Time Travel: A New Hypercomputational Paradigm

Assuming that all objections to time travel are set aside, it is shown that a computational system with closed timelike curves is a powerful hypercomputational tool. Specifically, such a system allows us to solve four out of five problems recently advanced as counterexamples to the fundamental principle of universality in computation. The fifth counterexample, however, remains unassailable, indicating that universality in computation cannot be achieved, even with the help of such an extraordinary ally as time travel.

[1]  D. Deutsch.  The fabric of reality , 1997, The Art of Political Storytelling.

[2]  Jim Harrington,et al.  Localized closed timelike curves can perfectly distinguish quantum states. , 2008, Physical review letters.

[3]  Albert Einstein,et al.  The collected papers of Albert Einstein , 1987 .

[4]  J. Gott,et al.  Closed timelike curves produced by pairs of moving cosmic strings: Exact solutions. , 1991, Physical review letters.

[5]  Hazel Richardson.  How to Build a Time Machine , 1999 .

[6]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[7]  Christof Teuscher,et al.  From Utopian to Genuine Unconventional Computers , 2006 .

[8]  J. Preskill.  Black Holes and Time Warps: Einstein's Outrageous Legacy , 1994 .

[9]  D. Wrzosek,et al.  Proceedings of the Royal Society of Edinburgh , 1940, Nature.

[10]  J. Heaton.  GÖDEL'S PROOF , 1960 .

[11]  Eitan M. Gurari,et al.  Introduction to the theory of computation , 1989 .

[12]  Kurt Gödel,et al.  An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation , 1949 .

[13]  James B. Morris.  Formal Languages and their Relation to Automata , 1970 .

[14]  K. Gödel.  An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation , 1949 .

[15]  Danny Hillis,et al.  The Pattern on the Stone , 1998 .

[16]  J. Gott.  Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time , 2001 .

[17]  Selim G. Akl.  Evolving Computational Systems , 2007, Handbook of Parallel Computing.

[18]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[19]  Selim G. Akl,et al.  Quantum Measurements and Universal Computation , 2006, Int. J. Unconv. Comput..

[20]  D. Siegel,et al.  The collected papers of Albert Einstein. , 2007, Isis; an international review devoted to the history of science and its cultural influences.

[21]  Selim G. Akl,et al.  On the Importance of Parallelism for Quantum Computation and the Concept of a Universal Computer , 2005, UC.

[22]  Selim G. Akl.  Three Counterexamples to Dispel the Myth of the Universal Computer , 2006, Parallel Process. Lett..

[23]  Selim G. Akl.  Even Accelerating Machines are Not Universal , 2007, Int. J. Unconv. Comput..

[24]  K. Thorne.  Do the Laws of Physics Permit Closed Timelike Curves? a , 1991 .

[25]  Scott Aaronson,et al.  Closed timelike curves make quantum and classical computing equivalent , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[26]  James L. Hein,et al.  Discrete structures, logic, and computability , 1994 .

[27]  K. Gödel.  Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I , 1931 .

[28]  Kip S. Thorne,et al.  Adventures in Space-Time. (Book Reviews: Black Holes and Time Warps. Einstein's Outrageous Legacy.) , 1994 .

[29]  K. Gödel.  Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I , 1931 .

[30]  D. Bacon.  Quantum computational complexity in the presence of closed timelike curves , 2003, quant-ph/0309189.

[31]  A. Einstein,et al.  Die Grundlage der allgemeinen Relativitätstheorie , 1916 .

[32]  Todd A. Brun.  Computers with Closed Timelike Curves Can Solve Hard Problems Efficiently , 2002, ArXiv.

[33]  Peter J. Denning,et al.  Machines, Languages, And Computation , 1978 .

[34]  C. D. Walter.  Algorithmics–The spirit of computing , 1988 .

[35]  I. Németi,et al.  A twist in the geometry of rotating black holes: seeking the cause of acausality , 2007, 0708.2324.

[36]  Selim G. Akl.  Unconventional Computational Problems with Consequences to Universality , 2008, Int. J. Unconv. Comput..

[37]  E. Newman,et al.  Metric of a Rotating, Charged Mass , 1965 .

[38]  Gregory J. Chaitin.  A century of controversy over the foundations of mathematics , 2000, Complex..

[39]  D. S. SzyId,et al.  Parallel Computation: Models And Methods , 1998, IEEE Concurrency.

[40]  A. Kox,et al.  THE COLLECTED PAPERS OF , 1996 .

[41]  Frank J. Tipler,et al.  Rotating cylinders and the possibility of global causality violation , 1974 .

[42]  Christos H. Papadimitriou,et al.  Elements of the Theory of Computation , 1997, SIGA.

[43]  P. Davies,et al.  How to build a time machine. , 2002, Scientific American.

[44]  R. Kerr,et al.  Gravitational field of a spinning mass as an example of algebraically special metrics , 1963 .

[45]  Deutsch,et al.  Quantum mechanics near closed timelike lines. , 1991, Physical review. D, Particles and fields.

[46]  Miguel Alcubierre,et al.  90 13 5 Se p 20 00 The warp drive : hyper-fast travel within general relativity , 2022 .

[47]  W. J. van Stockum,et al.  IX.—The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry , 1937 .

[48]  Gregory J. Chaitin.  A century of controversy over the foundations of mathematics , 2000 .