QGravity, masses and CKM matrix all for free

[arivero]

I'd like to know if someone has seen/read, at least in part, some of this rumbling anywhere (beyond my own speculations, this is). It should be nice to know if it coincides with some other "speculator".

Postulate an undeterminacy principle for GR:
when transforming locally to minkowskian coordinates, you can not determine, up to plank constant, the infinitesimal volume where the transformation applies.

Now, such infinitesim is given by a generic coordinate vector x and a infinitesimal displacement (dx0, dx1, dx2, dx3). From this displacement you can get a velocity vector (1,dx1/dx0,dx2/dx0,dx3/dx0). To get units of momenta, one multiplies it by a mass. ¿Plank mass? ¡No! you can -and you will- use a separate mass value for each coordinate: m_n, m_e, m_u, m_d.

In this way you have got a momentum (m_e dx1/dx0, m_u dx1/dx0. m_d dx3/dx0) for the infinitesimal volume, and now you are can impose the condition [x,p]=h. Note that m_n=0 at this order.

Now one must build the riemann tensor. but this procedure involves first and second derivatives of metric. Regretly (well, not) the left and right derivatives do not coincide anymore because the indeterminacy does not let us to take the zero limit in derivatives. Thus we will introduce a matrix to control the ambiguity process in each derivation. This will be the CKM matrix.

 

[Greg Bernhardt]

@arivero did you ever expand on this further?

 

[arivero]

I think I was trying to exploit https://aip.scitation.org/doi/10.1063/1.522810 ambiguities.

In my arxive I can see at least a related note https://arxiv.org/abs/physics/0007027

At that time at was unaware of Kaluza Klein interpretation of mass, so I was looking for something without extra dimensions, and then I though about ambiguities in quantization. I was expecting to be able to formalise them via the tangent groupoid, and then perhaps to connect with Connes-Lott-Chamseddine spectral triples. Ambitious, it was.

 

[arivero]

https://arxiv.org/abs/hep-th/9905021 was another in this topic, and surely most of my early notes from years 96 to 2000, they are just light scraps as at that time I was already outside the academy, working in computer science as a lot of my kin.