[adrianN]

There is no algorithm for checking whether a system can solve the halting problem or not, the reduction to the halting problem is quite simple. But that's besides the point.

If you found something that could solve the halting problem and you're lucky enough to be able to prove it for this special case, that would just mean that the assumption that everything physical can be computed by a Turing machine is wrong. It works the same way with anything else that we think of as "impossible". If you observed an apple falling towards the sky that doesn't mean that the apple is non-physical, it just points to a serious flaw in our understanding of gravity. Experiments trump all physical theories.