Twistor, cohomology, foundations of physics

A twistor framework for foundations of physics is outlined, in which (1) spacetime is secondary, derived from twistor constructions; (2) the primary physical agents are described by elements of sheaf cohomology defined on twistor space, which encode all information about the spacetime entities (fields and particles); (3) the dynamics of spacetime entities is encoded in the holomorphic structures of twistor space and revealed through Penrose transform and its generalizations (twistor diagrams); (4) the nonlinearity of gravity and nonabelian gauge interactions is a manifestation of the deformation of twistor space effected by the self-interacting twistor agents. A consistent framework of quantum gravity is attainable within twistor formalism because not only can gravity be derived from the primary physical agents of the formalism but also, and most importantly, the formalism itself can be proven intrinsically quantal without the necessity of imposing a quantum postulate upon it extrinsically through a quantization procedure. Indeed, the Planck constant and the whole quantum edifice built thereupon can be derived from formalism. Thus, the conflicts between the principles of general relativity and quantum theory are dissolved because both theories are consequences of twistor formalism, and the century-long debate concerning the possibility of a consistent framework of quantum gravity is closed. Many technical and conceptual issues must be clarified before the twistor formalism can be turned into a practical research framework. But the foundational pillars of the framework provided by twistor formalism are rock solid.