There could still be a persistence-based cosmological argument even if there were existential inertia

Suppose that today at noon, Felix the cat enters a time machine and travels back to the time of the dinosaurs, where he spends the rest of his life hunting small reptiles. According to the doctrine of existential inertia, objects have a blockable tendency to continue existing.

Question: If Felix has existential inertia, was his inertial tendency to continue existing blocked at noon when he time-traveled to the past, and hence failed to exist past today’s noon?

My intuition is that the answer is negative. Existential inertia seems to me to be about “having a future” and today at noon, Felix does have a future, even if that future is in the distant past. In other words, if there is such a thing as existential inertia, it concerns what I call “internal” rather than “external” time.

Beyond mere intuition, here is a reason for a defender of existential inertia to agree with me. If existential inertia concerns external time, then in a relativistic world it is a doctrine that says that an object that exists at point z of spacetime has a tendency to exist somewhere or other in the forwards lightcone centered on z. But there is something odd about a metaphysical principle, like existential inertia is supposed to be, that impels an object to continue to exist in some location or other in some infinite set of locations (say, the infinite number of locations in the forward lightcone one second away from the present in some reference frame), without impelling the object to exist in any particular location, or even imposing any kind of probability distribution on where it is to exist. Moreover, it is not clear why the forward lightcone would be so metaphysically special that a fundamental metaphysical principle would coordinate with lightcones so neatly.

Perhaps this is not completely convincing. But it has some legs. There is thus some reason to think that existential inertia applies to internal rather than external time. But if so, then existential inertia has not removed all that needs to be explained about persistence. For a normal cat not only tends to continue to exist in its internal-time future, but also tends to continue to exist in its external-time future, since normally there is no time travel. And this external-time persistence is not explained by existential inertia, if existential inertia concerns the external-time future. So there is a persistence to explain, and theism offers an explanation. There is still room for an argument for theism from persistence.

Here is a closely related explanatory problem: Why is it that internal and external time tend to be correlated, so that internal-time persistence tends to imply external-time persistence?

Suppose that, contrary to my relativity theory intuitions, one insists that existential inertia concerns external-time persistence rather than internal-time persistence? Then there is still something to be explained: the correlation between internal and external time.