Twistor theory encodes the conformal geometry of four-dimensional spacetime using incidence geometry in a complex vector space. In the flat correspondence, a spacetime point is a two-plane in a four-dimensional twistor space, and hence a projective line in projective twistor space. Null separation becomes intersection of these lines. Choosing a spacetime signature is an additional reality condition on the complex geometry.
Twistor theory is a mathematical framework developed by the British mathematician Roger Penrose in the 1960s. It is designed to provide a new perspective on the geometry of space-time and the fundamental structures of physical theories, particularly in the context of general relativity and quantum gravity. At its core, twistor theory transforms the conventional approach to understanding space-time by introducing a new set of mathematical objects called "twistors.
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