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 rn of the polynomial in question. They correspond to the balls t= rn 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.
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.
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.