Well there is such a thing as Planck units, including among other things the Planck length and Planck time. These are the shortest that are physically possible; to put it simply, Planck time is the shortest amount of time in which anything can happen. It's, quite literally, a 'tick' of the clock of the universe, much like FPS is for DF.
I'd say more like the shortest
observable tick of the clock/difference in position. I subscribe to the idea that sub-Planck physics is a deterministic but non-trivially complex environment which can only be observed at a resolution >= Planck*[x,y,z,t,etc]. A continuous and wave-function (or several, overlaid upon each other) thus appears as discrete an 'unpredictable' phenomena in time and space, inclusive of the kind of particle/anti-particle pairs that are key to Hawking radiation, that are (maybe) local maxima or minima in either the bare continuous waveform (as measured against one or more or all of the available dimensions, and possibly at higher orders or derivation).
That's if the universe's intrinsic mathematics is anything like the pure maths we like to work with, of course. I think I've mentioned before the possibility of a Conway's Game Of Life universe simulated by us, in which intelligent creatures could 'arise', but have no understanding of the silicon technologies and coding techniques used to implement their world, and who would have their own 'Planck distance' and 'Planck time' limits to detection that are greater than the cell-size/tick-length that we, as almighty lords and rulers of their universe, actually know to be the Truth. The scientific approximations adopted by the denizens to explain the world around them would by far more distant than Quantum Theory is to the Newtonian kind, and remain so, even when at their equivalent of Quauntum 'understanding'. Mainly because I suspect that our Quantum Theory is also a significant distance away from the Truth, in whataver form that may be. (Although I shall probably never accept the possibility of there being a set of Lord and Rulers behind us. Because then we're into Turtles All The Way Down territory.)
There, a little light philosophy to help me wind down for the day.