I once thought (tweeted) that physics is 'explaining the explainable (computable) part of the universe' as the rest can be seen as random. Now I'm not sure about this anymore.
The simplest example of non-computable physics I could think of is a realworld super-Turing machine, i.e. a physical law that states that certain physical essembles, which are parametrized by finite strings, behave in a certain experiment in correlation with the halting property of the program described in the string. In a sense, there is similarity to computable physics, as we can start an infinite experiment using infinite ressources, where we ask the system for the halting state of every problem while simultaneously running the programs and see if they halt. If the theory holds true, we would expect to see an infinite number of confirmations (programs halting where the experiment says they would) and no refutation.
But as we can never confirm the law in the cases of programs which don't halt and no proof exists for their non-halting, we could also assume that the output for those programs is random.
Would that turn our theory into a computable (but non-deterministic) one? What frameworks exist to evaluate those questions? How would Solomonoff induction treat a realworld super-Turing machine?