String Theory and Twistor Theory
As with string theory, the brilliant physicist Sir Roger Penrose’s twistor theory has provided some mathematical insights into the existing theories of physics, including some that lie at the heart of the Standard Model of particle physics.
For nearly four decades, Penrose has been exploring his own mathematical approach — twistor theory. Penrose developed the theory out of a strong general relativity approach (the theory requires only four dimensions). Penrose maintains a belief that any theory of quantum gravity will need to include fundamental revisions to the way physicists think about quantum mechanics, something with which most particle physicists and string theorists disagree.
One of the key aspects of twistor theory is that the relation between events in space-time is crucial. Instead of focusing on the events and their resulting relationships, twistor theory focuses on the causal relationships, and the events become byproducts of those relationships.
If you take all of the light rays in space-time, it creates a twistor space, which is the mathematical universe in which twistor theory resides. In fact, there are some indications that objects in twistor space may result in objects and events in our universe.
The major flaw of twistor theory is that even after all of these years (it was originally developed in the 1960s), it still only exists in a world absent of quantum physics. The space-time of twistor theory is perfectly smooth, so it allows no discrete structure of space-time.
It’s a sort of anti-quantum gravity, which means it doesn’t provide much more help than general relativity in resolving the issues that string theorists (or other quantum gravity researchers) are trying to solve.
Edward Witten and other string theorists have begun to investigate ways that twistor theory may relate to string theory. One approach has been to have the strings exist not in physical space, but in twistor space. So far, it hasn’t yielded the relationships that would provide fundamental breakthroughs in either string theory or twistor theory, but it has resulted in great improvements of calculational techniques in quantum chromodynamics.