Willem de Sitter - Time Quotes

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It is possible to relegate the epoch of the starting of the expansion to minus infinity, e. g. by using instead of the ordinary time the logarithm of the time elapsed since the beginning. But this is only a mathematical trick. We call zero minus infinity, but that only means that we allow the universe an infinite time to get well started on its course of expansion, but it does not make the time during which anything really happens any longer.

Willem de Sitter
Observations give us two data, viz. the rate of expansion and the average density, and there are three unknowns: the value of λ, the sign of the curvature, and the scale of the figure, i. e. the units of R and of the time. The problem is indeterminate.

Willem de Sitter
The triangles that we can measure are not large enough... to detect the curvature. Fortunately, however, we are, in a way, able to communicate with the fourth dimension. The theory of relativity has given us an insight into the structure of the real universe:... a four-dimensional structure. The study of the way in which the three space-dimensions are interwoven with the time-dimension affords a kind of outside point of view of the three-dimensional space... from this outside point of view we might be able to perceive the curvature of the three-dimensional world.

Willem de Sitter
The way in which the universe expands is determined by the variation of this [radius of curvature] R with the time. There are three types, or families, of non-static universes... the oscillating universes, and the expanding universes of the first and of the second kind.... each of these is a representative of a family, comprising an infinite number of members differing in size and shape.... In the expanding family of the first kind the radius is continually increasing from... zero... In the expanding series of the second type the radius has at the initial time a certain minimum value, different for the different members of the family. [Both kinds of expanding families] become infinite after an infinite time.

Willem de Sitter