close, there's a regional local solar time (you could just steal timezones for this one) and then there is global time, which is what we go by for everything. Local solar time is essentially just an offset to the global time for the relative nature of local time to global time.
i like how whenever i mention this, people seem to think i want to get rid of time instead of timezones
What you're describing is LITERALLY the system we have. UTC is a global, coordinated time that tracks solar time to a precision of less than a second. As far as my computer is concerned, my time is UTC (technically GMT, but they both refer to the same time) minus 6 hours. We all could choose to say, "hey, wanna meet for dinner at 3AM?" and have that be a normal thing to say in my area, and an odd thing to say odd in Europe... but nobody wants that.
yeah, my problem is that nobody use UTC. And we have problems like gas pumps in finland breaking because they programmed timezones incorrectly.
I'm imagining something more fluid, where the time it is depends on exactly where you're standing and the position of the sun in relation to it. You'd need to factor the direction you're traveling as well as the distance whenever you went anywhere. We'd have a lot more intimate relationship with our current celestial situation.
that's basically why timezones were created. before then, every town had its own local time.