A derivation of the first generation particle masses from internal spacetime

TL;DR

This paper derives ratios of fundamental particle masses, including quarks and electrons, from internal spacetime geometry using general relativity, achieving results consistent with lattice QCD without quantum field theory.

Contribution

It introduces a novel approach using internal spacetime geometry and Ricci tensors to derive particle mass ratios from first principles, avoiding quantum field theory.

Findings

Derived quark mass ratio m_u/m_d ≈ 0.4879 consistent with lattice QCD.

Calculated bare quark masses close to lattice QCD values.

Obtained constituent quark mass ratio near 1, aligning with quark models.

Abstract

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 $.473 \pm .023$, obtained at $2 \operatorname{GeV}$ in the minimal subtraction scheme using supercomputers. 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.