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The idea

Relativistic Comput ing by P é ter N é meti (joint work with Hajnal Andr é ka, Istv á n N é meti and Gergely Sz é kely ). The idea. after Black Hole Physics breaking the Turing Barrier becomes conceivable. you can MANIPULATE TIME (just like space). G. R.

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The idea

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  1. Relativistic ComputingbyPéter Németi (joint work with HajnalAndréka, István Németi and GergelySzékely) Relativistic Computing

  2. The idea after Black Hole Physics breaking the Turing Barrier becomes conceivable you can MANIPULATE TIME (just like space) G. R. Relativistic Computing Church Thesis was formulated in Newtonian worldview Turing Machine concept incorporates “ABSOLUTE TIME”

  3. plan of talk Relativistic Computing • Black hole computing • Wormhole computing (astrophysicist Igor Novikov) • Comparison, realisticity issues

  4. Gravitycausesslowtime • New physics brings in new horizons, new possibilities and breaks old barriers. Gravitycausesslowtime G. R. Relativistic Computing

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

  6. Computingbeyondtheturingbarrier Wewanttousethe GR effectthatgravitycausesslowtime todecide an arbitraryrecursivelyenumerableset. Wewill show the idea intwolevels of abstraction. InCartoon-likepictures The same idea inspacetimediagrams Relativistic Computing

  7. Speeding up time using gravity Relativistic Computing

  8. Speeding up time using gravity Relativistic Computing

  9. Speeding up time using gravity Relativistic Computing

  10. Secondlevel: spacetimediagrams Letusseein more mathematicaldetail howthisfairytalecan be implemented interms of GR spacetimediagrams. Relativistic Computing

  11. Ordinaryblackhole – computer’s view Relativistic Computing

  12. Ordinary black hole – programmer’s view Relativistic Computing

  13. Rotating black hole Malament-Hogarth event! Etesi-Nemeti paper: computations Infinite space inside Relativistic Computing

  14. Worries – one by one • Blue shift (communication) • Evaporation of BH • Strong Cosmic Censor Hypothesis • Instability of Cauchy Horizon • Blue shift (cosmic, distant galaxies) • Unlimited tape • Predictability, Repeatability, Radiation from singularity • Decay of protons • Heat Death Relativistic Computing

  15. Worries: 1. Communication blue shift already solved in [ND], Fig.5, sec.5.3.2, p.133 worldline of programmer Cauchy horizon worldline of computer outer event horizon photon signal communication messenger communication Relativistic Computing

  16. Worries: 2. Evaporation of BH • 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 BH’s.” • 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. Relativistic Computing

  17. Worries: 3. – 4. – 5. • 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 Relativistic Computing

  18. Forever expanding universe t cosmological event horizon worldlines of galaxies worldlines of galaxies photon geodesics photon geodesics Relativistic Computing

  19. Kerr-newmann wormhole in forever expanding universe Kerr-Newmann-deSitter space-time r = 0 singularity r = 0 1 I+ I+ BH interior 1: Inner event horizon (Cauchy horizon) 2: Outer event horizon 3: Cosmological event horizon distant galaxies (Olbers paradox) 2 3 worldline of computer Relativistic Computing

  20. Worries: 3. – 4. – 5. • 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. Relativistic Computing

  21. Worries: 3. – 4. – 5. • 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 Relativistic Computing

  22. Worries: 6. – 7. – 8. • 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 Relativistic Computing

  23. PART II: Wormholecomputing Relativistic Computing Wereviewed BH computing, nowcomes WH computing. This is anotherkind of thought-experiment, basedon a different GR space-time Both haveadvantages and disadvantages. WH computing: cancompute more complexproblems, is smaller, no needforNoahsArk

  24. Wormhole (asspace-structure) A B Long path (outside) Short path (inside) unfold B A Relativistic Computing

  25. Wormholeinspacetime diagram t Long path (outside) Short path (inside) B A B A Relativistic Computing

  26. Ordinary black hole – programmer’s view Relativistic Computing

  27. Manipulating time... 3 t Signal outside WH From A to B 6 2 5 Signal inside WH From B to A 4 Event horizon of BH 3 1 2 1 r B A r = 0 Relativistic Computing

  28. Manipulating time... 3 t Signal outside WH From A to B 6 2 5 Signal inside WH From B to A 4 Event horizon of BH 3 1 2 1 r B A r = 0 Relativistic Computing

  29. Inducing a time shift t 9 8 Signal outside WH From A to B 7 BlackHole disappears 12 6 11 10 9 5 8 7 4 6 5 4 BlackHole appears 3 3 Signal inside WH From B to A 2 2 1 1 r B A Relativistic Computing

  30. Designing thewormhole computer Task is: decideforanyrecursiveset S whether S is finiteorinfinite. S is specifiedby fixing a numbertheoretic 0 -formulaΦ(x) S   x : Φ(x) Wewillcheckwhetherthere is a greatest x withΦ(x). Relativistic Computing

  31. Entities of thewh computer Relativistic Computing • Ca – Turing machine(TM) at mouth A (see itsprogram later) • Ma – Mirror at mouth A (acts eitheras a mirror or a prism) • Mirror: reflects signals coming from the wormhole towards Mb outside the wormhole • Prism: filters red light, reflects green towards Mb • Cb – TM at mouth B (see itsprogram later) • Mb – Mirror at mouth B • Reflects light signals coming from Cbor Ma into the wormhole towards Ma • Pr – Programmer (checks incoming signals on Ma till TMH) • Red and Green light means there are finitelymany x suchthatΦ(x) • Only Red light means there are infinitelymany x suchthatΦ(x) • No signals means there is no x suchthatΦ(x)

  32. Σ2 Thought experiment Wormhole time gap (Malament-Hogard event) Wait TMH time Φ(x)& Flash Finitemany x Φ(x) Infinitemany x Φ(x) Pr Ca Ma Cb Mb Inside WH Outside WH Relativistic Computing

  33. Program of Cb Pr Ca Ma Cb Mb Relativistic Computing

  34. Program of Ca Pr Ca Ma Cb Mb Relativistic Computing

  35. Wormholescancompute more Relativistic Computing Howmuch more? Beyond-Turingcomplexityissues: JiriWiedermann, Philip Welch, MarekSuchenek, Mark Hogarth BH decidable problems are all

  36. Wormholescancompute more Relativistic Computing 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 candecideall  problems. Question: can WH decideall n problemsbyusingperhapsnWH-s?

  37. Comparisonbetween BH and WH computing BHsobserved Blue shift problem: BHsarefocusinglenses No timetravel WeneedbigBHs Programmertravels BH cancompute less WHsnotyetobserved WHsaredefocusinglenses (no bsroblem) Time travel WHsmay be small No needforNoahsArk WH cancompute more Relativistic Computing

  38. The way to get through the turing barrier THE END Orthefuture ? … Relativistic Hyper Computing

  39. 1.St question General Relativity Physics RELATIVISTIC COMPUTING Exotic Matter Cosmic censor conjecture ForSale!!! Singularities Closed time-like curves Cosmology Malament-HogartSpacetimes Relativistic Computing

  40. Questions… You can read more on IstvanNemeti’s homepage: http://www.renyi.hu/~nemeti/ Relativistic Computing

  41. People, history Relativistic Hyper Computing History of relativistic computing 1987 - start: Andréka & Németi Univ. Ames USA Lecture Notes 1992 - Independent start: Hogarth (Cambridge) Other authors: Pitowsky (Israel), Shagrir (Israel), Earman (Pittsburgh), Norton (Pittsburgh), Malament (USA), Etesi (Hungary, Dept. Phys.), Dávid (Hungary, Dept. Phys.), Tipler, Barrow, JiříWiedermann, Philip Welch, MarekSuchenek, Chris Wüthrich, B. Gyenis (Pittsburgh)

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