So this would be a totally separate source of indeterminism than quantum mechanics. So you could have a schrodinger's rocket fired at a indeterministic 3-body system which means multiple sources of indeterminism interact.
Entropy could be viewed as the simple addition of information due to indeterminism.
How can causality survive in a universe like that.
That only matters if you assume infinite measurement accuracy, and the scientific method has never assumed that.
Even if we assume the world is 100% fully deterministic, as long as our measurements are not 100% accurate we will have some amount of measurement noise which is completely indistinguishable, even in principle, from true fundamental randomness.
In fact, fundamental randomness is much easier to work around than measurement noise, since there is no risk of it being correlated with your experimental design. In contrast, measurement errors are often correlated to the measurement method, which makes them much harder to eliminate statistically.
Doesn't the Turing halting problem also imply that (some) things are not predictable (the halting of certain algorithms)? But I don't think that interferes with causality.
Causality in physics survived the discovery of quantum uncertainty, though it was changed by it. What parts of current physics would have to be abandoned if our current inability to predict outcomes with complete precision turned out to be fundamental?
A non-deterministic universe can have two kinds of events: caused events, and random events. That is, an event can simply happen, but it can also be caused by another event. For example, a ball could start moving on a pool table all on its own (random), but still any ball that is hit by another ball would start moving because of the impact (caused).
If the fully random events are rare enough, you can even still determine causality using statistical tests, just like we do today. Of course, you can never be 100% certain, but that is to be expected. This is anyway how experimental science worked even when the world was assumed to be 100% deterministic: true randomness is not really different to experimental science than measurement noise.
Entropy could be viewed as the simple addition of information due to indeterminism.
How can causality survive in a universe like that.