publication . Preprint . Article . 2011

A logic road from special relativity to general relativity

Hajnal Andréka; Judit X. Madarász; István Németi; Gergely Székely;
Open Access English
  • Published: 22 Mar 2011
Abstract
We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
Subjects
arXiv: Mathematics::LogicComputer Science::General Literature
ACM Computing Classification System: TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS
free text keywords: General Relativity and Quantum Cosmology, Mathematical Physics, Mathematics - Logic, Philosophy, General Social Sciences, Pure mathematics, Test theories of special relativity, Static interpretation of time, Principle of relativity, Four-force, Epistemology, Calculus, Special relativity (alternative formulations), Theory of relativity, Absolute time and space, Problem of time, Mathematics
25 references, page 1 of 2

[1] Andr´eka, H., V. Goranko, Sz. Mikula´s, I. N´emeti, and I. Sain. Effective first order temporal logics. pp. 51-129. In L. Bolc and A. Szalas (eds.) Time and Logic, a computational approach UCL, London, 1995.

[2] Andr´eka, H., J. X. Madar´asz, and I. N´emeti. On the logical structure of relativity theories. E-book, Alfr´ed R´enyi Institute of Mathematics, Budapest, 2002. With contributions from A. Andai, G. Sa´gi, I. Sain, and Cs. T˝oke. http://www.mathinst.hu/pub/algebraic-logic/olsort.html. 1312 pp.

[3] Andr´eka H., J. X. Madar´asz, and I. N´emeti. Logic of space-time and relativity theory. In M. Aiello, I. Pratt-Hartmann, and J. van Benthem, (eds.) Handbook of spatial logics, pp. 607-711. Springer-Verlag, Dordrecht, 2007.

[4] Andr´eka H., J. X. Madar´asz, and I. N´emeti. Logical axiomatizations of spacetime. Samples from the literature. In A. Pr´ekopa and E. Molna´r (eds.) NonEuclidean geometries, pp. 155-185. Springer-Verlag, New York, 2006.

[5] Andr´eka, H., J. X. Madar´asz, I. N´emeti, P. N´emeti, and G. Sz´ekely. Vienna Circle and logical analysis of relativity theory. In F. Stadler (ed.) Wiener Kreis und Ungarn. Vero¨ffentlishungen des Instituts Wiener Kreis, Springer-Verlag, to appear.

[6] Andr´eka, H., J. X. Madar´asz, I. N´emeti, and G. Sz´ekely. A logical investigation of inertial and accelerated observers in flat space-time. In F. G´ecseg, J. Csirik, and Gy. Tur´an (eds.) Kalm´ar Workshop on Logic and Computer Science, pp. 45-57, JATE University of Szeged, Szeged, 2003.

[7] Andr´eka, H., J. X. Madar´asz, I. N´emeti, and G. Sz´ekely. Relativity Theory on Logical Grounds. Course Notes, Budapest 2010. http://www.mathinst.hu/pub/algebraic-logic/kurzus10/kurzus10.htm

[8] Benda, T. A formal construction of the spacetime manifold. J. Phil. Logic, 37(5):441-478, 2008.

[9] Chang, C. C., and H. J. Keisler. Model theory. North-Holland Publishing Co., Amsterdam, 1990.

[10] d'Inverno, R. Introducing Einstein's relativity. Oxford University Press, New York, 1992.

[11] Einstein, A. Relativity. The Special and the General Theory. Penguin Classics, 2006. Translated by W. Lawson (original publication in German 1921).

[12] Enderton, H. B. A mathematical introduction to logic. Academic Press, New York, 1972.

[13] Goldblatt, R. Orthogonality and spacetime geometry. Springer-Verlag, New York, 1984.

[14] Henkin, L., J. D. Monk, and A. Tarski. Cylindric Algebras. Part I. NorthHolland Publishing Co., Amsterdam, 1971. [OpenAIRE]

[15] Hodges, W. Model Theory, Encyclopedia of Mathematics and its Applications, 42. Cambridge Univ. Press, Cambridge, 1993.

25 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue