The base-2 discrete scaling model known as Notation-67 is Planck length × 2⁶⁷ ≈ 2.385 × 10⁻¹⁵ m [1].
The second value, (rₑ ≈ 2.818 × 10⁻¹⁵ m at Notation ~67.24), represents the classical electron radius. [1]
Here is how both numbers compare:
- Notation-67 (\(\approx 2.385 \times 10^{-15} \text{ m}\)): In models like the Discrete Geometric Origin of the Standard Model, this notation is a fundamental base-2 geometric scale that brackets the classical electron radius, providing a natural ultraviolet cutoff for electromagnetic interactions.
- Classical Electron Radius (\(2.81 \times 10^{-15} \text{ m}\)): Also known as the Lorentz radius, this is a physical length scale derived by setting the electrostatic potential energy of a point charge equal to its rest-mass energy (via \(mc^{2}\)). [1, 2, 3]
NOTES: Directly related to the base-2 scaling models, the first value is the specific definition of Notation-67. [1]
- Discrete Geometric Origin of the Standard Model – 81018Apr 5, 2026 — 1. The Atomic Anchor: Why 137? * Planck Length (lP): 1.616255×10−35 meters. * Ratio: rₑ / ℓₚ ≈ 1.7435 × 10²⁰ *
- Flaw in the radius of a spherical electron model (classical electron radius).
- Dive into the Quantum universe where size truly defies imagination! Atom: The typical size of an atom is around 10^-10 meters. These tiny units form the building blocks of all matter. Nucleus: The nucleus of an atom is significantly smaller, approximately 1.2 x 10^-15 meters. This dense core contains protons and neutrons. Neutron-Proton: Neutrons and protons are about the same size as the nucleus, roughly 10^-15 meters. These particles are crucial for the structure of atoms. Quark: Quarks, the fundamental constituents of protons and neutrons, are considered point particles with no known internal structure. Their size is often described as smaller than 10^-18 meters, which represents our current limit of measurement rather than a definite size. Electron: Electrons are also considered point particles in quantum mechanics. They don’t have a definite size in the classical sense. The classical electron radius (about 2.8 x 10^-15 meters) is a theoretical concept and doesn’t represent a physical size. String (in string theory): Hypothetical strings, proposed in string theory, are believed to be incredibly small, on the order of ~10^-35 meters (close to the Planck length). Jul 10, 2025 — The classical electron radius is roughly 2.8 x 10^-15 meters. This value is not a direct measurement of the electron’s physical size.
- This chart will have several addendums: