Predictability Problems in Physics

[PdotdQ]

@dga471

it seems to me that even if there are cases in classical physics (space invaders, Norton’s dome, etc.) which are not predictable, most other situations we encounter in daily life are in principle predictable and deterministic.

Let me add a quick comment on this:
Norton’s dome is indeed not an issue, because it requires very specific configurations. However, space invaders are problematic because one does not know when/whether the invader appears prior to it appearing. In other words, in a world with only classical mechanics without SR, there is no way to know that we are in a daily life situation that are in principle deterministic.

@dga471

In the case of quantum mechanics, nothing has P(X) = 1. Thus, nothing is teleological.

As I mentioned in a previous post, if one gives up locality, it is possible to have a deterministic QM. One can also have a (in my opinion nonelegant) deterministic Relativistic QM. I believe the jury is still out on whether there is a field theory extension to deterministic QM. However, giving up locality might run afoul on how one would evaluate Eric’s P(X)'s in practice. I am not sure on this point.

@swamidass

I dispute this. Weather is not predictable. People are not predictable. Stocks are not predictable. All these are chaotic systems too. A large proportion of what we deal with in life is neither predictable nor deterministic from a human point of view.

Chaotic systems are an important example. They are, in principle, predictable. However not practically so, because we do not have perfect knowledge.

Chaos is an example where predictability can fail in the following sense: given any computational resolution, for a chaotic system I can come up with a configuration that a computer with said resolution will get the time evolution wrong.

I agree with @dga471 that we should separate determinism and predictability. However, I believe that if either determinism or predictability fails, Eric’s P(X) program is not tenable. If determinism fails, P(X) is never 1, while if predictability fails, it is not possible to evaluate P(X) to test the theory.