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created a minimum at Penrose-Hawking singularity theorem
Added some references to computable physics
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.
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.
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.
Do you have a feel for how this looks in SDG, e.g. via the work of Tim de Laat.
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…
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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