Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-15T05:28:18.724Z Has data issue: false hasContentIssue false
  • English
  • Français

VII.—On the Measurement of Spatial Distance in a Curved Space-time

Published online by Cambridge University Press:  15 September 2014

H. S. Ruse
Get access

Extract

The problem of defining the concept of spatial distance in a general riemannian space-time has been discussed by E. T. Whittaker, who showed how to translate into the terms of four-dimensional geometry the method adopted by astronomers in determining the distance of a star from the earth by means of a comparison of its absolute and apparent luminosities. The problem was further considered by the present writer, who derived a different formula for spatial distance by a method which was essentially one of partitioning the whole of space-time into space and time relative to the given observer. It was suggested that the new spatial distance might be that determined practically by parallax-measurements, though the evidence in support of this suggestion was perhaps hardly sufficient to carry conviction.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 53 , 1934 , pp. 79 - 88
Copyright
Copyright © Royal Society of Edinburgh 1934

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page 79 note * Proc. Roy. Soc., A, vol. cxxxiii, 1931, p. 93.

page 79 note † Proc. Roy. Soc. Edin., vol. lii, 1932, p. 183.

page 79 note ‡ The word distance will be used to mean spatial distance. Displacements between point-events in the four-dimensional world will be called intervals.

page 81 note * Eddington, Mathematical Theory of Relativity, 1924, p. 77.

page 83 note * See Veblen, Invariants of Quadratic Differential Forms (Camb. Math. Tract, No. 24, 1927), chap. vi.

page 83 note † This notation differs slightly from that of my previous paper, in which the coordinates of S were denoted by unaccented letters. In this paper x 0, x 1, x 2, x 3 are used exclusively for current coordinates.

page 85 note * Ruse, , Proc. London Math. Soc., vol. xxxii, 1931, p. 90.Google Scholar

page 86 note * Kermack, , M'Crea, , and Whittaker, , Proc. R.S.E., vol. liii, 1933, p. 35.Google Scholar

page 88 note * Eddington, op. cit., p. 156, equation (67.12) with R sin x=r.