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Showing posts from May, 2019

TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, and Twistors

There are two mysterious looking correspondences involving ADE groups. McKay correspondence between McKay graphs characterizing tensor products for finite subgroups of SU(2) and Dynkin diagrams of affine ADE groups is the first one. The correspondence between principal diagrams characterizing inclusions of hyper-finite factors of type II1 (HFFs) with Dynkin diagrams for a subset of ADE groups and Dynkin diagrams for affine ADE groups is the second one.

I have considered the interpretation of McKay correspondence in TGD framework already earlier

but the decision to look it again led to a discovery of a bundle of new ideas allowing to answer several key questions

of TGD.




Asking questions about M8-H duality at the level of 8-D momentum space led to a realization that the notion of mass is relative as already the existence of alternative QFT descriptions in terms of massless and massive fields suggests (electric-magnetic duality). Depending on choice M4⊂ M8, one can describe p…

McKay correspondence, ADE hierarchy, and inclusions of hyperfinite factors in number theoretical vision

There are two mysterious looking correspondences involving ADE groups. McKay correspondence between McKay graphs characterizing tensor products for finite subgroups of SU(2) and Dynkin diagrams of affine ADE groups is the first one. The correspondence between principal diagrams characterizing inclusions of hyper-finite factors of type II1 (HFFs) with Dynkin diagrams for a subset of ADE groups and Dynkin diagrams for affine ADE groups is the second one.

These correspondences are discussed from number theoretic point of view suggested by TGD and based on the interpretation of discrete subgroups of SU(2) as subgroups of the covering group of quaternionic automorphisms SO(3) (analog of Galois group) and generalization of these groups to semi-direct products Gal(K)&timesL SU(2)K of Galois group for extension K of rationals with the discrete subgroup SU(2)K of SU(2) with representation matrix elements in K. The identification of the inclusion hierarchy of HFFs with the hierarc…

An overall view about models of genetic code and bio-harmony

During last years kind of brain storming period has occurred in the TGD inspired models of bio-harmony and genetic code. A lot of ideas, some of them doomed to be short lived, have emerged, and it seems that now it its time for a thorough cleanup and integration with the general ideas of TGD inspired quantum biology.

TGD leads to 3 basic realizations of the genetic code. One can also consider 3 realization also for bio-harmony. The question is which of them is the realistic one or whether several options can be considered. In this article these ideas are discussed critically and open problems are summarized.

The three genetic codes correspond to a fundamental realization in terms of dark proton sequences (dark nuclei) with 3-proton representing codon. Second realization is the chemical realization and the third realization is in terms of dark photon 3-chords mediating the interaction between various realizations. Frequency resonance is very natural interaction between dark lev…

The problems leading to inflation and those created by inflation and TGD solution to them

The Wikipedia article about inflationary cosmology gives a good summary of inflation theory and its problems. What is nice that inflation theory is a solution to real problems. What is not nice is that it leads to new problems.




Horizon problem: temperature constant in extreme accuracy. No time to equilibrate.



Flatness problem: 3-space is unexpectedly flat suggesting critical 3-space so that 3-curvature vanishes. Here inflation theorists should have though a second though. Criticality suggests criticality in thermodynamical and even in quantum sense.



Monopole problem of GUTs. Monopoles are not observed. This is a problem of GUTs and thus all theories that are based on GUTs as QFT limit.





This is a nice starting point. The inflationary solution of the problems would be a rapid expansion.
Inflation theory relies on GUT paradigm and proposes exponentially fast expansion due to a decay of false vacuumwith non-vanishing energy density decaying to particles. Horizon size become…

Heavy element surprise

Again a surprise in astrophysics (see the popular articles here and here and the slides here. It is really amazing how little we actually know about the mechanism producing heaver elements.




Big bang produces H, He, and also Be but in trace amounts. Heavier elements are absent and are believed to be produced in stars. How the heavier elements are formed? This is the problem. One proposal is that during super-nova explosions so called r-process produces heavier elements outside supernova but SN1987A did not provide support for this.

One proposal is that the heavier elements are produced in the collisions of neutron stars. A further proposal is that they are produced in collapsing accretin disk when neutron star collapses to blackhole.



Standard hypothesis is that so called population III stars produce elements heavier than Be. These stars would be very large and very short lived - age would have been around 105-106 years. Not a single population III star has been however observed …

Solar surprise

Sabine Hossenfelder gave a link to a popular article about totally shocking new findings about Sun. There are 5 times more gamma rays than expected and the spectrum has a deep and narrow dip around 40 GeV. Spectrum continues to much higher energies than expected, at least up to 100 GeV. One proposal is that there could be dark matter in the interior of Sun yielding the gamma rays but is unclear how they could get to the surface without experiencing the same fate as ordinary gammas from nuclear reactions.

There is also a correlation with sunspot cycle. Basic data and observations related to correlations with the solar cycle are discussed in two articles (see this and this).




Power law spectrum is harder than for cosmic rays: spectral indices are n=-2.2 and n=-2.7 respectively (one has power law behavior En for the flux). The spectral intensity at 100 GeV is very nearly the maximum flux predicted by the model assuming that reflection of cosmic gamma rays gives to the ga…

Twistor lift of TGD and WCW geometry

In the following a view about WCW geometry forced by twistor lift of TGD is summarized. Twistor lift brings to the action a volume term but without breaking conformal invariance and without introducing cosmological constant as a fundamental dimensional dynamical coupling. The proposed construction of the gamma matrices of WCW giving rise to Kähler metric as anti-commutators is now in terms of the Noether super charges associated with the super-symplectic algebra. This I dare to regard as a very important step of progress. pu

Possible weak points of the earlier vision

To make progress it is wise to try to identify the possible weak points of the earlier vision.




The huge vacuum degeneracy of Kähler action defining the Kähler function of WCW Kähler metric is analogous to gauge degeneracy of Maxwell action and coded by symplectic transformations of CP2. It implies that the degeneracy of the metric increases as one approaches vacuum extremals and is maximal for the space-time surfac…