Electron Mass Emerging from the Vacuum Acceleration and the Hubble Parameter's Relation to the Fine Structure Constant in Six Dimensional Geometry

In this work, it is shown that the vacuum acceleration is related to the electron mass, and the Hubble parameter exhibits a reciprocal scaling law with respect to the square of the fine-structure constant, such that H₀ ∝ α^-2. The present model extends Kaluza-Klein theory to include an orthogonal compact timelike dimension, where the compact spacelike and timelike dimensions comprise a phase-plane. The division of energy and the projection onto 3+1D spacetime from this 4+2D geometry gives a_vac = (c H₀ / (4 √2)) ≈ 1.2 × 10⁻¹⁰ m/s². Coincidentally, this matches acceleration a₀ noted by Milgrom, where galactic rotation curves transition from Newtonian dynamics. We use this same geometric model to describe the closed topology of an electron satisfying
m_e = ((α² ħ² a_vac) / (16 G c²))^1/3.
This derivation comes from two postulates. First, that relativistic effects are a rotation of the vector x(t) towards an orthogonal plane. Second, that the particle's internal dynamics are in equilibrium with the vacuum acceleration. Measured values of the Hubble constant from SH0ES and Planck give us values that are a bit too high and a bit too low for the electron mass, respectively. When we input the precisely measured value of the electron mass into our equation, it yields the local Hubble constant as 71.3273 km s⁻¹ Mpc⁻¹, consistent with the Chicago-Carnegie Hubble Program.

Please cite  DOI 10.5281/zenodo.18917994 unless you are referencing specific equation numbers. Equation numbers have changed since version 3.1.0. Please contact the author if you require more information.