Physicists have said that time is not continuous, but moves in small increments. The smallest theoretical unit is called Planck time and is roughly the amount of time it takes from the moment my hand touches the door knob until my dogs start barking.
I'm not sure that there is a longest theoretical unit, but we took a stab at it at the post office this morning. Our recent inspections were thrown out in part because we received inadequate training in the proper way to fill out form 1838-C which accounts for every nanosecond of a carrier's time. We spent one and a half hours going over the form line by line, including lines that aren't there (line 20) and lines that refer to functions we haven't had in over 20 years (line 17, strapping out time). To plagiarize another writer, it began to seem that we would be delivering mail using continental drift.