Can twistor theory be used to describe everything?

[Suekdccia]

I've been looking at another Penrose's theory/model called twistor theory (https://en.wikipedia.org/wiki/Twistor_theory) that seems very interesting. From what I've read it seems to me that literally everything can be represented by twistors (or, rather, variations of twist theory).

The only things that I found that could not be properly described by them were neural networks (but the book itself where I read that said that some modification of it could do it) and renormalization group calculations as it is indicated here (https://physics.stackexchange.com/q...cattering-amplitudes-be-applied-to-reno/56111) but the comments and the answers say that while being not the best option (it makes mathematics difficult when trying to apply twistors there) it is not impossible.

I also read that in its original form, twistors could not be applied to other spaces than 4D and other metric signatures than (2,2), but that modifications of the theory have made it able to be applicable to every dimensions/signatures (https://mafiadoc.com/clifford-geome...linear-algebra-_5a33759f1723ddfb91c2e096.html)

Also, they have been related to other space time networks theories (like Wolphram's) and to the holographic principle (to my knowledge, a holographic principle based universe could represent everything we have in our own universe, so all mathematical/logical things could be represented in holography)

Here's the link (https://phys.org/news/2018-03-math-bridges-holography-twistor-theory.html)

I also find this entry (https://motls.blogspot.com/2017/02/a-story-about-roger-penrose.html) in Lubos Motl's blog that says "It's not quite clear whether twistors are totally sufficient to describe quantum gravitational phenomena in D=4" and in the spanish wikipedia entry of twistor theory it says "For a time it was hoped that the theory of twistors constituted by itself a direct path to quantum gravity, but this, at present, is considered unlikely".

All the things that twistor theory cannot be applied to or cannot describe seem to have problems with Penrose's original twistor theory or at least with twistors themselves (or "alone"). But would it be the same for a modified twistor theory (by adding something else to the theory for example)?

But this may be only my perception. So, my question is: Can literally all logical/mathematical things be represented by twistors and (variations of) twistor theory?

 

[AndyW]

I find the topic of twistor theory very intriguing and have done some research on it myself. From what I have gathered, it does seem that twistors are a powerful mathematical tool that can be used to describe a wide range of physical phenomena, including quantum gravity. However, as with any scientific theory, there are limitations and areas that are still being explored and developed.

As you mentioned, there are some instances where twistors may not be the most suitable tool for describing certain phenomena, such as neural networks and renormalization group calculations. However, as you also noted, there have been modifications and extensions of twistor theory that may make it more applicable in these cases. It is possible that with further development and refinement, twistors could potentially be used to describe all logical and mathematical concepts.

But, as Lubos Motl pointed out in his blog, it is not entirely clear at this point whether twistors alone are sufficient to fully describe quantum gravity in 4 dimensions. There may be other components or theories that need to be incorporated in order to fully understand this complex phenomenon. It is also important to keep in mind that science is always evolving and theories are constantly being revised and improved upon.

In summary, while twistors and twistor theory have shown great potential for describing a wide range of phenomena, there may still be some limitations and areas that require further development. It is an exciting area of research and I look forward to seeing how it continues to evolve in the future.