Abstract
In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of first-order logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom difference, however, leads to radical differences in the predictions of the two theories. One of their major differences manifests itself in the relation between relativistic and rest masses, see Thms. 5 and 6.
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Bibliography
H. Andréka, P. Burmeister, and I. Németi. Quasivarieties of partial algebras — a unifying approach towards a two-valued model theory for partial algebras. Studia Sci. Math. Hungar. 16, 1981, pp. 325–372.
H. Andréka, J. X. Madarász, and I. Németi. “Logical analysis of special relativity theory,” in: J. Gerbrandy, M. Marx, M. de Rijke, and Y. Venema (Eds.), Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Vossiuspers, Ams-terdam University Press, 1999. CD-ROM, ISBN: 90 5629 104 1, http://www.illc.uva.nl/j50.
H. Andréka, J. X. Madarász, and I. Németi. “Logical axiomatizations of space-time. Samples from the literature,” in: Non-Euclidean geometries, volume 581 of Mathematics and Its Applications. New York: Springer, 2006, pp. 155–185.
H. Andréka, J. X. Madarász, and I. Németi, “Logic of space-time and relativity theory,” in: M. Aiello, I. Pratt-Hartmann and J. van Benthem (Eds.), Handbook of Spatial Logics. Dordrecht: Springer, 2007, pp. 607–711.
H. Andréka, J. X. Madarász, and I. Németi, “On the logical structure of relativity theories.” Research report, Alfréd Rényi Institute of Mathematics, Budapest, 2002. With contributions from A. Andai, G. Sági, I. Sain and Cs. Tőke. http://www.mathinst.hu/pub/algebraic-logic/Contents.html. 1312 pp.
H. Andréka, J. X. Madarász, I. Németi, and G. Székely, “Axiomatizing relativistic dynamics without conservation postulates,” in: Studia Logica 89, 2, 2008, pp. 163–186.
J. Ax, “The elementary foundations of spacetime,” in: Foundations of Physics 8, 7–8, 1978, pp. 507–546.
S. A. Basri, A Deductive Theory of Space and Time. Amsterdam: North-Holland 1966.
T. Benda, “A Formal Construction of the Spacetime Manifold,” in: Journal of Philosophical Logic 37, 5, 2008, pp. 441–478.
C. C. Chang and H. J. Keisler, Model theory. Amsterdam: North-Holland 1973, 1977, 1990.
H. D. Ebbinghaus, J. Flum and W. Thomas, Mathematical logic. New York: Springer-Verlag 1994.
R. Goldblatt, Orthogonality and spacetime geometry. New York: Springer-Verlag 1987.
J. X. Madarász. Logic and Relativity (in the light of definability theory). PhD thesis, Eötvös Loránd Univ., Budapest, 2002.
J. X. Madarász, I. Németi, and G. Székely, “Twin paradox and the logical foundation of relativity theory,” in: Foundations of Physics 36, 5, 2006, pp. 681–714.
J. X. Madarász, I. Németi, and G. Székely, “First-order logic foundation of relativity theories,” D. Gabbay, S. Goncharov and M. Zakharyaschev (Eds.), in: Mathematical problems from applied logic II. New York: Springer, 2007, pp. 217–252.
J. X. Madarász, I. Németi, and Cs. Tőke. On generalizing the logic-approach to space-time towards general relativity: first steps. in: V. F. Hendricks, F. Neuhaus, S. A Pedersen, U. Scheffler and H. Wansing (Eds.), First-Order Logic Revisited, Logos Verlag, Berlin, 2004, pp. 225–268.
V. Pambuccian, “Alexandrov-Zeeman type theorems expressed in terms of definability,” in: Aequationes Mathematicae 74, 3, 2007, pp. 249–261.
G. Székely, First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers. PhD thesis, Eötvös Loránd Univ., Budapest, 2009.
J. Vaänänen, “Second-order logic and foundations of mathematics,” in: Bulletin of Symbolic Logic 7, 4, 2001, pp. 504–520.
J. Woleński “First-order logic: (philosophical) pro and contra,” in: V. F. Hendricks, F. Neuhaus, S. A. Pedersen, U. Scheffler and H. Wansing (Eds.), First-Order Logic Revisited. Berlin: Logos Verlag 2004, pp. 369–398.
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Madarász, J.X., Székely, G. (2011). Comparing Relativistic and Newtonian Dynamics in First-Order Logic. In: Máté, A., Rédei, M., Stadler, F. (eds) Der Wiener Kreis in Ungarn / The Vienna Circle in Hungary. Veröffentlichungen des Instituts Wiener Kreis, vol 16. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0177-3_7
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