Planck length

Planck built his natural units in 1899, a year before he invented the quantum, by asking what lengths, masses and times can be assembled from G, c and h alone. The answer for length is 1.6 × 10⁻³⁵ m: twenty orders of magnitude smaller than a proton, and about 10⁻²⁰ times any distance the LHC can resolve. Probing it directly would need a collider of galactic proportions.

The physical claim is that at this scale the Schwarzschild radius of a particle and its Compton wavelength coincide, so you cannot localise anything more finely without making a black hole — spacetime itself presumably stops being smooth. String theory and loop quantum gravity both place their structure near here, and black-hole entropy counts Planck areas on the horizon. Resist the common overreach: nothing in established physics says space is pixellated at l_P; it is where our theories are known to fail, not a measured grain size.