# Astronomy Edwin Hubble Essay Research Paper THE — страница 5

effect. These corrections have been mentioned in the Halley lecture (Hubble 1934b), but were not there discussed relative to the space curvature measurement. Part of the 1936 paper was concerned with the problem for the first time. Hubble concluded that his observed log N(m) distribution showed a large departure from Euclidean geometry, provided that the effect of redshifts on the apparent magnitudes was calculated as if the redshifts were due to a real expansion. A different correction is required if no motion exists, the redshifts then being due to an unknown cause. Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings he maintained this position, favouring (or at the very least keeping open) the model where no true expansion exists, and therefore that the redshift “represents a hitherto unrecognized principle of nature”. This viewpoint is emphasized (a) in The Realm of the Nebulae, (b) in his reply (Hubble 1937a) to the criticisms of the 1936 papers by Eddington and by McVittie, and (c) in his 1937 Rhodes Lectures published as The Observational Approach to Cosmology (Hubble 1937b). It also persists in his last published scientific paper which is an account of his Darwin Lecture (Hubble 1953). From the beginning of his career Hubble was intrigued with the distribution of nebulae. His work on the problem began with his Ph.D. research (Hubble 1920), elementary as this now appears. He returned to the subject time and again with ever-increasing sophistication until the end of his career. He had even begun a major count programme anew in 1949 using the just-completed Palomar 48-inch Schmidt telescope (unpublished investigation) in an effort to use the modern magnitude scales then being set up photoelectrically. The aim was to investigate again from scratch the space curvature measurement. In his paper of 1926 Hubble had used his estimate of the average space density of galaxies to calculate the space curvature of the static Einstein universe. This fact is of quite ironic interest because it was Hubble himself, more than anyone, who three years later set out the observational foundation for the non-static solutions to the Einstein field equations of gravity. His use, then, of a static model to calculate the space curvature shows that as late as 1926 he had believed in non-expanding models, despite the large velocities that had been observed by Slipher and the attempts by many astronomers to understand these velocities using particular cosmological models. Recall that the Friedmann non-static solutions had been discovered in 1922, evidently unknown at Mount wilson at the time. The next major observational development was the discovery of the redshift-distance relation in 1929. d). The redshift-distance relations. As is well known the Einstein field equations of gravity admit only three stationary solutions (Tolman 1929 and 1934 sections 133-145). By stationary is meant that the manifold is not expanding. The mathematical expression of this condition is that the coefficients of each of the spatial coordinates in the equation of the metric is not a function of time. The two stationary solutions of historical importance are those of Einstein (1917) and of de Sitter (1916a, b; 1917), neither of which later proved to describe the true situation. Einstein’s did not because it contained matter but no redshift (it was truly static both in space and time). De Sitter’s did not because it had no matter, but curiously did have spectrum shifts (both red and blue) of test particles placed in the space which it described. This was due to a scandalous space-dependent factor in the metric coefficient of the time dimension , despite the static nature of the space coordinates. The “de Sitter spectral shift effect” had been looked for by many astronomers (see Hubble’s history in his chapter V of The Realm of the Nebulae) without convincing success. Robertson (1928) had predicted a linear relation and believed he had found a suggestive effect that could be interpreted in this way. He had correlated Slipher’s redshifts with the distances he had estimated using apparent magnitudes. Robertson gave no details. His result was set out in a single paragraph in a highly theoretical paper, but he was clearly aware of the possibility of the Kr term in the velocity field and that the universe might not, after all, be static. As with Hubble’s Cepheid paper 5 years before, and his space distribution paper to come 5 years in the future, Hubble’s (1929b) discovery paper of the expansion was written so convincingly that it was

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