Relativistic computers and the Turing barrier

We examine the current status of the physical version of the Church-Turing Thesis (PhCT for short) in view of latest developments in spacetime theory. This also amounts to investigating the status of hypercomputation in view of latest results on spacetime. We agree with [D. Deutsch, A. Ekert, R. Lupacchini, Machines, logic and quantum physics, Bulletin of Symbolic Logic 6 (3) (2000) 265-283] that PhCT is not only a conjecture of mathematics but rather a conjecture of a combination of theoretical physics, mathematics and, in some sense, cosmology. Since the idea of computability is intimately connected with the nature of time, relevance of spacetime theory seems to be unquestionable. We will see that recent developments in spacetime theory show that temporal developments may exhibit features that traditionally seemed impossible or absurd. We will see that recent results point in the direction that the possibility of artificial systems computing non-Turing computable functions may be consistent with spacetime theory. All these trigger new open questions and new research directions for spacetime theory, cosmology, and computability.