Is Spacetime Smooth? Smooth: infinitely differentiable If there were a limit to the differentiability of matter's motion through time, I'd assume it would be at the quantum level (where particles are not actually point particles). Example: When I accelerate in my car, the value of my acceleration does not go from 0 to a. There is a non-zero jerk, the rate of change in acceleration. I'm fairly sure that I can also, with my human senses, detect a non-zero change in jerk (i.e. a higher nonzero derivative). My senses are not fine enough to detect much higher derivatives of motion, but I intuitively suspect that it would take infinite energy to move something in a spacetime that were not smooth. Is there a limit to the differentiation of motion through space with respect to time?