Sure, but time is not a field. What it is, is hard to say, but field isn't it. It's more of a function of being on the surface of a hyperdimensional sphere.
That was kind of my point. Perhaps time is a field (meaning it can have different magnitudes, though likely constrained orientation). The thought is that gravity is actually the result of mass interacting with time fields. If that thought is anywhere near correct, then one could test that by measuring time flow (via accurate clock) in deep space versus one at sea level. I would expect that two perfect clocks, one at sea level, one at 175,000 ft orbit would read one second different after about 86 years (the clock at sea level lagging the one in space). Has this difference ever been measured?