Abstract
For our present purpose, we shall merely note that in the extended theory of relativity, gravitation, just like inertia, depends on the essential nature of space and that the particular property of space that accounts for gravitation, namely its curvature, is clearly mathematical.
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Notes
Joannis Sarisberiensis, Polycraticus, Bk. 2, Ch. 21, Opera Omnia, Patrologie Migne, 2nd series (Paris, 1855), 199:447: Scio equidem lapidem vel sagittam, quam in nubes jaculatus sum, exigente natura recasurum in terram, in quam feruntur omnia nutu suo pondera, nec tamen simpliciter recidere in terram, aut quia novi recidere necesse est Potest enim recidere et non recidere. Alterum tamen, etsi non necessario, verum tamen est… Ceterum etsi non essepossit, nihil impedit esse Scientiam, quae non necessariorum tantum, sed quorumlibet existentium est, nisi forte et tu cum stoicis existentia censeas necessariis comparanda.
Leibniz, Nouveaux essais, Opera, ed. Erdmann (Berlin, 1840), p. 203 [New Essays on Human Understanding, trans. Peter Remnant and Jonathan Bennett (Cambridge: University Press, 1981), p. 66 (Berlin: Akademie-Verlag, 1962 pagination)].
Clark Maxwell, Scientific Papers (Cambridge, 1890) 2 115 ff., 311.
Emile Borel, Le hasard, 2nd ed. (Paris, 1914), pp. 3, 300. In his more recent book Borel further explains that “it is because it has effected the entry of universal gravitation into a more general conception of the world ... that Einstein’s theory of general relativity has been received with such admiration and passionate curiosity in scientific circles all over the world” (ET 40; Eng. 33).
Marcel Brillouin, ‘Propos sceptiques au sujet du principe de relativite,’ Scientia 13 (1913) 23. Cf. analogous statements made somewhat earlier by Sir Oliver Lodge, ‘The Aether of Space,’ Nature 79 (1909) 323, and Walther Ritz, ‘Die Gravitation,’ Scientia 5 (1909) 255.
At a time when the general theory of relativity still existed only in some kind of nascent state for Einstein, he indicated how important Eötvös’s experiments were for the theory. In these experiments, Eötvös demonstrated with a high degree of exactitude the identity of inertial and gravitational mass, “whose definitions are logically independent of one another” (‘Zum Relativitäts-problem,’ Scientia 15 [1914] 342). Weyl also pointed out the significance of this result (STM 225).
Edmond Bauer, in his excellent little book La théorie de la relativité (Paris, 1922, p. 63) makes this aspect of the theory quite clear: “Thus disappears from science the notion of the force of gravitation, of universal attraction — a mysterious property of matter that seemed to make itself felt instantaneously at a distance with no conceivable mechanism.”
Paul Langevin, AG 19, 22, and preface to Eddington, Espace, temps et gravitation, trans. Rossignol (Paris, 1920), p. ii. In order to justify this complete fusion of physics and geometry, which is one of the most essential characteristics of the new doctrine, the relativists take pains to emphasize that “it is only the whole composed of geometry and physics that may be tested empirically,” given that the observations themselves constantly involve assumptions such as the one equating the path followed by light rays with a straight line (Weyl, STM 93). Thus, “this seals the doom of the idea that a geometry may exist independently of physics,” and “the metrical… field is related to the material content filling the world” (STM 220), while, on the other hand, “gravitation is a mode of expression of the metrical field” (STM 226), so that “Geometry, Mechanics, and Physics form an inseparable theoretical whole,” which must be conceived en bloc (STM 67). In a more recent work this physicist declares, moreover, that the metrical structure is not rigidly given a priori, “but constitutes a field describing the state of physical reality causally dependent on the state of matter.” He adds this picturesque image: “Like the snail, matter itself constructs and forms its own home” (Mathematische Analyse des Raumproblems, Berlin, 1923, p. 44).
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© 1985 D. Reidel Publishing Company, Dordrecht, Holland
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Meyerson, É. (1985). Gravitation. In: The Relativistic Deduction. Boston Studies in the Philosophy of Science, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5211-9_7
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