Three shorter articles related to "TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors"

I decided to isolate from a rather long article TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors the following three shorter articles.

M⁸-H Duality and Consciousness.

This article is part of a longer paper "TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors". I found it convenient to isolate the part of paper related to the possible implications for TGD inspired theory of consciousness. M⁸-H duality is one of the key ideas of TGD, and one can ask whether it has implications for TGD inspired theory of consciousness. Certain aspects of M⁸-H duality indeed challenge the recent view about consciousness based on ZEO (zero energy ontology).

The algebraic equations for space-time surfaces in M⁸ state the vanishing of either the real or imaginary part (defined in quaternionic sense) for octonion valued polynomial with real coefficients. Besides 4-D roots one obtains as universal exceptional roots 6-spheres at boundary of the light-cone of M⁸ with radii given by the roots r_n of the polynomial in question. They correspond to the balls t= r_n inside Minkowski light-cone with each point have as fiber a 3-sphere S³ with radius contracting to zero at the boundary of the light-cone of M⁴. Could these balls have a special role in consciousness theory? For instance, could they serve as correlates for memories. In this article I consider several scenarios involving a modification of the recent form of ZEO. In the following are the abstracts of these articles.

M⁸-H Duality and the Two Manners to Describe Particles.

This article is part of a longer paper "TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors". I found it convenient to isolate the part of paper related to the notion of particle mass to a separate article. The basic new result is that M⁸-H duality allows to see particles in two manners. In M⁸ picture particles are massive and correspond to a fixed M⁴ subset M⁸: in this case symmetry group os $SO(4)$: this could correspond to low energy hadron physics. In H=M⁴× CP₂ picture particles are massless and symmetry group is SU(3): this picture would correspond to high energy hadron physics with massless quarks and gluons. It is shown that p-adic mass calculations performed M⁴× CP₂ picture are consistent with the massless of the particles: in zero energy ontology (ZEO) it is possible to have quantum superpositions of particles with different mass and this is consistent with the description of the situation in terms of p-adic thermodynamics.

Do Supertwistors Make Sense in TGD?.

This article is part of a longer paper "TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors". I found it convenient to isolate the part of paper related to supersymmetry. In twistor Grassmannian approach to N =4 SYM twistors are replaced with supertwistors and the extreme elegance of the description of various helicity states using twistor space wave functions suggests that super-twistors are realize at the level of M⁸ geometry. These supertwistors are realized at the level of momentum space.

In TGD framework M⁸-H duality allows to geometrize the notion of super-twistor in the sense that different components of super-field correspond to components of super-octonion each of which corresponds to a space-time surfaces satisfying minimal surface equations with string world sheets as singularities - this is geometric counterpart for masslessness.

The progress in understanding of M⁸-H duality throws also light to the problem whether SUSY is realized in TGD and what SUSY breaking does mean. It is now clear that sparticles are predicted and SUSY remains exact but that p-adic thermodynamics causes thermal massivation: unlike Higgs mechanism this massivation mechanism is universal and has nothing to do with dynamics. This is due to the fact that zero energy states are superpositions of states with different masses. The selection of p-adic prime characterizing the sparticle causes the mass splitting between members of super-multiplets although the mass formula is same for all of them. Super-octonion components of polynomials have different orders so that also the extension of rational assignable to them is different and therefore also the ramified primes so that p-adic prime as one them can be different for the members
of SUSY multiplet and mass splitting is obtained.

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

Articles and other material related to TGD.