Such a statement just means they can implement computation in this formalism. Not a huge surprise as you can implement computation with many other structures.
This is being downvoted, but I'd like an explanation of what the alternative is. Can someone to explain how this result differs from a claim "I can build a computer which turns a light on when a given program terminates, so therefore 'light on-ness' is undecidable".
Whether a light is on or off is contingent. This is more like proving the light would always be on as a fundamental fact of basic physics. Even if it were done by showing that the existence of a computer connected to the light, proving that from first physical principles would be a big achievement.
The Church-Turing thesis is an (unprovable) statement of faith, not a mathematical theorem.
Effectively, it states that "all algorithms can be computed on a Turing machine, and vice-versa".
Note that this thesis is not as radical as it first sounds; I'm assuming that if we ever do find a way of computing functions that cannot be computed on a Turing machine, then we'll just call it something else, not an 'algorithm'. This would make the Church-Turing thesis just a tautological circular definition.
> it states that "all algorithms can be computed on a Turing machine, and vice-versa".
It is about algorithms of a certain kind, the kind of computation that we do when we, say, factor polynomials or check a step in a euclidean geometry proof. That is the kind of computation called for in the Entscheidungsproblem. Turing's analysis of that kind of computation was very persuasive, and consequently influential.
But as to whether there is more, whether we can go farther with some kind of analog computation involving lasers and interference, or some kind of quantum stuff ... well, maybe. It doesn't seem impossible that Turing, in the 1930's, lying on the grassy river bank after a hard run and reflecting on what a device can compute, did not imagine it all. To date (as I understand it) no analysis of what can be done with a real device under current physics has for the community of experts the same persuasiveness of Turing's work.
This paper seems to me to at least hint that there may be things that nature computes, but which no Turing machine can compute. It makes me wish to understand the physics.
