ABSTRACT
SOPHIA: The issue about time and change does not concern merely the case where the universe expands for an infinite time. It also concerns the case where the universe stops expanding after a finite time, starts to contract, and finally comes to an end in the big crunch. If time does not require change, time could continue flowing on after the universe has contracted to a small point and vanished. There could be empty time elapsing after the universe has ceased to exist. Let us examine this general question for starters: if all change comes to a stop at some time in the future, must time come to an end?
