The mutable scenario is nice because it neatly sidesteps most paradoxes.  Time CAN change, in this scenario, and the resulting timeline is {past previous to the change} + {changed timeline that includes a time traveler}.  Of course, in order to understand what’s going on in the changed timeline, we have to consider (as Mark and I discussed the other day) the two unique constructions of mutable time: replacement, and multiply.

The replacement timeline is where the changed timeline just wholesale replaces the original timeline, past the change.  Any time travelers will still “remember” the old unchanged timeline if they lived through it, because their proper worldline (their path through time) – although loopy – is still internally consistent.  This is the first major divergence from the immutable construction, because in that world, there only ever was one timeline (talking of “alternate histories” is sort of meaningless in immutable time).

The multiply timeline is the one I am fond of: in this construction, each change to the timeline splits it in two, and the two resulting timelines are separate universes, A and B.  What is the change we’re talking about?  The introduction of a time traveler, of course!  This implies that a time traveler can’t ever “return” to the original timeline from which he or she originated, but one can assume that if the time traveler is going back and wreaking havoc changing things, going back isn’t foremost in the planning.

It is interesting how the multiply timeline shares traits with the Many Worlds theory of quantum mechanics: basically, that multiple-possibility states (Schroedinger’s Cat is both alive and dead inside the box) do not become one or the other via observation, but exist simultaneously in separate, noninteracting universes.  Observation merely tells the observer which of the many possible universes he or she is in.  The relationship between a quantum observer and a multiply-timeline time traveler feels weird to me: they clearly share properties, but the time traveler seems both more powerful (can move from one universe to another) and more constrained (can’t get into universes where time travelers aren’t).

Time travel is fun to think about.