Einstein–Perrin dilemma on the Brownian motion (Avogadro’s number) resolved?

Abstract

The general recognition of the existence of atoms and molecules occurred only at the beginning of the twentieth century. Many researchers contributed to this, but the ultimate proof of the molecular nature of matter that convinced even the last sceptics was the confirmation of Albert Einstein’s statistical-fluctuation theory of Brownian motion, a part of his comprehension of interdisciplinary atomism, by Jean Perrin’s experiments on colloidal gamboge particles. Einstein noticed a difference between the values of Avogadro’s constant derived from Perrin’s experiments and Planck’s calculation from black-body radiation. Einstein assumed the incorrectly evaluated size of the gamboge spherules to be a culprit of the difference and asked Perrin to check the assumption with additional experiments and using the viscosity formula introduced in his own dissertation. The result was a discrepancy that neither Einstein nor Perrin settled any further. In this communication, based on the survey of developments in colloid and polymer science and their comparison with relevant experiments, an explanation of the dilemma is given that now, after more than a century, proves Einstein correct. The comparison was de facto possible during his lifetime.