Forever Is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes
Earman (John) & Norton (John D.)
Source: Philosophy of Science, Vol. 60, No. 1 (Mar., 1993), pp. 22-42
Paper - Abstract

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Authors’ Abstract

  1. The standard theory of computation excludes computations whose completion requires an infinite number of steps.
  2. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length.
  3. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

Sections
  1. Introduction.
  2. Pitowsky Spacetimes
  3. Malament-Hogarth Spacetimes
  4. Paradoxes Regained?
  5. Characterization of M-H Spacetimes
  6. Are Supertasks in M-H Spacetimes to be Taken Seriously?
  7. Can M-H Spacetimes be Used to Gain Knowledge of the Truth- Value of Fermat's Conjecture?
  8. Can gamma-1 Carry Out the Assigned Infinite Task?
  9. Conclusion

Authors’ Conclusion
  1. Thomson lamps, super-pi machines, and Platonist computers are playthings of philosophers; they are able to survive only in the hothouse atmosphere of philosophy journals. In the end, M-H spacetimes and the supertasks they underwrite may similarly prove to be recreational fictions for general relativists with nothing better to do.
  2. But to arrive at this latter position requires a resolution of some of the deepest foundations problems in classical general relativity, including the nature of singularities and the fate of cosmic censorship. It is this connection to real problems in physics that makes them worthy of discussion.

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