planck ‹p{{n}}› planck · the stack, real, from 1 ℓP upn = 10²⁵
26.60
view width = n ℓP–
energy to see this size–
light crosses it in–
gravity vs electric, 2 protons8×10⁻³⁷
each sheet (real)256 Na⁺ · 256 Cl⁻
gold core (real)512 atoms, 1 layer
0.01 eV neutron wavelength2.860 Å
gold atom spacing2.884 Å
neutron caught by 1 gold layer1.9×10⁻⁷
its catch size (radius)70.7 fm
gold nucleus (radius)7.0 fm
Planck energy1.22×10²⁸ eV
the stack as small and as real as it goes. n is how many Planck lengths wide the view is: n = 1 is 1.616 × 10⁻³⁵ m, n = 6.2 × 10³² is a centimetre. a −+−+ sheet of 512 charges, each +1 or −1, is in real matter a sheet of rock salt: 256 sodium ions and 256 chloride ions, 2.82 Å apart, 16 × 32 = 4.5 × 9.0 nm. the gold core with the sheets' 512 is one layer of 512 gold atoms, 2.884 Å apart: 2.3% off the salt, close enough to sit on it. the layer gap (2.9 Å) is my choice. at the scaler's 0.01 eV a neutron is a wave 2.860 Å long, 0.8% off the gold spacing: it doesn't hit the core, it diffracts off it (first order at 46° from the salt's 3.99 Å surface cell; D₂ at 21°, the water ion at 9.5°). its chance of being caught by one gold layer is 1.9 × 10⁻⁷, though the gold nucleus looks ten times wider to it (70.7 fm) than it is (7.0 fm). below about 10⁻¹⁹ m nothing has been measured; from there down to 1 ℓP (16 powers of ten) the page draws nothing it can't back. gravity, weaker than the electric force by 10³⁶ between two protons, only catches up near 10¹⁸ GeV, within a factor of ten of the Planck energy.