Status of time in a Universe at maximum entropy In billions and billions (thanks Carl Sagan) of years I have heard that atoms will lose energy and their temperature will approach absolute zero and thus their entropy will approach a minimum level. If we take this to be true then it logically follows that there will be no way to distinguish one instant of time from a second instant of time.
So my question - is time still flowing? If a theoretical time traveler were to arrive in this period would time "Start" again until that object reached a minimum level of entropy?
 A: It's important to distinguish between time and the flow of time. In any universe we need four numbers to uniquely identify a spacetime point, and we conventionally choose one of the coordinates to be time and the other three space so the location of a spacetime point is given by $(t, x, y, z)$.
Assuming the universe doesn't hit a singularity then for every spacetime point $(t, x, y, z)$ there is a point $(t+dt, x, y, z)$ i.e. a point at the same place in space but a time $dt$ later. The metric tensor tells us how the spacetime changes between the two points.
So given that for any time $t$ there is a later time $t + dt$, the question is whether this constitutes a flow of time even if nothing in the universe has changed between $t$ and $t+dt$. My view is that there is still a flow of time because (apart from a few special cases) it is impossible for nothing to change between the times. Spacetime is still expanding so even at maximum entropy the scale factor changes between the two points even if no observer can detect the change.
A: I think the assumption of you question is wrong because entropy only increases. Indeed temperature in the universe tends to approach absolute zero and it will look less complex, but, every bit of radiation left will be so vastly distributed over space in a disordered way that you cannot say that the entropy is getting smaller.
That aside, considering that the universe indeed reach absolute zero and maximum entropy, time would stop flowing. The arrow of time is determined by the increase in entropy, if entropy stops increasing time stops ticking.
