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.

2. A spinor connection for M⁴ would induce a gauge potential of the gravitational field. Spin would take the role of gauge charge. The description of gravity and dimensional interactions would be exactly the same on a formal level. For both, the analogy of the classical energy-impulse tensor would occur at the vertices through modified gammas, and both would be gauge theories in a certain sense.

However, there are 4 problems that seem to destroy this vision, of which problems b,c,d were already solved towards the end of the last year .

1. The spinor connection can be dimensionally transformed to zero by a general coordinate transformation: no gravity at all!
2. In dimension D=4 for space-time, an infinite number of diffeo structures can be found and they differ from the normal s.e. it involves lower-dimensional defects. This is a catastrophe from the perspective of general relativity.
3. Fermion and antifermion numbers are separately conserved unless fermion pairs can be created in a vacuum. Fermion pair creation must be possible.
4. Furthermore, the modified Dirac effect which should give the vertices is exactly zero based on the Dirac equation. Could Dirac's equation break down in the defects and in this way produce the vertices looking like QFT vertices?

There is a common solution for all these four problems (see this)!

1. In Dirac's picture, the creation of a pair means that the fermion line reverses in time. This point would be exactly a defect for a standard diffeo structure when it is interpreted as an exotic for a diff structure! In that case, Dirac's equation does not apply at the defect and there is a delta function singularity that gives the vertex.
2. The creation of the pair is possible in dimension D=4 and only in dimension D=4!
3. The induced spinor connection can be converted to zero everywhere by a generalö coordinate transformation except in these diffeo-defects!! Gravitation can therefore be effectively eliminated by a general coordinate transformation, but not completely. This generalizes Einstein's elevator argument to the quantum level. This is nothing but the quantum version of the Equivalence Principle!

See the article What gravitons are and could one detect them in TGD Universe? or the chapter with the same title.

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.