In order to measure a physical quantity the measuring device must possess that quality. Just as a meter rod is physically one meter.
The same for a clock. It must possess that quality we call time. I call this "matter" time in that the clock if it is in motion will have slower time than when at rest. And empty time is the fastest.
I believe if time slows down there must be a kind of fastest time point from which to start the slowdown.
Mitch Raemsch