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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.
added pointer to today’s
added pointer to the recent preprint:
(by the discoverer of the Kerr black hole-solution, now aged 89)
doubting the conclusion of Penrose & Hawking’s singularity theorem.
If I understand well (just from cursory reading, and not being an expert on the matter), the main point of the article is to highlight that Penrose’s theorem derives (at best, Kerr has qualms about that, too) the existence of “finite affine length lightrays”(the “FALL”s appearing throughout the article) but not from this the fact that these end in a singularity, and hence not the existence of the singularity. Kerr claims to give counterexamples of FALLs not ending in a singularity (though in contexts where there is a singularity, elsewhere, if I understand well).
Another point seems to be the argument that singularities should not be expected to form “in reality”. Here I am unsure whether this is meant as an argument about vanilla GR or about some enhancement (cf. p. 15). The second point of view would be rather less iconoclastic, if not mainstream.
fixed bad Wikipedia link
from
- Wikipedia, Penrose-Hawking singularity theorem
to
- Wikipedia, Penrose-Hawking singularity theorems
Both forms work in the nForum but only the 2nd works in the nLab. The problem is the “en dash” character in the Wikipedia link. It is best to copy and paste the URL rather than manually trying to encode the page name.
Why an “en dash”? Wikipedia follows the somewhat general convention that it should be used to join two distinct people as opposed to using a hyphen in a hyphenated last name (even though the last names come from distinct people).
I see that informed commentary on Kerr’s paper is made in reply to Physics.SE:q/790724, especially Physics.SE:a/796154 which confirms my reading in #11.
added pointer to the original texts:
Roger Penrose: Gravitational Collapse and Space-Time Singularities, Phys. Rev. Lett. 14 (1965) 57 [arXiv:10.1103/PhysRevLett.14.57]
Stephen W. Hawking, George F. R. Ellis: The large scale structure of space-time, Cambridge Univ. Press (1973, 2010) [doi:10.1017/CBO9780511524646, Wikipedia entry]
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