The diffusion equation, a mathematical tool describing how particles spread out in space, has long painted a paradoxical picture: a disturbance, like ripples on Water, instantly engulfs the entire universe. This challenged the theory of relativity, which holds that nothing can move faster than light. The puzzle was deepened by the deep connection between diffusion and the growth of entropy — a measure of disorder in a system that, according to the second law of thermodynamics, inexorably increases. But if we sharpen our theoretical "snapshot" and zoom in to the microscopic level, it becomes clear: each individual particle moves strictly according to Einstein's laws, and there is no violation. The apparent superluminal speed is an artifact arising from too coarse, averaged description, much like a blurry photograph creates the illusion of motion where there is none.
Old paradoxes arose from a wrong perspective: the mathematical machinery of diffusion allowed "snapshots" that cannot be obtained in real experiments. In the real world, any signal carrying information or energy always propagates slower than light. To capture this, one must track not the averaged thermal motion but the movement of the particles themselves — then the illusion of instantaneity vanishes, and everything falls into place.
The thermal speed of water molecules is about 500 m/s, which is 600,000 times slower than light. In practice, diffusion never really violated the theory.