On Friday, February 23, 2018 at 11:12:32 AM UTC-6, Bruno Marchal wrote:
> On 23 Feb 2018, at 17:15, Lawrence Crowell <goldenfield...@gmail.com
> The MH spacetime in the case of the Kerr metric does permit an observer in
> principle to witness an infinite stream of bits or qubits up to the inner
> horizon r_- that is continuous with I^+ in the exterior spacetime. This
> means due to spacetime effects one could witness the diagonalization in a
> Zeno machine context. For instance a switch that is switched one in one
> second, off the next half second, on in the next quarter second and so
> forth will presumably have a final state. However, what does prevent this
> in a fundamental way is that a switch flipped in this chirped frequency
> will diverge in energy and become a black hole before returning a result.
> We could of course avoid the black hole with a ball that bounces, but of
> course one does not get an infinite number of little bounces at the end.
> Because of this an observer could in principle witness a universal Turing
> machine emulate all possible Turing machines. Thinking according to TMs is
> for me a bit simpler, but this does illustrate one could get around Godel.
> I am not sure the observer should not be itself implemented in the MH, and
> its first person perspective might not allow him to see the TM emulating
> all TMs. But even if it did, that would only be the implementation of a
> halting algorithm, which overcome the Turing limitations, but not the Gödel
> one: you will only get the sigma_truth completely, but “time” itself is
> such an oracle, and again, I am not sure if such an observer does not, from
> its personal point of view, have to live an infinite life to assess the
> result. But I have looked at the MH paper a long time ago, so take this
> with caution. Note that Gödel incompleteness cannot be escaped by *any*
> means, even infinite means, unless you directly refer to the semantics,
> which is not an effective process.
> However, quantum mechanics as I illustrate seems to throw a spanner in the
> works. This breaks the continuity between r_- and I_+. It also means the
> inner horizon is built from quantum fields from the exterior in ways that
> generates a mass inflation singularity. This is interesting to ponder with
> respect to the connection between quantum mechanics and general relativity.
> Yes, very interesting.
> In fact I think the two are simply aspects of the same thing. This means
> in some way the incompleteness theorems of Godel are involved with the
> foundations of physics.
> Very glad to hear that.
> Note that with Mechanism, incompleteness is responsible for the whole set
> of accessible phenomenologies including the physical one, so yes, it is
> hoped that physicists will someday study incompleteness (in a more serious
> (valid) way than Penrose which has detracted many physicists from Gödel,
> and many logicians from physics).
In effect quantum mechanics enters into the picture of MH spacetimes to
prevent physics from providing a loop hole out of Godel's theorem.
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