difficulties (contradictions) arising in the extension of the laws of physics to the universe as a whole or to a sufficiently large part of it. Thus, the extension of the second law of thermodynamics to the universe (without taking gravitation into account) has led in the past to the conclusion of the necessity of heat death. The age of the metagalaxy in the theory of an evolving universe proved until the 1950’s to be less than that of the earth.
However, two concrete paradoxes are usually included under the term “cosmological paradoxes,” both arising from the cosmological application of the laws of classical (Newtonian) physics: the photometric paradox (Chéseaux-Olbers paradox, named after the Swiss astronomer L. de Chéseaux, 1744, and the German astronomer H. B. Olbers, 1826) and the gravitational paradox (Neumann-Seeliger paradox, named after the German scientists K. Neumann and H. von Seeliger, 19th century). These paradoxes (cosmological paradoxes in the narrow sense of the term) have been overcome by relativistic cosmology.
Classical physics finds difficulty in explaining why it is dark at night: if radiating stars are present everywhere in the infinite space of a steady-state universe (or at least in a sufficiently large part of it), then some star should be encountered in any direction along the line of sight and the entire sky should be blindingly bright, as, for example, the sun’s surface. This contradicts actual observations and is called the photometric paradox. It does not arise in relativistic cosmology, since the brightness of remote objects decreases owing to the red shift. The gravitational paradox is less obvious in character and arises because Newton’s law of universal gravitation does not provide a rational answer to the problem of the gravitational field that is generated by an infinite system of masses (if no special assumptions are made regarding the nature of the spatial distribution of these masses). An answer on the cosmological scale is provided by A. Einstein’s theory, in which the law of universal gravitation is refined to include the case of very strong gravitational fields.
REFERENCESZel’manov, A. L. “Gravitatsionnyi paradoks.” In Fizicheskii entsiklopedicheskii slovar’, vol. 1. Moscow, 1960.
“Fotometricheskii paradoks.” In Fizicheskii entsiklopedicheskii slovar’, vol 5. Moscow, 1966.
Tolman, R. C. Relativity Thermodynamics and Cosmology. Oxford, 1934.
G. I. NAAN