I loved the maths that Goedel produced and his cosmological conclusions. Having said that, there is a good reason that Wheeler was recognized for the Wolf prize in physics, and Goedel was not. Goedel was awarded, however, the National Medal of Science! More goodies, I think, when our species can make the proper machinery, to test Wheelers' Geometrodynamics. Lots of goodies there,! Not just to answer 'deep questions.' On Wednesday, April 7, 2021 Lawrence Crowell <[email protected]> wrote: I am not following this thread any more. I noticed Bruno writing about Gödel's theorem and mechanism. The role of such is hard to nail down. My take on the role of undecidability theorems in physics is below. There is a famous story that JohnWheeler asked Kurt Gödel whether his incompleteness theorems played any role inquantum mechanics, where upon Gödel threw Wheeler out of his office. Most usualanswers about whether Gödel's theorem plays a role in physics is met withnegativity by both mathematicians and physicists. Gödel's theorems are about amathematical system with the power of first order logic or that is recursive notbeing able to make a complete list of all provable propositions about itself.Gödel showed this by illustrating how a free variable in a predicate can be theGödel number for that predicate, which as itself a Gödel number is outside alist of such number in the manner of Cantor's diagonalization. This is Gödel'sfirst theorem. The second theorem says that if there are unprovable theorems,which tacitly state their unprovability they must be true. This is because ifthey are false it leads to a contradiction that they are provable. However, thefirst theorem is most important here.
This would pertain to physics withthe question of whether physics can ever represent itself within itself. Thisruns into some issues, where Godel's theorem and the Cantor diagonalizationimplies an axiomatic system that has an infinite number of propositions. If weconsider a proposition as some set of bits or quantum bits, then clearly whatis accessible to any observer is finite. In fact the universe appears toconspire mightily to prevent any observer from accessing an infinite amount ofanything. Singularities are hidden behind event horizons, even if theobservable universe is infinite its expands in a way that leaves only a finiteportion observable. We may consider the issue ofhypercomputation. A trivial case of this is a switch that flips every halvingof each interval of time, so if the initial interval is a second then aninfinite number of switch flips occur in the next second. Malement-Hogarthspacetime have properties with Cauchy horizons that pile up incoming signals.It is then possible for an infinite computation to occur that can be accessedby an observer in a finite time. This hypercomputation permits a machine tocompute beyond the limits of the Church-Turing thesis. However, these spacetimesmay be pathological. In the case of the infinite flipping of the switch, theasymptotic divergence of the frequency of switch flipping means the ultimatelimit is energy large enough to cause the switch to become a black hole. Theinner horizon of a Kerr or Reisner-Nordstrom blackhole is continuous with I^+,so an infinite number of null rays pile up there in a Cauchy horizon. Thiscould be a set up for a hypercomputations. However, Hawking radiation decaysthe black hole so it is not eternal. Nature appears to conspire to prevent anycircumvention of the Church-Turing thesis. This is exactly what we might expectif Gödel's theorem plays a role in nature. The natural physics to look at isquantum mechanics, where the observer is ultimately a quantum system that isaccessing information about a quantum system. The observer plus system is awhole system that is in this setting self-referential. Recent work with theFrauchiger-Renner theorem and measurements related to the Wigner's friend havedemonstrated limits on the capacity of quantum mechanics to access informationabout itself. This may have ultimatelyconsequences for issues involving the foundations of quantum mechanics, inparticular the Born rule, and with cosmological issues for how the universe isstructured so that information physics conforms to the Church-Turing thesis. LC On Tuesday, April 6, 2021 at 10:32:57 AM UTC-5 [email protected] wrote: On Tue, Apr 6, 2021 at 11:05 AM Bruno Marchal <[email protected]> wrote: > I use the term “pagan” for “non confessional theology” Since you were the only one in the world who knows Brunospeak rather than telling us what the synonyms in your homemade language are it might be more interesting to all of us who don't speak that tongue if you would try doing some actual philosophy instead. On second thought that's probably not feasible because to do that you would be required to actually have something to say. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/75fd0d72-f881-4d9b-8f0a-56f37f17de69n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/129949319.536664.1617850050194%40mail.yahoo.com.
