By Albert Einstein
Albert Einstein's recognized lectures entitled Sidelights on Relativity
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Additional resources for Illuminated Geometry
The distribution of the visible stars is extremely irregular, so that we on no account may venture to set down the mean density of star25 Albert Einstein matter in the universe as equal, let us say, to the mean density in the Milky Way. In any case, however great the space examined may be, we could not feel convinced that there were no more stars beyond that space. So it seems impossible to estimate the mean density. But there is another road, which seems to me more practicable, although it also presents great difficulties.
Therefore the question whether the universe is spatially finite or not seems to me decidedly a pregnant question in the sense of practical geometry. I do not even consider it impossible that this question will be answered before long by astronomy. Let us call to mind what the general theory of relativity teaches in this respect. It offers two possibilities:— 1. The universe is spatially infinite. e. if the ratio of the total mass of the stars to the magnitude of the space through which they are scattered approximates indefinitely to the value zero when the spaces taken into consideration are constantly greater and greater.
If the ratio of the total mass of the stars to the magnitude of the space through which they are scattered approximates indefinitely to the value zero when the spaces taken into consideration are constantly greater and greater. 24 Illuminated Geometry 2. The universe is spatially finite. This must be so, if there is a mean density of the ponderable matter in universal space differing from zero. The smaller that mean density, the greater is the volume of universal space. I must not fail to mention that a theoretical argument can be adduced in favour of the hypothesis of a finite universe.
Illuminated Geometry by Albert Einstein