@qed.maths: How many Planck volumes fit in a proton? Its measured radius is r_p = 8.41 × 10⁻¹⁶ m, so V = 4πr³/3 = 2.5 × 10⁻⁴⁵ m³. The Planck length is l_P = √(ħG/c³) = 1.62 × 10⁻³⁵ m, so a Planck volume is l_P³ = 4.22 × 10⁻¹⁰⁵ m³ and N = V/l_P³ = 5.9 × 10⁵⁹. As a cube of the same volume the proton is n = 8.4 × 10¹⁹ Planck lengths wide: 66 halvings of its edge. From a person (1.7 m) down to that edge there are only 50. A model, not a map: the Planck length is a unit of length, not a measured pixel of space, r_p is a measure cited from memory, the proton has no sharp edge, and the Planck length is drawn as a dot. Checked by several routes per number and 51 assertions. #math #mathedit #mathanimation #fyp #planck

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Sunday 18 October 2026 07:32:59 GMT