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A derivation of the first generation particle masses from internal spacetime

Charlie Beil

TL;DR

The work proposes a classical GR framework with degenerate internal spacetime metrics to derive first-generation SM fermion masses without quantum field theory. Using four geometric configurations (ν_e, e, u, d) and the Einstein equations together with a generalized Poisson equation, it yields m_e = 0 and a bare-to-dressed mass structure that reproduces m_u/m_d ≈ 0.488 and a constituent ratio of about 0.979, with a dressed electron mass fixed at 0.511 MeV leading to bare quark masses near lattice QCD values. Energy-density analysis confirms the electron has zero bare density while up and down quarks carry positive densities and the electron neutrino can have negative density, which the author speculates could contribute to dark matter through gravitational effects. All results are claimed to follow from first principles with no free parameters, and the approach links spacetime geometry directly to mass scales in the light of lattice QCD benchmarks. The work thus offers a geometrical, non-QFT route to particle masses and hints at novel gravitational roles for neutrino components in cosmology.

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.

A derivation of the first generation particle masses from internal spacetime

TL;DR

The work proposes a classical GR framework with degenerate internal spacetime metrics to derive first-generation SM fermion masses without quantum field theory. Using four geometric configurations (ν_e, e, u, d) and the Einstein equations together with a generalized Poisson equation, it yields m_e = 0 and a bare-to-dressed mass structure that reproduces m_u/m_d ≈ 0.488 and a constituent ratio of about 0.979, with a dressed electron mass fixed at 0.511 MeV leading to bare quark masses near lattice QCD values. Energy-density analysis confirms the electron has zero bare density while up and down quarks carry positive densities and the electron neutrino can have negative density, which the author speculates could contribute to dark matter through gravitational effects. All results are claimed to follow from first principles with no free parameters, and the approach links spacetime geometry directly to mass scales in the light of lattice QCD benchmarks. The work thus offers a geometrical, non-QFT route to particle masses and hints at novel gravitational roles for neutrino components in cosmology.

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 . This value is within the lattice QCD value , obtained at 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 , these ratios yield the bare quark masses and , which are within/near the lattice QCD values and . Finally, using -accelerations, we derive the ratio of the constituent up and down quark masses. This value is within the 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.
Paper Structure (8 sections, 16 theorems, 91 equations, 1 figure, 3 tables)

This paper contains 8 sections, 16 theorems, 91 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Standard model particles from internal spacetime geometry
  3. Spacetime metrics for pointons, pointal spheres, and their unions
  4. A bare quark mass ratio and the bare electron mass
  5. Dressed electron/bare quark mass ratios
  6. Gravitational mass
  7. A constituent quark mass ratio
  8. The energy density of electron neutrinos

Key Result

Theorem 1

On an asymptotically flat internal spacetime, the Einstein field equation and generalized Poisson equation yield In contrast to the other masses, the neutrino mass $m_{\nu_e}$ is not fixed. Furthermore, the (gravitational) mass of each configuration is positive.

Figures (1)

  • Figure 1: Graphs of the energy densities $\rho_{\text{sp}}$, $n = \pm 1$, and $\rho_d$ over the $(r,r_0)$-plane. The graph of $\rho_{\text{sp}}$ with $n = -1$ (drawn in magenta) corresponds to the electron neutrino and lies below the $(r,r_0)$-plane.

Theorems & Definitions (35)

  • Theorem
  • Definition 2.1
  • Proposition 3.1
  • proof
  • Remark 3.2
  • Remark 3.3
  • Proposition 3.4
  • proof
  • Theorem 3.5
  • proof
  • ...and 25 more