Ah, but then whose time would that be? How do you keep track of what solar time was parallel to 'your' time?
Time is such a fickle thing. Every atom in the universe knows what time it is, but between the effects of gravity, the speed of light and some quantum stuff it is amazing that we can agree on this at any level at all. I spent a lot of time earlier this year getting some ultra stable clocks to run without shelling out 5 digits and it was a very interesting little detour. Eventually I settled on an old atomic clock module from a decommissioned cell tower, not quite 'miniature' but small enough (I've seen some of the newer ones and they are incredible). The thing is precise enough to show the day/night deviation in phase from DCF77 to my home a few hundred km away.