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 [Formula: see text]. This value is within the lattice QCD value [Formula: see text], obtained at [Formula: see text] in the minimal subtraction scheme using supercomputers. Moreover, using the Levi-Civita Poisson equation, we derive ratios of the dressed electron mass and bare quark masses. For a dressed electron mass of [Formula: see text], these ratios yield the bare quark masses [Formula: see text] and [Formula: see text], which are within/near the lattice QCD values [Formula: see text] and [Formula: see text]. Finally, using [Formula: see text]-accelerations, we derive the ratio [Formula: see text] of the constituent up and down quark masses. This value is within the [Formula: see text] range of constituent quark models. 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.