The current International Date Line and time zone system allows for an average of four minutes per degree of rotation of the earth, or 240 seconds.
If we were to revise our time system with a shorter second, this would create a rounding error with the existing longitude measurements. For every degree of rotation, then, the time would have to be 277.7777 (recurring) seconds, according to the 100 000 seconds in one day calculation.
We would have to address this issue, or simply recalibrate the lines of longitude. This is a work in progress.