nLab Malament–Hogarth spacetime

Idea

It has been argued that there are spacetimes which are such that they allow trajectories on which a computing device could travel indefinitely together with spacetime points at which an observer could observe the whole infinite history of the computer in finite time. If this indeed were physically realizable it would to some extent physically implement what is called hypercomputation. This would contradict, to some extent, the physical Church-Turing thesis, which asserts that no physical process can realize a computer more powerful than a Turing machine.

References

Original articles include

• M. Hogarth, Does General Relativity Allow an Observer to View an Eternity in a Finite Time?, Foundations of Physics Letters, 5, 173–181 (1992)

Reviews include

• Wikipedia, Malament–Hogarth spacetime

See also

• Gabor Etesi, Istvan Nemeti, Non-Turing computations via Malament-Hogarth space-times, Int.J.Theor.Phys. 41 (2002) 341-370 (arXiv:gr-qc/0104023)

Discussion relating to the cosmic censorship hypothesis is in

• Gabor Etesi, A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory (arXiv:1205.4550)