  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 $m_u/m_d = 9604/19683 \approx .4879$. This value is within the
lattice QCD value at $2 \operatorname{GeV}$ in the
$\overline{\operatorname{MS}}$-scheme, $.473 \pm .023$. 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 $.511 \operatorname{MeV}$,
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 lattice QCD values $m^{\overline{\operatorname{MS}}}_u =
(2.20\pm .10) \operatorname{MeV}$ and $m^{\overline{\operatorname{MS}}}_d =
(4.69 \pm .07) \operatorname{MeV}$. Finally, using $4$-accelerations, we 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 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.
