Abstract
It is shown that a uniformly-expanding universe, governed by the Cosmological Principle, exhibits a velocity space described by the hyperbolic geometry ofJ. Bolyai andN. Lobachevsky. This geometry provides a mathematical description of the free paths of lightrays and of material bodies, and has considerable theoretical, epistemological and practical implications. Its application is of particular importance for astronomical observations involving cosmological distances; this is exemplified in relation to the estimation of the size of objects (QSOs) with large (z>1) redshifts. It is suggested that Bolyai—Lobachevskian geometry is of general relevance to any expanding model of the universe.
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During 1976 with the Department of Philosophy, London School of Economics, Houghton Street, London, WC2A 2AE.
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Prokhovnik, S.J. The universe as a Bolyai—Lobachevsky velocity space. Acta Physica 41, 201–209 (1976). https://doi.org/10.1007/BF03159406
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DOI: https://doi.org/10.1007/BF03159406