In 1964, C. Alden Mead published a
paper in which he determined the effect of gravity on a phenomenon called diffraction, which describes what happens to light when you send it through a small aperture. Because gravity is so incredibly weak compared to the force that governs the behavior of light (the electromagnetic force), its effect is completely ignored in diffraction calculations. But Mead was curious about quantifying gravity's negligible effect. When you scatter a particle of light off another particle — say an atom — the atom's gravitational attraction to the light particle causes an intrinsic uncertainty in the atom's location. Mead used the uncertainty principle and the gravitational effect of the photon to show that it is impossible to determine the position of an object to a precision smaller than the Planck length.
So why is the Planck length thought to be the smallest possible length? The simple summary of Mead's answer is that it is impossible, using the known laws of quantum mechanics and the known behavior of gravity, to determine a position to a precision smaller than the Planck length. Pay attention to that repeated word "known." If it turns out that at very small lengths, some other version of quantum mechanics manifests itself or the law of gravity differs from our current theory, the argument falls apart. Since our understanding of subatomic gravity is incomplete, we know that the statement that the Planck length is the smallest possible length is on shaky ground. Still, until a better theory of quantum gravity is devised, the Planck length is the best estimate we have for a minimum length.
