Tuesday, August 11, 2020

Leaving space

Suppose that we are in an infinite Euclidean space, and that a rocket accelerates in such a way that in the first 30 minutes its speed doubles, in the next 15 minutes it doubles again, in the next 7.5 minutes it doubles, and so on. Then in each of the first 30 minutes, and the next 15 minutes, and the next 7.5 minutes, and so on, it travels roughly the same distance, and over the next hour it will have traveled an infinite distance. So where will it be? (This is a less compelling version of a paradox Josh Rasmussen once sent me. But it’s this version that interests me in this post.)

The causal finitist solution is that the story is impossible, for the final state of the rocket depends on infinitely many accelerations, and nothing can causally depend on infinitely many things.

But there is another curious solution that I’ve never heard applied to questions like this: after an hour, the rocket will be nowhere. It will exist, but it won’t be spatially related to anything outside of itself.

Would there be a spatial relationship between the parts of the rocket? That depends on whether the internal relationships between the parts of the rocket are dependent on global space, or can be maintained in a kind of “internal space”. One possibility is that all of the rocket’s particles would lose their spatiality and exist aspatially. Another is that they would maintain spatial relationships with each other, without any spatial relationships to things outside of the rocket.

While I embrace the causal finitist solution, it seems to me that the aspatial solution is pretty good. A lot of people have the intuition that material objects cannot continue to exist without being in space. I don’t see why not. One might, of course, think that spatiality is definitive of materiality. But why couldn’t a material object then continue to exist after having lost its materiality?


Peter said...

Once the rocket is no longer spatially related to anything outside of itself, could it still be temporally located to anything? If not, then we seem to have a case of something temporal causing a real change in something atemporal (the last acceleration of the rocket before it becomes atemporal causes the atemporality of the later rocket). Does this worry you, or is there a way around this?

IanS said...

On causal finitism, note that even ordinary real rockets accelerate at an infinite number of instants. So care is needed in defining and counting causes. If you allow continuously variable thrust, it does not seem easy to divide the plausible cases from the paradoxical ones by counting alone.

JCarver said...

"over the next hour it will have traveled an infinite distance"

Isn't it natural to think that an infinite distance can't be traversed, at all, no matter how fast you go?

Alexander R Pruss said...


Causal finitism is indeed costly: one has to deny that ordinary causal processes involve an infinite number of instants of causation. This can be done by holding that time is discrete or by one of the interpretations of physics in my infinity book.