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The Evolution of Theories of Space-Time and Mechanics

Published online by Cambridge University Press:  14 March 2022

W. H. McCrea
W. H. McCrea*
Affiliation:
The Queen's University of Belfast, N. Ireland
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Extract

In this paper I attempt to trace certain aspects of the evolution of theories of space-time and mechanics as revealed by a brief comparative study of Newtonian theory, Robb's theory, general relativity, and Milne's kinematical relativity. The first object is to emphasise how each theory leaves us in a position in which the succeeding one appears as a perfectly natural next step in the development of ideas. The second object is to show how, in spite of superficial differences in character, the theories all necessarily possess the same general structure constituted by the presence of hypotheses, from which certain general mathematical relations are deduced, which in their turn are used to predict relations between observable quantities.

Type
Research Article
Information
Philosophy of Science , Volume 6 , Issue 2 , April 1939 , pp. 137 - 162
Copyright
Copyright © The Philosophy of Science Association

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References

Notes

1 See in particular H. Dingle, Nature, 139 (1937), 784-786; Philosophy, 11, (1936), No. 41.

2 L. N. G. Filon, Mathematical Gazette, 22 (1938), 9-16.

3 We use “agreement” in the usual elementary sense, and do not here go into deeper questions of the significance of “experimental error.“

4 E. A. Milne, Relativity, Gravitation, and World-Structure (1935), 30. (This book will be referred to below as W. S.) See also H. Poincaré, La Science et l'Hypotkèse (1908), 5.

5 More properly, to describe certain phenomena occurring in nature in terms of forces and masses.

6 But particular reference should be made to H. Jeffreys, Scientific Inference (1937) Ch. IX.

7 Actually we subsequently conclude that no such theory is possible.

8 A. A. Robb, Geometry of Time and Space (1936), originally published as A Theory of Time and Space (1914) and summarised in The Absolute Relations of Time and Space (1921).

9 A. Einstein, Annalen der Physik, 49 (1916); Principle of Relativity (1923), 111-164.

10 O. Veblen and J. H. C. Whitehead, Foundations of Differential Geometry (Cambridge Tracts, No. 29) (1933). See p. 24.

11 See A. S. Eddington, Mathematical Theory of Relativity (1922), §§ 16-18.

R. C. Tolman, Relativity, Thermodynamics and Cosmology (1934), §§ 72-74.

W. Pauli, jr. Encykl, d. Math. Wiss., V2, 539-775. See §§ 52, 53.

12 B. Riemann, Math. Werke (1876), 254-269; W. K. Clifford, Math. Papers (1882) 55-71.

13 See, for example, H. Weyl, Das Raumproblem.

14 See A. Einstein, L. Infeld, and B. Hoffmann, Annals of Math., 39 (1938), 65-100.

15 Eddington, op. cit, 119, 212.

16 See for example W. H. McCrea, Zeits. für Astrophysik, 9 (1935), 290-314.

17 Veblen and Whitehead, op. cit., 32.

18 Clerk Maxwell, Scientific Papers, Vol. I (1890), 156.

19 E. A. Milne, W. S. and subsequent papers by Milne, A. G. Walker, and G. J. Whitrow, in Proc. Roy. Soc., Proc. London Math. Soc., and elsewhere. 20 W. S., § 15.

21 W. S., § 11.

22 W. S., Ch. III.

23 E. A. Milne, Proc. Roy. Soc. A.158 (1937), 324; see 325-6.

24 See the series of papers from 1929 onwards in Monthly Notices of the Roy. Astron. Soc.

25 These are discussed more fully by W. H. McCrea, Proc. Edinburgh Math. Soc. (1938), in press.

26 Milne, Proc. Roy. Soc., loc. cit., p. 326.

27 A. S. Eddington, Relativity Theory of Protons and Electrons (1936). See also Nature, 139 (1937), 1000-1001.

28 H. Jeffreys, Nature, 141 (1938), 672-6, 716-719, which see for a recent and concise discussion of this point.

29 Cf. Jeffreys, Nature loc. cit.

30 Clerk Maxwell, Scientific Papers, I (1890), 157.

31 In certain cases the predictions may refer to the statistical results of a set of observations.

32 C. G. Darwin, New Conceptions of Matter (1931), 4.

33 G. T. Whitlow, Quart. Journ. of Math. (Oxford Ser.), 4(1933), 161-172.