Editing Twistor theory (section)

===Palatial twistor theory<!--'Googly problem' and 'Palatial twistor theory' redirect here-->===
The nonlinear graviton construction encodes only anti-self-dual, i.e., left-handed fields.<ref name="Penrose1976"/> A first step towards the problem of modifying twistor space so as to encode a general gravitational field is the encoding of [[Chirality (physics)|right-handed]] fields. Infinitesimally, these are encoded in twistor functions or [[cohomology]] classes of [[Homogeneous function|homogeneity]] −6. The task of using such twistor functions in a fully nonlinear way so as to obtain a ''[[Helicity (particle physics)|right-handed]]'' nonlinear graviton has been referred to as the ('''gravitational''') '''googly problem'''<!--boldface per WP:R#PLA-->.<ref name="Penrose1000">Penrose 2004, p. 1000.</ref> (The word "[[googly]]" is a term used in the game of [[cricket]] for a ball bowled with right-handed helicity using the apparent action that would normally give rise to left-handed helicity.) The most recent proposal in this direction by Penrose in 2015 was based on [[noncommutative geometry]] on twistor space and referred to as '''palatial twistor theory'''<!--boldface per WP:R#PLA-->.<ref>{{Cite journal|doi=10.1098/rsta.2014.0237|title=Palatial twistor theory and the twistor googly problem|year=2015|last1=Penrose|first1=Roger|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=373|issue=2047|pmid=26124255|s2cid=13038470|page=20140237|bibcode=2015RSPTA.37340237P |doi-access=free}}</ref> The theory is named after [[Buckingham Palace]], where [[Michael Atiyah]]<ref>[https://www.quantamagazine.org/20160303-michael-atiyahs-mathematical-dreams/ "Michael Atiyah's Imaginative State of Mind"] – ''[[Quanta Magazine]]''</ref> suggested to Penrose the use of a type of "[[noncommutative algebra]]", an important component of the theory. (The underlying twistor structure in palatial twistor theory was modeled not on the twistor space but on the non-commutative [[holomorphic]] twistor [[Quantum group|quantum algebra]].)