Speaker
Description
Internal spacetime geometry was recently introduced to model certain quantum phenomena using spacetime metrics that are degenerate. I will describe how the Ricci tensors of these metrics can be used to derive a ratio of the bare up and down quark masses, obtaining $m_u/m_d = 9604/19683 \approx .4879$. This value is within the lattice QCD value $.473 \pm .023$, obtained at $2 \operatorname{GeV}$ using supercomputers. Moreover, I will show how the Levi-Cevita Poisson equation can be used to derive ratios of the dressed electron mass and bare quark masses. For a dressed electron mass of $.511 \operatorname{MeV}$, these ratios yield the bare quark masses $m_u \approx 2.2440 \operatorname{MeV}$ and $m_d \approx 4.599 \operatorname{MeV}$, which are within/near the respective lattice QCD values $(2.20\pm .10) \operatorname{MeV}$ and $(4.69 \pm .07) \operatorname{MeV}$. Finally, I will describe how the $4$-accelerations of these metrics can be used to derive the ratio $\tilde{m}_u/\tilde{m}_d = 48/49 \approx .98$ of the constituent up and down quark masses. This value is within the $.97 \sim 1$ range of constituent quark models. All of the ratios obtained are from first principles alone, with no free or ad hoc parameters. Furthermore, and rather curiously, the derivations do not use quantum field theory, but only tools from general relativity.
