Finally, Garrett's model with 3 generations

[martinbn]

Can someone give a brief description of the model, assuming that the reader is OK with the maths. Just the general idea.

 

[DaniV]

This video helps me understanding theorticlly without matematics this theory, it's very easy underdtanding the basis of the theory although video is not explaining the whole theory processes and its conclusions

 

[garrett]

Hello martinbn,
The general idea of the model is to begin with a high-dimensional Lie group, which has a natural connection and metric, then embed de Sitter spacetime in this Lie group and allow the Lie group to deform, described by variations of the connection, guided by a Yang-Mills-type action extended to fermions. By choosing a nice Lie group, and allowing deformations that preserve some of the Lie group's structure, one can obtain all of the particle-fields and dynamics for the Standard Model and gravity. The model proposed in this paper is a prequel, laying a geometric foundation for previous work on E8 theory, but can be readily adapted for use with other Lie groups.

 

[Alberto Garcia]

Hi Garrett, and what is the problem to calculate the bare mass of an elementary particle (fermion)?

In the paper you wrote:
'...we must presume that each generation of fermions is only accessible from one of three triality-related regions of E8; only then do each of these regional fermion generations correctly match known fermion properties. Each generation will transform under a different triality-related regional spin connection...'
'...all three generations of chiral fermions transform correctly, with no mirror fermions. Also, because the vacuum Higgs field may be different in each region, each generation of fermions may have a different bare mass...'
'...the triality-related boson generators in the three regions act on the corresponding fermions in agreement with their familiar Standard Model spins and charges...'

 

[garrett]

Well, this is the million dollar question. Somehow, according to this new theory, our spacetime must be a superposition of these three triality-related spacetimes, with fermions having masses related to the parameters of how these spacetimes are embedded and related. This would need to produce the (bare) masses and CKM/PMNS mixings we observe. The superposition currently posited in LGC is too simplistic to produce this -- I think the final description, if there is one within LGC, will be more... complex.

 

[Alberto Garcia]

To complete the theory, undoubtedly, a monumental amount of work has to be done , but maybe, you are in the right track, and your efforts could lead to the beginning of a new science revolution, which are stages required by history of science for the progress of knowledge, as T. Kuhn showed us.

 

[garrett]

Thank you, Alberto, that's very flattering. But it may also be that this new idea is wrong. I think it has a lot going for it, but I'm biased, and one always has to remember that, in science, human wishes and dreams, no matter how wonderful, can never change nature's mind. So if a theory is wrong, no matter how nice and popular it gets, it will keep being wrong.

 

[MTd2]

Garrett, I don't know if this exists, but, a Fourier transform is a relation that sends variables between a collection of variables where each one has a complex value. That is, it is a map that relates 2 2d spaces, where the observable is a 1D quanitty.

Your triality could mean mapping 4 3d spaces where the "meta- observable" is a 2D quantity, a complex plane. So, it's going to functions in 4 quaternions, and descending to a 2D space which is wavefunction of the the triadic object.

Depending on how you define the triality, it can yield a fermion on a boson when taking the "meta observable".