Abstract
Our objective is to formulate questions about time in their true setting — cosmology. Even to formulate these questions one needs a theory. But, for cosmology, the available theories are unsatisfactory and the slender empirical evidence admits a diversity of interpretations.
We review the evidence for an expanding, finite-age cosmos, using general relativity and in relation to questions about the global structure of time. In interpreting the evidence we emphasize the implicit assumptions, which often go unstated.
We conclude by formulating a number of questions about time. Is there a proper clock? What is the exact relationship between the time asymmetries? Is time asymmetry imperfect? Could it be local? Is the notion of an asymmetry conceptually adequate to capture a sufficient variety of structures of time?
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Notes and References
D.W. Sciama, In: Early Evolution of the Universe and Its Present Structure, G.O. Abell and G. Chincarini (eds), IAU, 1983, pp 493–506.
This paradox has a long history, dating back to centuries before Olbers. See, e.g. E. R. Harrison, Darkness at Night: A Riddle of the Universe (Cambridge, Mass.: Harvard Univ. Press, 1987 ). The name Olbers’ paradox seems to have been popularised by H. Bondi in his classic text on Cosmology, 2nd ed. ( Cambridge: Univ. Press, 1960 ).
E. R. Harrison, in: Proc. JAU No. 139, Galactic and Extragalactic Background Radiation, S. Bowyer and Ch. Lienert (eds), Kluwer Academic, Dordrecht, 1989, pp 3–17.
P.C.W. Davies, The Physics of Time Asymmetry, Univ. of Surrey Press, London, 1974; H. Bondi and T. Gold, Mon. Not. R. Astr. Soc., 108, 252 (1948).
For a clear exposition of the general relativistic redshift, see J.L. Synge, Relativity, the General Theory (Amsterdam, Elsevier, 1966 ). Briefly, every redshift, including the gravitational redshift, may be regarded as a Doppler shift.
W. de Sitter, Mon. Not. R. Astr. Soc., 78, 3 (1917).
One has to distinguish between an emission and absorption redshift. Both tend to be similar, though not identical. This is strange because one would expect the absorption redshift, due to absorption by intergalactic dust, to have a range of values all the way up to the emission redshift.
H. Arp, personal communication (1988).
R. K. Sachs and A. M. Wolfe, ‘Perturbations of model and angular variations of the microwave background’, Ap. J., 147, 73–90 (1967).
W.R. Stoeger, G.F.R. Ellis and B.G. Schmidt, ‘Gauge-invariant variation in the redshift and cosmic background radiation anisotropies’, Gen.Rel. Gray., 23, 1169–94 (1991).
A 15±4µK (5 ppm) anisotropy in the CMBR was detected by COBE (Cosmic Background Explorer). G. I. Smoot, C.L. Bennett, A. Kogut et al, Ap. J., 316, Ll (1992). For the interpretation of this anisotropy as favouring cold dark matter, see C.L. Bennett et al, Ap.J., 316, L7 (1992); R.L. Davis, H.M. Hodges, G.I. Smoot et al, Phys. Rev. Lett., 69, 1856 (1992).
The surface r = 2m has area 4orr2, but has infinite volume; curvature coordinates may not be used while going across the surface r = 2m.
S. W. Hawking and G.F.R. Ellis, The Large Scale Structure of Spacetime (Cambridge: Univ. Press, 1974, 1987 ) pp 286–7.
P.D. Lax, Hyperbolic Systems of Conservation Laws,American Mathematical Society Publications, Providence, Rhode Island, 1973. The example is that of the flow of a compressible fluid in a tube with the piston being pushed out with constant acceleration. This now-standard example may also be found in, e.g., R. D. Richtmyer, Principles of Advanced Mathematical Physics,Vol. I, Springer, Berlin, 1978, pp 388–90. The situation in GRT is analogous: a collapse, once initiated, must continuously accelerate, leading to a finite-time ‘blow up’ of smooth solutions.
For a review of the techniques and pitfalls here, see C. K. Raju, ‘Distributional matter tensors in relativity’, Proceedings of the Fifth Marcel Grossman Meeting, D.G. Blair et al eds, Wiley Eastern, Singapore, 1989) p 421. The background may be found in J. Phys. A: Math. Gen., 15, 381–96 (1982); 15, 1785–97 (1982).
Vera C. Rubin, ‘What is the matter in spiral galaxies?’ In: Large-Scale Structure of the Universe, V. C. Rubin and G.V. Coyne (eds) ( Princeton: Univ. Press, 1980 ).
K. Gödel, Rev. Mod. Phys., 21, 447–50 (1948).
S. Chandrasekhar, in: The Nature of Time, (ed) T. Gold, Cornell Univ. Press, Ithaca, 1967, pp 68–74.
Cited by S. Chandrasekhar, Ellipsoidal Figures of Equilibrium, Yale Univ. Press, New Haven, 1968.
As already noted by Gödel, on the speculation that galaxies may have formed due to inhomogeneities resulting from rotation, it is not essential that the axes of rotation should be preferentially oriented like those of the planets.
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© 1994 Springer Science+Business Media Dordrecht
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Raju, C.K. (1994). Cosmological Time. In: Time: Towards a Consistent Theory. Fundamental Theories of Physics, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8376-3_11
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DOI: https://doi.org/10.1007/978-94-015-8376-3_11
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