The most cursed time idea: infinite time zones and variable-duration time measurements.
Utilizing very accurate GPS, each chronometer identifies its exact coordinates, and thus the local sunrise/sunset times. Let 0600 equal sunrise at your location, and 1800 equal sunset at your location. The day is then divided into 12 day-hours and 12 night-hours, each of which are divided into to 60 day/night-minutes and 60 day/night-seconds.
Call it Neo-Sundial Time.