David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 24 (1-2):236 - 280 (1972)
Temporal betweenness in space-time is defined solely in terms of light signals, using a signalling relation that does not distinguish between the sender and the receiver of a light signal. Special relativity and general relativity are considered separately, because the latter can be treated only locally. We conclude that the (local) coherence of time can be described if we know only which pairs of space-time points are light-connected. Other consequences in the case of special relativity: (1) a categorical axiom system exists in terms of nondirected light connection alone, with neither particle nor time order as a primitive concept, though we do not actually present the axioms; (2) any concept definable by coordinates is also definable in terms of nondirected light signals if and only if it is invariant under Lorentz transformations, translations, dilations, space reflections, and time reflections; and (3) any transformation of space-time (not necessarily continuous) which preserves nondirected light connection is a product of transformations just listed above. The bulk of the paper is devoted to proving that the definitions we give correspond to their intended interpretations in the usual space-time continua.
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References found in this work BETA
Rudolf Carnap (1958). Introduction to Symbolic Logic and its Applications. New York, Dover Publications.
Hans Reichenbach (1969). Axiomatization of the Theory of Relativity. University of California Press.
Kurt Gödel (1949). An Example of a New Type of Cosmological Solutions of Einsteinâs Field Equations of Gravitation. Reviews of Modern Physics 21 (3):447–450.
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Citations of this work BETA
T. Budden (1997). A Star in the Minkowskian Sky: Anisotropic Special Relativity. Studies in History and Philosophy of Science Part B 28 (3):325-361.
Andreas Kamlah (1973). Invarianzgesetze Und Zeitmetrik. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 4 (2):224-260.
Tim Budden (1997). A Star in the Minkowskian Sky: Anisotropic Special Relativity. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (3):325-361.
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