Common solution of 4 killer problems of TGD

Towards the end of the last year, I made considerable progress in understanding particle vertices (see this). The question however remained, what exactly is a graviton and what is the vertex corresponding to graviton emission.

The help came from condensed matter physics. There is evidence for a chiral graviton in systems exhibiting quantum Hall effect (see this). Chiral graviton is not a true graviton. However, the article inspired a rethinking of the problem.

The result was a beautiful picture that combined the previously identified big problems for which a common solution was already found.

1. Quantum gravity in TGD can be understood as a gauge theory where the gauge group is the Lorentz group SO(1,3). The whole point is that this group is an isometry group related to the other half of the causal diamond. The necessary infinite-dimensional unitary representations of SO(1,3), which are a disaster in standard gauge theory, have a beautiful interpretation in zero-energy ontology because SO(1,3) acts as isometries of the causal diamond. The unitary irreps of SO(1,3) take the role of the unitary representations of the Poincare group. Poincare invariance is in turn realized in the moduli space of causal diamonds (CDs) forming the backbone of the “world of classical worlds” (WCW) (see see this)).

Here, surprisingly, a connection with Weinstein’s work emerges. Weinstein’s analogous attempt fails for many reasons, also because the unitary representations of SO(1,3) are infinite-dimensional and the usual measure theory does not work. I even wrote an article about this (see this). Thanks to Marko and others for directing attention to Weinstein, and to myself for taking Weinstein’s stuff so seriously that SO(1,3) was bothered.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.