>Prove that planck lengths aren't pixels
The planck lenght is simply where physical measurement becomes meaningless because beyond that scale we have nothing to measure things with.
Suppose you were to measure an object by firing photons at it and see if they bounce back. The smaller the photon, the smaller the object you can measure, like trying to pinpoint the exact location of a tree trunk by throwing a baseball at it, or a marble, and listening for a sound of impact. Obviously the smaller your projectile, the more accurately you can measure because it's easier to miss.
So, the smaller the wavelenght of a photon, the tighter its wavepacket, or the smaller its size, but as the wavelenght decreses the energy of the photon increases, and beyond the planck scale the energy of the photon would be enough to turn it into a tiny black hole. (proof: http://en.wikipedia.org/wiki/Planck_length#Value)
It doesn't mean that things smaller than the planck lenght cannot exist, it means that they are physically unreal from our point of view because we have no physical way of interacting with them. Many physics theories toy with the idea that there exists stuff below the planck scale that just occasionally pops into our reality by becoming larger, in the form of e.g. virtual particles, which would explain the Casimir effect.