The existence of Brownian motion is the physical proof for the existence of both atoms and molecules. At the later years of the 19th century, Boltzmann theorized the existence of atoms and molecules. Its conceptual development was opposed by the existing scientific positivist authorities headed by Ernst Mach (1838-1916). Consequently, continued intellectual isolation caused the ill and depressed Boltzman to kill himself in 1906, fully unaware of Einstein’s vindication a year earlier. This was accomplished by Einstein’s annus mirabilis of 1905. The same year he published the special theory of relativity and the Nobel Prize paper in photoelectric effect. The relevant paper on Brownian motion was titled: On the motion of small particle suspended in stationary liquids required by the molecular-kinetic theory of heat. By this theory, Einstein was also unaware that these phenomena were already observed and studied in detail by the Scottish botanist Robert Brown (1773-1858 ) in 1828. The beauty of Einstein’s analysis was the derivation of the formula for the mean squared distance traversed by the atoms or molecules within a specified time period: <��²>=������/�������� where �� is Boltzmann’s constant, �� is the viscosity of the liquid, �� is the radius of each atom or molecule, �� is the time, �� is the absolute temperature. Nevertheless, if Einstein’s formula gives values in the order of Planck length then it can be used to describe the Brownian motion of space-time charges of the quantum vacuum fluctuations of the squares of zero-point energies.