In both the solutions A and B the curvature is positive, in both three-dimensional space is finite: the universe has a definite size, we can speak of… - Willem de Sitter

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In both the solutions A and B the curvature is positive, in both three-dimensional space is finite: the universe has a definite size, we can speak of its radius, and, in the case A, of its total mass. In the case A... the density is proportional to the curvature... Thus, if we wish to have a finite density in a static universe, we must have a finite positive curvature.

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About Willem de Sitter

Willem de Sitter (6 May 1872 – 20 November 1934) was a Dutch mathematician, physicist, astronomer and cosmologist who applied the general theory of relativity to the early investigation of the structure of the universe.

Also Known As

Alternative Names: W. de Sitter
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Additional quotes by Willem de Sitter

Since we only consider the universe on a very large scale, and make abstraction of all details and local irregularities, our universe must be homogeneous and isotropic. It follows... that the three-dimensional space of it must be what mathematicians call a space of constant curvature.

We... come to the conclusion... that the actual universe is neither the static nor the empty one. It differs so much from both of these that neither can be used as an appropriate grand scale model. We must thus look for other solutions of the general field-equations. On account of the expansion our solution must necessarily be a non-static one, and it must have a finite density. There is only one possible static solution possessing a finite density, viz. our old friend A, but of non-static solutions with finite density there exists a great variety.

In electromagnetism... the law of the inverse square had been supreme, but, as a consequence of the work of Faraday and Maxwell, it was superseded by the field. And the same change took place in the theory of gravitation. By and by the material particles, electrically charged bodies, and magnets which are the things that we actually observe come to be looked upon only as "singularities" in the field. So far this transformation from the force to the potential, from the action at a distance to the field, is only a purely mathematical operation.

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