A new estimation of physical time in Monte Carlo simulations is derived from the requirement that the self-diffusion coefficient measured by Monte Carlo and molecular dynamics simulations have the same value. The dynamics of the particles using both simulation methods are compared by measuring velocity autocorrelation functions. Simulations of pure Lennard-Jones liquids and a binary Lennard-Jones solution show that at small time scales the particle dynamics are different, but at larger time scales they become similar. As a critical test crystal growth from the melt is simulated using the proposed time scale. Both for Monte Carlo and molecular dynamics a linear dependence of the growth rate on undercooling is found and the measured proportionality constant (the kinetic coefficient) is equal to within 6%, i.e., within the statistical error of both methods.