A derivation of the first generation particle masses from internal spacetime

Internal spacetime geometry was recently introduced to model certain quantum phenomena using spacetime metrics that are degenerate. We use the Ricci tensors of these metrics to derive a ratio of the bare up and down quark masses, obtaining mᵤ/md = 9604/19683. 4879. This value is within the lattice QCD value at 2 GeV in the MS-scheme,. 473. 023. Moreover, using the Levi-Cevita Poisson equation, we derive ratios of the dressed electron mass and bare quark masses. For a dressed electron mass of. 511 MeV, these ratios yield the bare quark masses mᵤ 2. 2440 MeV and md 4. 599 MeV, which are within/near the lattice QCD values m^{MS}ᵤ = (2. 20. 10) MeV and m^{MS}d = (4. 69. 07) MeV. Finally, using 4-accelerations, we derive the ratio mᵤ/md = 48/49. 98 of the constituent up and down quark masses. All of the ratios we obtain are from first principles alone, with no free or ad hoc parameters. Furthermore, and rather curiously, our derivations do not use quantum field theory, but only tools from general relativity.