Abstract
Modern scientific man has largely lost his sense of awe of the universe. He is confident that, given sufficient intelligence, perseverance, time and money, he can understand all there is beyond the stars. He believes that he sees here on earth and in its vicinity a fair exhibition of nature’s laws and objects, and that nothing new looms “up there” that cannot be explained, predicted, or extrapolated from knowledge gained “down here.” He believes he is now surveying a fair sample of the universe, if not in proportion to its size—which may be infinite—yet in proportion to its large-scale features. Little progress could be made in cosmology without this presumptuous attitude. And nature herself seems to encourage it, as we shall see, with certain numerical coincidences that could hardly be accidental.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
† G. O. Abell, Annual Review of Astronomy and Astrophysics 3, 1 (1965).
† For its interesting historical antecedents, see S. L. Jaki, “Olbers’, Halley’s, or Whose Paradox?” Am. J. Phys. 35, 200 (1967), which should also stand as a warning to all armchair historians.
† Nature 130, 9 (1932).
† This figure, as well as Figures 31, 33, and 34, is reproduced, by permission of the publishers, from the author’s article “Relativistic Cosmology” in Phys. Today 20, 23 (November 1967).
† Further details can be found in W. Rindler, Monthly Notices of the Royal Astronomical Society 116, 662 (1956).
† See, for example, H. Bondi, “Cosmology,” Chapter IX, Cambridge University Press, 1961. This is an extremely readable reference on all aspects of cosmology.
† One can further generalize this equation by including the effect of possible pressure: see the remark after equation (89.13) below.
† In this connection we may quote Eddington’s mystical argument for the Λ term (Mathematical Theory, page 154): “An electron could never decide how large it ought to be unless there existed some length independent of itself for it to compare itself with.”
† The R in this formula must not be confused with the expansion factor R. Unfortunately the traditional notations clash here. tSee, for example, R. C. Tolman, “Relativity, Thermodynamics, and Cosmology,” formulae (98.6), Oxford University Press, 1934. Tolman’s “mixed” components 8π T 1, 8π T2, etc., here correspond to G11/g11, G22/g22, etc. On the following pages Tolman reproduces Dingle’s expressions for the Tμ of a very general line element, and it is worth remembering where these can be found.
† See H. P. Robertson, Rev. Mod. Phys. 5, 62 (1933), especially Note D.
† Publ. Astron. Soc. Pac. 67, 82 (1955); Helv. Phys. Acta Suppl. IV, 128 (1955).
† Monthly Notices of the Royal Astronomical Society 132, 379 (1966).
† Robertson used t 0 and log ρ 0, assuming a definite value for H 0. But Tinsley’s coordinates (Beatrice M. Tinsley, Ph.D. Dissertation, University of Texas, 1967), have the advantage that the diagram need not be recalibrated whenever a new value of H 0 is announced. Furthermore, the empirical density restrictions are on σ 0 rather than on p0: The dynamical mass determinations of clusters of galaxies depend on observing relative motions, and these satisfy ν2 ∝ m/r; but ν is directly observable as red shift, whence m ∝ r. The density involves a further division by (distance)3, so that ρ ∝ (distance)-2 ∝ H 2—since the uncertainty in Hubble’s parameter R/R is only in the denominator, the numerator being again observable as a red shift.
† See, for example, C. W. Misner, in “Relativity Theory and Astrophysics,” J. Ehlers, editor, p. 160, Vol. I, Providence, R. I., American Math. Soc., 1967.
† I. Ozsváth and E. Schücking, in “Recent Developments in General Relativity,” p. 339, New York, Pergamon Press, 1962.
† K. Gödel, Rev. Mod. Phys. 21, 447 (1949).
† See, for example, I Ozsváth and E. Schücking, Nature 193, 1168 (1962).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1969 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rindler, W. (1969). Cosmology. In: Essential Relativity. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1135-6_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1135-6_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90201-2
Online ISBN: 978-1-4757-1135-6
eBook Packages: Springer Book Archive