This is a short note on a new way to describe Haug's newly introduced maximum velocity for matter in relation to the Schwarzschild radius. This leads to a probabilistic Schwarzschild radius for elementary particles with mass smaller than the Planck mass. In addition, our maximum velocity, when linked to the Schwarzschild radius, seems to predict that particles just at that radius cannot move. This implies that radiation from the Schwarzschild radius not can undergo velocity time dilation. Our maximum velocity of matter, therefore, seems to predict no time dilation, even in high Z quasars, as has surprisingly been observed recently.