Time without anything changing

Consider this valid argument:

1. Something that exists only for an instant cannot undergo real change.

2. Something timeless cannot undergo real change.

3. There can be no change without something undergoing real change.

4. There is a possible world where there is time but all entities are either timeless or momentary.

5. So it is possible to have time without change.

Premises 1 and 2 are obvious.

The thought behind premise 3 is that there are two kinds of change: real change and Cambridge change. Cambridge change is when something changes in virtue of something else changing—say, a parent gets less good at chess than a child simply because the child gets really good at it. But on pain of a clearly vicious regress, Cambridge change presupposes real change.

The world I have in mind for (4) is one where a timeless God creates a succession of temporal beings, each of which exists only for an instant.

(I initially wanted to formulate the argument in terms of intrinsic rather than real change. But that would need a premise that says that there can be no change without something undergoing real change. But imagine a world with no forces where the only temporal entities are two particles eternally moving away from each other at constant velocity. They change in their distance, but they do not change intrinsically. This is not Cambridge change, for Cambridge change requires something else to have real change, and there is no other candidate for change in this world. Thus it seems that one can have real change that is wholly relational—the particles in this story are really changing.)

All that said, I am not convinced by the argument, because when I think about the world of instantaneous beings, it seems obvious to me that it’s a world of change. But even though it’s a world of change, it’s not a world where any thing changes. (One might dispute this, saying that the universe exists and changes. I don’t think there is such a thing as the universe.) This suggests that what is wrong with the argument is that premise (3) is false. To have change in the world is not the same as for something to change. This is more support for my thesis that factual and objectual change are different, and one cannot reduce the former to the latter.