difficult to calculate, e.g., the magnitude of the Lamb shift, a slight change in the spectrum of the hydrogen atom due to quantum electrodynamics. That changed dramatically when Feynman, Tomonaga, and Schwinger figured out how to reorganize the QED equations. They were able to split up the equation into small bits, and group the bits in order by size (a "perturbation series"). Then Feynman came up with his famous diagrams as a shorthand for the terms in this series. That turned QED from an esoteric challenge (one hears stories about graduate students spending years on a single calculation), into an everyday job. With Feynman's version of things, college physics majors are able to do accurate QED calculations which Dirac himself would have found impossible.

Anyway, I think that twistors may be a modern version of this; in string theories, as in early-QED, many promising projects can get stalled when they run into a too-hard equation. Twistors may give us another way of organizing these theories in order to solve them. As such, I have heard that it is proving useful in making physics predictions for the Large Hadron Collider---it doesn't have any new guesses regarding black hole production, but it makes some Standard Model calculations easier.

Hope this helps,

-Ben