Penrose developed a theory called "twistor theory" that tries to describe the universe using twistors. (https://en.wikipedia.org/wiki/Twistor_theory)

From what I've read, there are a lot of papers researching on twistors and applying them to numerous processes and physical models/theories.

In 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".

Also, I found that neural networks could not be properly described by them (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 (Can modern twistor methods to calculate scattering amplitudes be applied to renormalization group calculations?) 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.

So how can twistor theory overcome these problems? If the original form of it cannot overcome these, would a modified version of twistor theory or a generalization of it (as in the case of neural networks I said before) do the job? (From what I've read it is usually said that twistors themselves have these problems, so maybe modifying or adding something to twistor theory or making a generalization of it could solve these) Is it there some specific example of what I'm looking for?

And if twistor theory in any form could do this, what about (also) Penrose's spin networks? (https://en.wikipedia.org/wiki/Spin_network)

  • $\begingroup$ Did you mean "neural networks"? Thats to do with machine learning not so much physics of particles $\endgroup$
    – user84158
    Feb 1, 2019 at 1:22
  • $\begingroup$ @zooby You are aware that Penrose has been promoting a crank theory of the brain, aren't you? I would guess this has something to do with that. $\endgroup$
    – user175150
    Feb 1, 2019 at 8:11
  • $\begingroup$ @frapadingue yes but that's more to do with wave-function collapse and "mircotublues" rather than twistors. $\endgroup$
    – user84158
    Feb 1, 2019 at 16:02
  • $\begingroup$ Mathematician Andrew Hodges (who studied under Penrose) has a site about twistor theory, with lots of links. $\endgroup$
    – PM 2Ring
    Feb 6, 2019 at 14:52

1 Answer 1

  1. Twistor space is a mathematical construction and/or reformulation, which are used in many parts of modern physics, e.g., string-like & YM-like models, such as, twistor string theory & the amplituhedron.

    Twistor theory as a physical theory of quantum gravity seems p.t. incomplete and/or speculative. [OP might want to specify which twistor theory proposal they are referring to. It goes without saying that it would be premature to rule out (or in) future twistor theory proposals.]

  2. Spin networks are typically an ingredient in LQG-like theories, and often based on an $SU(2)$ principal bundle & associated bundles thereof.

  • $\begingroup$ I was not referring to one specific version of twistor theory, I was asking whether there was some version of twistor theory that would overcome the problems that I've found and I've put in my original question. For example, you said that string theory uses twistors (I did not know that). Would string theory (based on twistors or simply using them) for example overcome these problems? Do spin networks also have the problems that twistor theory has? If yes, I have the same question for them. Is it there any version of spin networks that would solve/avoid these problems? @Qmechanic $\endgroup$
    – sztorwi
    Feb 6, 2019 at 10:09

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