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Redshift increases with distance

Hubble went on to estimate the distances to 24 extra-galactic nebulae, using a variety of methods. In 1929 Hubble examined the relationship between these distances and their radial velocities as determined from their redshifts. All of his estimated distances are now known to be too small, by up to a factor of about 7. This was due to factors such as the fact that there are two kinds of Cepheid variables or confusing bright gas clouds with bright stars. However, his distances were more or less proportional to the true distances, and combining his distances with measurements of the redshifts of the galaxies by Vesto Slipher, and by his assistant Milton L. Humason, he found a roughly linear relationship between the distances of the galaxies and their radial velocities (corrected for solar motion), a discovery that later became known as Hubble's law.

This meant that the greater the distance between any two galaxies, the greater their relative speed of separation. If interpreted that way, Hubble's measurements on 46 galaxies lead to a value for the Hubble constant of 500 km/s/Mpc, which is much higher than the currently accepted values of 74 km/s/Mpc (cosmic distance ladder method) or 68 km/s/Mpc (CMB method) due to errors in their distance calibrations.

Yet the reason for the redshift remained unclear. Georges Lemaître predicted on theoretical grounds based on Einstein's equations for general relativity the redshift -distance relation, and published observational support for it, two years before the discovery of Hubble's law. Although he used the term "velocities" in his paper (and "apparent radial velocities" in the introduction), he later expressed doubt about interpreting these as real velocities. In 1931 he wrote a letter to the Dutch cosmologist Willem de Sitter expressing his opinion on the theoretical interpretation of the redshift-distance relation:

"Mr. Humason and I are both deeply sensible of your gracious appreciation of the papers on velocities and distances of nebulae. We use the term 'apparent' velocities to emphasize the empirical features of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority."

Today, the "apparent velocities" in question are usually thought of as an increase in proper distance that occurs due to the expansion of the universe. Light traveling through an expanding metric will experience a Hubble-type redshift, a mechanism somewhat different from the Doppler effect (although the two mechanisms become equivalent descriptions related by a coordinate transformation for nearby galaxies).

In the 1930s, Hubble was involved in determining the distribution of galaxies and spatial curvature. These data seemed to indicate that the universe was flat and homogeneous, but there was a deviation from flatness at large redshifts. According to Allan Sandage,

"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."

There were methodological problems with Hubble's survey technique that showed a deviation from flatness at large redshifts. In particular, the technique did not account for changes in luminosity of galaxies due to galaxy evolution.Earlier, in 1917, Albert Einstein had found that his newly developed theory of general relativity indicated that the universe must be either expanding or contracting. Unable to believe what his own equations were telling him, Einstein introduced a cosmological constant (a " fudge factor ") to the equations to avoid this "problem". When Einstein learned of Hubble's redshifts, he immediately realized that the expansion predicted by general relativity must be real, and in later life, he said that changing his equations was "the biggest blunder of life." In fact, Einstein apparently once visited Hubble and tried to convince him that the universe was expanding.

Hubble also discovered the asteroid 1373 Cincinnati on August 30, 1935. In 1936 he wrote The Observational Approach to Cosmology and The Realm of the Nebulae which explained his approaches to extra-galactic astronomy and his view of the subject's history.

In December 1941, Hubble reported to the American Association for the Advancement of Science that results from a six-year survey with the Mt. Wilson telescope did not support the expanding universe theory. According to a Los Angeles Times article reporting on Hubble's remarks, "The nebulae could not be uniformly distributed, as the telescope shows they are, and still fit the explosion idea. Explanations which try to get around what the great telescope sees, he said, fail to stand up. The explosion, for example, would have had to start long after the earth was created, and possibly even after the first life appeared here." (Hubble's estimate of what we now call the Hubble constant would put the Big Bang only 2 billion years ago.)