Existence of Faster than Light Signals Implies Hypercomputation already in Special Relativity
Conference paper
Abstract
Within an axiomatic framework, we investigate the possibility of hypercomputation in special relativity via faster than light signals. We formally show that hypercomputation is theoretically possible in special relativity if and only if there are faster than light signals.
Keywords
Special Relativity Turing Machine Light Signal Coordinate Point Logic Language
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References
- 1.Andréka, H., Madarász, J.X., Németi, I., Székely, G.: A logic road from special relativity to general relativity. Synthese, 1–17 (2011) (online-first)Google Scholar
- 2.Andréka, H., Madarász, J.X., Németi, I., Székely, G.: What are the numbers in which spacetime? (2012), arXiv:1204.1350Google Scholar
- 3.Andréka, H., Németi, I., Németi, P.: General relativistic hypercomputing and foundation of mathematics. Nat. Comput. 8(3), 499–516 (2009)MathSciNetMATHCrossRefGoogle Scholar
- 4.Dávid, G., Németi, I.: Relativistic computers and the Turing barrier. Appl. Math. Comput. 178(1), 118–142 (2006)MathSciNetMATHCrossRefGoogle Scholar
- 5.d’Inverno, R.: Introducing Einstein’s relativity. Oxford University Press, New York (1992)MATHGoogle Scholar
- 6.Earman, J., Norton, J.D.: Forever is a day: supertasks in Pitowsky and Malament–Hogarth spacetimes. Philos. Sci. 60(1), 22–42 (1993)MathSciNetCrossRefGoogle Scholar
- 7.Etesi, G., Németi, I.: Non-Turing computations via Malament–Hogarth space-times. Internat. J. Theoret. Phys. 41(2), 341–370 (2002)MathSciNetMATHCrossRefGoogle Scholar
- 8.Friedman, M.: Foundations of Space-Time Theories. Relativistic Physics and Philosophy of Science. Princeton University Press, Princeton (1983)Google Scholar
- 9.Hogarth, M.L.: Does general relativity allow an observer to view an eternity in a finite time? Found. Phys. Lett. 5(2), 173–181 (1992)MathSciNetCrossRefGoogle Scholar
- 10.Madarász, J.X.: Logic and Relativity (in the light of definability theory). Ph.D. thesis, Eötvös Loránd Univ., Budapest (2002), http://www.math-inst.hu/pub/algebraic-logic/Contents.html
- 11.Madarász, J.X., Németi, I., Székely, G.: Twin paradox and the logical foundation of relativity theory. Found. Phys. 36(5), 681–714 (2006)MathSciNetMATHCrossRefGoogle Scholar
- 12.Manchak, J.B.: On the possibility of supertasks in general relativity. Found. Phys. 40(3), 276–288 (2010)MathSciNetMATHCrossRefGoogle Scholar
- 13.Matolcsi, T., Rodrigues Jr., W.A.: The geometry of space-time with superluminal phenomena. Algebras Groups Geom. 14(1), 1–16 (1997)MathSciNetMATHGoogle Scholar
- 14.Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W. H. Freeman and Co., San Francisco (1973)Google Scholar
- 15.Mittelstaedt, P.: What if there are superluminal signals? The European Physical Journal B - Condensed Matter and Complex Systems 13, 353–355 (2000)CrossRefGoogle Scholar
- 16.Németi, P., Székely, G.: Special relativistic hypercomputation is possible if there are faster than light signals (2012) (preprint version); arXiv:1204.1773 Google Scholar
- 17.OPERA collaboration: Measurement of the neutrino velocity with the OPERA detector in the CNGS beam (2011), arXiv:1109.4897Google Scholar
- 18.Petkov, V.: Relativity and the nature of spacetime, 2nd edn. Frontiers Collection. Springer, Berlin (2009)MATHCrossRefGoogle Scholar
- 19.Recami, E.: Tachyon kinematics and causality: a systematic thorough analysis of the tachyon causal paradoxes. Found. Phys. 17(3), 239–296 (1987)MathSciNetCrossRefGoogle Scholar
- 20.Recami, E.: Superluminal motions? A bird’s-eye view of the experimental situation. Found. Phys. 31, 1119–1135 (2001)CrossRefGoogle Scholar
- 21.Recami, E., Fontana, F., Garavaglia, R.: Special relativity and superluminal motions: a discussion of some recent experiments. Internat. J. Modern Phys. A 15(18), 2793–2812 (2000)MathSciNetGoogle Scholar
- 22.Rindler, W.: Relativity. Special, general, and cosmological, 2nd edn. Oxford University Press, New York (2006)Google Scholar
- 23.Selleri, F.: Superluminal signals and the resolution of the causal paradox. Found. Phys. 36, 443–463 (2006)MathSciNetMATHCrossRefGoogle Scholar
- 24.Stannett, M.: The case for hypercomputation. Appl. Math. Comput. 178(1), 8–24 (2006)MathSciNetMATHCrossRefGoogle Scholar
- 25.Székely, G.: First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers. Ph.D. thesis, Eötvös Loránd Univ., Budapest (2009)Google Scholar
- 26.Székely, G.: The existence of superluminal particles is consistent with the kinematics of Einstein’s special theory of relativity (2012), arXiv:1202.5790Google Scholar
- 27.Taylor, E.F., Wheeler, J.A.: Spacetime Physics. W. H. Freeman and Company, New York (1997)Google Scholar
- 28.Tolman, R.C.: The Theory of the Relativity of Motion. University of California, Berkely (1917)MATHGoogle Scholar
- 29.Weinstein, S.: Super luminal signaling and relativity. Synthese 148, 381–399 (2006)MathSciNetCrossRefGoogle Scholar
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