On the Formation of Clusters of Nebulae and the Cosmological Time Scale

Abstract

A. The Problem of the Short Time Scale in an Expanding Universe. - The red-shift in the spectra of nebulae is most easily interpreted as a Doppler effect caused by the mutual and approximately uniform recession of these nebulae from one another. This hypothesis of an expanding universe leads to an alarmingly short cosmological time scale with the consequence that some two billion years ago intergalactic space must have been practically non-existent and the nebulae were not clearly separable from one another. Nevertheless, the individual objects which constitute these nebulae such as the stars, and the double, triple and multiple systems of stars might well have existed in their present physical condition even in a very contracted universe. The argument that the earth and the stars have existed for periods longer than two billion years, and the fact that perhaps the present statistical distribution of stars could have been achieved only in a very much longer time than two billion years is therefore not sufficient to reject the hypothesis of the expanding universe. In order to show that the time scale demanded by this hypothesis is inacceptable we must endeavor to discuss objects which (a) in a contracted universe clearly could not have existed in their present form and (b) whose formation required intervals of time definitely larger than two billion years. If we succeed in finding any objects which meet these requirements (a) and (b) we shall have demonstrated the impossibility of a time scale which would allow us to interpret the nebular red-shift on the basis of an expanding universe.