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Budapest, September 10, 2012Relativistic ComputingPage: 1

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Church Thesis was formulated in Newtonian worldview Turing Machine concept incorporates ABSOLUTE TIME Budapest, September 10, 2012Relativistic ComputingPage: 2 you can MANIPULATE TIME (just like space) after Black Hole Physics breaking the Turing Barrier becomes conceivable

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Black hole computing Wormhole computing (astrophysicist Igor Novikov) Comparison, realisticity issues Budapest, September 10, 2012Relativistic ComputingPage: 3

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Budapest, September 10, 2012Relativistic ComputingPage: 4 Gravity causes slow time New physics brings in new horizons, new possibilities and breaks old barriers.

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Budapest, September 10, 2012 Relativistic Computing Page: 5 +45 μs/day because of gravity -7 μs/day because of the speed of sat. approx. 4 km/s (14400 km/h) Relativistic Correction: 38 μs/day approx. 10 km/day Global Positioning System

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Budapest, September 10, 2012Relativistic ComputingPage: 6 We want to use the GR effect that gravity causes slow time to decide an arbitrary recursively enumerable set. We will show the idea in two levels of abstraction. 1.In Cartoon-like pictures 2.The same idea in spacetime diagrams

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Budapest, September 10, 2012Relativistic ComputingPage: 7

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Budapest, September 10, 2012Relativistic ComputingPage: 8

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Budapest, September 10, 2012Relativistic ComputingPage: 9

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Budapest, September 10, 2012Relativistic ComputingPage: 10 Let us see in more mathematical detail how this fairy tale can be implemented in terms of GR spacetime diagrams.

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Budapest, September 10, 2012Relativistic ComputingPage: 11

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Budapest, September 10, 2012Relativistic ComputingPage: 12

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Budapest, September 10, 2012Relativistic ComputingPage: 13 Malament-Hogarth event! Etesi-Nemeti paper: computations Infinite space inside

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Budapest, September 10, 2012Relativistic ComputingPage: 14 1. Blue shift (communication) 2. Evaporation of BH 3. Strong Cosmic Censor Hypothesis 4. Instability of Cauchy Horizon 5. Blue shift (cosmic, distant galaxies) 6. Unlimited tape 7. Predictability, Repeatability, Radiation from singularity 8. Decay of protons 9. Heat Death

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Budapest, September 10, 2012Relativistic ComputingPage: 15 Cauchy horizon outer event horizon worldline of programmer worldline of computer photon signal communication messenger communication already solved in [ND], Fig.5, sec.5.3.2, p.133

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Budapest, September 10, 2012Relativistic ComputingPage: 16 Shielding (only gradually) CMB Apostolos book, p.146 Evaporation is only hypothetical Penrose 2004, p.848: … BH evaporation is an entirely theoretical … might be that Nature has other ideas for future of BHs. Papers: Nikolic, H., Black holes radiate but do not evaporate. arXiv:hep- th/0402145v3, Aug 2005. Helfer,A. D., Do black holes radiate? arXiv:gr-qc/0304042v1, Apr 2003. Therefore since we are using a huge BH for hypercomputing, Hawking radiation should cause no problem.

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Budapest, September 10, 2012Relativistic ComputingPage: 17 3. Strong Cosmic Censor 4. Instability of Cauchy Horizon 5. Blue shift (cosmic, distant galaxies) - Expansion of Universe forever - Asymptotically de Sitter background implies stability

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Budapest, September 10, 2012Relativistic ComputingPage: 18 worldlines of galaxies photon geodesics worldlines of galaxies t cosmological event horizon

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Budapest, September 10, 2012Relativistic ComputingPage: 19 r = 0singularity r = 0 I+I+ I+I+ BH interior distant galaxies (Olbers paradox) worldline of computer 1 2 3 1: Inner event horizon (Cauchy horizon) 2: Outer event horizon 3: Cosmological event horizon Kerr-Newmann-deSitter space-time

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Budapest, September 10, 2012Relativistic ComputingPage: 20 Papers for fall of censor: Joshi, P.S., Do naked singularities break the rules of physics? Scientific American, January 2009. Chambers, C. M., The Cauchy horizon in black hole-de Sitter spacetimes. arXiv:gr-qc/9709025v1, Sep 1997. German,W.S., Moss, I.A., Cauchy horizon stability and cosmic censorship. arXiv:gr-qc/0103080v1, Mar 2001. Lobo, F.X. N., Exotic solutions in general relativity: traversable wormholes and warp drive spacetimes. arXiv:0710.4474v1 Oct 2007.

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Budapest, September 10, 2012Relativistic ComputingPage: 21 Weak Energy Condition is not LAW: Barcelo, C., Visser, M., Twilight for the energy conditions?, Int. J. Mod. Phys. C 11 (2002), 1553. arXiv:gr-qc/0205066. Cosmology accelerated expansion, dark energy Wormholes boom implies new kinds of MH-regions

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Budapest, September 10, 2012Relativistic ComputingPage: 22 6. Unlimited tape information energy 7. Predictability Repeatability Radiation from singularity New orbit for programmer 8. Decay of protons Small enough particles do not decay (electron, positron, neutrino) 9. Heat Death

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We reviewed BH computing, now comes WH computing. This is another kind of thought-experiment, based on a different GR space-time Both have advantages and disadvantages. WH computing: can compute more complex problems, is smaller, no need for Noahs Ark Budapest, September 10, 2012Relativistic ComputingPage: 23

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AB Budapest, September 10, 2012Relativistic ComputingPage: 24 A B Long path (outside) Short path (inside) unfold

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AB Budapest, September 10, 2012Relativistic ComputingPage: 25 Short path (inside) AB t Long path (outside)

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Budapest, September 10, 2012Relativistic ComputingPage: 26

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Budapest, September 10, 2012Relativistic ComputingPage: 27 t 1 1 2 3 4 5 6 2 3 BA r r = 0 Signal outside WH From A to B Signal inside WH From B to A Event horizon of BH

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Budapest, September 10, 2012Relativistic ComputingPage: 28 t 1 1 2 3 4 5 6 2 3 BA r r = 0 Signal outside WH From A to B Signal inside WH From B to A Event horizon of BH

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Budapest, September 10, 2012Relativistic ComputingPage: 29 t 2 4 6 8 10 12 BA r Signal outside WH From A to B Signal inside WH From B to A 1 3 5 7 9 11 2 4 6 8 1 3 5 7 9 BlackHole disappears BlackHole appears

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Budapest, September 10, 2012Relativistic ComputingPage: 30 Designing the wormhole computer Task is: decide for any recursive set S whether S is finite or infinite. S is specified by fixing a number theoretic 0 -formula Φ(x) S x : Φ(x) We will check whether there is a greatest x with Φ(x).

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C a – Turing machine (TM) at mouth A (see its program later) M a – Mirror at mouth A (acts either as a mirror or a prism) Mirror: reflects signals coming from the wormhole towards M b outside the wormhole Prism: filters red light, reflects green towards M b C b – TM at mouth B (see its program later) M b – Mirror at mouth B Reflects light signals coming from C b or M a into the wormhole towards M a Pr – Programmer (checks incoming signals on M a till T MH ) Red and Green light means there are finitely many x such that Φ(x) Only Red light means there are infinitely many x such that Φ(x) No signals means there is no x such that Φ(x) Budapest, September 10, 2012Relativistic ComputingPage: 31

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Budapest, September 10, 2012Relativistic ComputingPage: 32 Wait T MH time Φ(x) & Flash Infinite many x Φ(x) Finite many x Φ(x) Pr CaCa MaMa MbMb CbCb Wormhole time gap (Malament-Hogard event) Inside WH Outside WH

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Budapest, September 10, 2012Relativistic ComputingPage: 33 Pr CaCa MaMa MbMb CbCb

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Budapest, September 10, 2012Relativistic ComputingPage: 34 Pr CaCa MaMa MbMb CbCb

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How much more? Beyond-Turing complexity issues: Jiri Wiedermann, Philip Welch, Marek Suchenek, Mark Hogarth BH decidable problems are all Budapest, September 10, 2012Relativistic ComputingPage: 35

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Theorem (P. Welch): BH can compute all problems if and only if one can create a computer which able to receive an arbitrary large (but finite) amount of information. WH can decide all problems. Question: can WH decide all n problems by using perhaps n WH-s? Budapest, September 10, 2012Relativistic ComputingPage: 36

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BHs observed Blue shift problem: BHs are focusing lenses No time travel We need big BHs Programmer travels BH can compute less WHs not yet observed WHs are defocusing lenses (no bs roblem) Time travel WHs may be small No need for Noahs Ark WH can compute more Budapest, September 10, 2012Relativistic ComputingPage: 37

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Budapest, September 10, 2012Relativistic Hyper ComputingPage: 38

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Budapest, September 10, 2012Relativistic ComputingPage: 39

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You can read more on Istvan Nemetis homepage: http://www.renyi.hu/~nemeti/ Budapest, September 10, 2012Relativistic ComputingPage: 40

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Budapest, September 10, 2012Relativistic Hyper ComputingPage: 41

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