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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 15th 2014
    • CommentRowNumber2.
    • CommentAuthorspitters
    • CommentTimeMar 16th 2014

    Added some references to computable physics

    • CommentRowNumber3.
    • CommentAuthorspitters
    • CommentTimeMar 17th 2014

    Apparently, there are deep connections between this theory, the cosmic censorship conjecture and computability; see this paper. I am not able to judge this paper quickly. If this mathematics works out, it should be interesting to understand how this allows us to decide the consistency of ZFC.

    • CommentRowNumber4.
    • CommentAuthorspitters
    • CommentTimeMar 17th 2014

    Updated computable physics with a quote from Geroch and Hartle, who are also thinking in the Type-I way.

    We propose, in parallel with the notion of a computable number in mathematics, that of a measurable number in a physical theory. The question of whether there exists an algorithm for implementing a theory may then be formulated more precisely as the question of whether the measurable numbers of the theory are computable. We argue that the measurable numbers are in fact computable in the familiar theories of physics, but there is no reason why this need be the case in order that a theory have predictive power. Indeed, in some recent formulations of quan- tum gravity as a sum over histories, there are candidates for numbers that are measurable but not computable.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 17th 2014
    • (edited Mar 17th 2014)

    Thanks for the pointer to the article by Etesi! That looks good and insightful. I have added a pointer to Malament–Hogarth spacetime and to cosmic censorship hypothesis.

    • CommentRowNumber6.
    • CommentAuthorspitters
    • CommentTimeMar 17th 2014

    Do you have a feel for how this looks in SDG, e.g. via the work of Tim de Laat.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMar 18th 2014
    • (edited Mar 18th 2014)

    Horizons, cosmic censorship and these hypercomputing spacetimes are all crucially global aspects of spacetimes, which cannot be detected by local, much less by differential observations. SDG as such won’t help here. Relevant is the causal structure of spacetime, its causet poset. That might be something to explore…

    • CommentRowNumber8.
    • CommentAuthorspitters
    • CommentTimeMar 18th 2014

    OK, so we should be using this domain theory PDF, but perhaps also presheaves on causal sets, as here. Smolin was quite excited about this at some point. There is a bit more work in this direction.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMar 18th 2014

    The first PDF you link to looks very reasonable. Something along these lines might be interesting to explore regarding hypercomputing spacetimes.

    I’d be very careful with these speculations about what this means for quantum gravity, though. There has been more excitement than results.

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