How does the twistorialization at imbedding space level emerge?

One objection against twistorialization at imbedding space level is that M⁴-twistorialization requires 4-D conformal invariance and massless fields. In TGD one has towers of particle with massless particles as the lightest states. The intuitive expectation is that the resolution of the problem is that particles are massless in 8-D sense as also the modes of the imbedding space spinor fields are. M⁸-H duality indeed provides a solution of the problem. Massless quaternionic momentum in M⁸ can be for a suitable choice of decomposition M⁸= M⁴× E⁴ be reduce to massless M⁴ momentum and one can describe the information about 8-momentum using M⁴ twistor and CP₂ twistor.

Second objection is that twistor Grassmann approach uses as twistor space the space T₁(M⁴) =SU(2,2)/SU(2,1)× U(1) whereas the twistor lift of classical TGD uses T(M⁴)=M⁴× S². The formulation of the twistor amplitudes in terms of strong form of holography (SH) using the data assignable to the 2-D surfaces - string world sheets and partonic 2-surfaces perhaps - identified as surfaces in T(M⁴)× T(CP₂) requires the mapping of these twistor spaces to each other - the incidence relations of Penrose indeed realize this map.

For details see the new chapter Some Questions Related to the Twistor Lift of TGD of "Towards M-matrix" or the article Some questions related to the twistor lift of TGD.

For a summary of earlier postings see Latest progress in TGD.

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