Planck length
If the speed of light "c", were somehow suddenly cut in half and changed to "c" (but with the axiom that "all" dimensionless physical quantities remain the same), then the Planck length would "increase" by a factor of 2 from the point of view of some unaffected observer on the outside. Measured by "mortal" observers in terms of Planck units, the new speed of light would remain as 1 new Planck length per 1 new Planck time – which is no different from the old measurement. But, since by axiom, the size of atoms (approximately the Bohr radius) are related to the Planck length by an unchanging dimensionless constant of proportionality: