Penrose on palatial twistors

The main purpose of this post is to publish a draft manuscript version of the research paper Chameleon Twistor Theory: a Geometric Programme for Describing the Physical World by Roger Penrose, with his permission. This will eventually appear in a book later this year and I will add the bibliographic information when I have it.

Roger Penrose talking about the paper in 2018

Abstract Original motivations are recalled, for the introduction twistor theory, as a distinctive complex-geometric approach to the basic physics of our world, these being aimed at applying specifically to (3+1)-dimensional space-time, but where space-time itself is regarded as a notion secondary to the twistor geometry and its algebra. Twistors themselves may be initially pictured as light rays—with a twisting aspect to them related to angular momentum. Twistor theory provides an economical conformally invariant description of quantum wave functions for massless particles and fields, best understood in terms of holomorphic sheaf cohomology, subsequently leading to a non-linear description of anti-self-dual (“left-handed”) gravitational (and Yang-Mills) fields. Attempts to remove this anti-self-dual restriction (the googly problem) led to a 40-year blockage to the development of twistor theory as a possible overall approach to fundamental physics. However, in recent years, a more sophisticated approach to this problem has been developed—referred to as palatial twistor theory—whose basic procedures are described here, where a novel generating-function approach to Λ-vacuum Einstein equations is introduced.

 

I will add my own thoughts on this paper here later.