I thought of this very idea once as well. It is actually pretty cool to think about. The nice thing about it is the consistency of the time relative to the sun.

I thought of this very idea once as well. It is actually pretty cool to think about. The nice thing about it is the consistency of the time relative to the sun. No matter where you go the "relative time" would match up with the suns position (per the season). But I also realized that when scheduling events you have to consider the time adjustment depending on the distance east-west the event will be from you. Since the Earth is approx. 25,000 miles around in 24 hrs you have to adjust plus or minus 3 to 4 seconds per mile of travel (if I haven't miscalculated). Of course, when coordinating events more than a few dozen miles away, one would surely use "absolute time" instead. I think watches that had both would be awesome. You could identify your exact longitude by the difference between your relative time and the absolute time.